Study on equivalent acceleration test method of bearing bench

Abstract

Accelerated testing using bearing test rigs is a critical method for evaluating bearing durability performance. Equivalent accelerated testing methods can significantly reduce testing cycles and minimize costs. To address the need for efficient durability assessment, this study reviews current equivalent accelerated testing methods for rolling bearings and proposes two novel methods based on the principle of energy conservation. Two novel accelerated testing methods were proposed based on the principle of energy conservation. The operational procedures for these methods were elaborated by integrating damage consistency criteria with experimental results. Additionally, insufficient consideration of energy loss in the proposed methods was addressed, and potential solutions were suggested. The results demonstrated that equivalent accelerated testing could be achieved theoretically through the energy equivalence method, which was grounded in energy consistency and combined with damage consistency criteria. The required parameters were obtained through motor monitoring, oil lubrication inlet/outlet temperature measurements, and external bearing temperature sensors. Damage consistency between accelerated and conventional tests was validated via artificially induced raceway defects and extended single-specimen testing. The difference in energy loss between the driving motor and bearings under conventional and accelerated testing conditions was found to be approximately equivalent, enabling the testing duration to be reduced without compromising reliability.

Keywords

rolling bearing accelerated test bearing test rig methodology energy-based equivalence damage consistency criterion

Introduction

The bearing of the high-speed train transmission system plays a vital role in train operation, and its performance directly relates to operational safety and smoothness. With the continuous development of high-speed train technology and the expansion of railway transportation networks, bearing reliability and safety performance have become crucial for ensuring normal train operation. After the design and processing of new bearing products, bearing performance is generally inspected through test rigs. Traditional bearing durability and life tests were found to require excessive time and effort, while test bearings needed to provide sufficient valid data. These conventional methods were considered unable to meet current bearing test requirements, leading to the common engineering practice of using accelerated life test methods for durability evaluation.^1–4

According to incomplete statistics, approximately 30% of rotating machinery failures are caused by rolling bearings. The actual service conditions of rolling bearings are complex, making a reasonable experimental design for bearing components a pressing issue. The principle of accelerated testing was to apply loads higher than benchmark levels during bearing tests, thereby accelerating failure and shortening test duration.^5,6 Parameters for achieving acceleration included temperature, speed, external load, corrosion, lubrication, or their combinations.^7–9

A primary challenge in accelerated life testing methodology is the limited ability of existing test rigs to account for the full range of acceleration parameters (e.g. temperature, lubrication). Since constructing new test rigs required substantial investment, the equivalent transformation of complex external factors into single test loads while fully utilizing existing equipment became a key research focus. Numerical calculation methods were demonstrated to provide effective solutions. Wang and Li¹⁰ analyzed aircraft engine bearing boundary conditions using quasi-dynamic methods, revealing relationships between actual conditions and state parameters. Their work established a theoretical basis for operating parameter selection and failure judgment in accelerated life testing. Zhang et al.¹¹ derived reliability functions for solid lubricated bearing failure modes based on Weibull distribution, describing accelerated stress effects through a generalized Eyring model. Jin et al.¹² simulated contact stresses for wind turbine main shaft bearings under both operational and accelerated conditions using ABAQUS, validating experimental design rationality by comparing theoretical and simulated acceleration factors. Nam et al.³ incorporated temperature effects on bearing life by combining life-load relationships with the Arrhenius model, proposing an accelerated zero-failure testing method for high-temperature operating conditions.

Current accelerated testing methods can be broadly classified into three categories: (1) Physics-based acceleration models, such as the inverse power law and Eyring model, which relate life to stress levels (e.g. Refs.^3,11). These models provide a theoretical foundation but often require simplification of complex service conditions; (2) Numerical simulation-based approaches, which use finite element or quasi-dynamic analysis to predict internal stress states under accelerated loads (e.g. Refs.^10,12). While insightful, these methods are computationally intensive and highly dependent on accurate modeling of complex boundary conditions, such as contact mechanics and thermal effects.^13–17 For instance, recent advancements in high-fidelity modeling, such as the 5-DOF dynamic modeling of rolling bearings with local defects considering comprehensive stiffness under isothermal elastohydrodynamic lubrication¹⁸ and the analysis of thermal elastohydrodynamic lubrication effects on vibration characteristics of ball bearings with local defects,¹⁹ have provided deeper insights into the complex interactions between lubrication, dynamics, and damage; (3) Test rig modification methods, which involve designing new test rigs or loading mechanisms to apply accelerated stresses, such as multi-bearing setups^20,21 or gyroscopic torque.^22,23 These can achieve significant time reduction but are platform-specific and not easily generalizable. Despite these advancements, a general, cost-effective, and easily implementable methodology that can be directly applied to existing bearing test rigs remains elusive. The need for a unified approach that simplifies complex external factors into a single controllable parameter, while ensuring damage equivalence with conventional testing, is evident. This study addresses this gap by proposing two novel energy-based equivalent acceleration methods.

To systematically evaluate the current landscape of accelerated testing methodologies, a SWOT (strengths, weaknesses, opportunities, and threats) analysis is presented, as shown in Table 1. This analysis provides a structured framework for understanding the relative merits and limitations of existing approaches, thereby identifying the research gap that the present study aims to address.

Table 1.

SWOT analysis of existing accelerated testing methods.

Method category	Numerical/simulation^3,10–17	Test rig modification^18–21	Physics-based models^3,11
Strengths	Can predict internal stress states; relatively low cost; enables parametric studies	Can achieve significant time reduction; direct physical testing	Theoretically grounded; provides acceleration factors
Weaknesses	Highly dependent on modeling assumptions; requires validation; computationally intensive for complex models	Platform-specific; expensive; not easily generalizable	Requires simplification of complex service conditions; limited to specific failure modes
Opportunities	Integration with AI/ML for faster predictions; improved multi-physics models	Standardization of accelerated test protocols; modular rig designs	Development of more comprehensive physics-of-failure models
Threats	Disconnect from real-world complexities; validation challenges	Rapid obsolescence; high development cost	Oversimplification leading to inaccurate predictions

To overcome these limitations, the present study proposes two novel energy-based equivalent acceleration test methods. The key innovation lies in applying the principle of energy conservation to bearing accelerated testing, controlling either the input energy (derived from motor electrical parameters) or the output energy (derived from bearing thermal dissipation). This approach provides a practical, unified framework that transforms complex, multi-factor influences into a single, measurable energy parameter, making it easily implementable on existing test rigs without major hardware modifications. A further significant contribution is the integration of a damage consistency criterion, validated through artificially induced raceway defect tests, to experimentally verify that the accelerated tests produce equivalent damage to conventional tests. This combined energy-damage framework offers a robust and generalizable methodology for significantly reducing testing time and cost while ensuring reliability.

Equivalent acceleration test method

Both methods proposed in this study are founded on the same core principle of energy conservation, aiming to achieve equivalent cumulative damage by ensuring equivalent total energy, whether considered at the system’s input or output. However, they are applicable under different experimental conditions and monitoring capabilities. The input energy equivalence method (Section 2.1) is suitable when high-precision monitoring of the driving motor’s electrical parameters (voltage, current) is available. It is particularly advantageous for tests where the primary interest lies in the total work done on the system. The output energy equivalence method (Section 2.2), on the other hand, is applicable when direct electrical measurement is challenging but thermal monitoring is feasible, such as in tests with complex lubrication systems or where heat dissipation is a critical performance indicator. It relies on measuring the thermal energy dissipated from the bearing, which is a direct consequence of frictional and rolling losses. Therefore, the choice between the two methods depends on the available instrumentation and the specific physical quantity that can be most accurately measured and controlled during the test.

The underlying hypothesis of the proposed energy-based equivalence is that the cumulative damage in a bearing is fundamentally driven by the total energy dissipated within the material. Under normal operating conditions, energy is input into the bearing system primarily via mechanical work from the motor. This energy is then partitioned into several forms:

(1) Elastic strain energy: Associated with reversible deformation of bearing components. While not directly causing damage, cyclic elastic deformation is a precursor to fatigue crack initiation.

(2) Plastic deformation energy (damage): Irreversible energy absorbed by the material at stress concentrations, leading to microstructural changes, dislocation movement, and eventual crack initiation and propagation. This is the primary form of energy directly linked to fatigue damage.

(3) Frictional energy (heat): Energy dissipated due to sliding and rolling friction at contact interfaces (roller-raceway, cage, seals). This energy manifests as a temperature rise and subsequent heat dissipation to the environment and lubricant. While frictional heat itself is not direct material damage, elevated temperatures can accelerate lubricant degradation, alter material properties, and exacerbate surface distress, indirectly influencing the damage rate.

(4) Kinetic energy: Associated with the motion of bearing components, which remains relatively constant under steady-state operation.

The proposed energy equivalence methods do not directly measure plastic deformation energy, which is challenging to quantify in-situ. Instead, they rely on the principle that for a given bearing system and failure mechanism, the total energy input (Method 1) or the total energy dissipated as heat (Method 2) is proportional to the damaging plastic deformation energy over the life cycle. This proportionality is the critical link that enables the use of total energy as a surrogate for damage. The damage consistency criterion, validated through artificial defect tests, serves to experimentally confirm this proportionality and ensure that the chosen energy threshold accurately represents equivalent damage under different loading rates.

The principle of energy conservation states that a system’s total energy remains constant under specific conditions. Energy cannot be spontaneously created or destroyed; it merely transforms between different forms or transfers between objects while maintaining constant total energy.²⁴ In bearing testing, actual components or specially designed test specimens are mounted on dedicated test rigs to evaluate performance and reliability. When considering the test bearing as an integrated system, the applied external loads can be assumed to impart equivalent energy quantities, thereby inducing identical damage patterns.²⁵ The energy-based methodology achieves equivalent accelerated testing by precisely controlling input-output energy consistency. This section details the theoretical foundation and derivation process for two energy-consistent acceleration methods.

Input energy equivalence method

During bearing testing, motor output power necessarily varies to maintain preset rotational speeds, whether due to loading condition changes or bearing damage. Assuming that the motor output power is P₀ when reaching the set speed under no load conditions, and the output power is P_F when reaching the set speed under load, with the motor voltage U and resistance R unchanged, it is as follows:

\begin{matrix} P_{0} = I_{0}^{2} \cdot R \\ P_{F} = I_{F}^{2} \cdot R \\ Δ P = P_{F} - P_{0} = (I_{F}^{2} - I_{0}^{2}) \cdot R = Δ I^{2} \cdot R \end{matrix}

(1)

To ensure that the measured ΔP accurately reflects bearing-related energy consumption, a pre-test calibration procedure is recommended. This involves:

(1) Measuring the power consumption P₀ at the target speed V_a with the bearing installed but unloaded, which captures all baseline system losses (motor losses, transmission friction, windage, etc.).

(2) Verifying the linearity of the drive system’s loss characteristics across the load range by measuring power consumption at intermediate load steps and confirming that the incremental power increase correlates linearly with applied load, as predicted by bearing friction models.

(3) If significant non-linearity is observed (indicating load-dependent system losses beyond the bearing), a correction factor can be derived from system identification tests using a dummy bearing or calibrated torque transducer.

Due to the applied load, the loading energy of a single cycle in the bearing experimental stage can be calculated by equation (2):

e_{1 i} = \int_{0}^{\frac{1}{f}} Δ {I_{i}}^{2} R d t

(2)

f is the rotation frequency of the bearing; e_1i is the energy loading on the bearing within a single cycle during the i-th intermediate test.

If the total number of loading experiments is n, the average single-cycle energy value under long-term loading, denoted as e₁, can be calculated using equation (3).

e_{1} = \frac{\sum_{i = 1}^{n} e_{1 i}}{n}

(3)

n is the total number of tests. If the fatigue life cycle number of the bearing under long-term loading test is N₁, then the total loading energy for the test is:

E_{1} = N_{1} \cdot e_{1}

(4)

Assuming that the bearing test rig is subjected to axial load F_a1 and radial load F_b1, under this loading condition, the speed is controlled at a certain value V_a, the energy of a single cycle load is e₁. The duration of the endurance test is t_a, at which point the energy consumption of a conventional endurance test can be calculated as E_a.

To achieve experimental acceleration while maintaining energy equivalence, the total energy input throughout the testing process was kept constant. The experimental loading configuration was modified to either: one is combined axial load (F_a2) and radial load (F_b2), another one is radial load only (F_b3). Notably, both axial and radial loads in the accelerated tests exceeded those applied in conventional durability testing. Under accelerated loading conditions, the rotational speed was maintained at a constant value (V_a), resulting in increased energy input per loading cycle from e₁ to e₂. The accelerated durability test duration (t_b) was derived from the following relationship with conventional testing parameters:

E_{a} = e_{1} \cdot t_{a} = e_{2} \cdot t_{b}

(5)

The energy-equivalent acceleration method achieves testing equivalence by increasing applied loads while proportionally reducing testing duration, thereby maintaining constant cumulative energy input. This approach requires all test bearings to be new and from the same production batch to ensure identical initial conditions. As illustrated in Figure 1, the test rig employs a motor-driven shaft to apply controlled loads for bearing performance evaluation. It should be noted that the current methodology intentionally excludes vibration effects, despite their established impact on bearing life,^26–28 due to three practical constraints: (1) the test rig actuator’s limited loading frequency range, (2) inherent difficulties in quantifying vibration energy contributions, and (3) measurement system limitations for capturing high-frequency dynamic responses.

Figure 1.

Schematic diagram of the bearing test rig configuration.

While input energy consistency is ensured, quantifying the exact energy portion absorbed by the bearing itself—as opposed to being dissipated elsewhere in the system—remains a challenge. A detailed numerical analysis of this energy allocation is beyond the scope of this paper for several reasons: (1) ISO 281 standard mentions that parameters such as internal clearances, grease/oil mass, contact parameters, oil film thickness, etc., will all affect the results in the calculation of bearing life, and these parameters will also affect the variation in energy values. (2) Although finite element methods have obtained a lot of simulation data, the differences in modeling methods, consideration of influencing factors, and engineers’ own experience lead to differences in finite element results. Finite element results can, to some extent, reflect the variation trend of the research factors, but further improvement is needed to obtain accurate results. (3) Well-known bearing manufacturers such as SKF and Schaeffler use supercomputers for bearing dynamic simulation modeling analysis during the calculation process, which requires high requirements for research equipment, consumables, software, and hardware. (4) In the bearing test process, it is impossible to monitor changes in the contact state inside the bearing. Current research is based on parameters such as acceleration and temperature under bearing in-service conditions to determine the internal state of the bearing and predict its life.^29–33

To ensure consistent input energy, this study needs to introduce a damage consistency criterion to quantitatively ensure the damage equivalence of accelerated tests.^34–37 To ensure that the accelerated testing does not alter the fundamental failure mechanism, this study introduces a damage consistency criterion validated through bearing raceway artificial defect detachment and extension single-specimen tests. The premise is that if the accelerated test produces the same microscopic damage characteristics (crack morphology, propagation path, fracture surface features) as the conventional test, then the failure mechanism can be considered unchanged. As shown in Figure 2, prefabricated defects of controlled dimensions are created on bearing raceways. After testing under both conventional and accelerated conditions (with equivalent total energy input), the bearings are sectioned and examined using scanning electron microscopy (SEM) to compare the crack initiation sites and morphology, crack propagation paths and rates, and the fracture surface features (striations, dimples, etc.). If the damage characteristics are statistically indistinguishable, this provides strong evidence that the accelerated test has reproduced the same failure mechanism, validating the energy-based equivalence approach.

Figure 2.

Bearing raceway artificial defect dimensions and actual machining results.

In summary, the total energy consumption during bearing operation can be reliably determined through routine monitoring of motor parameters (current and voltage), regardless of the specific loading conditions. Accelerated testing employs an amplified load ratio factor, which necessitates greater energy input from the motor when maintaining identical rotational speeds to routine tests. By preserving equivalent cumulative energy input, the duration of accelerated testing can be optimally designed according to experimental requirements. The validation of damage equivalence between routine and accelerated tests is achieved through comparative analysis of experimental results. When equivalence criteria are satisfied, the accelerated testing protocol is confirmed as meeting design specifications. Conversely, any observed deviations necessitate systematic analysis to identify underlying causes and implement appropriate scheme modifications.

Output energy equivalent method

The equivalence between higher loads applied for shorter durations and lower loads applied for longer durations is theoretically grounded in the Palmgren-Miner linear damage rule,^38,39 which states that fatigue damage accumulates linearly with the number of cycles, and failure occurs when the cumulative damage reaches unity. This rule, combined with the S-N (stress-life) relationship for bearings (typically following an inverse power law: L₁₀∝ (Cr/Pr or C_a/P_a)^*p*, where L₁₀ is life, Cr, Pr, C_a, P_a is the basic dynamic load rating and equivalent dynamic load of radial ball and thrust ball bearings, and *p* is the load-life exponent, approximately 3 for ball bearings and 10/3 for roller bearings per ISO 281⁴⁰), provides the mathematical basis for load-life equivalence.

Following system energy input, energy is dissipated through various pathways to satisfy conservation principles, where, in bearing performance testing, differences in external loading between conventional and accelerated tests alter the internal contact state distribution. Under constant rotational speed, the bearing’s contact position temperature exhibits a characteristic progression from initial ambient temperature to a stabilized operational range, primarily due to rolling friction at roller-ring interfaces, lubrication inefficiencies, and the conversion of motor-driven kinetic energy into internal energy that manifests as a measurable temperature rise in the constant-mass bearing assembly.^41–45 This thermal energy propagates from internal contact zones to external monitoring positions, enabling temperature observation via sensors, with quantitative analysis defining Q₀ as no-load heat dissipation at target speed (initial monitoring temperature t_c), Q_F as loaded heat dissipation (operational internal temperature t_d), and establishing the thermal relationship given constant bearing mass M and specific heat capacity C at monitored locations, then there are:

\begin{matrix} Q_{0} = M \cdot C \cdot t_{c} \\ Q_{F} = M \cdot C \cdot t_{d} \\ Δ Q = Q_{F} - Q_{0} = M \cdot C \cdot (t_{d} - t_{c}) = M \cdot C \cdot Δ t \end{matrix}

(6)

Due to the applied load, the energy of a single cycle of loading during the bearing test phase can be calculated by equation (7):

q_{1 i} = \int_{0}^{\frac{1}{f}} M \cdot C d t

(7)

q _1i represents the energy on the bearing in a single cycle during the i-th intermediate test. Assuming a total of n loading experiments have been conducted, the average single-cycle heat dissipation energy under long-term loading, denoted as q₁, can be calculated as shown in equation (8).

q_{1} = \frac{\sum_{i = 1}^{n} q_{1 i}}{n}

(8)

If the life cycle number of the bearing under long-term loading test is N₁, the total energy of the test loading is:

Q_{1} = N_{1} \cdot q_{1}

(9)

The equivalent accelerated testing methodology achieves testing acceleration through thermal energy dissipation consistency, where output energy equivalence is maintained by implementing equations (6)–(9). Under conventional testing conditions with unit cycle thermal dissipation q_a and loading duration t₁, and accelerated testing conditions with unit cycle thermal dissipation q_b and loading duration t₂, the equivalence relationship between both testing regimes is established as follows:

Q_{a} = q_{a} \cdot t_{1} = q_{b} \cdot t_{2}

(10)

Bearing test rigs are typically equipped with external temperature sensors. For oil-lubricated bearings, monitoring the lubricant inlet and outlet temperatures allows for a quantitative assessment of thermal effects. Bearing heating originates from four primary mechanisms: frictional heat generation, rolling losses, elastic hysteresis, and lubrication deficiencies.

Accelerated testing employs elevated loads, which intensify these mechanisms, leading to higher frictional forces and increased elastic deformation. This is analogous to the S-N relationship, where higher stress amplitudes result in fewer cycles to failure. The energy-equivalent acceleration methodology leverages this principle, assuming identical thermal conduction properties between test conditions. It accounts for two dominant energy dissipation pathways: frictional energy (quantified via temperature sensors) and rolling resistance losses (manifested as heat).

Elastic deformation effects are addressed through temporal scaling, where prolonged loading (t₁) with lower stresses produces incremental damage per cycle damage (d_s) is considered equivalent to shorter, more intense loading (t_s) with higher per-cycle damage (d_b), satisfying t₁·d_s≈t_s·d_b (where t₁ > t_s, d_b > d_s). Lubrication effects are controlled for by using new bearings from identical batches with confirmed optimal internal conditions.

Analysis of energy equivalent method using simulation data

This chapter presents illustrative simulation data for feasibility analysis and demonstration of the proposed energy-equivalent accelerated testing methodology. The data are generated to mimic realistic test scenarios and are used solely to elucidate the procedural workflow and demonstrate the theoretical concepts. Using high-speed train axle box bearings as test specimens, the experimental design incorporates actual service condition parameters provided by an industrial partner, with axial loads of −15, −10, 10, and 15 kN combined with radial loads of 30, 45, 60, and 70 kN. Motor current output was continuously monitored during testing, enabling calculation of cyclic energy via Joule’s law. Energy input variations under different loading conditions were determined by normalizing against no-load reference values. Comparative analysis of prefabricated defect propagation was performed under controlled energy input conditions, while synchronous monitoring of bearing vibration acceleration and temperature variations provided complementary damage evaluation metrics.

A standardized defect preparation protocol was implemented on bearing outer raceways, comprising: (1) defect zone demarcation using precision measurement tools (excluding 10 mm from each raceway end), (2) creation of defect features using a 3 mm spherical grinding wheel to produce an array of 2 mm diameter, 0.4 mm depth pits with 2 mm spacing along the raceway generatrix, and (3) quality verification ensuring burr-free surfaces. Detailed defect specifications conform to Section 2.1 requirements. The input energy equivalence method test results were systematically presented in Table 2 (Note: A, B, C, D represent the measured damage size for each test condition. The consistency basis requires A = B = C = D).

Table 2.

Experimental design for input energy equivalent method.

Test classification	Radial load (kN)	Axial load (kN)	Loading time (h)	Cycle energy (J)	Input total energy (J)	Damage Size (mm)
Normal	30	15	10	100	10E6	A
Accelerate 1	45	10	8	180	10E6	B
Accelerate 2	60	5	6	350	10E6	C
Accelerate 3	70	0	4	520	10E6	D
Consistency basis	A = B = C = D

The output energy equivalence method performs accelerated testing by quantifying thermal energy dissipation through two primary pathways: (1) bearing heat radiation and (2) lubricant heat transfer. Following speed stabilization, distinct thermal profiles emerge across different loading configurations, as evidenced by variations in both bearing outer ring temperatures and lubricant inlet/outlet temperature differentials. The experimental results obtained through this methodology were systematically summarized in Table 3.

Table 3.

Experimental design for output energy equivalent method.

Test classification	Radial load (kN)	Axial load (kN)	Loading time (h)	Cycle energy (J)	Out total energy (J)	Damage Size (mm)
Normal	30	15	10	100	10E6	A
Accelerate 1	45	10	8	180	10E6	B
Accelerate 2	60	5	6	350	10E6	C
Accelerate 3	70	0	4	520	10E6	D
Consistency basis	E = F = G = H

A detailed flowchart illustrating the complete workflow for both input and output energy-equivalent methods, including the damage consistency validation process, is provided in the Supplemental Materials (Figure S1) for readers interested in a visual summary of the procedural steps. To ensure that temperature-induced changes in lubricant properties do not alter the failure mode, the following measures are incorporated into the test protocol:

(1) Temperature monitoring: Three type-K thermocouples (accuracy ± 0.5°C) are mounted on the bearing outer ring at 120° intervals. Additionally, PT100 sensors monitor lubricant inlet and outlet temperatures continuously throughout the test.

(2) Lubricant viscosity tracking: Based on the measured temperatures, the actual operating viscosity ν of the lubricant is calculated using the ASTM viscosity-temperature relationship. The specific film thickness λ (ratio of minimum film thickness to composite surface roughness) is then estimated using elastohydrodynamic lubrication (EHL) theory to verify that the lubrication regime (boundary, mixed, or full-film EHL) remains consistent between conventional and accelerated tests.

(3) Thermal stabilization criterion: Testing proceeds only when the bearing outer ring temperature has stabilized (variation < ± 2°C over 30 min). If the stabilized temperature under accelerated loading exceeds the conventional test temperature by more than 20°C, the test is paused to allow cooling, or the load is reduced to maintain thermal equivalence.

(4) Upper temperature limit: A critical temperature limit T_crit is established based on the lubricant’s thermal degradation threshold (typically 20°C–30°C below the manufacturer’s specified continuous operating limit). If bearing temperature approaches T_crit, the test is immediately suspended to prevent lubricant degradation and associated failure mode changes.

Discussion

It is important to acknowledge that the results presented in this study are based on illustrative simulation data, not physical experiments. While these simulations effectively demonstrate the theoretical feasibility and procedural workflow of the proposed energy-equivalent methods, full experimental validation on a bearing test rig with real-time monitoring of motor parameters, temperatures, and defect propagation is the essential next step. Future work will focus on implementing the proposed methods on an actual test rig, such as the one schematically shown in Figure 1, to obtain experimental data that can definitively confirm the damage consistency predicted by the simulations. The detailed experimental protocol provided in Section 3 serves as a blueprint for such future experimental studies.

This study investigates the feasibility of two energy-based accelerated testing methodologies while acknowledging several unresolved technical challenges. These challenges primarily include:

(1) Energy loss problem of the drive motor in the bearing rig test

According to the fundamental principle of energy conservation, energy is transformed rather than disappears during operation. Although motor input energy can be precisely controlled, the actual energy transmitted to the bearing differs due to inevitable power losses. Four primary loss mechanisms are identified: (a) copper losses, (b) iron losses, (c) mechanical losses, and (d) stray losses. In conventional testing, relatively minor but sustained energy losses result from prolonged operation with lower loads, whereas in accelerated testing, higher instantaneous losses are exhibited due to increased loading, albeit within a significantly reduced testing duration. Approximate parity in cumulative motor energy losses between both testing modes is demonstrated by our proposed equivalent acceleration method when identical equipment configurations are used. Practical limitations are faced by current solutions employing motor energy recovery systems, as documented in references,^46,47 including prohibitive costs and stringent grid compatibility requirements that hinder widespread engineering implementation.

(2) Bearing energy loss

Energy losses are inevitably generated within bearings during both conventional and accelerated testing processes. These losses are primarily attributed to four factors: (1) roller-raceway friction, (2) seal friction, (3) lubricant viscous drag, and (4) inter-component friction. Under accelerated testing conditions, increased loading has been found to significantly alter three critical parameters: lubrication performance, friction coefficients, and contact position temperatures.^48–50 Similar to motor energy dissipation phenomena, the reduced testing duration in accelerated methods is considered to compensate for energy loss differentials between accelerated and conventional testing protocols.

Quantitative evaluation of bearing energy dissipation enables more precise equivalence determination. Two principal measurement methodologies have been established: the relative method and the absolute method. The relative method is performed by comparing power losses at rated speeds between test conditions, yielding relative loss values. While this approach is valued for its operational simplicity and minimal equipment requirements, its limitations include measurement inaccuracy, strict environmental control needs, and incompatibility with high-speed applications.

The absolute method, recognized for superior accuracy, comprises two variants: the thermal measurement method and the electrical measurement method. In the thermal approach, energy dissipation is calculated through temperature differential measurements across loaded bearing assemblies at constant speeds. This method is particularly recommended for high-speed bearing evaluation despite its specialized equipment needs and procedural complexity. The electrical method determines energy loss via voltage and current differential measurements, offering high sensitivity and precision with relatively simple instrumentation. However, stringent power supply stability requirements and elevated voltage/current specifications must be maintained. Bearing power loss may also be derived from rolling friction coefficients, rotational speeds, and loading parameters. For engineering optimization, power loss reduction has been demonstrated to enhance both service life and operational efficiency. Three primary improvement strategies have been widely adopted: (1) optimized bearing geometry design, (2) advanced lubrication system selection, and (3) operational environment enhancement.

During accelerated life testing, two critical stress thresholds must be strictly observed: yield strength and ultimate tensile strength. Exceeding these limits may induce plastic deformation or fracture, fundamentally altering failure mechanisms from material fatigue to overload-induced damage. In test rig configurations, traveling wind simulation systems are typically installed to partially replicate operational cooling effects, though with limited heat dissipation capacity. When bearing temperatures approach operational limits during accelerated testing, immediate test suspension is required until the assembly is cooled to ambient conditions. While this study focuses on total energy equivalence, a more granular analysis of energy forms could provide further refinement. The relationship between frictional energy (heat) and plastic deformation energy (damage) is complex and load-dependent. At higher accelerated loads, a larger proportion of input energy may be dissipated as heat due to increased friction, potentially leading to an overestimation of the damage-equivalent energy if only total input energy is considered. This highlights the importance of the damage consistency criterion, which serves as an empirical check to validate that the chosen energy-based acceleration factor indeed yields the same physical damage extent, implicitly accounting for the changing energy partition.

(3) Load-Dependent Transmission Losses

A legitimate concern in the proposed input energy equivalence method is that increasing the applied load may increase mechanical losses in the drive system components (couplings, shafts, support bearings) beyond the test bearing itself. While the differential measurement approach (P_F−P₀) partially mitigates this by subtracting baseline losses, it assumes that these ancillary losses are load-independent. In practice, some components (e.g. support bearings) do experience increased losses under higher loads. To address this, we recommend two complementary strategies:

(a) Conservative load limits: The accelerated loads should be selected such that the increase in ancillary losses remains small relative to the total bearing-related losses. This can be ensured by conducting a preliminary system characterization to identify the load range over which the drive system’s loss characteristics remain approximately linear.

(b) Future refinement with torque sensors: For ultimate precision, the method could be enhanced by incorporating in-line torque transducers between the motor and test bearing. This would directly measure the mechanical power delivered to the bearing, eliminating uncertainties from transmission losses. While this increases instrumentation complexity, it represents a pathway for future methodological refinement.

It is also worth noting that the output energy equivalence method (based on thermal dissipation) is inherently less sensitive to transmission losses, as it directly measures heat generated at the bearing. This provides a complementary validation approach when transmission loss concerns are paramount. During accelerated life testing, two critical stress thresholds must be strictly observed: the material’s yield strength and endurance limit. Exceeding the yield strength may induce plastic deformation or fracture, fundamentally altering the failure mechanism from high-cycle fatigue (HCF) to low-cycle fatigue (LCF) or overload-induced ductile fracture. This would invalidate any equivalence with conventional testing. Therefore, the accelerated loads must be selected such that the maximum contact stresses remain within the elastic regime, and the calculated life based on the S-N curve remains within the high-cycle fatigue region (>10⁵ cycles). A safety factor of at least 1.5 against yielding is recommended when designing accelerated test protocols.

While the proposed energy-based framework has been theoretically validated and shows promise for maintaining failure mechanism consistency within appropriate load limits, it is important to acknowledge that the fundamental assumption of unchanged failure mechanisms under accelerated conditions requires further experimental verification across a wider range of bearing types, materials, and operating conditions. Future work should include comprehensive fractographic analysis to definitively confirm that the damage morphology under accelerated conditions matches that under conventional loading.

(4) Thermal effects and lubrication regime preservation

A fundamental challenge in accelerated bearing testing is maintaining identical lubrication conditions across different load levels. Under higher loads, increased frictional heating can reduce lubricant viscosity, potentially shifting the lubrication regime from full-film elastohydrodynamic (EHL) to mixed or boundary lubrication. This transition fundamentally alters contact conditions, friction coefficients, and wear mechanisms, potentially invalidating any comparison with conventional tests. The proposed methodology addresses this through three complementary strategies:

(a) Thermal monitoring and control as detailed in Section 3.3, ensuring that temperature excursions are limited and the lubrication regime remains consistent.

(b) Lubricant selection: For accelerated tests where some temperature rise is inevitable, selecting lubricants with higher viscosity indices or synthetic base oils can help maintain film thickness across a wider temperature range.

(c) Output energy method as validation: The output energy equivalence method, which measures heat dissipation, provides a direct check on thermal consistency. If the heat dissipation per cycle under accelerated loading is disproportionately higher than under conventional loading (after accounting for load increase), this may indicate a lubrication regime shift, and the accelerated load should be reduced.

It is important to note that the damage consistency criterion (validated through artificial defect tests) serves as the ultimate verification. If the accelerated test produces identical crack morphology and propagation characteristics despite moderate temperature differences, this suggests that the failure mechanism has remained fundamentally unchanged, and the thermal effects are within acceptable limits.

Conclusion

This study has proposed and theoretically validated two novel energy-based equivalent acceleration test methods for rolling bearings, addressing the critical need for reducing testing time and cost while maintaining reliability. The scientific value and contributions of this work are summarized as follows:

(1) Two complementary methods are proposed—input energy equivalence (based on motor electrical monitoring) and output energy equivalence (based on thermal dissipation monitoring). This dual approach offers flexibility for different test rig configurations and monitoring capabilities, representing a practical advancement over existing methods that often require specialized equipment or extensive rig modifications. The methods are designed for implementation on existing test rigs, enhancing their practical applicability.

(2) A key scientific contribution is the integration of a damage consistency criterion, validated through artificially induced raceway defect tests. This provides an experimental mechanism to verify that accelerated tests produce physically equivalent damage to conventional tests, addressing a fundamental concern in accelerated testing—whether the accelerated conditions merely accelerate time or fundamentally alter failure mechanisms.

(3) The proposed methods enable significant test duration reduction (as illustrated in Tables 1 and 2, from 10 to 4 h for equivalent cumulative energy) while using readily available monitoring parameters (motor current, temperature sensors). This has substantial implications for industrial bearing development, allowing faster product validation, reduced time-to-market, and lower development costs without compromising reliability assessment.

(4) This study establishes a theoretical and methodological foundation for energy-based accelerated testing. Future work can build upon this framework by: (a) experimentally validating the methods on full-scale test rigs with diverse bearing types and operating conditions; (b) refining the energy-damage relationship through more detailed analysis of energy partitioning (elastic vs plastic deformation, frictional losses); (c) incorporating vibration energy considerations into the framework; and (d) developing standardized protocols for industrial application.

In summary, this manuscript advances scientific knowledge by providing a theoretically grounded, practically implementable methodology for bearing accelerated testing, establishing a direct link between laboratory acceleration and real-world damage equivalence.

Supplemental Material

sj-pdf-1-ade-10.1177_16878132261444648 – Supplemental material for Study on equivalent acceleration test method of bearing bench

Supplemental material, sj-pdf-1-ade-10.1177_16878132261444648 for Study on equivalent acceleration test method of bearing bench by Lida Cao in Advances in Mechanical Engineering

Footnotes

Handling Editor: Chenhui Liang

ORCID iD

Lida Cao

Author contributions

Lida Cao: Methodology, Investigation, Writing, Validation, Supervision.

Funding

The author disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The author sincerely appreciates the funding support of the key project of Jilin Province Education Science ‘14th Five-Year' Plan 2025' Research on the Construction of Four-chain Integrated Talent Training System for Railway Majors' Production, Education, Science and Innovation' from the perspective of new productivity' (Project Approval No. : ZD25179).

Declaration of conflicting interests

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data availability statement

Data included in this study are available upon request by contact with the corresponding author.*

Supplemental material

Supplemental material for this article is available online.

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