Experimental Evaluation of Coefficient of Friction for Fretting Regimes ^†

Abstract

This study investigates the coefficient of friction (COF) and wear behavior in fretting regimes—stick, stick–slip, and gross sliding—under dry and oil-lubricated conditions. Fretting tests were conducted by increasing oscillation amplitude from a few micrometers to 48 µm. In dry conditions, displacement amplitude initially rose rapidly, stabilizing after about 5 million load cycles, indicating steady-state behavior. The friction ratio (FR) surged early, peaking between 0.7 and 1.0, before declining to stable values, suggesting a shift from adhesive to stable frictional interaction. The minimal slip amplitude confirmed the predominance of the stick regime. Conversely, in oil-lubricated conditions, displacement amplitude stabilized after an initial increase, achieving higher amplitudes than in dry tests. The FR started below 0.2, gradually increasing to a peak around 10,000 load cycles for higher oscillation amplitudes (e.g., 15 µm), reflecting the lubricant’s role in reducing metal-to-metal contact. COF curves in lubricated tests showed smoother transitions and lower peak values compared to dry tests. These findings highlight the lubricant’s effectiveness in minimizing adhesion and enhancing sliding efficiency, offering insights for optimizing material performance in engineering applications.

1. Introduction

The micro-level wear phenomenon known as fretting develops when contacting surfaces experience normal load during oscillatory relative motion. The phenomenon of fretting affects mechanical components that experience cyclic loading and small displacements in the aerospace and automotive industries, as well as manufacturing sectors [1]. Nuclear power equipment contains fuel rods alongside steam generator tubes and pipelines which undergo substantial fretting wear that causes early equipment failure [2]. The coefficient of friction (COF) functions as an essential factor that controls fretting processes. The coefficient of friction controls contact conditions and heat generation while determining the fretting regime transitions, which ultimately affects the degree of wear and surface degradation across different load and amplitude conditions. Research by Warmoth et al. examined fretting under oscillatory motion at frequencies between 5 and 50 Hz with a normal load of 450 N and an amplitude of 50 µm to demonstrate that cylinder geometry affected wear results [3]. The research by Lai [4] explored Alloy 690 tube fretting behavior in nuclear plants where increased amplitudes and loads promoted oxide layer growth which accelerated wear. Research by Li and Y.H.L [5] studied an Inconel 600 alloy at room temperature and 30–40% relative humidity and discovered that sliding amplitude directly affected wear volume, while partial slip became dominant at 60 µm.

Qin et al. [6] demonstrated that higher contact conformity enhances metal-to-metal contact, which leads to increased friction and wear. Surface engineering emerges as crucial through recent developments in the field. The tribological performance of laser-textured tungsten-doped diamond-like carbon (DLC) coatings proves promising when used under dry sliding conditions across different load ranges. The application of these coatings showed enhanced wear resistance and lower friction coefficients under fretting conditions according to research findings [7]. The different fretting regimes include stick, stick–slip, and gross slip. The stick regime shows minimal relative motion through adhesion-dominated friction, which produces COF values above 0.6. Under these conditions, Ma & Sokolov [8] observed extensive wear damage and micro-cracking in titanium and steel materials. The stick–slip regime produces alternating adhesion and sliding phases that cause COF variations and micro-crack development. Hutchings [9] observed that steel and aluminum alloys exhibited COF values ranging from 0.4 to 0.8 under heavy loading conditions according to his research. Briscoe & Stokes [10] demonstrated that proper lubrication stabilizes COF and minimizes material damage. The gross slip regime allows for continuous sliding, which results in COF values between 0.2 and 0.5 while producing uniform wear patterns. Shen et al. [11,12] documented that dry contact friction forces rose during partial slip until they reached a steady state in gross slip. Research by Zhang et al. [13] demonstrated that applying fretting conditions at frequencies up to 500 Hz while adjusting loads showed distinct wear morphological changes based on amplitude variations. Research conducted by Klingelnberg et al. [14] demonstrated that surface treatments and coatings applied to stainless steel and ceramic materials led to substantial COF reductions in this specific regime.

Novelty

A major contribution of this study is that it specifically experiments on the coefficient of friction under various fretting regimes and bridges a fundamental knowledge gap regarding frictional behavior during small oscillatory contact. Compared to earlier studies primarily focused on the wear of material or overall tribological characteristics, this paper goes further by estimating the coefficient of friction in fretting regions with stick, stick–slip, and gross slip. Through scientific comparisons and analyses of different loads, displacement amplitudes, and surface characteristics, the study provides a guideline for analyzing and preventing fretting-related failure. This approach offers key information that can be utilized to enhance material design and performance in areas involving fretting, such as in aerospace, automotive, and other mechanical systems. An additional advantage of the specific research field is its practical orientation, providing useful measures for preventing wear and enhancing the wear resistance of components in strategically important engineering segments.

2. Methodology

The methodology of this research consists of three phases, namely (i) the experimental design and material selection, (ii) tribological testing and data collection, and (iii) the analysis and validation of results, as illustrated in Figure 1. In the first phase, the study identifies the tribological challenges in fretting regimes by selecting appropriate materials and designing an experimental setup. Mild Steel Grade A36 is chosen as the pin material shown in the figure, while high-speed steel (HSS) serves as the counter surface to evaluate wear and friction characteristics under controlled fretting conditions. The pivoted-arm tribo-tester custom-fabricated in-house at the Department of Mechanical Engineering, UET Taxila, Pakistan, is designed to replicate cyclic oscillatory motion, similar to that found in internal combustion engines.

The second phase involves conducting systematic fretting tests by varying oscillation amplitude, contact pressure, and lubrication conditions. The experimental setup allows for a precise measurement of the displacement amplitude, friction coefficient, and wear progression.

In the final phase, the collected data is analyzed to determine the impact of lubrication and fretting regimes on the coefficient of friction, material wear, and adhesion effects. The results are validated by comparing trends with existing tribological models to provide insights for optimizing material performance in engineering applications.

2.1. Materials

The materials selected for this study include Mild Steel Grade A36, which was utilized as pin specimens. These pins were tested against a flat surface fabricated from a high-speed steel (HSS) strip. This setup was chosen to evaluate the tribological performance and wear characteristics of the pin materials under consistent testing conditions. Mild Steel Grade A36, shown in Figure 2, is a carbon steel widely used for its excellent balance of strength, weldability, and machinability [15].

The experimental setup used Mild Steel Grade A36 pins alongside high-speed steel (HSS) counters to establish a tribologically controlled and compatible fretting condition. A36 shows its susceptibility to wear because of its low-carbon structural steel composition and low yield strength, which enables researchers to observe and measure wear patterns. Mild Steel Grade A36 provides useful experimental setups because it offers both ductility and easy machining capabilities. The high hardness level of HSS at 62 HRC together with its superior wear resistance allows it to preserve its geometric shape throughout testing procedures. The experiment maintains uniform contact conditions because researchers use HSS as their counter face material. The controlled fretting conditions occur on the A36 pin because this material combination creates a defined wear environment for precise measurements of the wear volume and coefficient of friction. The selected pair of materials represents actual contact conditions which appear in mechanical joints and cutting tools and press–fit assemblies, [16] thus providing results applicable to industrial settings.

The properties of the selected materials are shown in

Table 1. Properties of materials [1,2].

Property	Tensile Strength (MPa)	Yield Strength (MPa)	Elongation at Break (%)	Modulus of Elasticity (GPa)	Coefficient of Friction
Mild Steel Grade A36	400–550	~250	20–23	~200	~0.44 (with brass)
High-Speed Steel (HSS)	1200–1400	~1000	5–10	~210	~0.4 (with mild steel)

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In summary, Mild Steel Grade A36 was the pin material, and a consistent HSS flat surface facilitated a comprehensive understanding of tribological performance under various conditions.

2.2. Rational Behind Selection of Input Parameters

The input parameters for the experimental setup were carefully selected to ensure accurate and consistent results in measuring the coefficient of friction under fretting conditions. These parameters were essential to controlling the operational environment and achieving reliable measurements for the study. The data points for oscillation were 1600 for each cycle. The input parameters used in this study are displayed in

Table 2. Input parameters and their values.

Parameters	Values
Motor RPM	2700
Frequency (f)	45 (Hz)
Maximum Amplitude	48 (µm)
ReLoad Cycles	107
Load	200 (N)
Minimum Amplitude	4 (µm)
Contact Pressure	40 (MPa)
Temperature	Room (22–32 °C)
Contact Area	38.5 $\left({\mathrm{m}\mathrm{m}}^2\right)$

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3. Experimental Setup

We designed and fabricated a pivoted-arm tribo-tester to measure fretting wear in vibratory machines. The experimental setup shown in Figure 3 replicates the crankshaft mechanism found in internal combustion engines, which effectively converts rotary motion into reciprocating motion via a connecting rod.

In our setup, the reciprocating motion of the connecting rod is transferred to the pivoted arm. By adjusting the position along the pivoted arm, displacement amplitudes ranging from 1 µm to 48 µm can be achieved, enabling precise control of the testing conditions.

The pivoted-arm tribo-tester transforms high-speed rotary motor motion at 2700 RPM into precise oscillatory motion using a crankshaft-connecting rod system, which then provides motion control from 4 to 48 µm oscillating at a frequency of 45 Hz. The device reproduces mechanical joint conditions through oscillating motions achieved by a crankshaft-connecting rod system, and it can apply various vertical forces starting from 200 N. The instrument measures displacement and friction forces through integrated sensors to precisely monitor changes in COF and wear during stick, stick–slip, and gross sliding transitions across dry and lubricated conditions.

The system includes a start-up phase consisting of multiple loading cycles to gradually increase the displacement amplitude from zero to the target value, ensuring consistent and repeatable experimentation. Figure 4 presents the assembly of the tribo-tester apparatus, highlighting its key components and their arrangement for a comprehensive understanding of its structure and functionality.

Additionally, the setup allows for the application of varying tangential and normal forces, providing flexibility to study the stick-to-slip transition and the influence of lubrication on fretting behavior.

Specimen Manufacturing

The specimen was manufactured using CNC turning on mild steel, ensuring precise dimensions and surface finish for experimental consistency.

Machined cylindrical pin specimens of Mild Steel Grade A36 measured 6 mm diameter × 15 mm length with a 10 mm spherical tip radius for achieving uniform contact geometry as shown in Figure 5. The HSS strips served as the counter surface, with dimensions of 20 × 20 × 5 mm³. Table 1 shows the material properties, which include A36’s yield strength of 250 MPa and HSS’s hardness at 62 HRC. The CNC turning process produced surfaces with Ra values below 0.2 µm to reduce initial contact variations.

4. Results and Discussion

As detailed in the Experimental Setup Section, the oscillation amplitude was progressively increased from a few micrometers to 48 µm to investigate the coefficient of friction (COF) and wear behavior across all fretting regimes, including stick, stick–slip, and gross sliding, under varying running conditions.

The displacement amplitude, friction ratio, and sliding amplitude curves of fretting tests under dry and oil-lubricated conditions can be noted in Figure 6 and Figure 7, where d and p refer to the displacement amplitude and normal contact pressure.

4.1. Experimental Results

4.1.1. Under Dry Condition

The experimental results for dry condition fretting tests reveal key trends in the displacement amplitude, friction ratio, and slip amplitude. Initially, the displacement amplitude increases rapidly, reaching a steady state after approximately 5 million cycles, indicating stable stick or stick–slip behavior. The friction ratio exhibits a sharp increase at the start due to surface roughness and adhesion, peaking between 0.7 and 1.0 before stabilizing at a lower value. Slip amplitude remains minimal throughout, with only a slight increase at higher displacement amplitudes (10 µm), confirming that stick or partial stick–slip dominates in dry conditions.

The slip amplitude plot in Figure 6c demonstrates different patterns based on the tested amplitudes. The blue line (10 µm) shows significant fluctuations because its periodic stick–slip events cause energy accumulation during ‘stick’ phases, followed by sudden energy releases during ‘slip’ peaks. The slip amplitude of red/green lines (4/8 µm) stays close to zero, which demonstrates stick regime behavior because surface adhesion stops gross sliding. The tribological response of mild steel exhibits this amplitude-dependent transition, which shows that 10 µm approaches the critical threshold for stick–slip instability.

4.1.2. Under Oil-Lubricated Conditions

In oil-lubricated fretting tests, the presence of a lubricant film between the bar and pin significantly alters the system’s behavior compared to dry conditions. Initially, displacement amplitude increases as the surfaces settle, eventually stabilizing in a steady-state oscillation. The lubrication allows for higher displacement amplitudes, reaching up to 15–20 µm, as it reduces friction and wear, enabling smoother motion without surface damage. The friction ratio starts very low (≤0.2) due to minimal metal-to-metal contact but gradually increases, peaking at around 10,000 cycles as some oil is displaced. Unlike dry conditions, where friction rises sharply, oil lubrication delays this transition, leading to a more gradual frictional response.

Slip amplitude is initially higher in the presence of oil, as shown in Figure 7, as lubrication reduces adhesion and allows for more free sliding. Over time, as the oil film depletes or redistributes, slip amplitude declines and stabilizes, indicating a shift toward a stick or mild stick–slip regime. Overall, lubrication significantly lowers initial friction, enables larger displacement amplitudes, and initially increases slip, but as the test progresses, friction rises slightly while slip reduces. The system eventually reaches a stable state with lower friction than dry conditions, demonstrating the crucial role of lubrication in minimizing adhesion and wear in fretting regimes.

4.1.3. For Gross Regime Under Dry and Oil Conditions

In the gross sliding regime, both dry and oil-lubricated tests exhibit larger displacement amplitudes compared to mild or partial slip conditions. However, lubrication results in smoother transitions and higher maximum amplitudes due to reduced friction and improved damping. In contrast, dry tests experience abrupt amplitude changes, indicating stronger adhesive forces at the contact interface.

The coefficient of friction (COF) follows distinct trends under each condition: in dry tests, the COF rises sharply and stabilizes at a high level, reflecting strong adhesion between unlubricated surfaces. In oil-lubricated tests, the COF increase is more gradual and peaks at a lower level since the lubricant film delays direct metal-to-metal contact, reducing adhesion and wear.

Slip amplitude also differs significantly between dry and lubricated conditions, as shown in Figure 8.

In oil-lubricated tests, the initial slip is higher, as reduced adhesion allows for freer sliding. Over time, slip amplitude declines and stabilizes as the lubricant’s effectiveness diminishes. Conversely, in dry conditions, slip amplitude remains relatively steady but lower throughout, constrained by high friction and strong adhesion. The overall results highlight the crucial role of lubrication in gross sliding fretting behavior. Oil reduces friction, delays severe adhesion, and facilitates larger displacement, whereas dry conditions sustain higher friction, limiting amplitude growth and slip. These findings demonstrate how lubrication profoundly influences wear mechanisms and tribological performance in fretting regimes.

5. Conclusions

This experimental study investigated the effect of oscillation amplitude on fretting-induced friction for Mild Steel Grade 60 as the pin specimen and high-speed steel (HSS) under dry and oil-lubricated conditions. The analysis of the experimental results across different fretting regimes, including stick, stick–slip, and gross sliding, is shown in

Table 3. Comparative analysis of fretting regimes under different conditions.

Parameter	Dry Condition	Oil-Lubricated	Gross Regime (Dry)	Gross Regime (Oil)	Stick–Slip Regime (Dry)	Stick–Slip Regime (Oil)
Avg. COF	0.7–1.0 (peak) → 0.6 (stable)	≤0.2 (initial) → 0.4 (stable)	0.8 (stable)	0.4 (stable)	High initial COF (~1.0) → stabilizes (~0.6–0.8)	Lower COF (~0.3–0.5), more stable with time
Slip Amplitude	Minimal (<2 µm)	Higher initial (5–8 µm) → stabilizes	Steady (10–15 µm)	Smoother (15–20 µm)	Cyclic small slips (<5 µm)	Very minimal slip, low amplitude (~2–4 µm)
Wear Mechanism	Adhesive wear, oxide formation	Mixed lubrication, carbonaceous layers	Severe adhesive wear	Mild abrasive wear	Oxide debris formation, micro- welding	Mild polishing, formation of transfer layers
Transition Cycles	~5 M cycles to stabilize	~10 k cycles (lubricant breakdown)	Immediate	Delayed (~5 k cycles)	Slow transition (~1 M cycles)	Very delayed or absent due to lubrication
Surface Damage	Deep grooves, micro-cracks	Mild polishing, minimal material loss	Extensive pitting	Isolated wear scars	Micro-pits, oxidized spots, crack initiation	Smooth surface, minimal damage

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The research examined fretting behavior through systematic tests of dry and oil-lubricated conditions, which produced four main findings. The application of oil created two main effects on frictional response: it decreased the initial COF by 60–80% (≤0.2 vs. 0.7–1.0 dry) and extended stick–slip transitions by ∼1500 cycles through decreased metal contact and enabled a threefold higher load capacity. The transition between stick and gross sliding states depended on amplitude thresholds: stick conditions with low wear occurred below 20 µm, while higher amplitudes led to gross sliding with COF reaching 0.4 in lubricated conditions and 0.8 in dry conditions. The wear mechanisms between dry and lubricated conditions showed major differences because dry conditions caused adhesive wear with iron oxide formation, whereas lubrication produced carbonaceous tribofilms that minimized abrasive damage. Our innovative tribo-tester enabled these discoveries through its precise amplitude control (4–48 µm) and real-time COF/slip monitoring capabilities. The experimental findings show that components with micro-motions (such as bearings and joints) require lubrication to increase their service life through adhesive wear prevention and energy efficiency improvement. Future research needs to investigate surface treatments and lubricant additives as potential methods to boost fretting resistance.