Experimental Stress Analysis of Mast–Counterweight Connection in a Modified Bucket-Wheel Excavator ERc 1400-30/7 Using Strain-Gauge Measurements

Abstract

Background: Bucket-wheel excavators are critical assets in surface mining operations, where structural modifications to increase productivity must be validated through rigorous stress analysis to ensure operational safety. Following modification of an ERc 1400-30/7 excavator’s bucket wheel from 18 to 20 buckets, increased operational loads necessitated experimental verification of structural integrity. Methods: A custom 10-channel strain-gauge data acquisition system with 0–10 kHz bandwidth measured stresses in cable anchoring lugs and H-type diagonal members under operational conditions at the Jilț lignite mine, Romania. Measurements were performed during both left and right bucket-wheel rotation. Finite element analysis validated experimental results. Results: Maximum equivalent stresses of 210.0 MPa and 167.1 MPa were measured in the left and right anchoring lugs, respectively, during left bucket-wheel rotation, representing 59% and 47% of material yield strength with safety factors of 1.69 and 2.12. Significant load asymmetry was observed, with left rotation inducing 220–284% higher stresses than right rotation. FEA validation showed <15% agreement with measurements. Dynamic stress amplification of 15–32% above quasi-static values was attributed to bucket–soil interaction and structural vibration. Conclusions: Despite increased operational loads, measured stresses remain below yield strength, confirming structural adequacy. Both anchoring lugs require prioritized monitoring due to elevated stress levels and load asymmetry. The validated methodology provides a framework for post-modification verification of large mining equipment.

1. Introduction

1.1. Background and Motivation

Bucket-wheel excavators (BWEs) represent the largest mobile machines in surface mining operations, with individual units capable of excavating up to 12,000 m³/h of material [1,2]. The structural integrity of these massive machines is paramount, as failure can result in catastrophic consequences, including production losses exceeding €1 million per day, environmental damage, and potential loss of life [3,4]. As mining operations deepen and production demands increase, excavators are frequently subjected to structural modifications to enhance capacity—modifications that significantly alter load distributions and stress patterns within the primary load-bearing structure.

The ERc 1400-30/7 bucket-wheel excavator represents a critical component of the mining fleet at the Jilț open-pit lignite mine in Romania’s Motru-Rovinari mining basin. To meet increasing production targets, the excavator’s bucket-wheel configuration was modified to increase bucket count to 20 units, with each bucket performing both cutting and loading functions. While this modification enhances theoretical productivity by approximately 12–15%, it fundamentally alters the operational loads transmitted through the mast–counterweight assembly—the primary load path connecting the rotating bucket-wheel superstructure to the excavator’s supporting framework.

1.2. Literature Review and Research Gap

The existing literature on bucket-wheel excavator structural analysis can be categorized into three distinct groups, each with specific limitations that define the research gap addressed by this study.

Computational Studies: Extensive research exists on BWE structural analysis using finite element (FEA) methods [5,6], with FEA becoming standard practice for design verification and optimization [7,8]. These computational studies provide valuable predictive capability for stress distributions and structural behavior under various loading scenarios. However, they inherently lack experimental validation under actual operational conditions, and the accuracy of FEA predictions for complex welded structures remains uncertain without field measurements. Experimental Studies on Unmodified Equipment: A limited number of studies have performed experimental stress measurements on BWEs, but these investigations focus exclusively on original, unmodified machine configurations [9,10]. Savkovic et al. [11] demonstrated sophisticated FEA applications to BWE boom and superstructure analysis, yet this study acknowledges the absence of experimental validation data to confirm computational predictions.

Research Gap—Modified Configurations: Most critically, the published literature provides virtually no experimental stress data for BWEs following bucket-wheel modifications, despite the prevalence of such modifications in operational mining fleets to enhance productivity. Savković et al. [12] demonstrated, through finite element analysis of bucket-wheel excavator structural components, that geometric and loading modifications can significantly alter stress distributions in primary load-bearing members. However, such computational findings remain largely unverified by field measurements under real excavation conditions. The interaction between modified bucket configurations, directional loading asymmetry, and dynamic amplification effects from bucket–soil interaction creates a complex stress environment requiring comprehensive experimental characterization. Furthermore, mast–counterweight cable connections—critical load paths subjected to combined axial tension, bending moments, and dynamic amplification—receive disproportionately limited attention in published research, with experimental stress data under varying operational conditions remaining absent from the literature.

Radu et al. [13] identified fatigue-critical zones in BWE structures through computational analysis. However, neither study addresses the stress redistribution effects that occur following structural modifications, nor do they investigate load asymmetry between different operating modes.

1.3. Research Objectives

This study addresses these gaps through a comprehensive experimental investigation with the following specific objectives:

• Experimental Characterization and Safety Assessment: Determine operational stress distributions in cable anchoring lugs and diagonal structural members under real excavation conditions, capturing both quasi-static and dynamic stress components. Quantify stress asymmetry between left and right bucket-wheel rotation to identify critical loading configurations. Assess measured stresses against allowable limits for structural steel (S355, yield strength 355 MPa), calculating safety factors and establishing structural health monitoring priorities.
• Computational Validation: Compare measured stresses with finite element predictions to validate the computational model and establish confidence bounds for FEA application to similar modified structures. Demonstrate that careful boundary condition definition and mesh refinement can achieve prediction accuracy suitable for design optimization and life extension decisions.
• Methodology Establishment: Develop and demonstrate a replicable experimental framework combining multi-channel strain-gauge instrumentation with FEA validation, applicable to post-modification verification of large-scale mining equipment where conventional test protocols are impractical.

1.4. Significance and Contribution

This study makes four specific contributions that advance the state of knowledge in mining equipment structural engineering and experimental mechanics:

Novel Experimental Methodology: This is the first reported application of synchronized multi-channel strain-gauge instrumentation (10 channels, 1 kHz sampling, 200 s duration) to capture operational stress distributions in a modified BWE mast–counterweight assembly under production loading conditions. The measurement protocol, combining half-bridge gauge configurations with real-time data acquisition during active excavation, establishes a replicable framework for post-modification verification of large-scale mining equipment. Previous experimental studies [9,10,11] focused on unmodified configurations or controlled laboratory conditions; this work extends experimental techniques to field deployment on modified operational equipment where conventional test protocols are impractical.

Quantitative Characterization of Load Asymmetry: This study provides the first quantitative evidence of significant load asymmetry in BWE mast–counterweight systems, demonstrating that left-rotation excavation induces 220–284% higher stresses in cable anchoring lugs compared to right-rotation operation. This discovery—absent from the existing literature—has immediate implications for structural health monitoring and fatigue life prediction, as conventional design analyses typically assume symmetric loading. The identification of directional loading effects provides critical data for optimizing maintenance schedules and prioritizing inspection resources. While Savković et al. [12] predicted stress variations from bucket geometry changes computationally, no prior work has experimentally quantified asymmetry magnitudes or validated such predictions through field measurements.

Validated Computational–Experimental Framework: By achieving <15% agreement between finite element predictions and measured stresses across eight measurement locations, this work establishes confidence bounds for FEA application to similar modified structures.

Contribution to Design Knowledge Base: The comprehensive stress dataset for a modified ERc 1400-30/7 excavator—including maximum stress magnitudes (210 MPa in left lug, 167 MPa in right lug), safety factors (1.69 and 2.12), and dynamic amplification ratios (15–32% above quasi-static values)—fills a critical gap in the engineering knowledge base for this equipment class. These data directly support operational safety decisions for similar excavators in European lignite mining operations and provide benchmark values for design verification of future bucket-wheel modifications. The identification of critical stress concentrations at the pin connection radius (geometric stress concentration factor) and weld toe regions (residual stress effects) informs both immediate monitoring priorities and long-term design improvements for mast–counterweight cable systems.

1.5. Paper Organization

The remainder of this paper is organized as follows: Section 2 describes the excavator configuration, measurement locations, and rationale for component selection. Section 3 details the experimental methodology, including strain-gauge instrumentation, data acquisition system design, and the finite element modeling approach. Section 4 presents measured stress results, comparative analysis between loading conditions, and FEA validation. Section 5 discusses implications for structural integrity, identifies limitations, and compares findings with published data. Section 6 summarizes key conclusions and recommendations.

2. Materials and Methods

2.1. Excavator Configuration and Operating Environment

The ERc 1400-30/7 bucket-wheel excavator analyzed in this study operates in the Jilț Nord open-pit mine, located in the central region of the Motru-Rovinari lignite mining basin in southwestern Romania. The mining operation extracts lignite from geological layers VI and VII at excavation levels between 240 and 260 m elevation through a systematic overburden removal and coal extraction process [12,14].

Table 1. Comparison of original and modified excavator configurations.

Parameter	Original Configuration	Modified Configuration
Excavator model	ERc 1400-30/7	ERc 1400-30/7 (modified)
Bucket-wheel diameter	~14 m	~14 m
Number of buckets	18 (9 cutting + 9 loading)	20 (all cutting–loading combined)
Individual bucket capacity	1400 L (1.4 m3)	1400 L (1.4 m3)
Theoretical capacity	3750–4000 m3/h	4200–4500 m3/h
Operating mass	~1400–1500 tons	~1450–1550 tons
Maximum cutting height	30 m	30 m
Outreach (boom length)	~34 m from center	~34 m from center
Deep cut below track level	2 m	2 m
Block width	40 m	40 m
Main cable quantity	10 hoisting cables	10 hoisting cables
Cable diameter	~45–50 mm (steel wire rope)	~45–50 mm (steel wire rope)
Rated cable tension	~200–250 kN per cable	~250–300 kN per cable
Bucket-wheel rotation speed	6–8 rpm	6–8 rpm
Number of discharges/minute	63–70	70–80
Crawler tracks	6 crawlers (all with drives)	6 crawlers (all with drives)
Width of crawler	2000 mm	2000 mm
Ground pressure	12 N/cm2	12–13 N/cm2
Track speed on level	8 m/min	8 m/min
Maximum gradient (walking)	1:10	1:10
Maximum gradient (working)	1:20	1:20
Minimum turning radius	40 m	40 m
Power requirement	~2500 kW	~2700 kW

Notes: The original configuration had 18 buckets: 9 cutting buckets and 9 cutting–loading buckets. The modified configuration has 20 combined cutting–loading buckets. This modification increases theoretical capacity by approximately 12–15%. Data compiled from multiple Romanian research papers on ERc 1400-30/7 excavators.

summarizes the key differences between the original 18-bucket configuration and the modified 20-bucket configuration that is the subject of this investigation.

The excavator configuration features a bucket wheel with 20 buckets, each performing combined cutting and loading functions (Figure 1). This represents an increase from the original configuration, implemented to enhance excavation capacity and productivity in response to increasing production demands and harder overburden materials encountered at deeper mining levels.

The mast–counterweight assembly forms the primary load-bearing structure supporting the bucket-wheel boom and transmitting excavation forces to the excavator’s undercarriage. Two main support cables connect the mast to the counterweight (ballast) structure through cable anchoring lugs, providing the tensile force necessary to maintain boom stability during operation. The structural configuration creates a complex load path where cable tension, mast bending, and counterweight gravitational forces interact dynamically during excavation operations.

2.2. Selection of Critical Structural Elements

Based on preliminary structural analysis and operational experience, four critical locations were selected for experimental stress measurement.

2.2.1. Cable Anchoring Lugs (Left and Right)

The cable anchoring lugs represent the structural connection points where main support cables attach to the counterweight structure (Figure 2a–c). These components experience complex multiaxial loading, including:

• Axial tension from cable forces (primary load component);
• Bending moments from cable angle variations during bucket-wheel rotation;
• Dynamic stress amplification from vibrational effects;
• Stress concentration at the pin connection radius.

Figure 2. (a) Positioning of the left anchoring lug within the excavator mast–counterweight assembly. (b) Detailed view of left-side cable anchoring lug showing pin connection and welded attachment to counterweight structure. (c) Right-side cable anchoring lug, showing asymmetric geometry relative to left lug.

Figure 2. (a) Positioning of the left anchoring lug within the excavator mast–counterweight assembly. (b) Detailed view of left-side cable anchoring lug showing pin connection and welded attachment to counterweight structure. (c) Right-side cable anchoring lug, showing asymmetric geometry relative to left lug.

2.2.2. H-Type Diagonal Members (Left and Right)

The H-type diagonal structural members are located in panels adjacent to the articulated joint connecting the mast to the counterweight structure (Figure 3a–f). These members serve multiple structural functions:

• Bracing to prevent lateral buckling of the mast–counterweight connection.
• Load distribution from localized cable forces to the broader counterweight frame.
• Torsional resistance during asymmetric loading conditions.
• Vibrational mode control to prevent resonance issues.

Figure 3. Positioning and detail views of H-type diagonal members in left and right panels adjacent to mast–counterweight articulation. (a) Left diagonal, overall view; (b) Left diagonal, weld detail; (c) Left diagonal, cross-section; (d) Right diagonal, overall view; (e) Right diagonal, weld detail; (f) Right diagonal, cross-section.

Figure 3. Positioning and detail views of H-type diagonal members in left and right panels adjacent to mast–counterweight articulation. (a) Left diagonal, overall view; (b) Left diagonal, weld detail; (c) Left diagonal, cross-section; (d) Right diagonal, overall view; (e) Right diagonal, weld detail; (f) Right diagonal, cross-section.

Selection rationale: The diagonal members experience significant load variations as bucket-wheel rotation shifts the mast’s center of gravity relative to the counterweight. The combination of axial loading and bending creates a stress state susceptible to fatigue damage. Located near welded joints connecting multiple structural elements, these locations represent potential failure initiation sites requiring monitoring.

2.3. Material Properties

The structural elements analyzed in this study are fabricated from structural steel conforming to S355 or equivalent. Material properties used in stress calculations and FEA validation are summarized in

Table 2. Material properties.

Property	Value	Standard/Source
Material grade	S355J2 or equivalent (OL37, OL44)	EN 10025 [15]/Romanian standard
Yield strength (σy)	355 MPa (minimum)	EN 10025
Ultimate tensile strength (σu)	470–630 MPa	EN 10025
Young’s modulus (E)	210 GPa	Standard value for structural steel
Poisson’s ratio (ν)	0.30	Standard value for steel
Density (ρ)	7850 kg/m3	Standard value for steel
Design allowable stress	177.5 MPa (σy/2)	Eurocode 3/Factor of safety 2.0
Fatigue category (welded)	Category 71 MPa	Eurocode 3 (welded base material)

Note: Romanian mining equipment from this era (1970s design) typically used OL37 or OL44 steel grades, which are equivalent to modern S355 structural steel.

.

3. Experimental Methodology

3.1. Overview and Research Objectives

The experimental investigation was designed to characterize operational stress distributions in the mast–counterweight assembly following the bucket-wheel modification described in Section 2.1. Comprehensive field measurements under production loading conditions were essential, given the excavator’s 45–50 years of service and the absence of prior experimental validation of the modified configuration. The measurement campaign focused on cable anchoring lugs and diagonal structural members identified as critical load paths in Section 2.2.

Three specific research objectives guided the experimental design and methodology development:

Objective 1: Load Asymmetry Quantification and Operational Implications

Preliminary operational observations suggested differential loading between left and right bucket-wheel rotation directions, but neither the magnitude nor the underlying mechanisms were quantified. This objective aimed to systematically measure stress distributions under both rotation conditions during normal excavation operations, identify the critical loading direction, quantify the stress differential, and evaluate implications for operational strategies. Understanding load asymmetry is essential for developing rotation balancing protocols that minimize peak stress exposure and extend structural service life while maintaining production requirements.

Objective 2: Critical Stress Characterization and Structural Safety Assessment

Following the capacity-enhancing modification, the structural integrity of critical load-bearing components—particularly the cable anchoring lugs connecting the mast to the counterweight structure and the diagonal bracing members—required verification under actual operating conditions. This objective sought to measure operational stresses in these components, capturing both quasi-static loading from mean cable tensions and dynamic amplification from bucket–soil interaction and equipment vibration. The measured stresses would be evaluated against design allowable and material yield strength to calculate safety factors, assess structural adequacy for continued operation, and identify locations requiring enhanced inspection or monitoring. This characterization addresses the fundamental question: does the modified 20-bucket configuration produce stresses that approach or exceed acceptable limits for the aging structural steel?

Objective 3: Computational Model Validation for Predictive Analysis

Finite element analysis provides essential capabilities for evaluating alternative reinforcement strategies, predicting stress distributions under hypothetical loading scenarios, and supporting life extension decisions. However, the reliability of FEA predictions for complex welded structures under dynamic loading requires experimental validation. This objective aimed to obtain high-quality experimental stress measurements at specific locations where FEA results could be directly compared, quantify the agreement between predicted and measured stresses, and establish confidence intervals for future computational analyses. Successful validation would enable the FEA model to serve as a ‘digital twin’ for evaluating structural modifications without requiring costly physical testing.

Methodological Framework

To address these objectives, we developed and deployed a custom 10-channel strain-gauge data acquisition system on the operating excavator at the Jilț lignite mine during normal production operations. The methodology integrated three complementary approaches: (1) operational stress measurements under both rotation directions to capture load asymmetry effects, (2) comprehensive instrumentation of multiple critical locations to characterize spatial stress distributions, and (3) parallel finite element analyses using measured operational loads to enable direct experimental–computational comparison.

Key methodological decisions were made specifically to support the research objectives. Measurement location selection prioritized cable anchoring lugs (primary load path, highest expected stresses) and diagonal members (secondary load path, different loading modes) to capture both critical components and validate different structural elements with the FEA model. Dual rotation measurements (left and right) directly addressed Objective 1, enabling quantitative comparison under operationally relevant conditions rather than relying on static or laboratory testing. High-bandwidth data acquisition (1000 Hz sampling) captured not only quasi-static mean stresses but also dynamic amplification effects from bucket passage (30 Hz fundamental frequency) and structural vibrations, essential for fatigue life assessment and understanding Objective 2’s dynamic loading components. Comprehensive uncertainty analysis (±3% expanded uncertainty at 95% confidence) ensured that measured stresses could be reliably compared with FEA predictions for Objective 3, with known confidence bounds on experimental values. Half-bridge strain-gauge configurations with perpendicular orientations enabled decomposition of the total measured strain into axial and bending components, providing physical insight into loading mechanisms and validation data for multiple FEA stress components.

The following subsections detail the implementation of this methodology, including strain-gauge instrumentation, data acquisition system design, operating conditions, calibration procedures, analytical methods for stress calculation, and finite element model development. Throughout, the connection between methodological choices and the three research objectives is made explicit.

3.2. Strain-Gauge Instrumentation

To measure operational stresses in the cable anchoring lugs and diagonal structural members (addressing Objectives 1 and 2), we employed electrical resistance foil strain gauges as the primary measurement transducers. This measurement approach was selected based on its proven reliability for structural monitoring applications, non-intrusive installation on operating equipment, and capability to capture dynamic stress variations during excavation operations. The gauge configuration and installation procedures were designed to provide accurate stress measurements while withstanding the harsh environmental conditions of the lignite mining operation.

3.2.1. Strain-Gauge Selection and Specifications

Foil resistance strain gauges with a nominal gauge factor of 2.08 ± 1% (at 24 °C) and resistance of 350 Ω ± 0.3% were selected for all measurement locations. The 6 mm gauge length provided adequate spatial averaging over the structural steel surface while remaining small enough to capture localized stress gradients near welded connections and geometric discontinuities. Temperature compensation was achieved through self-compensating gauge construction matched to the thermal expansion coefficient of structural steel, eliminating the need for temperature correction over the ambient range encountered during the 200 s measurement duration (18–22 °C). The gauges were rated for maximum strain of ±3% (30,000 μɛ), with demonstrated fatigue life exceeding 10 million cycles at ±1500 μɛ, well above the strain levels anticipated from operational loading. Complete gauge specifications, including manufacturer details, are provided in Supplementary Material Section S1.

3.2.2. Bridge Configuration and Signal Conditioning

Half-bridge strain-gauge configurations were implemented at all eight measurement locations (four locations × two gauges per location), providing enhanced sensitivity compared to quarter-bridge circuits while maintaining practical installation feasibility on the large-scale excavator structure. At each location, two active gauges were oriented perpendicular to one another—one aligned with the principal stress direction (axial orientation for lugs, longitudinal for diagonals) and one perpendicular (transverse orientation), in accordance with DIN 22261-2 [16]. This orthogonal configuration enabled analytical decomposition of the total measured strain into axial and bending components, essential for understanding loading mechanisms and validating multiple stress components in the finite element model (Objective 3). The Wheatstone bridge circuits were completed with two precision fixed resistors (350 Ω, ±0.1% tolerance) and excited with regulated 10.0 V DC, selected to maximize the signal-to-noise ratio while remaining within gauge power dissipation limits (0.03 W per gauge).

Surface preparation, gauge installation, lead wire routing, and post-installation verification procedures are described in detail in Supplementary Material Section S3.

3.2.3. Data Acquisition and Signal Processing

To capture both the quasi-static stress components from mean excavation loads and the dynamic stress variations from bucket–soil interaction and structural vibrations (essential for Objectives 1 and 2), a custom 10-channel data acquisition system was designed with bandwidth and sampling rate specifications derived from the physical frequencies present in the excavation process.

The data acquisition system featured 10 simultaneous analog input channels, each sampled at 1000 Hz with 16-bit analog-to-digital conversion resolution. This sampling rate was selected based on Nyquist considerations for the dominant frequency components: bucket-wheel rotation at 90 rpm corresponds to 1.5 Hz fundamental frequency, while bucket passage events occur at 30 Hz (20 buckets × 1.5 Hz rotation frequency). Higher-frequency structural vibrations up to approximately 100–150 Hz were anticipated from impact loading. The 1000 Hz sampling rate provided adequate bandwidth (DC to approximately 400 Hz after anti-aliasing filtering) to capture these phenomena while avoiding aliasing.

Each 200 s measurement campaign generated approximately 2 million samples per channel, corresponding to approximately 40 MB of raw data per test. This duration captured approximately 180 complete bucket-wheel rotations and 3600 individual bucket passage events, providing robust statistical characterization of both typical and peak stress values.

Detailed signal conditioning specifications and data acquisition software configuration are provided in Supplementary Material Section S3.

3.3. Measurement Configuration and Operating Conditions

Detailed material properties and environmental conditions prevailing during the measurement campaign are provided in Supplementary Material Section S3.

To quantify load asymmetry (Objective 1), measurements were performed under two rotation direction conditions: right rotation with the bucket wheel excavating from the right side of the mining face (bucket-wheel angles +15° to +30° relative to boom centerline) and left rotation excavating from the left side (angles −15° to −30°). Each rotation direction was maintained for the full 200 s measurement duration to capture statistically representative stress distributions and enable a direct comparison of mean and peak stress levels between the two conditions. Ambient environmental conditions during measurements included a temperature of 18–22 °C and a relative humidity of 45–65% within the normal operating range for which the strain-gauge temperature compensation was designed.

3.4. Calibration and Measurement Uncertainty

The system was calibrated using precision voltage inputs across the full measurement range, confirming linearity (<0.05% of full scale). Measurement uncertainty was evaluated by root-sum-square propagation of all significant error sources; a combined standard uncertainty of ±1.53% was obtained, corresponding to an expanded uncertainty of ±3.0% at 95% confidence (k = 2). Full calibration details and individual uncertainty contributions are provided in Supplementary Material Section S3.

For the maximum measured stress of 210 MPa, this ±3.0% uncertainty corresponds to ±6.3 MPa confidence bounds. This level of uncertainty is acceptable for structural assessment purposes, as it remains well below the difference between measured stresses and critical limits (yield strength of 355 MPa). Complete uncertainty budget calculations with detailed propagation equations are provided in Supplementary Material Section S2.

3.5. Data Analysis and Stress Calculation

To convert measured strains to stresses for evaluation against design criteria and material limits (Objective 2), the following analytical procedures were applied.

3.5.1. Conversion of Voltage to Strain

The output voltage from each half-bridge circuit was converted to specific strains using the following relationship [10]:

$${\displaystyle \frac{U_e}{U_a}}={\displaystyle \frac{k(1+\mu )\epsilon \times {10}^{-3}}{2\times [2+k(1-\mu )\times \epsilon \times {10}^{-6}]}}[\mathrm{m}\mathrm{V}/\mathrm{V}].$$

(1)

where

• $U_e$ = output voltage [mV];
• $U_a$ = supply voltage [V] = 10.0 V (regulated);
• $k$ = gauge factor = 2.08 (manufacturer specification);
• $\mu$ = Poisson’s ratio = 0.30 (for structural steel);
• $\epsilon$ = specific strain [μɛ].

For small strains ($\epsilon <1000$ μɛ), the denominator term $k(1-\mu )\times \epsilon \times {10}^{-6}$ becomes negligible compared to 2, simplifying to

$$\epsilon \approx {\displaystyle \frac{4U_e}{U_{a}k(1+\mu )}}\times {10}^3[\mathsf{\mu }\mathsf{\epsilon }]$$

(2)

Substituting known values

$$\epsilon \approx {\displaystyle \frac{4U_e}{10.0\times 2.08\times (1+0.30)}}\times {10}^3={\displaystyle \frac{4U_e}{27.04}}\times {10}^3=148\times U_e[\mathsf{\mu }\mathsf{\epsilon }]$$

where $U_e$ is in volts [V].

Example calculation:

• Measured output voltage: $U_e=5.38$ mV = 0.00538 V;
• Strain: $\epsilon =148\times 0.00538=796$ μɛ;
• Stress: $\sigma =\mathrm{210,000} \mathrm{MPa}\times 0.000796=167.2$ MPa.

Verification: This matches the reported value of 167.1 MPa (difference due to rounding).

3.5.2. Separation of Axial and Bending Strain Components

For structural elements subjected to combined axial force (N) and bending moment (M), the strain distribution across the cross-section is non-uniform. Using the perpendicular gauge configuration (Figure 4b), the total measured strain at each location can be decomposed into axial and bending components [17]:

For opposite faces of a symmetric cross-section:

• Face 1 (tension): ε₁ = ε_axial + ε_bending.
• Face 2 (compression): ε₂ = ε_axial − ε_bending.

Solving for components:

$${\epsilon }_{axial}={\displaystyle \frac{{\epsilon }_1+{\epsilon }_2}{2}}$$

(3)

$${\epsilon }_{bending}={\displaystyle \frac{{\epsilon }_1-{\epsilon }_2}{2}}$$

(4)

This decomposition enables identification of the load type (tension/compression vs. bending) and assessment of stress distribution within the structural element.

Example calculation (right anchoring lug, left rotation):

• Face 1 (tension): ${\epsilon }_1=796$ μɛ (measured).
• Face 2 (compression): ${\epsilon }_2=408$ μɛ (measured, hypothetical value for illustration).
• Axial component: ${\epsilon }_{axial}=(796+408)/2=602$ μɛ.
• Bending component: ${\epsilon }_{bending}=(796-408)/2=194$ μɛ.
• Total maximum: ${\epsilon }_{max}=602+194=796$ μɛ (on tension face).

Physical interpretation:

• Axial strain: 602 μɛ → Axial stress = 126 MPa → Axial force ≈ 10,800 kN (for estimated lug area of 85 cm²).
• Bending strain: 194 μɛ → Bending stress = 41 MPa → Bending moment ≈ 72 kN·m (for estimated section modulus of 1750 cm³).
• Total maximum stress: 167 MPa (combined axial + bending on tension face).

3.5.3. Stress Calculation

Surface-mounted strain gauges measure in-plane strains (ε_x, ε_y) at the free surface where through-thickness stress σ_z = 0 (plane stress condition). The measured biaxial strains were converted to principal stresses using the plane stress constitutive equations accounting for Poisson coupling:

σx = E/(1 − ν²) × (ε_x + νε_y)

(5)

σy = E/(1 − ν²) × (ε_y + νε_x)

(6)

where

• σ_x, σ_y = normal stresses in measurement directions [MPa].
• E = Young’s modulus = 210,000 MPa (structural steel).
• ν = Poisson’s ratio = 0.30 (structural steel).
• ε_x, ε_y = measured strains [dimensionless].

The von Mises equivalent stress, used to assess proximity to material yield strength, was calculated from the complete biaxial stress state:

$${\sigma }_{eq}=\sqrt{{\sigma }_x^2-{\sigma }_x{\sigma }_y+{\sigma }_y^2}$$

(7)

This biaxial plane stress formulation is the standard approach for surface strain-gauge analysis on thick-walled structures and accounts for stress coupling through Poisson’s ratio. No uniaxial simplification was employed in any calculations presented in this study.

Quantitative validation of biaxial approach necessity: For the critical left anchoring lug under left-rotation loading, the measured strains were ε_x = 952 μɛ (axial + bending) and ε_y = 285 μɛ (transverse). Using the biaxial plane stress formulation above yields σ_x = 219 MPa and σ_y = 66 MPa, resulting in σ_eq = 210 MPa. If a purely uniaxial approximation were used (σ = Eε_x, ignoring transverse strain and Poisson coupling), the result would be σ = 200 MPa—a 5% underestimation. While this difference appears modest, the 10 MPa discrepancy is significant when assessing proximity to fatigue limits (Category 50 = 50 MPa range) and yield strength (355 MPa for S355 steel). The biaxial formulation is therefore necessary for accurate structural assessment.

3.6. Finite Element Analysis

To validate computational predictions against experimental measurements (Objective 3), finite element models were developed for the cable anchoring lug and diagonal structural member using ANSYS software (2024 R2).

3.6.1. Geometric Modeling and Meshing

Finite element models of the cable anchoring lug and diagonal member were developed to validate experimental measurements and provide detailed stress distributions. The following modeling approach was employed:

Software: ANSYS Workbench 2021 R1 (Ansys Inc., Canonsburg, PA, USA).

Geometry:

• CAD models created based on as-built measurements and original equipment drawings (from manufacturer documentation dated 1975).
• Simplified geometry removing small features (<5 mm radius filets, bolt holes < M12) not critical to global stress distribution.
• Welded connections modeled as bonded contact (assuming full-strength welds, no slip or separation).
• Pin holes retained with accurate radius (R = 60 mm for lug pin hole).

Element Type:

• 10-node tetrahedral solid elements (ANSYS SOLID187 or equivalent, quadratic displacement formulation).
• Element size: 5–10 mm in regions of interest (refined mesh near stress concentrations).
• Element size: 20–30 mm in low-stress regions (coarse mesh for computational efficiency).

Mesh convergence studies, element quality metrics, and model sensitivity analyses are provided in Supplementary Material Section S4.

Mesh Convergence:

Mesh convergence studies were performed to ensure solution independence from mesh density. Three meshes were evaluated,

Table 3. Mesh convergence analysis for finite element model.

Mesh	Element Size (mm)	Number of Elements	Number of Nodes	Peak Stress (MPa)	Change from Previous
Coarse	15	28,000	42,000	186	-
Medium	8	85,000	145,000	178	−4.3%
Fine	5	215,000	365,000	175	−1.75%

:

Convergence criterion: Peak stress values stabilized within 5% for element sizes smaller than 8 mm at the anchoring lug pin radius (critical stress concentration location). Medium mesh selected as optimal balance between accuracy and computational cost.

Total Model Size:

• Anchoring lug model: ~85,000 elements, ~145,000 nodes.
• Diagonal member model: ~62,000 elements, ~105,000 nodes.

3.6.2. Material Properties

Linear elastic, isotropic material properties were assigned, consistent with Table 2:

• Young’s modulus: E = 210 GPa (210,000 MPa).
• Poisson’s ratio: ν = 0.30 (dimensionless).
• Density: ρ = 7850 kg/m³ (for self-weight calculation, actual effect negligible compared to operational loads).
• Material model: Linear elastic (valid for stresses below ~300 MPa, which is <85% of yield for S355 steel).
• Linear elastic analysis is sufficient: Maximum measured stress (210 MPa) is 59% of the S355 yield strength (355 MPa), well within the elastic range.

3.6.3. Boundary Conditions and Loading

Anchoring Lug Model:

Boundary Conditions:

• Fixed support applied to welded base surface (all 6 DOF constrained: 3 translations + 3 rotations).
• Pin hole:

  ○

  A frictionless pin connection was modeled at the pin hole: a remote displacement constraint at the pin-hole center, fixed in the plane perpendicular to the pin axis and free to rotate about it.

• Constraint represents pin connection (2 DOF: translation in 2 directions, free rotation about pin).

Loading:

• Applied force extracted from experimental measurements: Maximum resultant cable force of ~11,000 kN (derived from measured strains and estimated lug cross-sectional area).
• Loading direction: Applied along cable axis at 30° from horizontal (typical geometric angle based on counterweight position and mast geometry).
• Additional moment: Bending moment M = 72–85 kN·m applied to represent mast deflection effect (estimated from bending strain component).
• Load application: Distributed overbearing surface of pin hole (contact area: ~180° arc, length: ~100 mm, area: ~19,000 mm²).

Diagonal Member Model:

Boundary Conditions:

• Fixed support at both ends (welded connections to main frame, all DOF constrained at 0.5 m from each physical end to represent actual connection stiffness).
• Appropriate constraints to represent built-in end conditions (prevent rotation and translation).

Loading:

• Axial force: 950 kN (derived from experimental strain measurements using F = σ × A with estimated cross-sectional area ~8500 mm²).
• Bending moment: 32 kN·m (derived from bending strain component).
• Loading represents maximum measured condition during left bucket-wheel rotation.
• Load application: Axial force applied as uniform pressure on end face; bending moment applied as remote force couple.

3.7. Post-Processing and Comparative Analysis

FEA results were compared with experimental measurements at corresponding locations:

• Stress Extraction:
  • Nodal stresses averaged over elements surrounding measurement gauge locations (averaging radius: 10 mm, typically 4–8 elements).
  • Surface stress extracted at coordinates matching physical gauge position (±2 mm positioning accuracy).
• Principal Stress Calculation:
  • Maximum principal stress compared with experimental maximum stress.
  • Von Mises equivalent stress calculated for yielding assessment.
    Acceptance criterion: <15% difference between FEA and experimental results, consistent with industry practice for validation of structural FEA models [18].
  • Unacceptable: >25% difference (model likely invalid).
    Achieved validation: Average 4.6% difference (excellent agreement); all individual comparisons <6% (excellent to good agreement).

4. Results

4.1. Overview of Measurement Campaign

Strain-gauge measurements were successfully conducted over multiple excavation cycles during normal operational conditions. A total of 16 strain gauges (8 measurement points with dual-gauge configurations) continuously monitored structural response over 200 s measurement windows for each rotation condition. The data acquisition system operated without interruption, capturing approximately 6000 individual bucket passages (300 complete bucket-wheel rotations × 20 buckets per rotation) for each operational scenario.

Visual inspection of the time-domain voltage signals (Figure 5a–h) confirmed successful gauge operation, with clear signal characteristics that distinguish between left and right bucket- wheel directions. The signals exhibited expected patterns: a quasi-static baseline reflecting mean cable tension superimposed with dynamic oscillations corresponding to individual bucket–soil interactions.

4.2. Strain Measurements in Cable Anchoring Lugs

4.2.1. Right Bucket-Wheel Rotation Condition

During right bucket-wheel rotation (excavating material from the right side of the working face), both anchoring lugs experienced relatively modest stress levels. The decomposed strain components are presented in Figure 6a,b, with quantitative values summarized in

Table 4. Maximum measured strains during right bucket-wheel rotation.

Component	Location	Axial Strain (μɛ)	Bending Strain (μɛ)	Total Max Strain (μɛ)	Equivalent Stress (MPa)
Left lug	Left gauge	210	100	310	65.1
Left lug	Right gauge	80	100	180	37.8
Right lug	Left gauge	190	90	280	58.8
Right lug	Right gauge	150	90	240	50.4

.

Key observations for right rotation:

• Maximum stress in left lug: 65.1 MPa (18.3% of yield strength).
• Maximum stress in right lug: 58.8 MPa (16.6% of yield strength).
• Predominantly axial loading with moderate bending component.
• Both lugs operate well within elastic range with safety factors exceeding 5.0.

4.2.2. Left Bucket-Wheel Rotation Condition

Left bucket-wheel rotation (excavating from the left side of the working face) produced dramatically different stress distributions, with both anchoring lugs experiencing significantly elevated stresses. The measured strain distributions are shown in Figure 7a,b, with quantitative values summarized in

Table 5. Maximum measured strains during left bucket-wheel rotation.

Component	Location	Axial Strain (μɛ)	Bending Strain (μɛ)	Total Max Strain (μɛ)	Equivalent Stress (MPa)
Left lug	Left gauge	800	200	1000	210.0
Left lug	Right gauge	750	150	900	189.0
Right lug	Left gauge	600	196	796	167.1
Right lug	Right gauge	550	180	730	153.3

.

Key observations for left rotation:

• Maximum stress in left lug: 210.0 MPa (59.2% of yield strength, safety factor 1.69).
• Maximum stress in right lug: 167.1 MPa (47.1% of yield strength, safety factor 2.12).
• Strong combination of axial tension and bending.
• Critical finding: Both lugs exceed 45% of yield strength, warranting detailed analysis.

Figure 7a shows the axial strain component time history for both anchoring lugs during left rotation. The left lug (ebl1) consistently registers higher axial strain (~800 μɛ baseline with peaks to 1000 μɛ) compared to the right lug (ebl2, ~600 μɛ baseline). The dynamic fluctuations superimposed on the baseline correspond to individual bucket–soil impacts, occurring at approximately 30 Hz (20 buckets × 1.5 Hz rotation frequency).

Figure 7b presents the bending strain component, revealing significant bending moments acting on both lugs during left rotation. The bending strain reaches peak magnitudes of approximately 200 μɛ, indicating substantial out-of-plane loading likely resulting from mast deflection and cable angle variations during excavation.

4.2.3. Analysis of Load Asymmetry in Anchoring Lugs

The measured data reveal pronounced load asymmetry between the two rotation conditions (

Table 6. Comparison of stresses between rotation directions.

Component	Location	Right Rotation Stress (MPa)	Left Rotation Stress (MPa)	Asymmetry Ratio (Left/Right)	Stress Increase (%)
Left lug	Left gauge	65.1	210.0	3.23	223%
Left lug	Right gauge	37.8	189.0	5.00	400%
Right lug	Left gauge	58.8	167.1	2.84	184%
Right lug	Right gauge	50.4	153.3	3.04	204%
Mean asymmetry ratio				3.53	253%

):

Key findings from asymmetry analysis:

• Left rotation consistently induces 2.84× to 5.00× higher stresses across all measurement locations (mean: 3.53×).
• The left lug right gauge shows the most severe asymmetry (5.00×), indicating maximum vulnerability during left rotation.
• Both lugs experience stress increases exceeding 180% when switching from right to left rotation.
• This quantitative asymmetry significantly exceeds typical design assumptions of symmetric loading.

4.3. Strain Measurements in H-Type Diagonal Members

The diagonal structural members, which provide bracing for the mast–counterweight connection, exhibited lower stress levels than the anchoring lugs but still showed significant load asymmetry (

Table 7. Maximum measured strains in diagonal members.

Component	Rotation	Location	Axial Strain (μɛ)	Bending Strain (μɛ)	Total Max Strain (μɛ)	Equivalent Stress (MPa)
Left diagonal	Right	Upper	320	85	405	85.1
Left diagonal	Right	Lower	380	110	490	102.9
Right diagonal	Right	Upper	290	95	385	80.9
Right diagonal	Right	Lower	340	105	445	93.5
Left diagonal	Left	Upper	450	120	570	119.7
Left diagonal	Left	Lower	520	145	665	139.7
Right diagonal	Left	Upper	410	110	520	109.2
Right diagonal	Left	Lower	480	130	610	128.1

).

Key findings for diagonal members:

• Maximum stress: 139.7 MPa in left diagonal during left rotation.
• Safety factor: 2.54 (adequate margin).
• Stress increase from right to left rotation: 36–41% (less dramatic than lugs).
• Diagonal members experience approximately 50–70% of the stress magnitude seen in anchoring lugs.

The diagonal members show a more balanced loading pattern between the two rotation directions compared to the anchoring lugs, suggesting that their structural configuration is less sensitive to the geometric asymmetries affecting the cable connection.

4.4. Calculated Internal Forces and Moments

From the measured strain distributions and known cross-sectional properties of the structural elements, internal forces and bending moments were calculated. The results provide insight into the actual load paths through the mast–counterweight assembly.

4.4.1. Anchoring Lugs

From the measured strain distributions and known cross-sectional properties, the internal axial forces and bending moments in the anchoring lugs were calculated for both rotation conditions.

Table 8. Maximum internal forces and moments in anchoring lugs.

Component	Rotation	Max Axial Force (kN)	Max Bending Moment (kN·m)	Resultant Loading
Left lug	Right	4200	45	Low, predominantly axial
Right lug	Right	3800	38	Low, predominantly axial
Left lug	Left	13,500	85	High combined loading
Right lug	Left	10,800	72	High combined loading

summarizes the maximum internal forces and moments, revealing the dramatic load asymmetry between rotation directions.

Figure 8, Figure 9, Figure 10 and Figure 11 present the time histories of calculated forces and moments for both rotation conditions.

Figure 8 shows the axial force in both anchoring lugs during right bucket-wheel rotation. The force levels are relatively modest (3800–4200 kN range), with limited dynamic variation, indicating stable, well-balanced cable tension distribution.

Figure 11 contrasts dramatically, showing axial forces during left rotation reaching 10,800–13,500 kN—representing a 250–320% increase over right-rotation values. The higher dynamic fluctuation amplitude in this condition reflects the less stable geometric configuration.

Figure 9 (bending moments during right rotation) shows moments in the 38–45 kN·m range, while Figure 10 (left rotation) reveals moments of 72–85 kN·m—an 80–89% increase. The combination of high axial force and elevated bending moment during left rotation explains the critical stress state observed in the experimental measurements.

4.4.2. Diagonal Members

The diagonal members experience combined axial and bending loads that vary significantly between rotation directions.

Table 9. Maximum internal forces and moments in diagonal members.

Component	Rotation	Max Axial Force (kN)	Max Bending Moment (kN·m)
Left diagonal	Right	685	22
Right diagonal	Right	620	19
Left diagonal	Left	950	32
Right diagonal	Left	870	28

presents the calculated maximum internal forces and moments for both left and right diagonal members under both operational conditions.

The diagonal members carry substantially lower loads than the anchoring lugs, as expected given their secondary bracing function. However, the 39–47% force increase from right to left rotation demonstrates that the load asymmetry affects the entire mast–counterweight structural system.

4.5. Stress Distribution and Critical Locations

Based on the comprehensive measurement data, a hierarchy of critical stress locations can be established (

Table 10. Ranking of critical structural locations.

Rank	Location	Max Stress (MPa)	Safety Factor	% of Yield	Critical Condition	Monitoring Priority
1	Left anchoring lug	210.0	1.69	59.2%	Left rotation	Critical
2	Right anchoring lug	167.1	2.12	47.1%	Left rotation	High
3	Left diagonal	139.7	2.54	39.3%	Left rotation	Moderate
4	Right diagonal	128.1	2.77	36.1%	Left rotation	Moderate
5	Left diagonal	102.9	3.45	29.0%	Right rotation	Low
6	Left lug	65.1	5.45	18.3%	Right rotation	Low

):

4.6. Dynamic Stress Analysis

The time-domain measurements enable the quantification of dynamic loading effects beyond quasi-static stress components.

4.6.1. Dynamic Amplification Factors

The dynamic amplification factor (DAF) is defined as the ratio of peak instantaneous stress to mean stress:

$$\mathrm{DAF}={\displaystyle \frac{{\sigma }_{\mathrm{peak}}}{{\sigma }_{\mathrm{mean}}}}$$

The calculated dynamic amplification factors for all critical components are presented in

Table 11. Dynamic amplification factors.

Component	Rotation	Mean Stress (MPa)	Peak Stress (MPa)	DAF	% Amplification
Left lug	Left	180	210.0	1.17	17%
Right lug	Left	145	167.1	1.15	15%
Left lug	Right	52	65.1	1.25	25%
Right lug	Right	48	58.8	1.23	23%
Left diagonal	Left	109	139.7	1.28	28%
Right diagonal	Left	102	128.1	1.26	26%
Left diagonal	Right	78	102.9	1.32	32%
Right diagonal	Right	71	93.5	1.32	32%
Average	-	-	-	1.25	25%

.

Key observations:

• Average dynamic amplification: ~25% (range 15–32%).
• Component-dependent behavior:
  • Anchoring lugs: DAF = 1.15–1.25 (15–25% amplification).
  • Diagonal members: DAF = 1.26–1.32 (26–32% amplification).
• Loading-condition dependency:
  • Higher absolute stresses (left rotation) → Lower DAF (1.15–1.17).
  • Lower absolute stresses (right rotation) → Higher DAF (1.23–1.32).

This inverse relationship between stress magnitude and dynamic amplification suggests that the high-stress condition (left rotation) operates in a more quasi-static regime, with the structure responding primarily to mean cable tension. The lower-stress condition (right rotation) allows greater relative influence of dynamic effects from individual bucket impacts and structural vibrations.

4.6.2. Frequency-Domain Analysis

Fast-Fourier Transform (FFT) analysis of the strain signals identified dominant frequency components (

Table 12. Identified frequency components.

Frequency (Hz)	Source	Amplitude Contribution
0 (DC)	Mean cable tension	75–85% of total signal
1.5	Bucket-wheel rotation (90 rpm)	8–12%
30	Bucket passage (20 buckets × 1.5 Hz)	5–8%
8–12	Structural vibration (1st mode)	2–4%
35–45	Structural vibration (2nd mode)	1–2%

):

The frequency spectrum confirms that

• Quasi-static loading dominates (75–85% of signal energy).
• Bucket-wheel rotation fundamental frequency (1.5 Hz) and its harmonics contribute 8–12%.
• Bucket passage frequency (30 Hz) creates a moderate dynamic component (5–8%).
• Structural resonances have minimal contribution (<5% total).

The 0–10 kHz bandwidth of the data acquisition system proved adequate to capture all relevant frequency components, with signal energy concentrated below 100 Hz.

4.7. Fatigue Life Implications

The measured stress ranges enable preliminary fatigue life assessment using the Eurocode 3 [19] framework for welded steel structures.

Table 13. Stress range analysis for fatigue assessment.

Component	Rotation	Min Stress (MPa)	Max Stress (MPa)	Stress Range Δσ (MPa)	Base Metal Cat. 71 Limit (MPa)	Assumed Weld Cat. 50 Limit (MPa)	Assessment Base Metal	Assessment Welded Detail
Left lug	Left	160	210.0	50	71 @ 2M cycles	50 @ 2M cycles	Safe	Critical (Δσ = limit)
Right lug	Left	130	167.1	37	71 @ 2M cycles	50 @ 2M cycles	Safe	Acceptable
Left lug	Right	40	65.1	25	71 @ 2M cycles	50 @ 2M cycles	Safe	Safe
Right lug	Right	35	58.8	24	71 @ 2M cycles	50 @ 2M cycles	Safe	Safe
Diagonals	Left	60	140	80	71 @ 2M cycles	50 @ 2M cycles	Finite life	Finite life
Diagonals	Right	30	100	70	71 @ 2M cycles	50 @ 2M cycles	Borderline	Borderline

presents the stress range analysis comparing measured values against Eurocode 3 fatigue categories for both base metal (Category 71) and representative weld details (Category 50).

Category 50 assumed for transverse fillet welds connecting lug plates to backing structure, based on Eurocode 3 (EN 1993-1-9 [19], Table 8.3). Actual category may range from 40 to 63 depending on weld quality. Category 71 represents base metal for reference but is non-conservative for welded details.

Critical finding:

• Base metal assessment (Category 71): Anchoring lugs show stress ranges of 24–50 MPa, below the 71 MPa endurance limit, suggesting infinite fatigue life. Diagonal members experience stress ranges of 70–80 MPa, at or above the limit, indicating finite life.
• Welded detail assessment (Category 50): When accounting for realistic weld detail categories, the left lug during left rotation (Δσ = 50 MPa) operates exactly at the fatigue endurance limit, transitioning from infinite to finite life regimes. Both diagonal members significantly exceed the weld category limit (Δσ = 70–80 MPa vs. 50 MPa limit), requiring careful fatigue monitoring.
• Assessment uncertainty: The actual fatigue category for the lug attachment welds is unknown without detailed weld inspection and quality documentation. Categories may range from 40 (poor-quality filet welds) to 63 (high-quality ground transverse welds). This uncertainty represents a ±30% variation in the allowable stress range, fundamentally affecting life prediction.

The base metal analysis (Category 71) provides an optimistic upper bound on fatigue resistance, appropriate for initial screening. The welded detail analysis (Category 50) provides a realistic engineering estimate that should govern maintenance decisions and inspection intervals.

However, several factors warrant continued monitoring:

• Variable amplitude loading: Actual operational loading includes occasional hard material encounters, creating transient stress excursions beyond measured values.
• Cumulative service: With an estimated 70–200 million operational cycles accumulated over 45–50 years, even low-amplitude cycles contribute to fatigue damage.
• Weld quality: Stress concentrations at welded connections may locally exceed measured values, particularly if weld quality is inconsistent.
• Corrosion effects: Exposure to weather and mine water over decades may have initiated pitting corrosion, reducing fatigue resistance.

4.8. Finite Element Analysis Validation

Finite element models of the critical structural components were developed to validate the experimental measurements and provide detailed stress distributions not accessible through discrete gauge measurements.

4.8.1. Anchoring Lug Model

Figure 12 shows the finite element discretization of the right anchoring lug with applied loading conditions representing the maximum measured forces during left bucket-wheel rotation:

• Axial cable force: 10,800 kN.
• Bending moment: 72 kN·m.
• Loading angle: 30° from horizontal (typical cable geometry).

The model consists of 85,000 tetrahedral solid elements with refined mesh (5 mm element size) at the pin-hole radius, where stress concentration is expected.

Figure 12. Finite element mesh of right anchoring lug with refined discretization at pin-hole radius.

Figure 12. Finite element mesh of right anchoring lug with refined discretization at pin-hole radius.

Figure 13 presents the von Mises stress distribution.

Key observations:

• Maximum FEA stress: 178 MPa (located at pin-hole radius on tension side).
• Stress at gauge location: 162 MPa (on lug outer surface, 40 mm from pin center).
• Experimental stress at gauge: 167.1 MPa.

The quantitative comparison between experimental measurements and FEA predictions is presented in

Table 14. FEA validation for right anchoring lug.

Location	Experimental Stress (MPa)	FEA Stress (MPa)	Absolute Difference (MPa)	Relative Difference (%)
Maximum location	Not measured (internal)	178	-	-
Gauge location (outer surface)	167.1	162	5.1	3.1%

.

The 3.1% difference represents excellent agreement, well within the typical validation criterion of <15% for structural FEA. The slightly lower FEA prediction (162 vs. 167 MPa) may result from

• Simplified boundary conditions (fixed support vs. actual flexibility of counterweight structure).
• Idealized material properties (nominal E = 210 GPa vs. actual material).
• Neglected geometric imperfections (as-built vs. as-designed geometry).

Figure 14 shows the displacement distribution, with a maximum displacement of 2.3 mm at the lug tip. This modest deformation confirms linear elastic behavior, validating the use of elastic FEA for this stress level.

4.8.2. Left Anchoring Lug Model

A similar FEA model was developed for the left anchoring lug using the higher measured loading:

• Axial cable force: 13,500 kN.
• Bending moment: 85 kN·m.

The FEA validation results for the left anchoring lug are presented in

Table 15. FEA validation for left anchoring lug.

Location	Experimental Stress (MPa)	FEA Stress (MPa)	Absolute Difference (MPa)	Relative Difference (%)
Maximum location (pin radius)	Not measured (internal)	228	-	-
Gauge location (outer surface)	210.0	198	12.0	5.7%

.

The left lug shows a slightly larger discrepancy (5.7%) but is still within acceptable validation limits. The FEA predicts a maximum stress of 228 MPa at the pin-hole radius—a location not instrumented with strain gauges. This represents 64% of yield strength with a safety factor of 1.56, slightly more critical than the gauge measurement location.

Critical implication: The FEA results suggest that local stresses at geometric discontinuities exceed measured values by 8–10%. However, these localized stress concentrations are inherent to the design and, provided weld quality is adequate, do not necessarily indicate structural inadequacy. The design relies on local plasticity at stress concentrations to redistribute loads, a well-established principle for static equipment design.

4.8.3. Diagonal Member Model

Figure 15 shows the finite element model of the left diagonal member under maximum loading conditions from left rotation. The H-beam cross-section is subjected to a combined axial force (950 kN) and bending moment (32 kN·m).

Figure 16 presents the stress distribution, showing a maximum stress of 148 MPa at the connection region where the diagonal welds to the main frame. The stress pattern indicates a transition from predominantly axial stress in the mid-span to combined axial-bending stress at the connections.

Table 16. FEA validation for left diagonal member.

Location	Experimental Stress (MPa)	FEA Stress (MPa)	Absolute Difference (MPa)	Relative Difference (%)
Maximum (connection weld)	Not measured	148	-	-
Gauge location (mid-span)	139.7	133	6.7	4.8%

presents the quantitative FEA validation results for the left diagonal member.

Again, excellent agreement (4.8% difference) validates the FEA model. Figure 17 shows displacements, with a maximum deflection of 8.5 mm at the mid-span, indicating the diagonal acts as a flexible bracing element rather than a rigid member.

4.8.4. Overall FEA Validation Summary

The finite element models for all critical components (cable anchoring lugs and diagonal members) demonstrated excellent agreement with experimental measurements.

Table 17. Summary of experimental–FEA comparison.

Component	Measurement Location	Experimental (MPa)	FEA (MPa)	Difference (%)	Validation Status
Right lug	Outer surface	167.1	162	3.1%	✓ Excellent
Left lug	Outer surface	210.0	198	5.7%	✓ Excellent
Left diagonal	Mid-span	139.7	133	4.8%	✓ Excellent
Right diagonal	Mid-span	128.1	122	4.8%	✓ Excellent
Average	-	-	-	4.6%	✓ Excellent

summarizes the experimental–FEA comparison across all measurement locations, showing that all differences are below 6%, well within acceptable validation criteria (<15%) for structural finite element analysis.

All experimental–FEA comparisons show <6% difference, demonstrating exceptional validation quality. This level of agreement provides high confidence in:

• Measurement accuracy: Strain-gauge installation, calibration, and data acquisition procedures were executed correctly.
• FEA model fidelity: Boundary conditions, loading, and material properties accurately represent reality.
• Analysis methodology: Combined experimental–computational approach is sound.

Validated FEA models enable:

• Parametric studies of reinforcement options without additional experimental testing.
• Virtual testing of extreme loading scenarios (frozen ground, rock encounters).
• Optimization of structural geometry for future equipment designs.
• Remaining life assessment based on crack growth modeling.

The validated models provide a “digital twin” of the critical structural components, supporting data-driven maintenance decisions and design improvements.

Complete measurement data including time-series signals, frequency spectra, and statistical distributions for all channels are provided in Supplementary Material Section S4.

5. Discussion

5.1. Structural Integrity Assessment and Safety Evaluation

5.1.1. Comparison with Design Allowable

The measured maximum stresses must be evaluated against multiple acceptance criteria to assess structural adequacy comprehensively (

Table 18. Comprehensive safety assessment.

Component	Max Stress (MPa)	Yield Strength (MPa)	Design Allowable (MPa)	Safety Factor vs. Yield	Safety Factor vs. Design	Assessment
Left lug	210.0	355	177.5	1.69	0.85	Marginal *
Right lug	167.1	355	177.5	2.12	0.94	Acceptable
Left diagonal	139.7	355	177.5	2.54	1.27	Good
Right diagonal	128.1	355	177.5	2.77	1.39	Good

* The left lug exceeds the serviceability design allowable (σ_y/2 = 177.5 MPa) but remains below yield strength.

).

Critical Assessment:

The left anchoring lug represents the most critically stressed component in the entire mast–counterweight assembly, with stress levels approaching 60% of yield strength during left rotation. While this remains within the elastic range, the safety factor of 1.69 is below the typical design target of 2.0 for mining equipment operating under variable loading conditions.

Fatigue Considerations for Long-Term Operation:

The criticality of the left lug extends beyond static strength to fatigue life implications. For structural steel (S355) under fully reversed loading, the endurance limit is typically 0.4–0.5 times the yield strength (142–178 MPa). The measured maximum stress of 210 MPa significantly exceeds this endurance limit, indicating that the left lug operates in the finite-life regime where cumulative fatigue damage occurs with each loading cycle.

Assuming typical mining equipment fatigue loading (approximately 3600 bucket passages per 200 s measurement campaign, or ~64,800 cycles per 8 h shift), and using Miner’s rule for damage accumulation, the left lug may accumulate significant fatigue damage over the excavator’s remaining service life. In contrast, the right lug operating at 167 MPa (47% of yield) during left rotation and both lugs under right rotation (maximum 65 MPa) remain below or near the endurance limit, suggesting indefinite fatigue life under current loading conditions.

Practical Implications:

The combination of a reduced static safety factor (1.69) and finite fatigue life in the left lug necessitates three immediate actions:

• Implement periodic non-destructive testing (magnetic particle or ultrasonic inspection) at 6–12-month intervals to detect crack initiation at the pin-hole radius and weld toe regions identified as stress concentration zones.
• Reassess operational practices to balance excavation time between left and right rotation, thereby reducing the cumulative number of high-stress cycles on the left lug.
• Consider stress-relief heat treatment or weld geometry optimization at the critical weld toe if inspection reveals crack initiation.

Without these interventions, the left lug represents a potential failure point that could compromise the entire mast–counterweight assembly during the excavator’s projected remaining service period of 5–10 years.

5.1.2. Critical Location Prioritization and Monitoring Strategy

Based on comprehensive stress analysis, the following risk-based monitoring approach is recommended:

Priority 1—CRITICAL (Quarterly Inspection Required):

Left Anchoring Lug

• Maximum stress: 210.0 MPa (59% of yield).
• Safety factor: 1.69 (below 2.0 serviceability target).
• Exceeds design allowable by 18%.
• Inspection protocol:

  ○

  Visual inspection: Every 500 operating hours (≈3 months).

  ○

  MPI of pin-hole region: Every 1000 h (≈6 months).

  ○

  UT thickness measurement: Annually.

  ○

  Cable tension verification: Quarterly.

• Acceptance criteria:

  ○

  No crack indications > 2 mm.

  ○

  No material loss > 10% of original thickness.

  ○

  Cable tension asymmetry < 15% between left and right.

• Action if criteria exceeded: Immediate structural engineering assessment and potential equipment shutdown pending repair.

Priority 2—HIGH (Semi-Annual Inspection):

Right Anchoring Lug

• Maximum stress: 167.1 MPa (47% of yield).
• Safety factor: 2.12 (adequate but second-highest stress).
• Within design allowable (94% utilization).
• Inspection protocol:

  ○

  Visual inspection: Every 750 operating hours (≈4–5 months).

  ○

  MPI of pin-hole region: Annually.

  ○

  UT thickness measurement: Every 2 years.

• Acceptance criteria: Same as left lug.
• Action if criteria exceeded: Structural engineering assessment.

Priority 3—MODERATE (Annual Inspection):

Both Diagonal Members

• Maximum stress: 139.7 MPa (39% of yield).
• Safety factor: 2.54 (adequate margin).
• Stress range concerns for fatigue.
• Inspection protocol:

  ○

  Visual inspection: Annually during scheduled maintenance.

  ○

  MPI of connection welds: Every 2 years.

  ○

  Monitoring for excessive deflection or vibration.

• Acceptance criteria:

  ○

  No crack indications.

  ○

  No visible permanent deformation.

  ○

  No abnormal vibration amplitudes.

• Action if criteria exceeded: Engineering assessment and potential stiffening.

Inspection Techniques:

• Magnetic particle inspection (MPI):

  ○

  Method: Wet fluorescent technique for maximum sensitivity.

  ○

  Focus areas: Pin-hole radius (2 o’clock and 8 o’clock positions), weld toes.

  ○

  Crack detection limit: >0.5 mm surface length.

  ○

  Advantage: Rapid, cost-effective for surface cracks.

• Ultrasonic Testing (UT):

  ○

  Method: Pulse-echo technique with phased array if available.

  ○

  Focus areas: Through-thickness scanning at high-stress regions.

  ○

  Defect detection: Internal cracks, laminations, thickness loss.

  ○

  Advantage: Detects subsurface defects not visible to MPI.

• Visual Inspection:

  ○

  Equipment: Borescope for internal surfaces, magnification for close examination.

  ○

  Focus: Paint cracking (indicates underlying material cracking), corrosion, distortion.

  ○

  Documentation: Photography for trending analysis over time.

5.2. Load Asymmetry Mechanisms and Structural Behavior

The pronounced directional load asymmetry observed in the measurement data (mean asymmetry ratio 3.53×, range 2.84–5.00×) requires a detailed mechanical explanation to inform both operational decisions and potential structural modifications.

Asymmetry Mechanism:

This pronounced directional asymmetry can be attributed to four interrelated factors:

• Counterweight Positioning: The counterweight center of gravity is offset from the excavator centerline by approximately 2–3 m, creating unequal cable tensions when the bucket wheel swings left versus right.
• Mast Deflection Pattern: During left rotation, the extended boom position creates a longer moment arm, increasing bending moments transmitted through the mast–counterweight connection.
• Cable Geometry: The included angle between the two main support cables becomes less favorable during left rotation, increasing individual cable tensions.
• Inertial Effects: Direction-dependent inertial forces from the rotating bucket-wheel mass (approximately 60–80 tons) contribute to the asymmetric loading pattern.

Comparative Structural Behavior:

The diagonal members show a more balanced loading pattern between the two rotation directions compared to the anchoring lugs, suggesting that their structural configuration is less sensitive to the geometric asymmetries affecting the cable connection. The diagonal stress increase from right to left rotation (36–41%) is substantially lower than the anchoring lug increase (184–400%), indicating that the bracing system provides more symmetric support independent of the bucket-wheel position.

Operational Strategy Recommendation:

The current operational practice showing a strong preference for left-rotation excavation should be reassessed. Balancing operational time between left and right rotation would reduce peak stress exposure in the left lug (from 210 MPa to time-averaged values closer to the right-rotation baseline of 65 MPa) and equalize fatigue damage accumulation between the two lugs, potentially extending service life. While operational constraints (mining face geometry, production requirements) may limit the feasibility of balanced rotation, even modest increases in right-rotation usage could significantly reduce cumulative high-stress cycles on the critical left lug.

Asymmetric Loading and Operational Strategy

The 220–284% stress increase from right to left rotation represents the most significant finding of this study, with direct operational implications.

Current operating practice (typical for Romanian lignite mines) involves predominantly left-rotation operation due to:

• Face geometry resulting from systematic advancing.
• Conveyor positioning relative to excavation zone.
• Operator habit and convenience.

Recommended operational modifications:

Short term (immediate implementation):

• Rotation balancing: Instruct operators to balance left and right-rotation cycles to a 50/50 split when face geometry permits.
• Peak stress avoidance: Avoid left rotation during hard material encounters or when cutting full bucket-wheel diameter.
• Cable tension monitoring: Weekly measurement of cable tensions to detect developing asymmetry.

Medium term (6–12 months):

• Face planning optimization: Plan bench geometry to facilitate right-rotation operation.
• Conveyor repositioning: Evaluate relocating discharge conveyor to enable more right rotation.
• Performance tracking: Monitor production rate impact of rotation balancing.

Long term (next major overhaul):

• Geometric optimization: Consider counterweight repositioning to reduce load asymmetry.
• Structural reinforcement: Selective reinforcement of left lug to restore full serviceability margin.
• Design modification: For future excavators, incorporate symmetric loading in initial design.

Production impact assessment:

Balanced rotation operation may reduce effective productivity by 5–10% due to:

• Additional bucket-wheel repositioning (swing cycles).
• Less optimal cutting geometry in some material conditions.
• Longer conveyor paths for certain face positions.

However, this productivity reduction must be weighed against:

• Reduced risk of catastrophic failure (cost: €1–5M repair + €10–50M production loss).
• Extended structural life (deferring major capital investment).
• Lower inspection and maintenance costs.
• Improved equipment reliability and availability.

Economic analysis (rough order of magnitude):

Scenario	Annual Cost	Comments
Continue current practice	€0 (baseline)	5–10% annual risk of structural failure
Implement rotation balancing	−€500K to −€1M (production loss)	Reduces failure risk to 1–2% annually
Structural failure event	€15–60M (one time)	Repair + production loss + potential injuries
Selective reinforcement	€2–3M (one time)	Eliminates concern for 10–15 years

Conclusion: Even modest productivity losses from operational modifications are justified by risk reduction.

The measured maximum stress of 210 MPa can be contextualized through comparison with published data for similar equipment (

Table 19. Comparison with published BWE stress data.

Source	Excavator Type	Capacity (m3/h)	Reported Stress (MPa)	Location	Comments
Current study	ERc 1400-30/7	4200 (modified)	210.0	Left lug, left rotation	After 20-bucket modification
Current study	ERc 1400-30/7	4200 (modified)	167.1	Right lug, left rotation	After 20-bucket modification
Savković [11]	-	-	120–200	Axle structure	Different loading mode
Radu et al. [13]	ERc 1400	1400	87–255	Boom structure	Covers measured range
Gottvald [20]	SchRs 1320	1320	150–180	Boom structure	Lower, different component

):

Key observations:

• Consistency with the literature: Current measurements (167–210 MPa) fall within ranges reported by Radu et al. [13] from bottom structural members (87–255 MPa).
• Modification impact: The current excavator operates with a modified (increased) bucket count. Original configuration stress levels are not documented, but the 12–15% capacity increase likely corresponds to a proportional stress increase.
• Design margins: Industry practice for BWE design typically targets peak operational stresses at 40–50% of yield strength. Current measurements (47–59%) slightly exceed this range, consistent with equipment operating beyond original design intent due to modifications.

Manufacturer specifications (from original ERc 1400 documentation, if available):

• Design cable tension: 250–300 kN per cable.
• Design stress in anchoring lugs: 120–150 MPa (typical for S355 under service loads).
• Intended safety factor: 2.0–2.5 for variable loading.

Industry standards comparison:

• FEM Rules for BWE Design (German standard):

  ○

  Recommended safety factor: 2.0–2.5 for variable loading.

  ○

  Current equipment: 1.69–2.12 (below recommendation for left lug).

• ISO 5049 [21] (Mobile Mining Machines—Safety):

  ○

  Requires structural analysis under maximum intended loading.

  ○

  Annual inspection of load-bearing structures.

  ○

  Current practice: Consistent with ISO requirements.

• Eurocode 3 (Steel Structures):

  ○

  Serviceability limit state: σ ≤ σ_y/2.0 = 177.5 MPa.

  ○

  Current equipment: Left lug exceeds by 18%.

Conclusion: The measured stress levels are high but not unprecedented for aging BWE equipment with production enhancements. The stress magnitudes are consistent with the published literature for similar equipment, providing confidence in measurement accuracy. However, the exceedance of serviceability design allowables warrants the enhanced monitoring and operational modifications recommended in Section 5.2.

5.3. Dynamic Loading Characteristics and Frequency Response

The dynamic amplification factors and frequency-domain analysis provide insight into the relative contributions of quasi-static versus dynamic loading components.

Dynamic Amplification Interpretation:

The inverse relationship between stress magnitude and dynamic amplification factor (higher stresses → lower DAF, lower stresses → higher DAF) suggests that the high-stress condition (left rotation) operates in a more quasi-static regime, with the structure responding primarily to mean cable tension. The lower-stress condition (right rotation) allows greater relative influence of dynamic effects from individual bucket impacts and structural vibrations.

This behavior indicates that the critical loading condition (left rotation, 210 MPa) is dominated by geometric and gravitational effects rather than transient dynamic phenomena. Consequently, structural modifications or operational changes targeting the quasi-static load path (cable routing, counterweight repositioning) will be more effective than damping or vibration isolation approaches.

Frequency-Domain Significance:

The frequency spectrum analysis confirms several important characteristics:

• Quasi-static loading dominates (75–85% of signal energy), validating the use of static analysis methods for primary stress assessment.
• Bucket-wheel rotation fundamental frequency (1.5 Hz) and its harmonics contribute 8–12%, representing the cyclic loading component relevant for fatigue analysis.
• Bucket passage frequency (30 Hz) creates a moderate dynamic component (5–8%), corresponding to individual bucket–soil impact events.
• Structural resonances have minimal contribution (<5% total), indicating that the structure is sufficiently stiff to avoid resonant amplification at operational frequencies.

5.4. Fatigue Assessment and Long-Term Service Considerations

While the stress range analysis (Table 13) indicates that anchoring lugs remain below the Eurocode 3 Category 71 fatigue limit (71 MPa at 2 million cycles), several factors warrant continued monitoring and conservative fatigue assessment.

Factors Requiring Continued Monitoring:

Variable Amplitude Loading: Actual operational loading includes occasional hard material encounters, creating transient stress excursions beyond measured values during routine lignite excavation.

Cumulative Service: With an estimated 70–200 million operational cycles accumulated over 45–50 years, even low-amplitude cycles contribute to fatigue damage accumulation.

Weld Quality: Stress concentrations at welded connections may locally exceed measured surface values, particularly if weld quality is inconsistent or if subsurface defects exist.

Corrosion Effects: Exposure to weather and mine water over decades may have initiated pitting corrosion, reducing the effective cross-sectional area and fatigue resistance.

Weld-Specific Fatigue Considerations and Detail Category Assessment

The preliminary fatigue assessment presented in Table 13 applies Eurocode 3 Category 71 (base metal) as a conservative baseline; however, a more rigorous treatment must acknowledge that the anchoring lugs are welded structures, for which fatigue strength is governed by the weld detail category rather than base metal properties. This distinction has critical implications for long-term structural integrity assessment.

Weld Detail Category Classification

According to Eurocode 3 (EN 1993-1-9 [19]), welded structural details are classified into fatigue categories (36, 40, 50, 56, 63, 71, 80, 90, 100, 112 MPa) based on geometric configuration, weld type, and loading direction relative to the weld. The anchoring lugs incorporate multiple weld types:

• Cable attachment welds (connecting lug plate to backing structure): Likely Categories 50–63 based on filet weld geometry and transverse loading orientation. These welds experience the full measured stress range (24–50 MPa for lugs).
• Pin-hole reinforcement welds (if present): Categories 40–50 due to high stress concentration at the circular discontinuity combined with weld geometry effects.
• Structural plate welds (joining lug components): Categories 63–80 for longitudinal butt welds; Categories 50–63 for transverse connections.
• The use of Category 71 (base metal) in Table 13 is appropriate for initial screening but represents a non-conservative assumption for final fatigue life assessment of welded details. Applying appropriate weld categories would reduce the allowable stress range by 30–50% compared to base metal values.

Revised Fatigue Assessment for Welded Structures

Assuming that the critical cable attachment welds fall into Category 50 (a reasonable engineering estimate for filet welds under transverse loading), the allowable stress range at 2 million cycles becomes 50 MPa rather than 71 MPa. Under this classification:

• Left lug, left rotation: Δσ = 50 MPa = 1.00 × Category 50 limit → Finite life, critical.
• Right lug, left rotation: Δσ = 37 MPa = 0.74 × Category 50 limit → Acceptable for 2M cycles, finite life beyond.
• Both lugs, right rotation: Δσ = 24–25 MPa = 0.48–0.50 × Category 50 limit → Likely infinite life if weld quality is good.

This refined analysis indicates that the left lug during left rotation operates at the fatigue limit for Category 50 welded details, not comfortably below it. The accumulated 70–200 million cycles over 45–50 years of service may have consumed a significant fraction of the available fatigue life.

Stress Concentration Effects at Welds

Beyond the nominal weld detail category, several localized effects further reduce fatigue resistance:

• Weld toe stress concentration: Geometric discontinuity at the weld toe creates stress concentration factors of 2.0–4.0, depending on weld profile quality. Local stresses at the weld toe may reach 100–200 MPa (2–4× the measured surface stress of 50 MPa), potentially exceeding even the base metal endurance limit.
• Residual stresses: Welding-induced residual tensile stresses (typically 50–80% of yield strength in the as-welded condition) combine with operational stresses. Although stress relief may have been performed during original fabrication, 45–50 years of service may have redistributed residual stress patterns.
• Heat-affected zone (HAZ) properties: The HAZ adjacent to welds exhibits an altered microstructure with potentially reduced ductility and toughness compared to the base metal. For S355 steel, the HAZ may have higher hardness but lower fracture toughness, making it susceptible to brittle crack initiation under cyclic loading.
• Weld defects and discontinuities: Even high-quality welds contain microscopic discontinuities (porosity, slag inclusions, lack of fusion) that act as crack initiation sites. After 45–50 years and ~100 million cycles, sub-critical defects may have grown to detectable crack sizes (>2–3 mm).

Variable Amplitude Loading and Cumulative Damage

The constant amplitude fatigue assessment (Table 13) provides only a first-order estimate. Actual operational loading is variable amplitude, incorporating:

• Routine lignite excavation: Δσ = 24–50 MPa (measured values), 64,800 cycles/shift.
• Hard material encounters (estimated 5–10% of time): Δσ = 60–80 MPa (1.2–1.6× measured), ~6000 cycles/shift.
• Overload events (rock layers, frozen ground): Δσ = 100–150 MPa (2–3× measured), ~500 cycles/shift.
• Cable re-tensioning cycles: Large-amplitude stress cycles during maintenance.

Using Miner’s rule for cumulative damage assessment, D = Σ (n_i/Ni) where n_i = actual cycles at stress range i, N_i = allowable cycles from the S-N curve.

For the left lug over 45 years (assuming 8000 operating hours/year × 45 years = 360,000 h):

• Routine cycles: ~23 billion cycles at Δσ = 35 MPa (mean).
• Hard material: ~2.2 billion cycles at Δσ = 70 MPa.
• Overload events: ~180 million cycles at Δσ = 120 MPa.

A preliminary Miner’s sum calculation (assuming Category 50 detail and standard S-N slope m = 3) suggests cumulative damage D = 0.3–0.8 (where D = 1.0 indicates predicted failure). This rough estimate confirms that the structure may have consumed 30–80% of its fatigue life, supporting the concern that continued operation without mitigation warrants close monitoring.

Significance of 60% Yield Stress Operation

The maximum stress of 210 MPa, representing 59.2% of yield strength (355 MPa), is particularly significant for fatigue assessment. Industry guidelines for cyclic loading applications (offshore structures, crane structures, mining equipment) typically recommend limiting operational stresses to 40–50% of yield strength to ensure adequate fatigue margins. The exceedance of this threshold by 10–20% indicates that:

• The original design intent (for 18-bucket configuration) likely targeted peak stresses of 140–180 MPa (40–50% of yield), with appropriate fatigue margins for the intended service life.
• The 20-bucket modification has elevated stresses beyond the original fatigue design envelope, potentially reducing the intended design life by a factor of 2–4, depending on the S-N curve slope.
• Even if ultimate strength failure is not imminent (safety factor 1.69 against yield), the structure operates in a regime where fatigue becomes the governing failure mode rather than static overload.

Applicability Limits of Current Fatigue Assessment

The current study provides essential baseline data but has inherent limitations for quantitative fatigue life prediction:

• No direct weld inspection data: Strain gauges measure surface stresses on parent metal, not local stresses at weld toes or roots where cracks typically initiate. Actual stress ranges at critical weld details may be 2–4× higher than measured values.
• Assumed weld quality: Analysis assumes “adequate weld quality” without radiographic or ultrasonic examination to confirm absence of significant defects. Weld quality variations could reduce fatigue life by factors of 2–10 compared to defect-free conditions.
• Limited load spectrum: 200 s measurement windows during routine lignite excavation do not capture the full operational stress spectrum, particularly extreme events that contribute disproportionately to cumulative fatigue damage.
• Single-equipment dataset: Results represent one excavator at one mine. Fleet-wide fatigue behavior may vary due to differences in operational practices, maintenance history, and as-built weld quality.
• Deterministic vs. probabilistic: The assessment uses deterministic criteria (stress < allowable) without probabilistic treatment accounting for uncertainties in loading, material properties, weld quality, and S-N curve scatter (typically a factor of 3–10 in fatigue life at a given stress range).

These limitations do not invalidate the findings but constrain the ability to make quantitative remaining life predictions. The appropriate conclusion is that the structure is adequate for continued operation with enhanced monitoring, not that it is certified for a specific additional service period.

Academic Implications and Research Directions

From a research perspective, this study raises several important questions regarding fatigue assessment of aged, modified large-scale welded structures:

• Transition from design life to extended operation: How should fatigue assessment criteria evolve when equipment operates beyond its original design life? Current codes provide design criteria but limited guidance for in-service assessment of aged structures.
• Weld detail categorization for complex geometries: The anchoring lug geometry combines multiple weld types in a three-dimensional stress field. Existing detail category classifications may not accurately represent fatigue behavior. Full-scale fatigue testing or advanced crack growth modeling would provide a better understanding.
• Effect of service aging on fatigue resistance: Does 45–50 years of cyclic loading and environmental exposure degrade fatigue resistance beyond what is captured in laboratory S-N curves developed on virgin specimens? This has implications across mining, marine, and civil infrastructure sectors.
• Validation of remaining life prediction methods: Probabilistic fracture mechanics approaches are theoretically superior to Miner’s rule but require detailed inputs often unavailable for operating equipment. Comparative studies would advance practical assessment capabilities.
• Risk-based inspection optimization: How should inspection intervals and methods be optimized to balance detection probability, consequence of failure, and economic considerations?

Recommended Future Investigations

To transition from preliminary assessment to quantitative remaining life prediction, the following investigations are recommended:

• Weld inspection campaign: Magnetic particle inspection (MPI) of accessible weld toes, ultrasonic testing (UT) of weld roots, and radiographic examination of complex joints to establish actual weld quality, detect existing crack-like indications, and provide a baseline for future comparison.
• Material property testing: Extract material samples from decommissioned sister excavator to determine actual yield strength, cyclic stress–strain properties, crack growth rate da/dN vs. ΔK, and fracture toughness K_IC after 45–50 years’ service.
• Extended stress monitoring: Install permanent strain-gauge instrumentation for 6–12-month continuous monitoring to capture complete operational load spectrum, including rare extreme events, seasonal variations, and actual left/right-rotation usage patterns.
• Probabilistic fatigue assessment: Develop a Monte Carlo simulation incorporating uncertainties in weld quality, load spectrum, initial flaw size, and material properties to yield probability distributions of remaining life, supporting risk-informed decision making.
• Comparative fleet study: Replicate measurements on multiple ER-1400 family excavators to quantify equipment-to-equipment variability and establish whether current findings represent best-case, worst-case, or typical conditions.

Preliminary Fatigue Life Estimate: Applying Miner’s cumulative damage rule to the left anchoring lug under left rotation (Δσ = 50 MPa at Category 50 limit), and assuming constant amplitude loading at 90 rpm bucket wheel rotation (47 million cycles per year), the theoretical fatigue life is N = 2 million cycles, corresponding to approximately 14 months of continuous operation. However, actual operational practice includes periods of right rotation (Δσ = 25 MPa, infinite life regime) and equipment downtime, extending practical life. With an estimated 50% left-rotation usage and 60% operational availability, the projected service life extends to approximately 4–5 years before reaching the fatigue limit. This preliminary estimate provides order-of-magnitude guidance for inspection scheduling; comprehensive remaining life prediction requires detailed variable amplitude load spectrum analysis, accounting for load history effects, weld quality variations, and potential fatigue crack initiation sites, which will form the basis of future work under extended monitoring programs.

Fatigue Monitoring Recommendation:

Despite analytical predictions of infinite life based on measured stress ranges, both anchoring lugs should be inspected annually using non-destructive testing (magnetic particle inspection or ultrasonic testing) to detect fatigue crack initiation before propagation to critical size. This precautionary approach is justified by the excavator’s extended service history, the criticality of the left lug (safety factor 1.69), and the potential for stress concentrations at unmeasured locations (weld roots, internal discontinuities) to exceed surface strain-gauge readings.

5.5. Computational Model Validation and Confidence Bounds

The exceptional agreement between finite element predictions and experimental measurements (average difference 4.6%, maximum 5.7%) establishes high confidence in the computational modeling approach and enables extension of the validated models to scenarios not directly measured.

Quality of Validation:

The 3.1–5.7% differences between FEA and measurements represent excellent agreement, well within the typical validation criterion of <15% for structural FEA applied to large-scale welded structures. This level of agreement is particularly noteworthy given the complexity of the loading conditions (combined axial bending, variable cable angles, dynamic effects) and the scale of the structure.

The slightly lower FEA predictions compared to measurements (162 vs. 167 MPa for right lug, 198 vs. 210 MPa for left lug) likely result from (1) simplified boundary conditions representing the counterweight structure as rigid constraints rather than modeling full structural flexibility; (2) idealized nominal material properties (E = 210 GPa) rather than specimen-tested values; and (3) as-designed geometry without accounting for manufacturing tolerances or 45–50 years of service-induced geometric changes.

Stress Concentration Implications:

The FEA results indicate that local stresses at geometric discontinuities (pin-hole radius, weld toes) exceed surface strain-gauge measurements by 8–10%. For the left lug, the predicted maximum stress of 228 MPa at the pin radius represents 64% of yield strength (safety factor 1.56), slightly more critical than the gauge measurement location (210 MPa, 59% of yield, safety factor 1.69).

However, these localized stress concentrations are inherent to the design geometry and, provided that weld quality is adequate and no crack-like defects exist, do not necessarily indicate structural inadequacy. The design philosophy for such structures relies on limited local plasticity at stress concentrations to redistribute loads—a well-established principle for static and quasi-static loading of ductile steel structures. The key requirement is that global yielding does not occur, a condition satisfied by the measured and predicted stress levels.

Utility of Validated Models:

The validated FEA models enable several important applications without requiring additional costly field measurements:

• Parametric studies of reinforcement options (doubler plates, geometry modifications) to evaluate structural improvements before implementation.
• Virtual testing of extreme loading scenarios (frozen ground, rock layer encounters, maximum production rates) to establish operational limits.
• Optimization of structural geometry for future equipment designs or planned modifications.
• Foundation for crack growth modeling and remaining life assessment using fracture mechanics approaches.

6. Conclusions

This experimental investigation of a modified ERc 1400-30/7 bucket-wheel excavator advances the understanding of structural behavior in large-scale mining equipment following capacity-enhancing modifications. Beyond the specific findings for this installation, the study establishes a validated methodology for post-modification structural verification and identifies fundamental loading characteristics relevant to the broader class of articulated excavation machinery.

6.1. Principal Findings

The comprehensive strain-gauge measurement campaign, encompassing eight critical structural locations under dual operational loading conditions, yielded four principal findings with implications extending beyond this specific equipment:

Structural Adequacy with Reduced Margins: The 11% increase in bucket count (18 → 20) elevated operational stresses in cable anchoring lugs to 47–59% of material yield strength—approaching or exceeding typical serviceability design thresholds (50% of yield) but remaining below ultimate capacity. Safety factors of 1.69–2.12 in critical components confirm adequate load-carrying capacity for continued operation, though with reduced design margins relative to the original configuration. This finding establishes that bucket-wheel capacity enhancements, while structurally feasible, necessitate transition from passive monitoring to active structural health management.

Severe Directional Load Asymmetry: Left-rotation excavation induces stresses 2.8–3.2 times higher than right-rotation operation in mast–counterweight connections—a phenomenon unreported in the prior literature and unaccounted for in conventional symmetric loading design assumptions. This asymmetry, attributable to counterweight geometric offset (2–3 m from excavator centerline), direction-dependent mast deflection patterns, and inertial effects from the rotating bucket-wheel mass, demonstrates that articulated mining structures exhibit fundamentally different loading behavior than predicted by quasi-static analysis. The practical implication—that operational practice (rotation direction preference) determines structural loading as significantly as equipment design—establishes operational management as a critical variable in structural integrity assessment.

Moderate Dynamic Amplification: Dynamic stress amplification of 15–32% above quasi-static levels, with frequency content dominated by quasi-static components (75–85% of signal energy) and minimal contribution from structural resonances (<5%), indicates that bucket–soil interaction effects are significant but do not fundamentally alter the loading regime. This finding validates the application of quasi-static computational methods for design evaluation while demonstrating the necessity of including moderate dynamic factors (1.15–1.30) in fatigue life calculations. The inverse relationship between static stress magnitude and the dynamic amplification factor reveals that high-stress operational conditions paradoxically exhibit more predictable, quasi-static loading behavior.

Exceptional Computational–Experimental Agreement: Finite element predictions achieved 3–6% agreement with measured stresses across all validation locations—significantly exceeding typical structural FEA validation criteria (<15%) and approaching the precision of laboratory test articles. This level of agreement, obtained for a complex multi-tone welded assembly under combined axial-bending loading, establishes confidence in computational prediction accuracy when models are carefully calibrated with boundary conditions representative of actual installation geometry and loading distributions. The validated models enable parametric investigation of reinforcement strategies, virtual testing of extreme loading scenarios, and probabilistic life assessment without requiring additional field measurements.

6.2. Significance and Broader Implications for Large-Scale Mining Equipment

The findings transcend the specific excavator investigated and contribute to a broader understanding of structural integrity assessment for aging, modified large-scale mining equipment.

6.2.1. Post-Modification Structural Verification Paradigm

Mining equipment frequently undergoes capacity-enhancing modifications (increased bucket counts, enlarged bucket volumes, higher rotation speeds) to meet escalating production targets, yet systematic structural verification of modified configurations remains uncommon in industry practice. This study demonstrates that post-modification stress levels can approach or exceed original serviceability design envelopes even when ultimate strength margins appear adequate, necessitating experimental validation rather than reliance on engineering judgment or simplified scaling assumptions.

The validated methodology—combining strategically positioned strain gauges (8–10 measurement points suffice for critical location identification), short-duration operational measurements (200 s windows capture representative loading), and computational validation—provides a cost-effective framework applicable to bucket-wheel excavators, draglines, walking draglines, electric mining shovels, and other large-scale excavation equipment classes. The total measurement campaign cost (€50,000–100,000 including instrumentation, installation, data acquisition, and analysis) represents <1% of excavator replacement cost (€15–30M) and <0.1% of production loss cost from premature structural failure, establishing favorable cost–benefit economics for proactive structural assessment.

Critically, this approach shifts structural integrity assessment from reactive (respond to failures) to predictive (identify critical locations before failure initiation), enabling risk-based maintenance resource allocation and supporting continued operation of aging equipment fleets with quantified confidence rather than empirical precedent.

6.2.2. Operational Loading Characterization in Articulated Structures

The documented 2.8–3.2× directional load asymmetry challenges conventional design assumptions of symmetric loading in articulated mining structures and demonstrates that geometric configuration (counterweight offset, cable routing, boom position) interacts with operational parameters (rotation direction, excavation depth, material resistance) to create loading conditions fundamentally different from those predicted by static equilibrium calculations.

This finding has broad implications for structural design philosophy: equipment specifications typically define loading by production capacity (m³/h) and material properties (cutting resistance, bulk density), but operational loading depends equally on how the equipment is used—rotation preferences, face geometry planning, cycle sequencing. Design codes for mining equipment (DIN 22261-2 [16], ISO 5049 [21]) do not currently account for operational asymmetry effects of this magnitude, suggesting that industry standards may benefit from revision to incorporate directionally dependent load factors derived from field measurements on representative installations.

Furthermore, the discovery that operational practice modifications (rotation balancing) can reduce peak stress exposure by factors of 2–3 without capital investment establishes operational optimization as a previously underappreciated structural integrity management strategy. Training programs, operator guidance systems, and production planning tools incorporating structural loading considerations represent low-cost interventions with potentially significant life extension benefits.

6.2.3. Integration of Experimental and Computational Methods

The exceptional FEA–experimental agreement (3–6% difference) achieved in this study demonstrates that careful computational modeling, when validated against field measurements, can reliably predict stresses in complex large-scale structures—a result with implications extending across civil, mechanical, and mining engineering applications involving aging infrastructure assessment.

The integrated approach—experimental measurements identify critical locations and validate model accuracy; validated models enable parametric studies of scenarios impractical to measure directly—provides a scalable methodology for structural assessment programs. This is particularly valuable for aging equipment fleets where individual unit measurement is economically prohibitive: measure representative units to validate computational models, then apply validated modeling approaches to fleet-wide assessment with periodic experimental verification.

The validated models also enable probabilistic structural reliability assessment incorporating uncertainties in loading (variable amplitude spectra), material properties (service-induced degradation), and geometric tolerances (as-built vs. as-designed), supporting risk-informed decision making for life extension, reinforcement prioritization, and inspection interval optimization—capabilities that advance structural integrity management from deterministic pass/fail criteria toward quantitative risk assessment aligned with modern asset management practices.

6.2.4. Fatigue Assessment in Welded Large-Scale Structures

The investigation highlights fundamental challenges in applying laboratory-derived fatigue assessment methods to aged, welded, large-scale industrial structures: measured stress ranges suggest favorable fatigue life when assessed against base metal criteria, yet accounting for realistic weld detail categories (Categories 40–50 vs. Category 71 base metal) transitions the assessment from infinite to finite life—a 30–50% reduction in the allowable stress range with profound implications for remaining life prediction.

This underscores a broader issue in structural integrity assessment of operating equipment: standard design codes (Eurocode 3 [16] AWS D1.1 [18], ASME) provide fatigue strength data for idealized conditions (virgin materials, controlled weld quality, laboratory loading), but field conditions involve complexities (service-induced material degradation, unknown weld quality, variable amplitude loading with rare overload events) that introduce substantial uncertainty. The preliminary cumulative damage assessment (Miner’s rule) suggests that 30–80% of fatigue life may have been consumed over 45–50 years of service—a result that, while uncertain due to input parameter assumptions, demonstrates the necessity of transitioning from deterministic “infinite life” declarations to probabilistic remaining life assessments acknowledging uncertainty.

The appropriate response is not to declare equipment unsafe based on conservative fatigue calculations, but rather to implement enhanced monitoring (semi-annual NDT inspections targeting weld locations) that detects crack initiation before propagation to critical size—a risk management approach balancing continued productive utilization against proactive intervention when physical evidence indicates deterioration. This philosophy—operate with enhanced monitoring rather than premature retirement based on conservative analytical predictions—is broadly applicable to aging infrastructure across mining, marine, and civil engineering sectors.

6.3. Methodology Transferability and Industry-Wide Applicability

While the quantitative stress values obtained in this study are specific to the ERc 1400-30/7 excavator with 20-bucket modification operating at the Jilț mine, the experimental–computational methodology is transferable to:

• Other bucket-wheel excavator classes (SchRs, SRs, ERs series) requiring post-modification verification or periodic structural assessment.
• Draglines, walking draglines, and electric mining shovels—articulated structures with comparable complexity and loading characteristics.
• Large-scale material handling equipment (stackers, reclaimers, ship loaders) where critical load paths require verification.
• Aging equipment fleets (30–50+ years’ service) where original design documentation is incomplete or operating conditions have evolved beyond the design basis.
• Equipment subjected to operational modifications (increased speeds, altered loading patterns, environmental condition changes) requiring structural impact assessment.

The methodology’s key attributes facilitating transfer include:

Modest instrumentation requirements: 8–16 strain-gauge channels are typically sufficient for critical location identification and validation.

Short measurement duration: 200 s operational windows capture representative loading; extended monitoring (days/weeks) is not required for initial assessment.

Standard equipment compatibility: Measurements conducted during normal production operation without equipment disassembly or production interruption.

Computational validation framework: FEA validation establishes model accuracy for parametric studies and scenario evaluation without repeated field measurements.

Risk-based decision support: Quantitative stress data enables prioritization of monitoring and reinforcement resources based on measured criticality rather than theoretical assumptions.

Adoption of this methodology by mining operators, equipment manufacturers, and engineering service providers would support systematic structural integrity assessment across operating fleets, potentially preventing costly failures while enabling continued productive utilization of aging capital equipment with quantified confidence in structural adequacy.

Quantitative Transferability Criteria

The experimental–computational methodology presented is applicable to bucket-wheel excavators and comparable articulated mining equipment satisfying the following similarity conditions:

Geometric Similarity:

• Boom length: 80–120 m (±30% of ERc 1400 configuration).
• Mast height: 15–25 m.
• Bucket-wheel diameter: 10–16 m.
• Counterweight offset from boom axis: 1.5–3.5 m.

Mass Scaling and Dimensionless Ratios:

• Operating mass: 1000–2000 tons.
• Bucket-wheel mass/Total operating mass: 0.03–0.06 (dimensionless).
• Counterweight mass/Bucket-wheel mass: 0.8–1.5 (dimensionless).

Operational Similarity:

• Material hardness: Unconfined compressive strength (UCS) < 15 MPa (lignite, soft coal, overburden).
• Bucket-wheel rotation speed: 60–120 rpm.
• Nominal excavation rate: 2000–6000 m³/h.

Structural Similarity:

• Welded steel construction (S355 or equivalent grades, 275–355 MPa yield).
• Cable-suspended counterweight systems (as opposed to rigid frame).
• Articulated boom–mast connections (pinned or bolted joints).

Excavators outside these parameter ranges require independent verification measurements, though the general methodological framework (critical location identification based on preliminary FEA → strategic strain-gauge deployment → operational loading characterization → refined FEA validation → safety assessment) remains conceptually applicable with adjusted instrumentation specifications and boundary conditions.

For equipment within the specified similarity bounds, the methodology can be applied with high confidence that critical structural locations, loading patterns, and analysis approaches will be representative. For equipment at or beyond the similarity limits, preliminary FEA screening is recommended to assess whether the identified critical locations (cable anchoring lugs, diagonal members) remain governing or whether alternative locations dominate the structural response.

6.4. Practical Recommendations

For the specific excavator investigated, comprehensive analysis supports continued safe operation subject to:

Enhanced monitoring: Semi-annual non-destructive testing (magnetic particle inspection, ultrasonic testing) of cable anchoring lugs, with acceptance criteria: no crack indications >2 mm.

Operational optimization: Target balanced excavation time between left and right rotation (50 ± 10%) to reduce peak stress exposure and equalize fatigue damage accumulation.

Strategic reinforcement: Evaluate selective structural reinforcement during next major overhaul (2–5 years) to restore full serviceability margins.

More broadly, mining operations managing aging excavator fleets should consider:

Fleet-wide risk assessment: Identify highest-risk equipment based on service history, modification status, and operational loading patterns.

Prioritized measurement campaigns: Deploy experimental validation on representative high-risk units to calibrate computational models for fleet-wide assessment.

Operator training programs: Educate operational personnel on structural loading implications of operational choices (rotation preferences, excavation sequencing).

Integration with asset management: Incorporate structural integrity assessment into enterprise asset management systems for data-driven maintenance decision making.

6.5. Study Limitations and Recommended Future Research

The current investigation provides essential baseline data and validated methodology, yet several limitations constrain quantitative life prediction and fleet-wide generalization:

Limited temporal scope: Short measurement windows capture routine operational loading but not seasonal variations, extreme events, or long-term degradation trends.

Single-equipment dataset: Results represent one installation; fleet-wide variability in geometry, operational practice, and material condition remains uncharacterized.

Material property assumptions: Nominal design properties assumed; actual properties following 45–50 years’ service (microstructural changes, corrosion effects) not measured.

Preliminary fatigue assessment: Constant amplitude S-N curve approach provides screening-level evaluation; detailed remaining life prediction requires comprehensive variable amplitude load spectrum analysis and probabilistic treatment of uncertainties.

Advancing the field requires:

Extended monitoring programs: Continuous stress measurement over 6–12-month periods, capturing complete operational loading spectra, including rare extreme events.

Material characterization from service-exposed components: Destructive testing of decommissioned excavator structures to establish actual (degraded) material properties and S-N curves.

Comparative fleet studies: Replicate measurements across multiple excavators to quantify equipment-to-equipment variability and identify fleet-wide risk factors.

Probabilistic life assessment frameworks: Monte Carlo simulation incorporating uncertainties in loading, material properties, weld quality, and inspection detection probability to yield probability-of-failure distributions supporting risk-informed decisions.

Development of industry standards: Synthesis of field measurement data from multiple installations to establish design guidelines for post-modification verification and aging equipment assessment applicable across the mining equipment industry.

6.6. Concluding Remarks

This investigation demonstrates that large-scale mining equipment subjected to capacity-enhancing modifications can continue safe, productive operation when structural assessment transitions from passive reliance on original design margins to active integrity management based on validated experimental–computational methods. The documented methodology—combining strategic field measurements with computational validation—provides a cost-effective, transferable framework applicable across the mining equipment sector for post-modification verification, aging equipment assessment, and operational optimization.

The fundamental contribution extends beyond confirmation of structural adequacy for this specific installation: this study establishes that operational loading in articulated mining structures exhibits complexities (directional asymmetry, dynamic amplification patterns) not captured by conventional design analysis, necessitating field validation even when computational predictions suggest acceptable stress levels. Furthermore, the discovery that operational practice modifications can reduce peak stress exposure by factors of 2–3 elevates operational management from a production optimization concern to a critical structural integrity parameter.

As mining operations worldwide confront the dual challenge of aging equipment fleets and escalating production demands, systematic structural integrity assessment becomes essential for balancing continued productive utilization against catastrophic failure risk. The validated methodology presented in this study—applicable to bucket-wheel excavators, draglines, and comparable large-scale mining equipment—provides the technical foundation for quantitative, risk-informed asset management decisions that extend equipment life, optimize maintenance resource allocation, and support safe, economically viable operations of critical mining infrastructure.