Contact Load Research Articles

Study on gear contact stiffness and backlash of harmonic drive based on fractal theory

Contact stiffness and backlash in the harmonic drive significantly impact a robot's positioning accuracy and vibration characteristics. The height of the harmonic drive tooth pair is typically less than 1 mm, making the measurement and modeling of backlash and contact stiffness inherently complex. This paper proposes a contact stiffness and backlash model by establishing a correlation between fractal parameters and tooth contact load. To obtain the fractal roughness parameters of the real machined tooth surface, a combination of a noncontact optical profiler and the RMS method is employed. Subsequently, the study explores the influence of rough tooth surface and contact force fractal parameters on contact stiffness and gear backlash. The results demonstrate the substantial impact of surface topography parameters and contact force on contact stiffness and backlash. Specifically, an increase in the fractal dimension correlates with a reduction in gear backlash and contact stiffness. Conversely, the fractal roughness parameter exhibits the opposite effect. Notably, an increase in contact force enhances contact stiffness.

Influence of different heat treatments on fracture behavior of rolling element bearing steels

Rolling element bearings (REB), one of the critical components of mechanical power transmissions, operate under high contact loads concentrated over small volumes of material. The damage caused by fatigue to REBs happens in two stages: the initiation of cracks and the propagation of cracks from areas of stress concentration. To select bearing steels for different applications, it is important to have knowledge about the material’s ability to resist fracture. This study presents results from an experimental investigation of bearing steels manufactured using different heat treatments. Steels were induction-hardened, carburized, and through-hardened, generating varying microstructures. Fracture mechanics tests were conducted using ASTM standards. The data generated is useful for predicting crack initiation and growth behavior under different loading conditions. Microscopic-level investigations are also presented to discern the fracture mechanisms associated with different microstructures.

Influences of external moment on the contact characteristics of angular contact ball bearings under combined loads

Angular contact ball bearings are widely used in rotating machinery. The external moment about the bearing lateral direction (i.e. the lateral moment) applied to a bearing affects the service life and performance of the bearings by influencing its internal contact characteristics. This work established a quasi-dynamic model of the ball bearing by comprehensively considering the inclination angle of the inner ring due to external lateral moment, the viscous drag, the inertial force and moment of the ball, the spin and sliding of the ball in the contact ellipse. On this basis, the operation process of angular contact ball bearings was simulated under combined radial and moment loads. The effectiveness of the model was verified experimentally, and the influences of external moments about different directions on the contact angle, slip-roll ratio, and load distribution under combined loads were analyzed. The results show that the increase in moment intensifies the spin-sliding of the rolling element. When the lateral moment and the radial load are applied together, the lateral moment can reduce the maximum load of the rolling element and causes the maximum load of the rolling element to deviate from its original position. When the lateral moment is combined with the axial and radial loads, the bearing load zone is concentrated by the rolling elements near the lateral direction. The curve of the load distribution changes from an ideal oval to a distorted oval. The research results can be used to guide the design, service life calculation, and performance evaluation of rolling bearings.

Influence of shear yield strength of rail material on the shakedown limit in shakedown map

Rail materials with different shear yield strengths can exhibit different rolling contact fatigue (RCF) damage response during cyclic contact loading. The objective of this work is to achieve the actual shakedown limits in the shakedown map for rail materials with different shear yield strengths through RCF simulation tests of wheel-rail, and to investigate the relationship between the shear yield strength (ke) and the shakedown limit. Rolling-sliding tests were performed to investigate the RCF damage states of three types of rail materials with different shear yield strengths. Then, according to the differences of RCF damage states for each rail material and the method of nonlinear curve fitting, the actual shakedown limits for three types of rail materials were obtained. The actual shakedown limits for the three types of rail materials were lower than the original one in the classical shakedown map. With an increase in the shear yield strength (ke) of the rail material, the actual shakedown limit is reduced. Moreover, a relationship emerged which allowed a simple method to be proposed to obtain the actual shakedown limit based on the shear yield strength. The changing process and differences in the impact of different shear stress levels on the microstructural damage transformation of rail materials from the perspective of contact mechanics have been discussed. The behavior of severe accumulation of residual stresses during cyclic loading and more likely initiation of microcracks are the main reasons why rail materials with a higher shear yield strength (ke) under great contact loads are more prone to developing RCF crack damages. That is, the shakedown limit for the material with a higher shear yield strength (ke) is much lower. In view of the application of the shakedown map in the evaluation and prediction for RCF damage of rail materials with different shear yield strengths, different shakedown limits should be applied to different rail materials when analyzing their likely performance.

Effect of dented residual stress on the surface-defect-induced pitting under rolling contact loading of M50 bearing steel

Surface-defect-induced pitting gradually becomes the limitation of the rolling contact fatigue life of the M50 bearing steel as the subsurface initiation spalling probability decreases recently. Dent formation lives residual stress (RS). However, it was ignored in past studies on surface-initiated pitting. Therefore, this study established a continuous simulation model from particle compression to cycle rolling contact loading to study the dent-induced RS effects on damage evolution. The constitutive model of damage evolution incorporated continuum damage mechanics and cohesive mechanics. The results show that the depth-width ratio of the dent and RS increases as the load and hardness increase. RS makes both subsurface-initiation-damage and surface-initiation-damage advance, and affects the direction and speed of the surface damage evolution. Moreover, the size of the pitting in the rolling direction increases as hardness increases.

Combined musculoskeletal finite element modeling of femur stress during reactive balance training

The purpose of this study was to determine the material stresses experienced in the femoral neck during the stepping phase of recovery from a forward loss of balance achieved both using release from a static forward lean and rapid treadmill accelerations in 8 older adults. A scalable musculoskeletal model with 23 degrees of freedom and 92 force actuators was used to calculate joint reaction forces. A finite element model of the femur used joint reaction forces calculated by the musculoskeletal model to calculate the material stresses during stepping. Balance recovery from a static forward lean angle had a greater joint contact force and greater maximum tensile stress than a recovery from treadmill induced perturbations both before and after a training session. Hip joint contact loads were found to be large in magnitude, however, all stresses experienced by the bone are less than critical yield stresses for trabecular bone. We suggest that stepping balance recovery is safe for older adults with no obvious loss of bone density or strength and that analyses such as finite element analysis are necessary to understand stresses in the material at the joint level.

Experimental study on boundary lubricity of superficial area of articular cartilage and synovial fluid

The boundary lubrication mechanism at the articulating surface of natural synovial joints has been the subject of much discussion in tribology. In this study, to elucidate the lubricating function of the superficial area of articular cartilage and synovial fluid (SF), cartilage specimens were processed with four different treatments: gentle and severe washing with detergent, incubation in NaCl solution, and trypsin digestion to selectively remove certain constituents from the cartilage surface. Subsequently, the frictional characteristics were examined in phosphate-buffered saline (PBS) and SF against glass. Angularly reciprocating sliding tests with a spherical glass probe and square articular cartilage specimens were performed at low contact loads in the mN range to extract the frictional behavior in the superficial area of the cartilage specimens. Meanwhile, the cartilage surface was observed to confirm the effects of treatments on the morphology of the cartilage surface using a fluorescence microscope and water-immersion methods. The coefficient of friction (COF) of the prepared cartilage specimens was varied from 0.05 to over 0.3 in PBS. However, a certain group of cartilage specimens exhibited a low COF of less than 0.1 with limited variation. For the low COF group of specimens, all four treatments increased the COF in PBS to different extents, and fluorescence microscopy revealed that the integrity of the cartilage surface was deteriorated by treatments. This means that the intact cartilage surface had lubricating constituents to maintain low friction, and the removal of such constituents resulted in the loss of the intrinsic boundary lubricity of the cartilage surface. The variation in the COF of the cartilage specimens was suppressed in SF because it had a clear boundary lubrication effect on the cartilage surface. The lubricating effect of SF could be confirmed even after degenerative treatment.

Influence of different combinations of high-order topological modification on contact pattern and load distribution of helical gear

An integrated model is proposed to evaluate the contact pattern and load distribution of helical gear with different combinations of high-order topological modification, which is established combining the finite element method (FEM), the analytical method (AM), and the nonlinear programming method. Based on the elastomer contact model of tooth surface, the FEM is used to separate the flexural-shear deformation of the teeth, while the contact AM is introduced to derive the local contact deformation. The contact characteristics of gears can be finally obtained by solving the nonlinear programming model with the constraints of deformation and load and finally verified by the finite element analysis. The results show that the longitudinal crowning can significantly improve the load distribution and the edge contact of the tooth. When the modified curve becomes a parabola of higher order, the contact characteristics change obviously. The pressure of double-crowned (4) gears was uniform and the amplitude decreased, but the amplitude of pressure of double-crowned (6) gears increases and the variance of load sharing ratio is more obvious at the beginning of the middle meshing period.

Investigation of tribological properties of MoS2 and CaF2 particles as oil additives and their effects on surface contact

AbstractNowadays, researches on the use of alkali metal salts as friction‐reducing and anti‐wear oil additives are continuing. In this study, the tribological effects of heavy metal containing MoS2 and alkali metal salt CaF2 additives on pure engine oil (20W50) were investigated using block‐on‐ring tester configured as surface contact geometry. The tests were performed at various contact loads, revolutions, and additive ratios. The crystal structure of the additives and their effects on surface quality and surface roughness analysed by x‐ray crystallography, scanning electron microscope and profilometry. Moreover, Energy dispersive spectrometry was used for element detection on worn surfaces. Results indicated that additives of MoS2 and CaF2 can reduce the friction, increase the capacity of load‐carrying and the wear resistance of surfaces. The additives improved the operation of the base oil in boundary lubrication zone by increasing the tribofilm forming effect. It was observed that the CaF2 additive exhibited more stable friction behaviour, while the MoS2 additive has better protective effects against scratches on the block surface.

Effect of Indentation Depth on Friction Coefficient in Adhesive Contacts: Experiment and Simulation.

The quasi-static regime of friction between a rigid steel indenter and a soft elastomer with high adhesion is studied experimentally. An analysis of the formally calculated dependencies of a friction coefficient on an external load (normal force) shows that the friction coefficient monotonically decreases with an increase in the load, following a power law relationship. Over the entire range of contact loads, a friction mode is realized in which constant shear stresses are maintained in the tangential contact, which corresponds to the "adhesive" friction mode. In this mode, Amonton's law is inapplicable, and the friction coefficient loses its original meaning. Some classical works, which show the existence of a transition between "adhesive" and "normal" friction, were analyzed. It is shown that, in fact, there is no such transition. A computer simulation of the indentation process was carried out within the framework of the boundary element method, which confirmed the experimental results.

Influence of Axle Weight and Frequency on the Tribological Properties of Laser-Repaired 316L Stainless Steel Coatings in Railway Wheel Tread Braking

The impact of the complex braking environment on the service performance of the repair fusion cladding was studied, which is of great significance to improve the ability of the train wheel track system to resist the extremely harsh environment. In this paper, a 316L stainless steel coating was prepared using laser fusion cladding repair technology for the local damage location of the train wheel tread. The MS-HT1000 high-temperature wear tester was used for the experiment. Then, the influence of different braking conditions on the friction and wear performance of the repaired specimens at room temperature and high temperature was analyzed. The results showed that the microstructure of the laser-repaired 316L stainless steel coating was dendritic and eutectic, and its physical phase was mainly composed of austenite, Fe-Cr, and carbides. The wear rate increases with the rise in the shaft weight load, indicating that the higher the contact load, the more severe the wear. In contrast, the influence of the friction coefficient in a room temperature environment is less variable. With an increase in the braking frequency, the wear of the specimen firstly rises and then decreases, and when the frequency is 1 Hz, the value of the wear rate at room temperature is the largest, and the wear surface appears as more peeling layers, and a large amount of wear debris is randomly distributed, which manifests as the wear mechanism being characterized by abrasive wear and adhesive wear. Therefore, different factors affect the wear level of the material differently, with the axle weight load having the greatest influence. The relevant results help to provide corresponding theoretical references for the optimization of parameters under the braking condition of the wheel tread, which ensures the normal operation of the braking system when driving.

Contact mechanics modeling of fractal surface with complex multi-stage actual loading deformation

The contact mechanical behavior of rough surfaces is related to the friction and wear of mechanical components, and also has an important impact on the dynamic performance and force transfer characteristics of assembly surfaces. This paper aims to solve the complex multi-stage mechanical deformation mode of the loading surface, and establishes all multi-stage contact mechanical models involved in the actual loading deformation process from the perspective of the actual deformation and critical deformation of the asperity. Firstly, based on the three-dimensional fractal contact theory, the force deformation relationship of a single asperity during the full deformation stage of loading is constructed. Then, six critical contact areas and four critical deformation quantities of a multi scale asperity are derived. Finally, the complex multi-stage deformation contact mechanical models of three-dimensional fractal surfaces under actual loading are established. The area power spectral density (APSD) function spectrum of rough surface under different fractal parameters, as well as the variation of contact load, contact stiffness, and contact area are analyzed numerically. Compared with several classical models, the rationality of the proposed model is verified. This study can be used as the basis for constructing the overall dynamic model of an assembly system

Relationship between the contact load and time-loss injuries in rugby union.

Quantifying and managing the matches and training loads of players is important for injury prevention. As rugby union is a full-contact sport and frequent contact injuries occur, it might also be important to quantify and manage players' contact loads. This study aimed to clarify the relationship between contact load and injury incidence in elite rugby union players. Forty-eight elite rugby union players (27.0 ± 3.5 years) in Japan were monitored during one season (8 months). The contact load, an index of training load, was evaluated as collision count and collision load measured using a global positioning system device, and then calculated using the acute:chronic workload ratio (ACWR) based on the exponentially weighted moving average (EWMA). The association between the EWMA-ACWR of contact load and injury incidence was analyzed using generalized estimating equations. Of the 58 injuries during one season, 70.7% were contact injuries. Collision counts and collision load calculated by EWMA-ACWR were associated with the risk of injury (p < 0.01 both), with the odds ratios were 4.20 [95% confidence interval (CI): 1.74-10.11] and 4.44 (95% CI: 1.95-10.13), respectively. Contact load calculated using EWMA-ACWR was associated with injury in elite rugby union players.

Stabilization of roughness parameters of rolls of temper mill during idle running in stand

The main results of improving in the condition of the surface layer of the working rolls of the training mill with their joint rotation pressed against each other in a state without a trained strip, are considered in order to further minimize changes in the roughness parameters of the trained strip from roll to roll. The analysis of changes in the roughness parameters of the working rolls during their running-in as a result of the elastic-plastic interaction of the microsteps of their surfaces is carried out. Mathematical dependences are obtained for calculating of the roughness parameters of the working rolls during their idle running in the stand, taking into account the ergodicity function of the process. It is shown that the permissible degree of reduction of the height parameters of the rough layer of the working rolls before stabilization during their running is determined by contact loads, physical and mechanical properties of the material of the rolls, the initial parameters of the microgeometry of their surfaces and friction conditions, and the time to stabilize of the roughness parameters depends mainly on the contact load and the speed of running-in, decreasing with decreasing load and increasing speed. It is determined that the maximum possible reduction in the initial roughness of the roll treated with shot after idle running them in a stand with a coefficient of friction of 0.3 is on average 57 %. A further change in roughness is associated with the effect of wear of the rough layer during the training of a cold-rolled strip. The obtained mathematical dependencies allow you to assign processing parameters, such as the compression force of the rolls, the speed or at a given speed — the running-in time.

Contact load practices and perceptions in elite English rugby league: an evaluation to inform contact load guidelines.

Athlete exposure to contact could be a risk factor for injury. Governing bodies should provide guidelines preventing overexposure to contact. Describe the current contact load practices and perceptions of contact load requirements within men's and women's rugby league to allow the Rugby Football League (RFL) to develop contact load guidelines. Participants (n=450 players, n=46 coaching staff, n=32 performance staff, n=23 medical staff) completed an online survey of 27 items, assessing the current contact load practices and perceptions within four categories: "current contact load practices" (n=12 items), "perceptions of required contact load" (n = 6 items), "monitoring of contact load" (n=3 items), and "the relationship between contact load and recovery" (n=6 items). During men's Super League pre-season, full contact and controlled contact training was typically undertaken for 15-30 minutes per week, and wrestling training for 15-45 minutes per week. During the in-season, these three training types were all typically undertaken for 15-30 mins per week. In women's Super League, all training modalities were undertaken for up to 30 minutes per week in the pre- and in-season periods. Both men's and women's Super League players and staff perceived 15-30 minutes of full contact training per week was enough to prepare players for the physical demands of rugby league, but a higher duration may be required to prepare for the technical contact demands. Men's and women's Super League clubs currently undertake more contact training during pre-season than in-season, which was planned by coaches and is deemed adequate to prepare players for the demands of rugby league. This study provides data to develop contact load guidelines to improve player welfare whilst not impacting performance.

Thermal contact conductance model of rough surfaces with inclination based on three-dimensional fractal theory

PurposeThe purpose of this study is to establish a thermal contact conductance model of rough surfaces with inclination based on three-dimensional fractal theory.Design/methodology/approachThe effects of contact load, inclination angle, fractal dimensional and fractal roughness on thermal contact conductance of rough surfaces were studied using numerical simulation.FindingsThe results show that the thermal contact conductance of the rough surface increases with the increase of contact load and fractal dimension and decreases with the increase of fractal roughness and inclination angle. The inclination angle of the rough surface has an important influence on the thermal contact conductance of the rough, and it is a factor that cannot be ignored in the study of the thermal contact conductance of rough surfaces.Originality/valueA thermal contact conductance model of rough surfaces with inclination based on three-dimensional fractal theory was established in this study. The achievements of this study provide some theoretical basis for the investigation of the thermal contact conductance of rough surfaces.

Assessment of the load-loading capacity of bolted joints during bolt bending and the combination of materials used

Abstract: based on the physical model of a hinged-bolt joint, which takes into account the possible bending of the bolt and, consequently, the real nature of the distribution of contact loads, the influence of the main design parameters of the joints on the distribution of loads between individual elements depending on the combination of their materials is analyzed. Dependencies for determining normal stresses in a given section of a connection element are presented, variants of the structural and technological design of typical hinge-bolt connections are analyzed according to the degree of influence of their geometric and material science features on the level of contact loads.

Enhanced corrosion resistance of CoCrMo by laser-based surface modification

Biomedical grade cobalt–chromium–molybdenum (CoCrMo) alloys are extensively used for load-bearing biomedical applications such as hip and knee implants due to their exceptional biocompatible and biomechanical properties. However, the strain-induced martensite ε-phase development during contact loading results in thin oxide layers that are prone to fracture leading to corrosion. The formation of thin oxide layers is undesirable for long-term deployment. We employed laser-texturing to enhance the corrosion resistance of the material in simulated body fluid by the formation of hcp ε-phase martensite and via the formation of oxide layers. However, partial formation of hcp ε-phase martensite was observed. By means of central composite design-based response surface methodology, three laser parameters such as average laser power, texture density and the number of passes were optimised for maximal open circuit potential, an indicator for minimal corrosion. The textured surfaces were found to assist in the cellular proliferation of fibroblasts and inhibit bacterial growth.

A nonlinear dynamic approach for analyzing dynamic stiffness of ball bearings at different raceway diameters and guiding clearances

In this work, the stiffness matrix model is integrated into the dynamic model of ball bearings, in which the dynamic forces real-timely affect the stiffness calculation to form the dynamic stiffness, which is a novel solution for the dynamic performance analysis of ball bearings under different loads, assemblies and bearing structures. Then, the main influencing factors for the magnitude of bearing stiffness are analyzed. Next, the fluctuation mechanism of bearing stiffness is revealed. Subsequently, the effects of raceway diameters and guiding clearances on the dynamic stiffness of ball bearings are investigated. The obtained results suggest the ball diameter and the number of balls at various raceway diameters alter contact loads, contact angles, contact deformations and offset distances to change the bearing stiffness, and the combinations of inner and outer raceway diameters should be compromised to attain the favorable magnitude and fluctuation of bearing stiffness. Moreover, guiding clearance should be adjusted to achieve the desired trajectory of cage to degrade the fluctuation of bearing stiffness.

Modeling and braking analyses of longitudinal-vertical coupling towbarless aircraft taxiing system

The variation of tire vertical load has effects on the vehicle braking performance, which may lead to the misjudgment of braking distance and increasement of the accident risks. In order to evaluate the braking distance of the towbarless aircraft taxiing system (TLATS) accurately, a longitudinal-vertical coupling model of the TLATS is established, in which the effects of the vertical vibration on braking dynamics is considered. An 11-degrees of freedom (DOF) dynamic model of the TLATS, which consists of the system longitudinal motion, vertical vibration, and an advanced Lugre tire model, is proposed. The tire vertical dynamic loads are obtained by calculating system vibration differential equations as the input for the Lugre tire model, in which an arbitrary pressure distribution function over the contact patch and load related parameters are used. The Lugre tire model parameters are identified based on the virtual experiment results in ADAMS/Car software through a multi-objective optimization (MOO) method. The proposed tire model is more accurate by comparing with the models using other pressure distribution functions. The advanced Lugre model is integrated into the longitudinal-vertical coupling dynamic model of the TLATS, and the fuzzy PID control method is used to achieve the optimal slip rate during the braking procedure. The tire friction and TLATS’s braking performances in terms of the slip rate, braking speed and braking distance are compared between the coupling and uncoupling models under different traction velocities and the road excitations when a same fuzzy control method is used for the system braking. The results show that the proposed longitudinal-vertical coupling TLATS dynamic model could assess the braking behaviors of the TLATS more accurately than the simplified uncoupling model, which could decrease the potential safety risk of the aircraft towing operation on the airport apron.