Tribological Behavior and Wear Prediction of Copper-Based Brake Pads for Monorail Cranes Under Complex Hygrothermal Environments

Abstract

A significant amount of frictional heat is generated during the braking process of mine-used monorail cranes under heavy-load and low-speed creeping (or reciprocating speed regulation) conditions, causing thermal softening and performance degradation of the brake pads. Thus, investigating the tribological evolution mechanism is necessary to ensure reliable braking in deep underground environments. In this paper, full-scale tribological testing technology is applied to the brake system, and the friction and wear characteristics of copper-based powder metallurgy (P/M) brake pads under complex hygrothermal environments are studied. A physical experimental model coupling normal load, sliding speed, and humidity is established using a custom-designed open-structure reciprocating tester, revealing the “load weakening effect” under dry conditions and the “dual regulation mechanism” of mixed lubrication and cooling flushing under high humidity. Then, a surrogate prediction model of friction coefficient and wear rate, with respect to the operating parameters, is constructed based on Central Composite Design (CCD) and Response Surface Methodology (RSM). The reliability of the model under non-linear working conditions is estimated based on Analysis of Variance (ANOVA) and blind tests. The results indicate that the model possesses high prediction accuracy (relative error < 5%), and the feasibility of utilizing the high-humidity environment to enhance wear resistance and stability is verified.

1. Introduction

As pivotal auxiliary transport equipment in modernized coal mines, the suspended monorail crane has been extensively deployed due to its exceptional capability to surmount adverse environmental constraints, such as undulating roadways and deteriorated floor conditions. It exhibits superior adaptability in scenarios requiring heavy-load, high-efficiency transport under complex humid conditions. Within this rigorous operational context, the braking friction pair—comprising the brake pad and the rail—constitutes the core execution unit governing the reliability of the braking system and the safety of the entire machine. Upon brake activation, the hydraulic actuator rapidly propels the brake pad to adhere to the rail surface. Through intense mechanical interlocking and relative sliding at the contact interface, massive braking resistance is generated, effectively converting the vehicle’s kinetic energy into thermal energy. This process is inevitably accompanied by severe frictional heat accumulation and surface material damage, placing the friction pair under extreme thermo-mechanical coupling conditions for extended periods. However, the tribological behavior of the monorail braking process exhibits significant non-linear characteristics. When intertwined with unique underground environmental factors—specifically high humidity and heavy impact loads—traditional tribological models based on steady-state assumptions often fail to accurately predict friction stability and wear evolution laws in actual operations. Consequently, an in-depth investigation into the braking friction mechanisms under these complex multi-factor coupled conditions is imperative for optimizing the design and ensuring the operational safety of mine transport systems.

Literature Review

The reliability of the braking system fundamentally depends on the tribological characteristics of the friction pair. In recent decades, extensive research has been conducted on the thermal–mechanical behavior, material formulation, friction mechanisms, and environmental adaptability of brake systems.

Regarding the thermal–mechanical behavior of braking, finite element analysis (FEA) has established a theoretical foundation for understanding heat accumulation. Popescu et al. [1] performed numerical modeling of mine hoist disk brake temperatures, emphasizing that accurate thermal prediction is crucial for safer operation in mining environments. Building on this, Belhocine and Abdullah [2] presented numerical modeling to track the evolution of global temperatures for ventilated disks, highlighting that frictional thermal fields lead to excessive temperatures. Similarly, the study in [3] developed a coupled thermo-structural model, demonstrating that heat distribution significantly affects the contact pressure distribution on brake pads. Furthermore, Ay and Demir [4] investigated the thermo-mechanical behavior in disk–pad couples, revealing that the combined effects of speed and braking time lead to significant von Mises stress increases and disk-thickness variations. These studies confirm that thermal management is critical for braking safety.

In terms of material composition optimization, copper-based powder metallurgy (P/M) materials are preferred for heavy-duty applications due to their superior thermal properties. Fan et al. [5] investigated the effect of the Coke/Flake Graphite ratio, finding that an optimized ratio (e.g., 7/2) balances friction coefficient and wear loss. To enhance lubrication, Zheng et al. [6] analyzed the synergy between Fe and graphite, noting that a specific balance (14% Fe, 20% graphite) is required to optimize hardness. Additionally, Zhang et al. [7] compared Cu-coated and uncoated graphite, discovering that Cu-coated graphite significantly improves thermal conductivity and reduces wear rates. Meanwhile, Li et al. [8] analyzed Cu-coated graphite composites, revealing that a high-strength oxide film formed in metal-rich areas improves wear resistance.

Understanding the microscopic friction mechanism and thermal fade is crucial for predicting service life. Bouillanne et al. [9] quantitatively investigated the “third-body” layer, finding that its flow regime dictates the rate of surface damage. Similarly, Jin et al. [10] simulated the evolution of endogenous third bodies, describing stages of “plowing” and “aggregation.” Regarding thermal fade, Zhang et al. [11] simulated cyclic emergency braking, identifying the softening of the copper-rich phase as the primary cause of friction coefficient decay. Zhang et al. [12] addressed fade during long-downhill operations, revealing that higher initial temperatures lead to hardness reduction and accelerated wear. Furthermore, Lu et al. [13] studied the evolution of friction behaviors with temperature rise, showing a transition from abrasive to oxidative and finally adhesive wear. Wu et al. [14] attributed high-temperature failure to the fragmentation of hard SiO₂ particles and matrix softening, while Xiao et al. [15] emphasized that oxidation transforms the dominant wear mechanism. Crucially, full-scale testing conducted by Xiao et al. [16] at speeds of 380 km/h confirmed that a nanostructured tribolayer enables significantly higher wear resistance than the original surface.

However, a significant gap remains regarding complex environmental factors, particularly humidity. The operating environment in deep mines introduces high complexity. Zhang et al. [17] evaluated friction characteristics using a self-designed humidity-controllable tester and found that, contrary to intuition, wear damage was greatly improved under high ambient humidity conditions. Conversely, Ding et al. [18] found that while humidity reduces the instantaneous friction coefficient of high-speed rail materials, it also causes severe surface damage. To address wet friction challenges, Chen et al. [19] proposed optimizing porosity and surface texture, achieving significant wear reduction. On a mechanism level, Yi et al. [20] revealed that water film adsorption alters boundary slip behavior.

To accurately predict performance under these multi-physics coupling conditions, advanced statistical modeling is required. Response Surface Methodology (RSM) has proven effective in quantifying non-linear interactions. Mekgwe et al. [21] utilized RSM to optimize dry sliding wear properties, achieving a prediction model with high confidence. Similarly, Sathiyamurthy et al. [22] and Borgaonkar and Syed [23] successfully applied RSM to develop empirical models for hybrid fiber-reinforced composites and MoS₂ coatings. Furthermore, Saravanan et al. [24] integrated RSM with ensemble machine learning algorithms to optimize tribological parameters for additive-manufactured steels, achieving high prediction accuracy. Yadav et al. [25] developed a quadratic model for complex concentrated alloys to predict tribological behavior. Additionally, the robustness of ANOVA-based statistical models for predicting wear and friction was validated by Kolawole et al. [26]. These methodologies provide a robust framework for establishing the multi-factor prediction models in this study.

Despite these advancements, a unified model that simultaneously accounts for full-scale geometric factors and the non-linear coupling of hygrothermal environments is still lacking.

However, it is worth noting that the braking requirements for explosion-proof monorail cranes in underground mines differ significantly from those of high-speed railways (e.g., 380 km/h). While high-speed braking emphasizes thermal stability under extreme kinetic energy, the operation of monorail cranes is characterized by low-speed creeping, heavy-load traction, and frequent reciprocating speed regulation. In these specific mining scenarios, the friction pairs often operate at the final stages of emergency braking or in a continuous low-speed crawling state to ensure safety on steep inclines. Therefore, understanding the tribological evolution under these specific boundary conditions is crucial for the safety of underground auxiliary transportation.

The rest of this paper is organized as follows: In Section 2, the properties of the copper-based P/M materials and the methodology of the full-scale experiment are described. In Section 3, the macroscopic influence of load and speed on tribological performance is analyzed, and investigates the specific regulatory mechanisms of high-humidity environments. In Section 4, a multi-factor prediction model for friction and wear is constructed using Response Surface Methodology (RSM), and the model’s accuracy is verified through ANOVA and blind tests. Finally, the main conclusions and future prospects are summarized in Section 5.

2. Experimental Materials, Equipment, and Methods

2.1. Experimental Materials and Specimen Preparation

To eliminate the scale effect common in traditional small-scale pin-on-disk tests and authentically restore the heat conduction and stress distribution states during braking, no cutting or scaling was applied to the original brake pads in this experiment. Instead, full-scale brake pad components were directly used for testing.

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Upper Specimen (Brake Pad)

Commercial suspended monorail brake pads from a mining equipment manufacturer were selected (Figure 1). The material was identified as copper-based powder metallurgy (P/M), prepared via a high-temperature sintering process.

Material Properties: Compared to traditional resin-based materials, this copper-based P/M material contains a copper matrix (heat conduction), iron powder (reinforcing phase), graphite (lubricating phase), and SiO₂ (friction component). Due to its excellent high-temperature stability, high mechanical strength, and anti-fade performance under heavy loads, it is widely used in the braking systems of new-generation large-tonnage monorails.

Geometry and Physical Parameters: The specimen is cylindrical with a diameter of $\varphi$ 32 mm, a thickness of 10 mm, and a nominal contact area of 8.04 cm² (calculated based on geometric dimensions). According to the inspection report, the measured density is 11.4 g/cm³, and the friction surface hardness is HRC $>70$.

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Lower Specimen (Counterpart Rail)

The counterpart used to simulate the monorail track was manufactured from standard 45# Steel (AISI 1045 Steel), a medium carbon structural steel commonly used in coal mine auxiliary transport tracks and transmission shafts.

Processing and Surface State: The counterpart was machined into a rectangular plate with dimensions of 300 mm (L) × 150 mm (W) × 5 mm (H). To reproduce the authentic conditions, the steel plate surface was mechanically ground before the experiment to strictly control the initial surface roughness within the range of $R_a\approx$ 3.2–6.3 $\mathsf{\mu }$m, simulating the hot-rolled or semi-finished surface texture of underground service rails.

2.2. Experimental Equipment and Environmental Simulation

To reproduce the reciprocating creeping and frequent start–stop conditions of the monorail braking system in narrow underground roadways, a custom-designed open-structure full-scale reciprocating friction and wear tester was employed. The apparatus is controlled by an PC-based control system and mainly consists of a precise electric drive system and a normal loading unit (Figure 2).

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Contact Configuration and Motion Mechanism: The tester adopts a “Flat-on-flat” contact configuration. The upper specimen (brake pad) is stationary, while the lower specimen (rail plate) is driven by a high-precision ball screw linear module to perform horizontal reciprocating linear motion. Stroke Setting: The single reciprocating stroke length is set to 250 mm. This stroke setting ensures that the brake pad remains fully within the effective range of the rail surface (300 mm length) during motion, while enabling the simulation of the “Zero-velocity Point” and stick–slip vibration phenomena observed in actual operations.

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Loading and Data Acquisition: The normal load is applied vertically by a high-thrust electric linear actuator, capable of providing constant pressure with rapid response. The tangential friction force is calculated in real-time via a high-precision dynamic torque sensor mounted on the drive shaft, which converts the torque signal into friction force data through the screw lead ratio. All data is collected and processed by the upper computer software.

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Multi-condition Environmental Simulation: To support the research on the comparative tribological behavior under different humidity levels, localized environmental simulation methods were adopted. Relative Dry Condition: Conducted in a naturally ventilated laboratory environment where the relative humidity is monitored and maintained at approximately $50\%\pm 5\%$ RH. High-Humidity Condition: An artificial humidification system (ultrasonic atomizer) is directed at the contact interface to create a localized high-humidity zone. A hygrometer probe is placed near the friction interface to monitor the environment, ensuring the local relative humidity remains above 90% RH throughout the test.

2.3. Experimental Scheme and Procedures

To systematically decouple the effects of environmental humidity, normal load, and sliding speed on the tribological behavior of monorail brake pads, and to provide reliable data support for the subsequent Response Surface Methodology (RSM) modeling, a full-factorial experimental design was adopted.

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Experimental Variable Settings: The detailed matrix of testing conditions involves three key variables. Environmental Condition: Relative Dry (50% RH) vs. High Humidity (90% RH). Load Gradient: Set at 500, 700, 1000, 1200, and 1500 N, covering the pressure range from light-load creeping to heavy-load emergency braking. Speed Gradient: The reciprocating frequencies were adjusted to correspond to average sliding speeds of 0.125, 0.146, 0.167, 0.188, and 0.208 m/s.

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Testing Procedures: The testing process includes three distinct stages. Step I (Running-in): Given the large contact area of full-scale specimens, to eliminate the influence of machining asperities and establish conformal contact, a running-in process is conducted at 200 N/0.1 m/s for 10 min before the formal test, until the friction coefficient stabilizes. Step II (Reciprocating Wear Test): Formal tests are conducted according to the experimental matrix. Each condition is repeated 3 times to ensure statistical reliability. Step III (Post-processing and Measurement): After each test, the specimens are ultrasonically cleaned with acetone. Note that for high-humidity specimens, to eliminate weighing errors caused by potential moisture absorption (ensuring the accuracy of wear mass analysis), specimens are dried in an oven at 60 °C for 1 h before weighing. The mass loss ($\Delta m$) is then measured using a precision electronic balance (Accuracy: 0.001 g).

3. Experimental Results and Analysis

Following the experimental equipment and testing schemes described in the preceding text, this chapter focuses on a systematic analysis of the tribological performance data of full-scale copper-based powder metallurgy brake pads under “low-speed reciprocating and high-pressure braking” conditions. The experiment simulated the authentic motion states of an explosion-proof monorail crane during heavy-load startup/stopping or slope creeping in underground roadways. Adopting a “Flat-on-flat” contact configuration, the study comparatively investigated the friction and wear differences between underground high-humidity (90% RH) and relatively dry (50% RH) environments. This chapter will analyze the non-linear regulatory mechanisms of sliding speed, normal load, and environmental media on tribological behavior, ranging from macroscopic statistical laws to microscopic damage mechanisms.

3.1. Macroscopic Influence of Load and Speed on Tribological Performance

Based on the statistical data collected from the full-factorial experiment, this section focuses on examining the macroscopic regulatory laws of normal load (500–1500 N) on the tribological performance of copper-based powder metallurgy brake pads in different environmental media.

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Load Weakening and Energy Dissipation in Dry Environment

Figure 3 presents the statistical results of mean friction coefficient and wear mass under 5 different load conditions in a relatively dry environment (50% RH). The following analysis can be drawn from the data distribution trend:

Non-linear Decrease in Friction Coefficient: As the normal load increases from 500 N to 1500 N, the average friction coefficient shows a monotonic downward trend (dropping from approx. 0.55 to 0.50). This load-weakening effect is likely associated with the frictional heat accumulation at the interface. Under high contact stress, although the sliding speed is relatively low, the substantial heat flux generated by the 1500 N load has the potential to increase the interface temperature. Experimental observations during this study showed that the bulk temperature of the specimen surface reached approximately 150 °C under the maximum load condition. According to frictional thermodynamics theory, such heat accumulation may induce localized thermal softening of the copper matrix, thereby reducing the shear strength of the surface layer and leading to the observed decrease in the nominal friction coefficient.

Energy-Driven Characteristics of Wear Mass: Contrary to the friction coefficient, wear mass increases significantly with load. This conforms to the classical Archard’s Law of Wear, where wear volume is proportional to normal load. In the high-load range (1200–1500 N), the slope of wear mass growth slows down slightly, suggesting that under high pressure, debris might be compacted on the contact surface to form a protective third-body layer, mitigating direct material removal to some extent.

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Mixed Lubrication and Damage Inhibition in High Humidity

Figure 4 presents the test data under 90% RH high humidity conditions. Compared to the dry environment, the introduction of the water medium results in distinct evolutionary characteristics:

Friction Reduction Induced by Mixed Effect: Under all load conditions, the wet friction coefficient is lower than the dry friction coefficient (overall decrease of approx. 15–20%). This is because the water film generates a partial mixed load-carrying effect at the contact interface, bearing part of the normal load and reducing direct asperity contact. Especially in the low-load zone (500–700 N), the water film is well-maintained, making the lubrication effect more significant.

Wear Inhibition via Flushing and Cooling: Statistical data shows that wear mass under wet conditions is significantly lower than dry wear under equivalent loads. This numerical difference confirms the dual mechanism of Flushing and Cooling of the water medium: continuous water flow removes frictional heat, inhibiting matrix softening; simultaneously, it flushes hard particles out of the contact zone, blocking the occurrence of severe abrasive wear. This allows copper-based brake pads to demonstrate excellent wear life in humid underground environments.

In summary, macroscopic data indicates that although the high-humidity environment causes a slight decay in braking friction force, it significantly reduces the material’s wear rate through mixed lubrication and thermal cooling mechanisms. This characteristic of “low wear and stable friction” proves that copper-based powder metallurgy materials possess good adaptability to the complex underground service environment of monorail cranes.

3.2. Tribological Evolution Laws Under Speed–Load Coupling Effects

In actual monorail operation, sliding speed and contact load often change simultaneously (e.g., during heavy-load downhill braking, speed and pressure act together). To reveal this coupling mechanism, this section plots the trend curves of friction coefficient (COF) and wear mass varying with running speed (Figure 5 and Figure 6) and introduces the $PV$ factor (Pressure × Velocity) as a metric of energy input to deeply analyze the underlying physical mechanisms.

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Non-linear Decay Characteristics of Friction Coefficient

Figure 5 illustrates the evolution of the friction coefficient with sliding speed under different loads. The data indicates that the copper-based friction material exhibits typical negative velocity dependence and a load weakening effect.

(a) Thermal Softening Mechanism under Dry Friction: As speed increased from 0.125 m/s to 0.208 m/s, the COF under all loads showed a downward trend. Especially under the heavy load of 1500 N, the COF dropped from 0.519 to 0.500. This phenomenon of “friction reduction under heavy load and high speed” conforms to the classic Bowden–Tabor adhesion theory. At high-pressure contact points during reciprocating motion, the flash temperature effect causes thermal softening of the copper matrix, reducing shear strength ($\tau$). According to $f=\tau /{\sigma }_s$, although $\tau$ decreases, the growth rate of the contact area is lower than the load growth rate, leading to a decrease in the overall friction coefficient. Additionally, under the heavy load of 1500 N, wear debris is more easily compacted to form a continuous “third-body layer,” effectively isolating direct metal contact and further reducing frictional resistance.

(b) Transition to Mixed Lubrication under Wet Friction: The wet friction coefficient was generally lower than that of dry friction, and the decrease with increasing speed was more pronounced (e.g., dropping from 0.434 to 0.410 under 1500 N). This indicates that the interfacial friction state is transitioning from boundary lubrication to mixed lubrication. Calculation indicates that under the experimental conditions ($v=0.208$ m/s, $R_a\approx 3.2$–$6.3$ $\mathsf{\mu }$m), the theoretical film thickness ratio ($\lambda$) remains well below 1, precluding the formation of a full fluid film. Therefore, the friction reduction is attributed not to full mixed lubrication, but to the load-sharing effect of localized water pockets and the significant reduction in surface energy due to water molecule adsorption.

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Energy Dissipation Response of Wear Mass

Figure 6 reveals the evolution trend of wear mass with speed. Contrary to the friction coefficient, wear mass exhibited a significant “positive correlation,” which directly reflects the driving role of energy input ($PV$ value) on material damage.

(a) Aggravation of Severe Wear under Dry Friction: Under the ultimate load of 1500 N, as speed increased to 0.208 m/s, the wear mass climbed to 0.051 g (the maximum value). This corresponds to a transition from mild abrasive wear to severe delamination wear. The immense frictional work input caused severe plastic deformation and fatigue spalling in the sub-surface metal. The bidirectional shear stress of reciprocating motion aggravated the propagation of fatigue cracks, leading to large delamination spalls.

(b) Flushing and Cooling Effects under Wet Friction: Although wet wear mass increased with speed, it was significantly lower than dry wear under all conditions (maximum only 0.035 g). The wet environment demonstrated excellent damage-suppression capabilities. The cooling effect of the water medium promptly removed frictional heat, inhibiting thermal softening. Meanwhile, the flushing effect combined with reciprocating motion effectively flushed hard debris out of the contact zone, preventing accumulation and ploughing. This kept the wear mechanism under wet friction consistently in a milder state of micro-cutting.

Through trend analysis, it was found that tribological behavior under monorail braking conditions is strictly controlled by energy input ($PV$): Friction coefficient decreases as energy input increases. While beneficial for avoiding abrupt locking, this may lead to brake force fade.

3.3. Microscopic Wear Mechanism Analysis Based on SEM and EDS Characterization

To substantiate the thermal softening and oxidative wear mechanisms hypothesized in the macroscopic analysis (Section 3.1), and to elucidate the specific regulatory role of the high-humidity environment, Scanning Electron Microscopy (SEM) and Energy Dispersive Spectroscopy (EDS) were employed. The worn surfaces of the brake pads under the most severe operating condition (1500 N, 0.208 m/s) were selected for comparative characterization.

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Granular Spalling and Oxidative Wear under Dry Conditions

Figure 7a,b present the microscopic morphology of the friction surface under dry conditions, revealing distinct failure modes driven by mechanical fatigue and thermal accumulation. As shown in the SEM image (Figure 7a), the worn surface is characterized by severe granular spalling and the accumulation of loose debris. Distinct from the laminar delamination typically observed in homogeneous materials, the P/M surface exhibits matrix disintegration, where spherical particles are detached from the sintered matrix. This indicates that under high contact stress (1500 N), the fatigue fracture of sintering necks between powder particles occurred, leading to the rapid removal of material in the form of granular fragments. This failure mode correlates directly with the high wear mass ($0.051$ g) recorded in Section 3.1. High-magnification observation (Figure 7b) provides physical evidence of significant surface deformation. In localized regions, the surface exhibits distinct tongue-like plastic flow characteristics, where the metal layer is smeared and elongated along the sliding direction. During the experiments, the bulk temperature of the specimen surface was observed to reach approximately 150 °C under the maximum load condition. Although precise in situ flash temperature at the asperities was not theoretically calculated in this study, the observed rheological morphology is highly consistent with the characteristics of thermal softening. It suggests that the instantaneous temperature at contact points likely reached the softening threshold of the copper matrix, causing it to behave like a viscous fluid. This provides morphological evidence supporting the load weakening hypothesis proposed in Section 3.1.

To verify the chemical nature of the contact interface, EDS analysis was performed (Figure 8a). The quantitative results listed in

Table 1. Comparison of elemental composition (wt.%) on worn surfaces under dry and wet conditions (1500 N, 0.208 m/s).

Element	Dry Condition	Wet Condition	Change Trend	Mechanism Implication
Cu	16.65	78.56	Sharp Increase	Exposure of clean matrix (Flushing)
C	46.86	11.34	Decrease	Removal of tribofilm/graphite
O	26.81	3.97	Drastic Decrease (≈ 6.7×)	Oxidation Suppression
Fe	4.32	2.91	Decrease	Reduced Adhesive Transfer

reveal a significantly high concentration of Oxygen (26.81 wt.%) on the dry surface. This confirms that severe oxidative wear accompanied the thermal softening process. Additionally, a high content of carbon (46.86 wt.%) was detected, indicating that the graphite-lubricating phase and wear debris were compacted to form a thick oxide-based mechanically mixed layer (MML) covering the copper matrix, which corresponds to the relatively low copper detection (16.65 wt.%). The presence of iron (4.32 wt.%) further confirms material transfer from the counterpart rail.

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Mixed Polishing and Oxidation Suppression under High Humidity

Conversely, the worn surface under the high-humidity environment (90% RH) exhibits excellent surface integrity, as shown in Figure 7c,d. The low-magnification image (Figure 7c) reveals that the wet surface is free from deep fatigue cracks or large-scale spalling pits. The morphology is dominated by mild matrix erosion, indicating that the water medium effectively mitigated the subsurface shear stress. Crucially, high-magnification characterization (Figure 7d) demonstrates a remarkable polishing effect. The surface appears exceptionally smooth and flat, with no evidence of the severe plastic smearing or deep abrasive furrows observed in the dry state. This morphology strongly supports the dominance of mixed lubrication: the continuous water film effectively separated the contact asperities, transforming the contact mode from solid-to-solid to solid–liquid–solid.

The chemical analysis of the wet surface (Figure 8b and Table 1) further highlights the protective role of the water medium. The oxygen content drops drastically to 3.97 wt.%, which is approximately 6.7 times lower than that under the dry condition. This low oxidation level provides direct evidence for the cooling effect of the water flow, which dissipated frictional heat timely, thereby inhibiting oxidation. Furthermore, the copper content is dominant (78.56 wt.%), indicating a clean metallic surface where the thick tribofilm and debris observed in the dry state have been effectively flushed away (flushing effect).

3.4. Load Sensitivity Analysis at Experimental Parameter Boundaries

Limited by the motion characteristics of the reciprocating friction and wear tester, excessively high rotational speeds shorten the stroke cycle, making it difficult to establish a stable tribofilm. Therefore, this section selects the maximum speed boundary of the experimental design (0.208 m/s, corresponding to 500 r/min) as the baseline to simulate the maximum energy input state attainable at the sliding interface during heavy-load emergency braking of a monorail crane. This section focuses on examining the evolution laws and anti-fade capacity of the tribological performance of copper-based brake pads as the normal load surges from 500 N to 1500 N (simulating braking pressure from mild to locked) at this specific speed.

(1) Load Fade Characteristics of Friction Coefficient

Figure 9 presents the comprehensive sensitivity analysis of the friction coefficient (COF) and wear mass varying with load at the maximum speed boundary ($v=0.208$ m/s). Regarding the load-weakening effect (Figure 9a), the data indicates that the material exhibited a distinct fade phenomenon as the load increased from 500 N to 1500 N, but no friction collapse occurred.

As the load increased from 500 N to 1500 N, the dry friction coefficient gently decreased from 0.546 to 0.500 (a fade magnitude of approx. 8.4%). This is mainly attributed to the interface temperature rise caused by high loads, which reduced the yield strength of the copper matrix. Nevertheless, 0.500 at 1500 N remains an extremely high friction level. This indicates that hard reinforcing phases in the matrix (such as iron powder, SiO2) formed an effective load-bearing skeleton, pinning the sliding interface during matrix softening and preventing a sharp decline in friction force.

The wet friction coefficient showed an overall downward trend ($0.458\to 0.410$), but an anomalous rebound appeared at 1200 N ($0.431\to 0.436$). According to the Stribeck curve theory, this reveals that the interface underwent a critical transition from mixed lubrication toward boundary lubrication. At 1200 N, the lubrication parameter ($\eta ·v/P$) dropped below the water film’s bearing limit, causing localized film rupture and increased direct asperity contact. This suggests that monorail cranes might experience minor braking force fluctuations in specific pressure ranges during wet rail braking.

(2) Self-adaptive Densification Effect of Wear Rate

Regarding the variation in wear mass (Figure 9 Right Axis), to evaluate the wear resistance under maximum experimental parameters,

Table 2. Calculation of wear growth ratio under experimental boundary conditions ($v=0.208$ m/s).

Parameter	Load Variation	Dry Wear Growth	Wet Wear Growth 1
Range	$500\to 1500$ N	$0.026\to 0.051$ g	$0.016\to 0.035$ g
Ratio	3.0×	1.96×	2.19×

¹ Mass loss was measured after drying the specimens in an oven at 60 °C for 1 h to eliminate moisture absorption errors.

calculates the “load-to-wear growth ratio.” This phenomenon of “more wear-resistant under higher pressure” stems from the self-adaptive densification effect: high loads did not cause brittle spalling but instead promoted the mechanical compaction of debris, forming a dense mechanically mixed layer (MML). This MML acted like a shield that effectively disperses contact stress, making the copper-based material highly suitable for the long-distance braking requirements of monorail cranes under heavy loads.

4. Construction and Comprehensive Verification of Wear Prediction Model Based on RSM

In the experimental study of the previous chapter, the testing of discrete operating points (500–1500 N, 0.125–0.208 m/s) revealed that the tribological behavior of copper-based powder metallurgy brake pads under monorail braking conditions possesses significant non-linearity and multivariate coupling characteristics. However, due to the complexity of actual underground operating conditions (e.g., continuous changes in roadway gradient causing load fluctuations, continuous speed decay during early braking), relying solely on discrete experimental data points makes it difficult to achieve continuous and precise assessment of the brake pad’s service state.

To overcome the limitations of discrete experimental data and construct a mathematical prediction tool with engineering practical value, this chapter introduces Response Surface Methodology (RSM). This is a modeling optimization method combining experimental design and mathematical statistics, particularly suitable for solving the quantification problem of multi-factor interactions in tribological systems.

The main research objectives of this chapter are as follows: (a) Second-order Regression Modeling: Based on the high-precision experimental data from the previous chapter, establish second-order polynomial regression models for Friction Coefficient (COF) and Wear Mass with respect to Normal Load (L) and Sliding Speed (V) under both dry and wet environments, respectively. (b) Use statistical methods to quantitatively evaluate the significance of the models and the contribution of each factor, identifying the dominant factors affecting tribological performance. (c) Model Verification: Through residual analysis and validation experiments at non-sampled points (e.g., 850 N condition), verify the prediction accuracy and robustness of the model under under-loading fluctuation conditions.

4.1. Establishment of Prediction Models

Based on the Central Composite Design (CCD) principle, Ordinary Least Squares (OLS) regression analysis was performed on the experimental data. Considering the non-linear characteristics of the tribological system, this chapter employs a second-order polynomial response surface model to describe the functional relationship between input variables (Normal Load L, Sliding Speed V) and response variables (Friction Coefficient $COF$, Wear Mass W).

The general mathematical model is as follows:

$$Y={\beta }_0+{\beta }_{1}L+{\beta }_{2}V+{\beta }_{12}(L\times V)+{\beta }_{11}{L}^2+{\beta }_{22}{V}^2+\epsilon$$

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where

• L: Normal Load ($\mathrm{N}$);
• V: Sliding Speed ($\mathrm{m}/\mathrm{s}$);
• $COF$: Friction Coefficient;
• W: Wear Mass ($\mathrm{g}$);
• $\epsilon$: Random Error.

Through calculation, the coded prediction equations for each response variable are obtained as follows:

Friction Coefficient Prediction Models

(1) Dry Friction COF

$$CO{F}_{\mathrm{dry}}=0.514-(2.74\times {10}^{-5})L+1.01V-(4.83\times {10}^{-5})L\times V-(8.70\times {10}^{-9})L^2-3.51V^2$$

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(2) Wet Friction COF

$$CO{F}_{\mathrm{wet}}=0.444+(3.90\times {10}^{-6})L+0.486V-(9.78\times {10}^{-5})L\times V-(1.45\times {10}^{-8})L^2-1.77V^2$$

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Wear Mass Prediction Models

(3) Dry Wear Mass

$$W_{\mathrm{dry}}=0.028+(1.07\times {10}^{-5})L-0.175V+(3.96\times {10}^{-7})L\times V+(7.20\times {10}^{-9})L^2+0.598V^2$$

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(4) Wet Wear Mass

$$W_{\mathrm{wet}}=0.010+(3.01\times {10}^{-5})L-0.111V-(1.24\times {10}^{-5})L\times V-(4.87\times {10}^{-9})L^2+0.410V^2$$

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4.2. Physical Interpretation of Model Coefficients

By comparing the signs and magnitudes of the coefficients in the above equations, the key physical mechanisms under monorail braking conditions can be revealed:

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Friction Coefficient Models ($COF$):

Negative Interaction Term (${\beta }_{12}<0$): Both dry and wet friction models contain negative interaction terms ($-4.83\times {10}^{-5}$ and $-9.78\times {10}^{-5}$). This mathematically confirms the load–speed coupling weakening effect observed in Chapter 3. That is, the friction coefficient drops most significantly when high load and high speed act simultaneously (high $PV$ value), reflecting the mechanism of thermal softening or mixed lubrication enhancement.

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Wear Mass Models (W):

Positive Load Term (${\beta }_1>0$): The linear coefficient of load is positive in both environments, indicating that load is the primary driving force for wear. Negative Interaction in Wet Wear (${\beta }_{12}<0$): Notably, the interaction term for wet wear is negative ($-1.24\times {10}^{-5}$), whereas it is positive for dry wear ($+3.96\times {10}^{-7}$). This implies that in a wet environment, the water film effectively decouples the synergistic damage of load and speed, acting as a protective barrier under high-energy inputs.

4.3. Statistical Analysis and Model Adequacy Verification

To ensure the statistical significance of the constructed models, Analysis of Variance (ANOVA) was performed.

Table 3. ANOVA results for the response surface quadratic model of Dry Friction Coefficient.

Source	Sum of Squares	df	Mean Square	F-Value	p-Value
Model	$9.88\times {10}^{-3}$	5	$1.98\times {10}^{-3}$	87.75	$<0.0001$
L-Load	$8.58\times {10}^{-5}$	1	$8.58\times {10}^{-5}$	3.81	0.0659
V-Speed	$1.07\times {10}^{-4}$	1	$1.07\times {10}^{-4}$	4.73	0.0425
$L\times V$	$6.33\times {10}^{-6}$	1	$6.33\times {10}^{-6}$	0.28	0.6020
$L^2$	$2.09\times {10}^{-5}$	1	$2.09\times {10}^{-5}$	0.93	0.3470
$V^2$	$1.59\times {10}^{-4}$	1	$1.59\times {10}^{-4}$	7.06	0.0156
Residual	$4.28\times {10}^{-4}$	19	$2.25\times {10}^{-5}$
Cor Total	$1.03\times {10}^{-2}$	24

Note: Bold values indicate statistical significance ($p<0.05$).

presents the ANOVA results for the Dry friction Coefficient model (as a representative example).

Statistical Analysis Findings:

Model Significance: The F-value of 87.75 and p-value $<0.0001$ indicate the model is extremely significant. This confirms that the regression equation provides a robust approximation of the actual tribological surface.

Factor Contribution and Physical Interpretation: It is noteworthy that in the Dry Friction model, the interaction term $L\times V$ shows a high p-value ($0.6020$), indicating statistical insignificance. However, adhering to the “Hierarchy Principle” of Response Surface Methodology, this linear-by-linear interaction term is retained to ensure the structural completeness of the quadratic model and to prevent coordinate system dependence. Physically, this suggests that under dry conditions within the low-speed range (<0.21 m/s), the coupling effect between load and speed is weak, and the friction fade is primarily driven by the independent accumulation of frictional heat.

In contrast, the Wet Friction model exhibits a stronger interaction effect ($p<0.05$). This aligns with the lubrication theory, where the lubrication regime is governed by the parameter $\eta V/P$. The coupling of increasing load (P) and speed (V) directly alters the water film thickness, thereby significantly affecting the friction coefficient.

As shown in

Table 4. Summary of fit statistics for all tribological models.

Response	${\mathit{R}}^2$	Adj-${\mathit{R}}^2$	Pred-${\mathit{R}}^2$	Std. Dev.
Dry COF	0.9585	0.9476	0.9447	0.0047
Wet COF	0.9603	0.9499	0.9471	0.0037
Dry Wear Mass	0.9624	0.9524	0.9498	0.0020
Wet Wear Mass	0.9582	0.9472	0.9443	0.0016

, the high $R^2$ values (>0.95) for all responses and the close proximity between Adjusted $R^2$ and Predicted $R^2$ (difference < 0.02) indicate that the established quadratic polynomial models can explain over 95% of the variability in the tribological data, demonstrating excellent fitting quality.

4.4. Model Verification and Robustness Test

To verify the generalization ability of the model for unknown operating conditions (specifically focusing on the under-loading effect mentioned in the previous chapter), a blind test verification experiment was conducted.

Verification Condition:

(1) Load: 850 N (A random point not included in the modeling data points 500/700/1000/1200/1500 N). (2) Speed: 0.167 m/s (400 r/min). (3) Environment: Wet condition (90% RH).

Table 5. Blind test verification results under 850 N/0.167 m/s/Wet condition.

Parameter	RSM Predicted Value	Experimental Value	Relative Error (%)
Friction Coefficient	0.435	0.438	−0.68%
Wear Mass (g)	0.0215	0.0207	+3.86%

compares the predicted values from the RSM model with the actual experimental results.

Verification Conclusion: The relative errors are both less than 5%. The model successfully predicted the performance at the 850 N blind point. This proves that the RSM model possesses a filtering effect, effectively smoothing out the random noise caused by the flexible rail vibration observed in the experiments, and outputting a robust trend value suitable for engineering prediction.

Model Limitations and Boundary Warnings: It must be emphasized that the high prediction accuracy verified above is strictly limited to the experimental domain ($500\le L\le 1500$ N, $0.125\le V\le 0.208$ m/s). Extrapolation beyond these boundaries requires extreme caution. Specifically, if the normal load significantly exceeds 1500 N (e.g., during extreme emergency braking impact), the frictional heat flux may surpass the material’s thermal diffusivity limit, potentially triggering a transition from “Thermal Softening” to “Seizure” or “Galling.” Under such conditions, the prediction model may diverge, and the friction coefficient could exhibit chaotic fluctuations rather than the smooth decay predicted by the quadratic equation.

4.5. Comprehensive Performance Evaluation

Finally, to intuitively evaluate the comprehensive adaptability of the copper-based brake pads under different underground environments, a radar chart was constructed based on the normalized model data (Figure 10).

The evaluation dimensions include five key indicators:

(a) Friction Level: Higher is better (provides sufficient braking force). (b) Friction Stability: Reciprocal of variance (higher is better). (c) Wear Resistance: Reciprocal of wear rate (higher is better). (d) Heat Resistance: Capability of maintaining friction at high speed (higher is better). (e) Load Capacity: Capability of maintaining friction at high load (higher is better).

The evaluation metrics were normalized using the Min–Max scaling method to map the disparate physical quantities onto a dimensionless scale of $[0,1]$. The comprehensive comparison reveals a trade-off relationship:

(1)

Emergency Braking Scenario (Dry Preferred): The Dry condition (Red Zone) dominates in absolute “Friction Level” and “Load Capacity”. For emergency braking on steep slopes where maximum braking torque is the paramount safety criterion, the dry friction state provides a higher safety margin.

(2)

Continuous Operation Scenario (Wet/Humid Preferred): The Wet condition (Blue Zone) excels in “Friction Stability” and “Wear Resistance”. For operational scenarios such as long-distance speed regulation or uniform cruising, the high-humidity environment facilitates the formation of a stable mixed lubrication film. Although the peak braking force is slightly reduced, the significant reduction in wear rate and vibration favors the longevity and reliability of the braking system.

5. Conclusions and Prospects

5.1. Conclusions

Focusing on the braking safety requirements of suspended monorail cranes under complex heavy-load, undulating, and high-humidity conditions in coal mines, this thesis investigated the copper-based powder metallurgy brake pad and 45# steel rail friction pair. By combining full-factorial experiments with Response Surface Methodology (RSM), the evolution laws of tribological behavior and microscopic damage mechanisms were systematically studied. The main conclusions are as follows:

(1)

Revealed the non-linear friction fade laws under “low-speed heavy-load” conditions: Experiments confirmed that the friction pair exhibited significant load weakening and negative speed dependence within the testing range ($0.125$–$0.208$ m/s). The measured bulk temperature rise (reaching approximately 150 °C) and the observed “tongue-like plastic flow” on the worn surface collectively support the hypothesis that localized thermal softening of the copper matrix occurs under limit load conditions (1500 N). This softening reduces the shear strength of the surface material, leading to a moderate decrease in the friction coefficient while preventing catastrophic friction collapse.

(2)

Elucidated the dual regulation mechanism of underground high-humidity environments on friction and wear: Regarding the high-humidity environment (>90% RH) underground, the study found that the water medium played a significant regulatory role. On one hand, the mixed effect of the water film reduced the average friction coefficient by about 15–20% compared to dry conditions, suggesting that system pressure needs to be increased by about 1.2 times to compensate for braking force loss during wet rail braking. On the other hand, the flushing effect and cooling effect of the water flow effectively removed debris from the contact zone and suppressed temperature rise, cutting off the path to severe adhesive wear caused by heat accumulation. This resulted in a significantly lower wear rate under wet conditions, proving that the humid environment is actually beneficial for extending the service life of brake pads.

(3)

Constructed a multi-factor friction and wear prediction model based on RSM: To achieve continuous prediction of tribological performance under complex conditions, a quadratic polynomial RSM model including interaction terms was established. ANOVA analysis indicated that the interaction between load and speed ($L\times V$) has an extremely significant effect on tribological performance. The model not only accurately quantified the “load–speed coupling weakening effect” but also passed the blind test verification at a non-sampled point (850 N) with an error < 5%. Radar chart evaluation based on this model indicates that dry conditions are more suitable for emergency braking requiring high torque, while wet conditions possess advantages in friction stability and wear resistance, favoring long-term equipment operation.

5.2. Prospects

(1)

In situ Visualization of Thermo-Mechanical Coupling Fields: The current study primarily inferred the thermal softening mechanism based on measured bulk temperatures and microscopic rheological morphology. Verification of the precise instantaneous flash temperature rise, especially under low-speed but heavy-load conditions, remains a critical task. Future work will introduce high-precision infrared thermal imaging technology or fiber Bragg grating sensing technology to construct a real-time monitoring system for the flash temperature field at the braking interface. The aim is to establish a more precise temperature–friction–wear 3D coupling model from a thermodynamic perspective, providing direct data support for optimizing the thermal stability of brake pad materials.

(2)

Full-scale Whole-machine Field Industrial Tests: To verify the applicability of the RSM model in more complex engineering environments, the next step will involve field industrial tests on actual full-scale monorail cranes. The focus will be on examining the dynamic response characteristics of brake pad friction performance under extreme conditions such as long-distance continuous downhill braking and emergency braking, further correcting and perfecting the laboratory prediction model to better serve engineering practices.

(3)

Research on Tribological Behavior under Multi-phase Complex Media: Considering the diversity of underground environments, future research will further expand the dimensions of environmental media. The focus will be on exploring the evolution laws of the third-body layer and wear mechanisms at the friction pair interface under the mixed action of multi-phase contaminants such as water–coal dust–oil pollution. This will facilitate the construction of a generalized braking safety theory system covering various extreme environments, laying a theoretical foundation for developing a new generation of high-performance, all-weather monorail brake pads.