Contact Load Distribution Research Articles

A comprehensive sliding wear prediction method for planetary roller screw mechanism

The thread-pairs wear has a significant role in the transmission accuracy, operational stability and service life of planetary roller screw mechanism (PRSM). Nevertheless, the previous literatures still lack the investigation on the wear evolution of roller, nut and screw. Hence, an accumulative wear depth (AWD) prediction model is proposed for PRSM with reciprocating motion. The presented model is validated by the measured wear phenomena of thread pairs and the experimental results in the literature. The equivalent sliding wear experiment of PRSM is designed and the sliding wear coefficient of PRSM material is obtained by the equivalent sliding wear experiment. Considering the thread profile error caused by AWD of roller, nut and screw, the load distribution (LD) and sliding velocities on screw-roller (SR) and nut-roller (NR) sides are calculated. More importantly, the interactions between the AWD, LD and sliding velocity are investigated. Furthermore, the effects of axial load on the AWD, sliding velocities in contact regions and load distribution coefficient are analyzed.

Study on internal load distribution of deep groove ball bearings considering raceway surface waviness

Abstract A full circumferential contact mechanics modeling study considering the effect of waviness mesoscopic profile and rolling element contact relationship on bearing load distribution is carried out. In the model, a sinusoidal function is adopted to simulate the profile of the waviness section. According to the contact tangency condition, a model of the contact deformation relationship between a single rolling element and the raceways is established. On this basis, a full circumferential rolling elements contact load distribution model of the bearing is established by introducing the contact deformation of all rolling elements with the raceway surfaces. Focusing on contact deformation of a full circumferential rolling elements with the raceways, this model can conduct more accurate modeling and reflect the load distribution state inside the bearing more realistically. The correctness of the mechanical analysis model proposed in this paper is proved by an average error of 3.38%, which is the comparison result between the mechanical analysis model and the finite element model. Meanwhile, computational efficiency is improved. Further, based on the model, the influence of the waviness parameters on the load distribution inside the bearing under the action of different types of loads is analyzed.

Modeling of double-row cylindrical roller bearing under combined loads and angular misalignment

Abstract To enhance the reliability of the double-row cylindrical roller bearing (DCRB), a new quasi-static model, which is capable of considering inner ring misalignment and combined loads, has been established. This model was used to calculate the distribution of internal loads and contact pressure. First, the model was verified with published data. Secondly, systematic parameter analyses are conducted to investigate how axial load, inner ring misalignment and roller profile influence the contact performance. The results indicate that when the bearing is subjected to a combined load, the difference between the radial loads borne by the two rows increases with the increase of axial load. The combined load and misalignment of the inner ring would cause significant changes in the numerical value and distribution of contact load and pressure between the rollers and raceways. The roller profile optimization can reduce contact pressure and alleviate the edge effect.

Mathematical model for mesh analysis of gear pair in gear-shaft-bearing systems with localized failure on raceway

To investigate the influence of bearing failures on the mesh characteristics of gear pairs, this paper presents a mathematical model for gear-shaft-bearing systems. Within this simulation method, the model of defective bearings and the contact analysis methodology of gear pairs are integrated into the system equations. Additionally, the coupling mechanism between system components is determined by addressing the misaligned shafts induced by asynchronous bearing vibrations. Furthermore, the torsional deformation of gear teeth generated by uneven load distribution is considered, and a calculation method for mesh stiffness in complex environments is developed. By employing the comprehensive model, the effect of raceway failures on the mesh behavior is lucidly explained, the real-time distribution of contact stress and load on the tooth surface can be obtained, and the optimal modification strategies for gears are formulated. Finally, the proposed model is confirmed through the finite element (FE) model and experimental observation, which provides a potent tool for the performance optimization of gearboxes.

Computational assessment of ratcheting in rail-wheel contact with solid contaminant

A numerical method for the fast evaluation of ratcheting in solid-contaminated contact between rollers was developed. The physical problem was simplified with a plane-strain half-infinite body, with a distribution of pressure and tangential stress on the contact surface obtained by considering the presence of evenly spaced solid contaminant particles between the contacting bodies. Such a distribution was obtained by an analytical method, which considered the material of the contacting bodies as linear elastic. The stresses under the contact surfaces were calculated using the Boussinesq-Cerruti model. Subsequently, the plastic strain accumulated in the roller after each application of the contact load was calculated by means of a non-linear kinematic-hardening constitutive law, also considering the effect of wear in removing material layers from the surface.First, the effects of the introduced approximations were evaluated. In particular, the error in calculating the plastic strain using contact load distributions from a theory based on linear elastic behavior was evaluated by comparison with the results of finite element models. Subsequently, the method was used to assess the experimental results of previously published studies on sand-contaminated contact between rail and wheel materials. Despite the approximations and indetermination of some model constants, the method was proven to be able to qualitatively explain many of the damage mechanisms related to the interaction of the contacting bodies with the contaminant particles.

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 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.

Load Distribution Analysis and Contact Stiffness Prediction of the Dual-Drive Ball Screw Pair Considering Guide Rail Geometric Error and Slide Position

The dual-drive ball screw pair serves as a crucial element within the fixed gantry machine tool with cross-rail movement. When in service, the dual-drive ball screw pair experiences variations in axial load, impacting the contact load distribution of the ball screw pair. A calculation model for determining the axial load offset of the dual-drive ball screw pair is proposed to investigate the variation in axial load. The impact of the geometric error associated with the guide rail and the position of the slide are considered. This paper presents the contact load distribution model for the dual-drive ball screw pair. This study investigates the contact load and contact angle distribution of the dual-drive ball screw pair during the machine tool in service. Additionally, based on fractal theory, the stiffness models of individual micro-convex body and contact surfaces have been established. This study provides a comprehensive analysis of the contact stiffness of the ball screw pair, considering the influence of guide rail geometric error and slide position. In addition, the three-dimensional surface morphology of ball screw pair is obtained by experiments. This paper investigates the contact stiffness distribution of dual-drive ball screw pair during service.

Study on multibody contact load distribution characteristics of scraper conveying system of continuous miner

Understanding the interaction of the scraper chain–sprocket–tail drum–chain path is of great significance to improving the transportation efficiency and service life of the intermediate scraper conveying system of fully mechanized excavation equipment. The dynamic characteristics of the internal tension, running resistance, and multicontact interface load of the scraper chain are the theoretical basis of the research. Firstly, a method for obtaining periodic cyclic dynamic load history is proposed, and then the model of a single-chain scraper conveyor for a continuous shearer is constructed by using RecurDyn and simulation structures. Finally, the influence of parameters such as conveying inclination angle and running speed of the sleeve scraper chain on the reliable operation of the conveying system is determined. The results show that when the conveying angle is 12°, the scraper conveying system runs stably and the impact between multirigid bodies is small. As the chain speed increases from 0.85 to 2.4 m/s, the wear of the conveying system gradually increases, and the contact load distribution of upper chain plate 2, upper chain plate 3, and lower chain plate 3 is seriously worn.

Calculation Model of Contact Load and Axial Stiffness of Planetary Thread Roller Bearing Based on Direct Stiffness Method

AbstractPlanetary Threaded Roller Bearing (PTRB) is a new bearing suitable for the heavy load linear drive mechanism. The load is transferred internally through annular threads, affecting the bearing capacity of the thread's contact load distribution characteristics. The structure of PTRB is discretized to study the contact load distribution of PTRB. The axial stiffness of the thread's teeth, its axial stiffness, and the contact stiffness of contact points are calculated. Moreover, a 1D equivalent spring network model is proposed based on discretized structure and stiffness. The PTRB contact load calculation model is proposed using the direct stiffness method and a 1D equivalent spring network model. Finally, the accuracy of the model proposed in this paper for calculating the contact load distribution of threaded teeth is verified by comparing the results obtained from theoretical model calculations, finite element methods, and experiments. The theoretical model proposed in this paper can provide theoretical guidance for PTRB parameters.

A Contact Load Distribution Model to Capture the Influence of Structurally Compliant Rotating Ring Gear on the Dynamic Response of Epicyclic Gear Sets

AbstractEpicyclic gears, also commonly referred to as planetary gears, are power transfer components that are commonly used in several industrial applications. The structural compliance of thin-rimmed annular ring gear can significantly influence the performance of an epicyclic gear set. As powertrain components are continually being optimized to their design limits, this influence becomes prominent and can no longer be ignored. Therefore to capture the influence associated with ring gear flexibility, the current study will incorporate a finite element-based ring gear formulation into the three-dimensional planetary dynamic load distribution model (Ryali, and Talbot, 2021, “A Dynamic Load Distribution Model of Planetary Gear Sets,” Mech. Mach. Theory, 158, p. 104229). The proposed contact model employs a modified simplex algorithm to iteratively solve for the elastic gear mesh contacts in conjunction with a numerical integration scheme, which enables it to inherently capture the influence of several components and system-level design variations without the need for an empirical mesh stiffness formulation or transmission error excitation of the system. The developed formulation will be used to study the dynamic response of planetary gear sets where the ring gear is a rotating member. The discussed results demonstrate the fidelity of the developed model, thus making it an excellent tool for the design and analysis of planetary gears.

Determination of Rock Tensile Strength Based on Arc Loading Splitting Test considering Modulus Effect

Tensile strength is an important control parameter for the design and stability analysis in rock engineering. In order to reveal the influence of elastic modulus on tensile strength test results, Brazilian splitting tests were carried out on specimens with different strengths, such as mudstone, white sandstone, green sandstone, red sandstone, and marble. Longitudinal and transverse strains were monitored to analyze the influence of elastic modulus on the maximum contact angle and peak contact load between head and disc. A numerical model of Brazilian splitting tests was built, and the contact load between the head and rock disc were detailed revealed. Based on the experimental and numerical results, a modified formula to calculate tensile strength considering the modulus effect was proposed theoretically. Results show that the maximum pressure between the head and disc increases and the contact angle decreases with the increasing of elastic modulus, which show great influence on the splitting failure; the distribution of contact load can be divided into three types: parabolic I, sinusoidal, and parabolic II, which are suitable for soft rock, medium-hard rock, and hard rock, respectively; the new models can improve the calculation accuracy of rock tensile strength.

Research on Non-Circular Raceway of Single-Row Four-Point Contact Ball Bearing Based on Life Optimization

The traditional slewing bearing with circular raceway has the problem of stress concentration under the large overturning moment. In this paper, a new non-circular raceway of a slewing ball bearing was presented to conquer this problem. To obtain the new non-circular raceway, first, the static equilibrium equations of the slewing ball bearing was established by the vector method, which is a constraint condition for life optimization; secondly, the life optimization function was established to calculate the contact load distribution in the bearing when the bearing life is at its maximum; finally, through the contact deformation with the contact load, the non-circular inner raceway corresponding to the maximum bearing life was obtained, and the non-circular shape corresponding to the raceway under axial load and overturning moment was studied. The results show that the non-circular raceway devised by this method can evenly reduce the contact force of the raceway and effectively improve the bearing capacity. Moreover, the position where the non-circular raceway deformation occurs is the position where the contact force is different before and after optimization. Therefore, the overturning moment has an effect on the shape of the raceway, whereas the axial load only affects the amplitude of the deformation, and has no obvious effect on the shape of the raceway.

Loaded contact pressure distribution prediction for spiral bevel gear

Contact pressure and load distribution are key indices used in the performance evaluation of spiral bevel gears, and their calculation accuracy and efficiency continue to be the focus of active research. An accurate and efficient numerical approach for predicting the contact pressure and load distribution of a spiral bevel gear is presented based on multi-tooth deformation compatibility. First, an improved discrete tooth surface contact analysis (DTCA) method is developed to obtain the contact characteristics of the gear set under the no-load condition. This method is a geometric approach that avoids numerical instability. A local triangular mesh refinement algorithm is proposed to improve the accuracy and efficiency of the DTCA method. Subsequently, the deformation compatibility relationships of a spiral bevel gear set are derived for single-tooth and multi-tooth meshing. By combining the deformation compatibility relationship and the influence coefficient method, a multi-tooth loaded contact analysis (MLTCA) model of the spiral bevel gear set is established. Moreover, an iterative algorithm based on the conjugate gradient and fast Fourier transform method is proposed to determine the mesh force and contact pressure distribution. Finally, the proposed method is tested using numerical examples to demonstrate its accuracy and efficiency by comparison with finite element simulations and experiment results.

A simple method to introduce the centrifugal effects in an angular contact ball bearing

An analytical model was developed for angular contact ball bearings running at high speeds. The model presented in this paper was designed for the 7206 C angular contact ball bearings and considers the geometrical parameters as well as the interactions between the raceways and the rolling elements involved while bearings are in operation. Using an original methodology, the effects of centrifugal forces generated by the rolling elements have been evidenced both on the normal contact load distribution and contact angles between balls and the two races. The effect of centrifugal forces was considered as a “supplementary clearance” included in a general model developed by Houpert for static conditions. Some simulations for various axial and radial loads and high rotational speeds have been presented. The results confirm important deviations of the static contact angle and the load distribution on both races.

Static Modelling and Analysis of a Novel Movable Tooth Drive with Logarithmic Spiral Tooth Profiles

This paper presents a static model for a novel movable tooth drive with logarithmic spiral tooth profiles, to research contact force and load distribution during the meshing period. According to the geometric properties of the conjugate tooth profiles, their compatibility law considering the multi-tooth elastic meshing effect are investigated to reveal load distribution characteristic of the teeth. The static model of the mechanism is thus developed to systematically analyze variation in contact force during the rise travel. The results indicate that the contact force between the tooth and ring gear is proportional to the curvature radius of the contact point, and it increases exponentially and monotonically corresponding to the curvature radius of logarithmic spiral tooth profile; in the multi-tooth meshing condition, the load distribution of the teeth coincides with the ratio of the curvature radius of each contact point, and periodical pulsations of total contact force occur at the alternation of the teeth. Finally, the proposed model is validated by the FEM simulation of a prototype, and the influence of dimensional parameters is further discussed for the self-locking and force transmission characteristics of the tooth. The outcomes provide critical technical support for the static modelling and design of such transmission mechanism.

An improved contact parameter model with elastoplastic behavior for bolted joint interfaces

In this study, considering the elastoplastic behavior of contacting asperities on micro-scale and the contact pressure distribution of bolted joint interfaces on macro-scale, an improved contact stiffness model is presented. Firstly, the bolted T-stub joint is chosen as the object of study, and the distribution of normal contact load over the interface under preload conditions is studied. Then, combining the continuity, smoothness and monotonicity of the constitutive relations of normal contact load-deformation in three different regimes of plastic- elastoplastic-elastic of contacting asperities, the contact stiffness of individual asperity is analytically derived. Meanwhile, the relation between the distribution of contact stiffness and the distribution of normal contact load for bolted joint interfaces is determined based on fractal theory. The presented model overcomes the shortcomings of the contact stiffness without elastoplastic behavior obtained from the MB model and reveals the inhomogeneous distribution features of interfacial contact stiffness in bolted joints. Finally, the finite element (FE) analysis for flange-bolted joints incorporating the proposed model and the relevant experimental verification are performed. The results show that the average error of the first 4-order natural frequencies between the FE results and the experimental ones is only 0.72%, and the predicted results in frequency-domain are consistent with the measured ones, which illustrates that the proposed model can be used in interface modeling of jointed structures.

P4. Independent expansion of the anterior and posterior height of a lateral expandable cage can improve the contact area and load distribution at the cage-endplate interface

<h3>BACKGROUND CONTEXT</h3> Compared to their traditional static counterparts, expandable cages offer clinical advantages by allowing for the use of smaller surgical access corridors to achieve similar lordosis correction without endplate damage from large impaction forces. However, as with static cages, the risk of implant subsidence due to stresses on the vertebral endplate remains an area of concern. Although early clinical outcomes have been reported for individual expandable cage designs, how the endplate contact area and load distribution are affected by specific cage expansion trajectories remains unclear. <h3>PURPOSE</h3> To assess and quantify differences in contact area and load distribution from different lateral expandable interbody cage designs. <h3>STUDY DESIGN/SETTING</h3> Comparative biomechanics analysis using established synthetic spine units. <h3>OUTCOME MEASURES</h3> Cage-endplate contact area, anterior-posterior load distribution, segmental lordosis angle. <h3>METHODS</h3> Discectomies and cage placement were performed on synthetic functional lumbar spine units (n = 3). Three different expandable cage designs were evaluated, each with their own unique expansion trajectory: cranio-caudal, arc-based, and independent anterior and posterior height expansion. For the third cage, a differential expander was used to increase the two heights, anterior and posterior, according to the path of least resistance. A Tekscan calibrated pressure mapping sensor was placed between the cage and the synthetic endplate. The functional spine units were mounted on a servo-hydraulic testing frame and a constant 250N compressive axial preload was applied with unconstrained rotations and translations. The cages were then fully expanded and segmental lordosis angle along with pressure measurements were collected. To allow for a consistent comparison among cages, the surface contact area was normalized by the footprint of each respective cage. To determine the uniformity in the contact load profile, the local load distribution was demarcated in half along the anterior-posterior (A-P) aspect of the cage. The symmetry of the loading profile was characterized by dividing the cumulative anterior force magnitude by the overall force (50% indicates perfectly balanced A-P loading) quantified using the pressure mapping sensor. Friedman's test was performed (α = 0.05) to compare the effect of expansion trajectory on the outcome measures (values reported as median [range]). <h3>RESULTS</h3> Expansion trajectory had a significant effect on cage-endplate contact area and the resultant A-P loading distribution (p = 0.050), but not segmental lordosis angle (p = 0.097). Independent expansion resulted in the highest cage-endplate contact area (93% [92 to 98%]) compared to cranio-caudal (84% [81 to 90%]) and arc-based (62% [56 to 63%]) expansion. Furthermore, independent expansion resulted in a near-even A-P loading distribution (48% [42 to 51%]), compared to cranio-caudal (34% [22 to 36%]), and arc-based (97% [94 to 99%]) expansion. <h3>CONCLUSIONS</h3> Of the cage designs evaluated, the expandable cage with independent anterior and posterior height expansion resulted in the highest cage-endplate contact area and most uniform load distribution, both important considerations fundamental for a successful fusion procedure and the mitigation of implant subsidence risk. With a larger sample size, our continuing studies will investigate the interaction of various cage placement options and expansion mechanisms. <h3>FDA DEVICE/DRUG STATUS</h3> MOD-EX XLIF Interbody System (Approved for this indication), RISE-L Spacer (Approved for this indication)

Design of Downhole Robot Actuator System and Mechanical Behavior Analyses of the PRSM by Considering Elastic Errors and Radial Loads

This paper designs a new class of actuators for the downhole traction robot system to achieve high-accuracy transmission, which is realized by the planetary roller screw mechanism (PRSM). As the downhole environment is a non-structure one, which increases the difficulty of the load analyses and distributions of the downhole robot system to complete a predesigned mission. Traditional achievements about the mechanical behavior analyses of PRSM ignore the effects of radial loads and torque elastic deformation errors, which are inevitable for the downhole robot actuator, and the results of which would affect the load distribution and fatigue life of the PRSM-aided actuator. To assist the complex task, in this study the mechanical behavior analyses of PRSM for the downhole robot system are investigated by considering axial loads, torque elastic deformation errors, and radial loads. Moreover, the calculation models for contact load distribution and fatigue life are established by utilizing the equivalent contact load and Hertz contact theory. Two cases for the robot actuator in the downhole environment are addressed, the results of which indicate that the contact load change and decrease with the thread growth direction of the PRSM, the first several threads bore most of the loads, and the last several threads only took a few loads. Additionally, the fatigue life reduces sharply under the condition that the axial loads, radial loads, and rotation speeds increase. Compared with the other two effectors, the fatigue life is more sensitive to the radial loads. The results show the sustainability of the presented screw–roller–nut and provide a potential reference for the downhole robot actuator motion analyses.

A computerized method of contact pressure and load distribution for crossed beveloid gears

Exact contact pressure and load distribution are key evaluation indices for beveloid gear design. A numerical calculation approach of contact pressure and load distribution for crossed beveloid gears is proposed, as opposed to the traditional method based on a finite element modeling software package. To acquire the flexibility properties of beveloid gear tooth surfaces, an accurate finite element (FE) model about a beveloid gear tooth with root fillets is first built. A solution model for crossed beveloid gears is developed using the influence coefficients technique. An enhanced solving approach is presented to improve the robustness of the solving model by addressing the limitation of the influence coefficients method. In addition, a unique contact pressure is presented. The numerical example proposed can be used to test the proposed methodology.