Multiscale Modeling and Data-Driven Life Prediction of Kinematic Interface Behaviors in Mechanical Drive Systems

Abstract

The multiscale coupling characteristics of the kinematic interface behavior of mechanical transmission systems are the core factors affecting system accuracy and lifetime. In this paper, we propose an innovative framework to achieve multiscale modeling from surface topographic parameters to system-level dynamics response through four stages: microscopic topographic regulation, mesoscopic wear modeling, macroscopic gap evolution, and system vibration prediction. Through the active design of laser-textured surfaces and gradient coatings, the contact stress distribution can be regulated to keep the wear extension; combined with the multiscale physical model and joint simulation technology, the dynamic feedback mechanism of wear–gap–vibration is revealed. Aiming at the challenges of data scarcity and mechanism complexity, we integrate data enhancement and migration learning techniques to construct a hybrid mechanism–data-driven life prediction model. This paper breaks through the limitations of traditional isolated analysis and provides theoretical support for the design optimization and intelligent operation and maintenance of high-precision transmission systems.

1. Introduction

Mechanical systems are complex, integrated assemblies that achieve specific functions through the coordinated operation of multiple components. Widely applied in industrial manufacturing, transportation, medical equipment, and other fields, their performance and reliability directly determine production efficiency and product quality [1]. Mechanical transmission systems, as the core carrier for energy transfer, are to efficiently and accurately transmit energy from the power source to actuators [2,3]. The key to the transmission process is the relative movement between the mechanical transmission components, usually achieved through the kinematic pairs, which are closely related to the interface [4,5,6]. The behaviors at interfaces, such as contact, friction, and wear, play a crucial role in determining the operational efficiency and dependability of a system. In demanding conditions like high speeds and heavy loads, the interfaces of kinematic pairs exhibit notable multiscale coupling features. The fractal characteristics of surface topography at the microscale affect the friction response through contact stress concentrations; wear at the mesoscale leads to the clearance dynamic evolution; and non-uniform clearance at the macroscale induces system-level nonlinear vibrations [7,8]. This multiscale dynamic correlation makes the interface behavior a key issue that restricts the accuracy and lifetime of the transmission system [9,10,11].

However, traditional design approaches are often based on modularization ideas and focus on the independent performance of subsystems [12,13] while ignoring the spatiotemporal evolutionary complexity of interface behavior [14,15]. This complexity stems from the multiscale nature of interfacial behavior: the interface is not only a geometrical contact surface but also an interfacial layer with transitions of changing mechanical gradients. In the interfacial layer, the intrinsic properties of the system are transformed from one phase to another according to a certain law, forming a transition zone of changing properties [8]. The surface morphology and mechanical gradient of the interfacial layer can be actively designed through coating technologies such as laser melting coating, thus enabling the regulation of stress and friction. The modulated coating can coordinate the microscopic wear evolution and effectively inhibit the nonlinear expansion of the gap [16,17]. Sudden changes in contact state under dynamic loading [18], random expansion of fretting wear, and nonlinear vibration induced by clearance [19] are urgently needed to reveal their inherent mechanisms through multiscale modeling and data-driven techniques [20,21]. At the same time, through multiscale modeling and data-driven technology, we reveal the dynamic feedback mechanism of wear–vibration and systematically explore the dynamic feedback mechanism of the two under cyclic loading, such as how the vibration energy accelerates the local wear and breaks through the limitations of the traditional isolated analysis.

An extensive examination of motion interface behavior in mechanical transmission systems is crucial for maintaining the smooth operation of such systems. Recent advancements in science and technology, such as multiscale physical modeling [22,23], simulation technology [9,19], and big data analysis [24,25], have introduced novel theories and methodologies for investigating motion interface behavior. Multiscale physical models achieve theoretical coupling in different scales [26] and build a multiscale correlation path from surface microtopography to macroscale dynamics [27]. Simulation techniques integrate finite element analysis [28] and multi-body dynamics [29] to reproduce the multiscale evolution of interface behavior in a virtual environment. Data-driven methods break through the bottleneck of scarce experimental data through data augmentation [30,31,32] and transfer learning [33] to realize life prediction under various working conditions [34,35,36].

Based on the above background and research status, this paper systematically reviews the research advances on interface behavior in mechanical transmission systems. Firstly, it explores the application of multiscale physical models in interface behavior analysis and reveals the impact of surface topography and friction wear on the clearance and dynamic behavior of kinematic pairs; secondly, it analyzes the regulation rule of the interface clearance and contact state on the system’s vibration characteristics through multiscale simulation; in addition, it focuses on the innovative application of data augmentation technology and transfer learning methods in interface behavior modeling and life prediction.

Through systematic sorting and analysis, this paper aims to summarize the research progress of interface behavior in mechanical transmission systems, reveal the influence mechanism of interface behavior on system performance, and provide a reference for future research and engineering applications.

2. Physical Model of Multiscale Interface Behavior

The interface behavior of a mechanical transmission system is essentially a multiscale coupling process of microtopography evolution [37], mesoscale wear accumulation [38], and macrodynamic response [39,40] (Figure 1). At the microscale, the fractal features of surface roughness dominate the local stress concentration through the Hertz contact [41,42], which directly affects the friction coefficient and wear rate [37]. Furthermore, it induces the non-uniform evolution of the clearance at the mesoscale, which triggers a nonlinear leap in the contact state [43]. At the macroscale, the geometric aberration and dynamic distribution of the clearance are further amplified into vibration instability and transmission accuracy deterioration at the system level [7].

Traditional single-scale analysis methods have limitations in explaining the multiscale coupling mechanism of interface behavior. For example, the static contact model is unable to characterize the surge of fretting wear rate under alternating load [44], and the pure macroscale kinetic simulation ignores the role of microtopography in regulating the contact force distribution. Therefore, the accurate modeling of interface behavior needs to realize the multiscale correlation system of “morphology parameters–wear path–clearance model–dynamic response” [45].

2.1. Contact Properties and Frictional Wear Modulation by Surface Microforms

The surface microtopography directly regulates the interfacial tribological properties of mechanical transmission systems. The combination of machining errors and wear leads to the formation of a random rough surface consisting of irregular convex peaks and concave valleys [46,47,48]. These surface contact behaviors occur only at local high points and significantly affect the interface stress distribution and frictional response [49,50]. The optimization of tribological properties needs to be approached from both morphological design and material modification. Morphological modulation can be achieved by storing lubricants or abrasive debris, such as laser weaving of surfaces, to reduce wear and lower the coefficient of friction [51], while material modification can be achieved by doping nanoparticles to enhance the hardness and toughness of the coatings and to inhibit crack propagation [52] (

Table 1. Glossary of terms.

Symbol	Definition	Description
k	Wear coefficient	Material-dependent factor in Archard’s law
H	Material hardness	abrasion resistance
Ra	Arithmetic roughness	Average vertical deviation of surface profile
$\mu$	Friction coefficient	Ratio of frictional force to normal load
Rq	Root mean square value of surface roughness	The spatial distribution dispersion degree of morphology
D	Fractal dimension	Multiscale roughness descriptor
Fn	Normal contact force
s	Sliding distance

).

2.1.1. Quantitative Characterization of Surface Morphology and Active Design

According to the fractal theory, the surface microtopography parameters can be quantitatively characterized [53,54,55], and the nonlinear relationship between the contact area $A_c$ and the expected load $F_n$ can be established based on the Hertz contact theory [56,57,58]:

$$A_{\mathrm{c}}\propto {\displaystyle \frac{F_n^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}{E^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{R}_a^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}}$$

where E is the modulus of elasticity. This law indicates that the stress concentration effect still has a large impact on local wear despite the increased load enlarging the contact area [9,40].

To overcome the uncontrollability of random rough surfaces, tribological properties can be improved by active design of surface morphology [59,60,61]. As shown in Figure 2 Aymard et al. propose a generic surface design strategy to prepare dry rough interfaces—meta-interfaces—with predefined friction behaviors by laser. This strategy is able to achieve a specific friction law by adjusting the height of the surface microstructure, thus enabling precise control of the friction behavior without the need to change the material body or surface chemistry. Experiments have shown that it is possible to specify the friction coefficient by adjusting the surface topology to achieve a linear friction law that matches the target slope while keeping the material pair constant [62]. The laser surface texturing technique significantly optimizes the contact stress distribution and lubrication state by constructing regular microstructures (e.g., pits and grooves). Micro-pit arrays can store abrasive debris under dry friction conditions, resulting in a 30% reduction in the coefficient of friction [63], while gradient roughness surfaces (R_a = 0.1–0.5 μm) inhibit crack extension by dispersing contact stresses and reduce wear rate by 35% [64]. The engineering value of this type of interface design has been demonstrated in transmission components such as gears and bearings. He et al. investigated the deposition of diamond-like films on titanium alloy surfaces and prepared DLC films with different micro-pit densities by in situ texturing, and the results of this study showed that textured diamond-like films with 52% micro-pit density exhibited the lowest average coefficient of friction and wear rate [63]. Liem et al. investigated the effect of geometrical parameters (shape, size, distribution) of surface microtextures on friction properties by laser technique on textures designed for different crankshaft bearings and found that the hybrid spherical and square cylindrical textures reduced the coefficient of friction by 22% under boundary lubrication conditions, whereas wedge-shaped textures exhibited optimal antiwear properties under high load conditions [64,65].

2.1.2. Coating Material Modification Co-Optimization

The coating gradient structure can effectively inhibit interfacial stress concentration by moderating the abrupt hardness change. CAI et al. used the DC reactive magnetron sputtering deposition technique to prepare nano TiN gradient coatings with gradual hardness change on the surface of titanium alloys [66]. The bonding force between the coating and the titanium alloy substrate was as high as 81 N, which was much higher than that of the single-layer TiN coating, and the friction factor was only 0.24, which had good wear resistance. Shan Xiangheng [67] found that for the Nb₂O₅/Nb₂O₅-Ti/Ti gradient coating, the addition of the intermediate layer impeded the continuity of columnar crystal growth and improved the coating densification, and the volumetric wear rate was 2.56 × 10⁻⁵ mm³N⁻¹m⁻¹, compared to the substrate, Nb₂O₅ single-layer coating, and Nb₂O₅/Ti bilayer coating by 90.42%, 89.28%, and 86.28%, respectively. Tao Ye [68] deposited a dense TiN interlayer on the surface of TC4, which increased the bond strength to 2.3 times that of the substrate and improved the wear resistance by 80%.

2.2. Interface Wear–Joint Clearance Coevolution

The surface topography directly affects the interface contact state, while the dynamic change in the contact state further drives the wear and clearance evolution [69,70,71]. Interfacial wear and clearance evolution exhibit significant nonlinear dynamic coupling characteristics [45]. An improved model based on Archard wear theory provides a quantitative analytical framework for this process [68], and its dynamic wear depth $h_w$ can be characterized as follows [11,72]:

$$h_w=k·{\displaystyle \frac{F_n·s}{H}}$$

where $F_n$ is the normal contact force; $s$ is the sliding distance; $H$ is the material hardness; and k is the wear coefficient related to the material properties and working conditions [73].

2.2.1. Non-Uniform Evolution of Interfacial Distributions

Mukras et al. [40] experimentally verified the heterogeneity of the wear depth distribution (Figure 3A), where the geometric asymmetry of the gap exacerbates the local stress concentration, and the peak contact pressure is 2–3 times higher than the mean value, accelerating the local wear. Their simulated maximum wear depth was 0.4524 mm, and the experimental maximum wear depth was 0.4850 mm, and the error between the two at the maximum wear depth was 6.7%, which verified the reliability of the simulation model.

Figure 3. (A) Non-uniform wear profile of the bushing of the crank–slider mechanism (maximum depth of 0.485 mm). (B) Dynamic migration path of the pin-bushing contact area with gap expansion, with red arrows indicating high-wear-risk areas [40].

Figure 3. (A) Non-uniform wear profile of the bushing of the crank–slider mechanism (maximum depth of 0.485 mm). (B) Dynamic migration path of the pin-bushing contact area with gap expansion, with red arrows indicating high-wear-risk areas [40].

It is noteworthy that the scale effect of wear evolution has been confirmed by in situ observation. Tsinghua University developed an experimental setup through the total reflection principle [74] to realize in situ observation of the dynamic evolution process of micrometer-scale contact patches. It was found that the formation of micrometer-scale furrows changes the contact force distribution, which in turn induces the vibration of the macroscale system through a multi-body coupling mechanism [75]. Further, Shenghao Lu et al. in this team revealed through an experimental-model fusion approach that processing and assembly errors lead to non-uniformity of normal stress distribution at the contact interface, which triggers contact stress fluctuations (Figure 4) [76].

However, the total reflection principle can only be measured on transparent materials, and acoustic emission techniques are more widely used in practical engineering applications [77,78]. Literature reports have shown a strong relationship between the multiple interactions of acoustic emission sources in sliding contacts and the root mean square (RMS) value of acoustic emission signals [79,80,81]. In the study of contact parameters at wheel–rail interfaces, ultrasonic measurement technology was applied to establish the calibration curve of ultrasonic reflectivity and contact pressure, and the actual measured ultrasonic reflection signals were converted to pressure values. This conversion enables the determination of the contact pressure distribution at the interface [81,82,83]. Hossein Towsyfya used the acoustic emission technique to monitor the signals of mechanical seals under different operating conditions. They combined it with a wear model to construct a closed loop of “topographic degradation–signal characteristics”. Morphological degradation leads to changes in acoustic emission signal characteristics, such as amplitude and frequency, which can be analyzed to monitor the mechanical seal operating conditions and faults (Figure 5) [79].

Figure 4. Dynamic evolution of contact interfaces. (A) Total reflection principle [84]. (B) Measuring device [85]. (C) Actual contact area at the interface [85]. (D) In constant normal force and variable normal force experiments, the distribution changes in equivalent stress across different time scales [76], (a,b): The change of equal effect force distribution P at different time scales in constant and variable normal force experiments.

Figure 4. Dynamic evolution of contact interfaces. (A) Total reflection principle [84]. (B) Measuring device [85]. (C) Actual contact area at the interface [85]. (D) In constant normal force and variable normal force experiments, the distribution changes in equivalent stress across different time scales [76], (a,b): The change of equal effect force distribution P at different time scales in constant and variable normal force experiments.

2.2.2. Coating Technology Enhances Wear Resistance

The key to wear suppression is the reduction in contact stress concentrations and the optimization of wear resistance. Coating technology can enhance interfacial hardness and reduce wear, which can significantly slow down the wear process. Gradient design and nanocompositing of coating compositions are key strategies for improving wear resistance. For example, multilayer coatings can reduce the wear rate by 58% compared with single-layer coatings by alternately depositing hard and ductile layers and dispersing the gradient of interfacial stress [80]; the strengthening effect of nanoparticles in nanocomposite coatings leads to increased hardness and reduced wear rate [81,82].

For sealing structures, the treated CrN coatings exhibited a lower wear rate of 46.0% relative to the untreated coatings. The surface of titanium alloy can form a gradient hardness interfacial layer by physical vapor deposition coating technology, and its wear resistance is enhanced to 3–5 times that of the substrate, while the nano-smooth surface of DLC coating significantly prolongs the life of the sliding vice by inhibiting adhesive wear [59].

In addition, wear can be further reduced by optimizing the coating structure and process. For the pore defects of CrN coatings, electrochemical polarization was used to seal the micropores, and the densities of the coatings increased by 20%. Under high humidity conditions, the wear rate of the coating after polarization treatment was reduced by 37.5%, which has been successfully applied to seals for marine power systems (

Table 2. Typical coating performance comparison [83,85].

Coating Type	Hardness	Applicable Working Conditions
CrN	20–25	High load gears and bearings
DLC	15–20	Vacuum and dry friction
MoS2	0.5–1.0	Aerospace lubrication and cryogenic environments

) [83,84].

2.3. Clearance Dynamic Contact State Modeling Method

As an important characteristic parameter of system operation, the clearance of kinematic pairs in mechanical transmission systems directly affects the system’s operational dynamics and service dependability. The nonlinear collision effects and dynamic contact state jumps induced by the clearance invalidate the traditional continuum assumption and need to be quantitatively characterized by dedicated contact models [86,87]. Since the beginning of the research to date, three commonly used methods for modeling the dynamics of clearance-containing mechanisms, namely, the two-state model, the continuous contact model, and the three-state model, have been gradually developed, as shown in Figure 6.

The two-state model considers that there are two states of motion between the members of the clearance kinematic pair: contact force constraints are generated between the members in the contact state, and the constraints are lost when they are in the free state, which can be judged by calculating the distance between the members. This method shows high efficiency in the dynamic analysis of deployable mechanisms, but it is unable to characterize the transient impact effects under high load conditions [88,89].

The continuous contact model assumes that components remain in contact all the time, i.e., the members are considered to have a very short time to undergo a separation collision [90]. By equating the clearance to a massless rigid rod, the clearance-containing system is transformed into a conventional multibody dynamics problem [91]. This simplified model is widely used in the rapid design of engineering systems such as automobile suspensions. Nevertheless, its assumption of ignoring contact deformation leads to high errors in high-precision scenarios (

Table 3. Comparison of three clearance modeling methods.

Clearance Modeling Methods	Advantages	Drawbacks	Applicable Occasions
Two-state model	Closer to reality and more accurate modeling	Computationally complex and difficult to use for multiple clearance systems	Single-clearance systems
Continuous contact modeling	simple calculation	Unable to reflect crash impacts	Small clearance and multiple clearance systems
Three-state modeling	Consistent with the actual situation	Complex modeling and computational instability	Fewer applications

).

The three-state model (contact–separation–collision) accurately describes the transient dynamics progress of the kinematic pairs through Lagrange’s equation [92], which adds the collision state compared to the two-state model and utilizes the momentum theorem, and the velocity change in the component before and after the collision is calculated by the recovery coefficient. Its advantage lies in its ability to capture the force pulse characteristics at the moment of collision, with less error in precision systems such as satellite antenna deploying mechanisms [41], but the frequent occurrence of state switching in multi-clearance mechanisms leads to a decrease in computational efficiency. Meanwhile, periodic steady-state solutions are difficult to obtain. In recent years, hybrid modeling approaches have gradually become a new direction to break through the limitations of a single model. Xia et al. proposed an adaptive contact stiffness model, which achieves a balance between accuracy and efficiency in a multi-gap parallel mechanism by adjusting the stiffness values in real-time to match the different contact phases (separation/sliding/collision) [93,94]. Mukras’ team further combined the discrete element idea with the Gaussian integration method to successfully predict the clearance expansion paths due to wear and collision forces in a crank–slider mechanism, and its collision force time series curve has a high correlation with experimental results [40].

Corresponding clearance modeling methods need to be deeply coupled with the wear evolution. The degradation of surface morphology due to wear significantly changes the contact stiffness and damping values, which in turn affects the accuracy of dynamics simulations [95,96]. Researchers have improved the accuracy of positioning error prediction for mechanisms with wear clearance by establishing a nonlinear mapping relationship between wear location and wear amount through neural networks [97]. This closed-loop association of “morphology–wear–model parameters” implies a paradigm shift in clearance modeling from phenomenal description to mechanism-driven modeling.

2.4. Dynamic Modeling of Clearance-Containing Mechanisms

The dynamic behavior of mechanism dynamics with clearance is a concentrated manifestation of multiscale effects at the system level. As a core component of mechanical transmission, the dynamics of multi-body mechanisms (e.g., satellite antenna unfolding systems, industrial robot joints, etc.) are directly affected by the clearance of the kinematic pairs; microscale surface wear evolves through the mesoscale clearance, ultimately triggering the macroscale nonlinear vibration and motion instability [98,99].

The dynamics of mechanical systems with clearances can systematically characterize the impact of clearances on the operation and vibration behavior of mechanisms, achieved by integrating multibody system equations of motion with contact mechanics theory [100]. At the core is the creation of multibody dynamic equations with coupled contact forces. Here, the choice of contact force model directly affects the nonlinear characteristics of clearances. For example, a virtual prototype simulation based on a three-state collision model can effectively reproduce the attitude oscillation phenomenon in a precision system. The experimental results show that the simulation results and the measured data have good consistency [101]. The dynamic modeling method combined with neural networks significantly improves the accuracy of motion trajectory prediction by adaptively correcting the contact parameters [102].

To cope with the time-varying characteristics and uncertainties of the clearance, researchers have developed a multi-body dynamics framework incorporating Monte Carlo methods to reveal the main causes of the dispersion of motion accuracy in multi-clearance systems [103,104,105]. Such models are of great value in engineering practices, such as optimizing mechanical system design to improve positioning accuracy or evaluating the service reliability of complex mechanisms in extreme environments. However, the dynamic coupling mechanism between wear and kinetic parameters is still insufficiently characterized by existing models; the alterations in surface topography and contact characteristics due to wear have not yet been fully integrated into the dynamic equations. Future research needs to deeply integrate the wear evolution mechanism with the dynamic modeling method to construct a whole life cycle prediction system from microscale damage to macroscale system response. This integration will offer theoretical support for designing, operating, and maintaining high-reliability driveline systems.

In the satellite biaxial drive mechanism, the clearance size is exponentially correlated with the velocity error and acceleration fluctuation, and the clearance reduces the positioning accuracy and operational stability of the satellite system and exacerbates the wear and tear of the reaction wheels and reduces their service life [106,107,108]. Dynamics simulations of crank–slider mechanisms show that periodic collisions triggered by the clearance of the moving pair excite broadband vibration energy and significantly exacerbate structural fatigue damage [109]. Some researchers further revealed experimentally that the root mean square (RMS) of the slider acceleration error showed a monotonically increasing trend when the clearance value was increased from 0 to 0.025 mm, and the acceleration error RMS reached a peak value of 1.4520 in the interval of 0.01–0.025 mm of clearance, which showed obvious nonlinear characteristics [110]. It is worth noting that this kinetic degradation has a self-enhancing effect: the increased vibration leads to an increased wear rate, which further enlarges the clearance size, forming a vicious cycle of “wear–vibration–secondary wear” (Figure 7).

3. Multiscale Interface Behavior Simulation Models

Although the multiscale physical model theoretically reveals the multiscale correlation law of interface behavior, its engineering applicability still needs to be verified and expanded by multiphysics field simulation technology. By combining with the theoretical model, multiscale simulation is capable of reproducing the dynamic behavior of a system within a virtual environment, which provides more data support for optimized design and fault diagnosis.

Among them, dynamic simulation achieves the quantification of the impact of clearances on overall mechanism dynamics (e.g., vibration spectrum broadening and motion accuracy attenuation) through multibody system modeling (e.g., ADAMS and RecurDyn) [111,112,113], whereas finite element analysis (e.g., Abaqus and ANSYS) analyzes the mechanism of contact stress concentration and wear hotspot formation at the microscale [114,115]. The deep integration of the two can not only reproduce the transient impact characteristics of the hinge collision of the wing deployment mechanism but also allow for the prediction of bearing surface wear [116,117], providing multiscale data support for the digital empowerment study (Figure 8). Researchers can predict the evolution trend in interface behavior under extreme operating conditions (e.g., heavy load impact, temperature alternation) at the design stage [118], significantly reducing experimental cost and shortening the R&D cycle, marking the paradigm shift from empirically driven to model-driven research on mechanical transmission systems.

3.1. Interface Contact–Wear Joint Simulation

Interface contact wear simulation is the core link of multiphysics field simulation technology, which systematically reveals the effect of interface behavior on the impact on mechanical transmission system performance by coupling contact mechanical analysis and the wear evolution model. Contact analysis focuses on the stress distribution and deformation characteristics in the contact region of kinematic pairs, and the finite element method shows significant advantages in this field [119,120,121]. For example, Cai et al. revealed the spatial and temporal evolution of the contact state in the early stage of fretting wear by using finite element simulation and found that the localized stress concentration can directly induce the emergence and expansion of surface micro-cracks [122]; Zhu et al. further compared the effects of different fretting pad geometries on the stress gradient in the contact area and confirmed that the curved profile can reduce the peak stress compared with the planar structure, which is a theoretical foundation for predicting fretting wear fatigue life [123].

Based on the consequence of contact analysis, wear simulation quantifies the material removal rate and surface morphology evolution by introducing physical models such as the Archard equation [124,125,126]. Zhao et al. build a finite element model for fretting wear according to the Archard model and reveal the wear patterns under partial slip and total slip states by simulating the fretting wear behavior of zirconium alloys: the former is dominated by oxide layer flaking, while the latter exhibits a composite pattern of adhesive wear and abrasive wear [127,128]. This refined modeling approach not only predicts the wear amount but also resolves the migration paths of wear products and their feedback effects on the clearance evolution [129].

In recent years, researchers have begun to deeply integrate finite element analysis (FEA) with dynamics analysis for a more comprehensive understanding of the properties of mechanical systems. Dynamics analysis places emphasis on the overall motion behavior and dynamic response of the system, while finite element analysis provides detailed information on microscale contact and wear behavior (Figure 9) [130]. For example, in the research on the fretting wear of the control rod cladding, finite element simulation and experimental observations were combined, and the numerical calculation results validate the model’s accuracy [131]. The dynamic load data of the kinematic pairs under typical working conditions were obtained through a dynamics simulation model and imported into the finite element model as boundary conditions. The wear depth of kinematic pairs was accurately predicted by integrating finite element simulation to analyze contact stress distribution and employing a modified Archard wear model. This approach establishes a scientific foundation for investigating the wear characteristics of such pairs [132,133]. This closed-loop framework of “macroscale load input–microscale wear output” effectively overcomes the limitations of the traditional single-scale simulation and provides methodological support for the life prediction and reliability device of complex mechanical transmission systems (Figure 10).

3.2. System Dynamics Simulation

System dynamics simulation is a key technical means to reveal the dynamic response of the kinematic pair interface to the macroscale system, which quantifies the impact of clearance on motion accuracy, vibration characteristics, and stability by constructing a multi-body dynamics model with coupled equations of contact forces. Early research focused on the exploration of the fundamental laws of simple mechanisms, such as Flores et al., based on the ADAMS platform to establish the crank–rocker mechanism model, and found that the single clearance vice has a limited impact on the output speed. Still, it will lead to periodic fluctuations in acceleration. In contrast, the double clearance vice leads to the acceleration spectrum broadening, which is more directly connected to the actual working conditions of the nonlinear characteristics and lays the methodological foundation for the simulation of complex systems [134].

Subsequently, researchers began to focus on more complex mechanisms and systems. The impact of joint contact force models, clearance size, and crank input speed on the dynamic performance of RSSR space mechanisms was analyzed by simulation [72,101]. Collision contact points between the ball head and ball socket tend to concentrate in two specific regions within the clearance ball. Moreover, clearance size emerges as the primary factor influencing both the fluctuation of the mechanism’s crank output angular acceleration and the joint contact force at the ball joint. The size of the clearance size exhibits a nonlinear positive correlation with the changes in crank angular acceleration and the size of joint contact force (Figure 11) [135,136,137,138].

In recent years, multi-physics field coupling and extreme working condition simulation have become a cutting-edge direction. Zhang et al. investigated the deployment characteristics of a solar sail panel with clearance and its impact on the spacecraft’s motion attitude using Adams12.0 software in conjunction with the two-state model and Lagrangian multiplier equation. This study not only considered the dynamics of the mechanical system but also combined the multi-physics field coupling problem of the spacecraft, which provided a significant reference for the design and optimization of the spacecraft [139,140]. In addition, based on Adams’s simulation, Zhang Jianchao et al. examined how crank speed and clearance size impact the accuracy of the lower dead center in presses. The research identified possible failure modes and forecasted the trend in failure development by simulating the system response under real operating conditions. These findings offer valuable data to enhance press design optimization and fault diagnosis [141].

4. Data Empowerment Interface Behavior Analysis and Life Prediction

Data modeling and analysis of interface behavior is a key step to capture the dynamic evolution law and quantify the coupling effect of multi-physical fields, which is an inevitable requirement to realize intelligent prediction and active regulation of mechanical transmission systems. Traditional physical models are limited by single-scale deterministic assumptions, making it difficult to portray the multiscale dynamic correlation of interface behavior. Meanwhile, purely data-driven methods are capable of mining complex patterns due to the scarcity of small-sample data and the lack of physical mechanisms, resulting in insufficient extrapolation capability and poor interpretability.

Breakthroughs in AI technology provide new ideas for the following dilemmas: data augmentation [142,143] techniques generate multiscale virtual data to compensate for the lack of samples due to high experimental costs; transfer learning enables cross-scenario reuse of models by multiplexing domain knowledge [144]; and mechanism–data-driven models ensure adherence to data-driven frameworks by integrating physical equations based on conservation laws [145,146,147]. These techniques synergistically promote the research of interface behavior from “empirical assumption-driven” to “data–mechanism synergy-driven”, which has made significant progress in the credibility of data generation, interpretability of multiscale correlation, and real-time edge computing and provides theoretical tools for intelligent operation and maintenance of high-reliability mechanical systems. It offers theoretical tools and methodological support for the intelligent operation and maintenance of highly reliable mechanical systems.

4.1. Enhanced Strategies for Data Scarcity Scenarios

The acquisition of interface data (e.g., friction, wear, and vibration signals) is limited by factors such as high measurement cost, complex working conditions, and multi-physical field coupling and generally presents the characteristics of small samples, uneven distribution, multi-domain heterogeneity, and complex mechanisms [148]. To overcome the issue of limited interface data, a dual-track approach is essential. This strategy involves both generating augmented data and transferring knowledge across domains [149,150]. By broadening data distribution and leveraging domain expertise, this approach surpasses constraints related to data volume and variety (Figure 12 and

Table 4. Comparative analysis of two methods of feature space expansion and generative adversarial networks [151].

Method	Core Problem-Solving	Technical Advantages
Feature space expansion	Sparse data in a single domain; for example, the Random Forest model has a 20% increase in generalization ability in sparse data scenarios	Highly interpretable and computationally efficient
Generative Adversarial Networks	Complex/extreme conditions data generation; for example, CGAN generates bearing failure data with 92% classification accuracy	Generate high-dimensional and complex data to break through distribution boundaries

).

4.1.1. Data Enhancement Techniques: From Interpolation to Physical Constraint Generation

The data enhancement technology method realizes targeted breakthroughs through a hierarchical strategy. Feature space expansion and generative adversarial networks form a hierarchical enhancement framework of “filling–expanding” (Figure 13), which consolidates the data foundation and expands the data distribution. Feature space expansion expands data in a single domain by means of interpolation or extrapolation, which is suitable for scenarios where the laws in the domain are clear. Still, the data are sparse [152,153], while the generative adversarial network extends the distribution boundary by virtue of its powerful generative ability while increasing the diversity and quantity of data [154,155].

Feature space expansion enhances small-sample performance using limited experimental data by combining physical mechanisms with data-driven methods. This approach is particularly beneficial in situations where the mechanism is well-defined, but the available data are scarce. Its core lies in utilizing domain knowledge to constrain the data generation process and ensure the physical rationality and interpretability of the expanded data. Two typical algorithms for feature space expansion are Random Forest [156,157,158] and synthetic minority oversampling technique (SMOTE) [159,160,161]. By constructing multiple decision trees, Random Forest is suitable for scenarios where the data distribution is sparse. Still, the regularity in the domain is clear and can improve the data density and model generalization ability. At the same time, SMOTE specifically solves the data imbalance problem and enhances the recognition ability of the minority class samples by linearly interpolating between the nearest neighbors of the minority class samples.

Generative Adversarial Networks (GANs) [162,163,164] show unique value in data enhancement for mechanical transmission systems by generating realistic and diverse synthetic data through adversarial training of generators and discriminators. Typical approaches for different engineering requirements include Conditional Generative Adversarial Networks (CGANs) [143] and Temporal Generative Adversarial Networks (TimeGANs) [165]. These two approaches address the bottleneck in enhancing mechanical transmission data by focusing on directional control and temporal fidelity. Their engineering applications have spanned critical components, including gears, bearings, and rotors.

CGAN controls the direction of data generation by introducing condition labels (e.g., fault type, load level) to achieve directional simulation of failure modes [159]. An improved algorithm based on a CGAN was used to synthesize rolling bearing fault samples under new conditions by M. Ahang et al. This method solves the problem of scarce fault data in industrial environments by generating fault data from standard data and experimentally demonstrates the high similarity and classification accuracy of the generated data with accurate data [166].

The time-series generation adversarial network maintains the time-series continuity of vibration, noise, and other signals through time-dependent modeling, adapting to the needs of life prediction and dynamic analysis [167]. For the case of bearing data acquisition, TimeGAN can be used to generate vibration time series data from regular to failure, with running time as the input label. The Pearson’s correlation coefficient values of the frequency domain waveforms of the generated data and the real data all exceeded 0.9 and reduced the lifetime prediction error compared to the conventional method [168]. Aiming at the situation that it is hard to model the non-stationary properties of the vibration signals under the variable speed condition of the rotor system, combining TimeGAN and Wigner–Ville distribution, the vibration time–frequency maps under the time-varying speed condition can be generated. The results show that the generated data successfully captures the frequency modulation phenomenon triggered by the sudden change in rotational speed, and the detection rate of rotor unbalance faults is greatly improved [169].

Figure 13. Similarity among real and synthetic data for a 0.014-inch failure of the inner ring of a bearing at 0 hp operating load [168].

Figure 13. Similarity among real and synthetic data for a 0.014-inch failure of the inner ring of a bearing at 0 hp operating load [168].

4.1.2. Cross-Domain Transfer Learning

The idea of addressing the small sample learning problem mainly draws on the human strategy of relying on experience to acquire new knowledge quickly. By training on plenty of similar samples, a model is able to learn transferable knowledge, which is then utilized to understand and predict more efficiently in new classes with only a small number of samples [170]. This strategy is categorized as a form of transfer learning, and a prevalent approach involves initially pre-training a model on a sizable dataset to establish a robust foundational knowledge base. Subsequently, fine-tuning this pre-trained model on a new task enhances its applicability to the specific requirements of the new task (Figure 14). This pre-training and fine-tuning strategy makes the model more stable on the new task and has better generalization ability.

Cross-domain migratory learning solves the problem of insufficient data in the target domain by sharing knowledge from the source domain (laboratory) and the target domain (actual working conditions). In engineering practice, domain-adversarial transfer learning (DANN) and pre-training–fine-tuning are two typical types of methods [171].

DANN employs adversarial training to align the feature distributions between the source and target domains [172]. Khan introduced a methodology utilizing an auxiliary classifier generative adversarial network (ACGAN) to generate mechanical sensor signals, addressing data augmentation and training data imbalance issues. By employing transfer learning, this approach generates synthetic data of high quality that closely resemble authentic data in statistical features and classification accuracy [173,174,175].

Pre-training–fine-tuning migration, on the other hand, is achieved by pre-training the model on large-scale source-domain data and then fine-tuning the adaptation with a little amount of target-domain data [176,177,178]. Lei et al. addressed the problem of the dynamic change in joint friction characteristics of industrial robots by constructing a pre-training model for the simulation environment and then combining it with fine-tuning of measured data at the service stage, which reduced the friction coefficient prediction error under different temperature operating conditions [179]. In the space mechanism, the researchers first use the ground vacuum chamber data to align the feature distribution with the in-orbit simulation data and then interpolate in the target domain to generate the dynamics data with different combinations of unfolding speed and temperature. By increasing the diversity and volume of data within the target domain, the accuracy of predictions regarding mechanism unfolding can be enhanced. This approach was validated in the Non-Cooperative Spacecraft Attitude Estimation Challenge 2021 (SPEC2021) conducted by the European Space Agency and Stanford University, yielding outstanding outcomes that underscore the method’s precision and resilience in spacecraft attitude estimation tasks. ESA has subsequently introduced a two-stage enhancement strategy [141,180,181].

4.2. Mechanism-Data Fusion Approach to Life Prediction

4.2.1. Data-Driven Model

The data-driven approach mainly depends on historical data and real-time monitoring signals. It establishes the statistical mapping relationship of state–life by mining the implicit laws in these data [34]. The essence of this approach centers on integrating and refining diverse data from various origins to accurately evaluate the condition and forecast the lifespan of the mechanical transmission system. This is accomplished through time–frequency feature analysis, deep learning modeling, and other methodologies. The time–frequency method is the mathematical expression of physical laws, which is suitable for scenarios with precise mechanisms and scarce data (

Table 5. Differences between time–frequency feature-driven and deep learning approaches.

Dimensionality	Theoretical Foundation	Feature Extraction Method	Interpretability
Time–frequency characteristic drive	Signal Processing and Statistics	Artificial design features (time-domain statistics, frequency-domain energy, etc.)	Characteristics and physical phenomena can be directly correlated
Deep learning	Neural Networks and Pattern Recognition	Automatic learning of features (convolutional kernels, attention weights, etc.)	Black box model and reliance on visualization tools

) [182,183,184]. Deep learning methods are abstract modeling of data laws and are ideal for scenarios with complex patterns and sufficient data (Figure 15) [185,186,187].

Time–frequency feature extraction techniques are utilized to create degradation metrics through the extraction of time-domain, frequency-domain, and time–frequency-domain characteristics from signals such as vibration and acoustic emission [188,189,190]. These features can reflect the dynamic behavior of mechanical transmission systems in different time scales and frequency scales and provide key information for life prediction [191]. He et al. introduced a novel approach involving the development of a dynamic model for mechanical end seals. This model integrates spectral analysis and numerical simulation methods to predict and assess lubrication and wear patterns in mechanical end seals utilized in hydraulic pumps for aeronautical and space applications under challenging operational environments [41]. Novelo’s team develops an online health monitoring system for nut production equipment based on vibration signal crags and envelope spectral features to shorten the response time for fault identification and reduce maintenance costs (Figure 16) [192]. Xu et al. introduce a fault diagnosis approach for electric motors utilizing a multimodal time series and an integrated Transformer network. By integrating time–frequency analysis techniques with deep learning methods, they demonstrate the efficacy of time–frequency feature fusion in enhancing the characterization of non-smooth signals (Figure 17) [187].

Deep learning models have the capacity to automatically learn and extract intricate features from data, facilitating precise modeling and prediction of system states [194,195,196]. By utilizing deep neural networks, such as convolutional neural networks (CNNs), recurrent neural networks (RNNs), and their variations like long short-term memory networks (LSTMs), time-series data and diverse data sources can be effectively processed, uncovering profound patterns within the data [197,198]. Deep learning prediction techniques offer notable advantages in handling extensive datasets, enhancing the accuracy and dependability of life prediction. Zhang et al. introduced a novel approach, a multi-head double sparse self-attention network based on an enhanced Transformer, for predicting the remaining useful life of mechanical systems. The model extracts the key information in the data through the self-attention mechanism, which improves the accuracy and interpretability of the prediction [199]. AN et al. introduced a novel hybrid model that integrates a convolutional neural network (CNN) with stacked bidirectional and unidirectional long short-term memory (LSTM) networks to forecast the residual service life of milling cutters. The CNN component is employed for feature extraction and dimensionality reduction, whereas the unidirectional LSTM component serves to remove noise and encode past information. Empirical findings demonstrate the efficacy of the hybrid model in accurately predicting the remaining service life of milling cutters [200].

4.2.2. Fusion Enhanced Robust Prediction

The fusion-enhanced prediction method enhances model generalization and robustness by integrating diverse data sources and features, along with employing data augmentation techniques [201]. This approach enhances the representation of data by fusing various features such as time–frequency features and deep learning features. Additional training samples are generated using methods like Generative Adversarial Networks (GANs) or data augmentation to further enhance model robustness and predictive performance (Figure 18).

Behera et al. introduced a Conditional Generative Adversarial Network (CGAN) approach to enhance the model’s generalization and prediction accuracy. This method involves generating multivariate failure instances and subsequently predicting Remaining Useful Life (RUL) using a Deep Gated Recurrent Unit (DGRU) network that integrates the generated failure data with conventional data [202]. Fan et al. introduced a feature representation-driven transfer learning approach to forecast the remaining useful life (RUL) of a device under unobserved conditions and failures in the target domain. Their method leverages a consensus self-organizing model (COSMO) to extract transferable features that delineate distinctions among devices and their equivalents. Subsequently, a Random Forest regression model is employed for RUL estimation. Through empirical validation using the NASA turbofan engine degradation simulation dataset, the efficacy of the transfer learning technique is confirmed in enhancing RUL prediction accuracy, particularly in scenarios where the complexity of the target domain surpasses that of the source domain [203].

4.2.3. Mechanism–Data-Driven Fusion

Despite the advantages of data-driven methods in complex pattern mining, their insufficient physical interpretability and weak extrapolation ability limit their application in engineering decision-making. To this end, physical degradation mechanisms need to be deeply fused with data models to form an interpretable and generalizable prediction framework (Figure 19). The mechanism–data fusion-driven approach constructs a fusion-driven prediction method with both mechanism credibility and data adaptability through the deep coupling of physical degradation models and machine learning algorithms [175,204,205,206]. Mechanism–data fusion-driven methods are mainly series hybrid models and parallel hybrid models in applications (Figure 20) [201,207].

Tandem models use data-driven models to generate input or correction parameters for physical models to optimize the prediction results further or use the number of physical outputs to bootstrap corrections to the numerical model. The advantage of this approach is that it requires less accuracy in the mechanistic modeling results, and the data-driven approach automatically maps the relationship between the inputs and outputs after taking as inputs the mechanistic results that have relevance to the prediction target [208,209,210]. Fan et al. developed a data-driven approach with physical feature enhancement by combining the physical model parameters with the sensor data and utilizing a deep neural network prediction model. The model performs exceptionally well on the CMAPSS dataset FD002 in the presence of data scarcity [211]. Cao estimates the degradation parameters by means of an Extended Kalman Filter (EKF), which provides information about the physical model. The EKF output is integrated with sensor data features and serves as input for a deep learning model designed as a mechanism–data fusion model [212].

Parallel hybrid modeling is the mechanistic model results and data-driven results, which can be processed to obtain the results by factor multiplication, weighted summation, and other methods (Figure 21). This modeling method needs to ensure that both the mechanistic model results and data-driven results have high accuracy, and the weights need to be adjusted to achieve better results [143,213]. Jianxiong Hu et al. used a weighted summation to combine the mechanistic and data models linearly and balance the contributions of the two types of models through weight adjustment [214]. Although this method verifies the validity of the fusion model through quantitative assignment, the weight coefficients are static and fixed, which makes it challenging to adapt to the dynamic change scene and does not realize the deep information interaction. For this, the limitation of static weights can be broken through particle filtering technology. The researcher uses particle filtering technology to fuse the results of mechanism–data models, and compared with the weighted summation approach, the weights of particle filtering technology can be dynamically adjusted with the error, advancing towards dynamic fusion modeling [215]. The approach involves integrating the theoretical aspects of the mechanistic model with the statistical characteristics derived from data into a cohesive target space. This integration is achieved through information mapping, followed by regression analysis to uncover the intricate relationships between these two sets of features. By doing so, this method surpasses the conventional fusion constraints at the outcome level. It enables the alignment of physical constraints with data patterns, facilitates cross-validation of multidimensional features, and enables in-depth exploration of nonlinear regression connections at the feature level [23]. This reflects the development trend in the field of fusion modeling— ranging from mechanical combination to intelligent fusion, and from result correction to process synergistic evolution—with the ultimate goal of constructing a new generation of predictive models with strong generalization ability and interpretability through the deep coupling of physical laws and data intelligence [204].

5. Conclusions

Aiming at the challenges of multiscale coupling and uncertainty of interface service behavior in mechanical transmission systems, this paper proposes a trinity-integrated research paradigm of “physical modeling, simulation verification, and digital empowerment” (Figure 22). This paradigm surpasses conventional methods by combining theoretical modeling, multiscale simulation, digital enhancement, and data-driven technologies to break their limitations.

This paper realizes theoretical breakthroughs in the following four dimensions:

• Multiscale Parameter Transfer Mechanism: To realize the correlation between different scales by modeling the behavior of multiscale physical interfaces and to realize the mapping and transfer of microscale parameters to macroscale dynamics models.
• Dynamic Two-Way Coupling Technique: To establish a positive link of “contact stress–wear depth clearance expansion–dynamics response” in the simulation link, and at the same time, to identify the distribution of wear hotspots through the inversion of vibration signals, so as to form the closed-loop feedback of wear and vibration.
• Uncertainty Quantification System: This system aims to establish a statistical mapping between vibration signals and component lifespan using a data-driven approach to address uncertainties arising from random interface parameters and environmental disturbances.
• Combination of Mechanism–Life Systems: This system is designed to quantify uncertainties related to interface parameters and environmental disturbances by integrating physical constraints into a neural network using a mechanism–data fusion approach, enabling an interpretable analysis of wear damage mechanisms.

6. Prospects and Challenges

Although significant results have been achieved in the research of multiscale modeling and life prediction of interfacial behavior of mechanical transmission systems, the transition from ‘phenomenal description’ to ‘mechanistic regulation’ still faces many challenges, which need to be explored in depth.

• In terms of multiscale modeling, there are theoretical bottlenecks in the dynamic transfer mechanism of parameters at different scales, the nonlinear mapping relationship between microscopic fractal features and macroscopic kinetic response has not yet been established, and the dynamic evolution of the surface gradient structure and the interaction mechanism between system vibration and energy in the process of wear has not yet been quantitatively characterized. In the future, we need to develop multiscale coupling algorithms based on adaptive weights to achieve real-time simulation of extreme working conditions.
• There is also room for improvement in the data-driven approach. Although Generative Adversarial Network (GAN) has potential, the physical credibility of synthetic data are insufficient, and the correlation between the time–frequency characteristics of vibration signals and the real wear mechanism is insufficient, which leads to a large generalization error of the life prediction model, so we can try to break through the adversarial generation framework based on physical constraints. Migration learning also faces the problem of feature drift and needs to build a multidimensional migration mapping network.
• Gradient coating design, due to the complexity of the process and high-cost limitations of the application, can be developed based on a machine learning coating composition–performance reverse design platform to achieve intelligent mapping. At the same time, the stability of the coating interface in extreme environments under the lack of research needs to establish an assessment system.
• The current interface data are severely restricted by the confidentiality agreement, and it is urgent to build a big data platform to break through the limitations; for high-precision machine tools, aerospace hinges, and other extreme scenarios, a large amount of measured data accumulation is needed to test the applicability of the framework under different working conditions, quantify the model robustness through multi-field coupling experiments, and promote the in-depth integration of theory and engineering.

These improvement directions are expected to provide more practical technical support for the reliability improvement of mechanical transmission systems and promote the further development of related technologies.