Elliptical Contact Research Articles

Application of machine learning for film thickness prediction in elliptical EHL contact with varying entrainment angle

This contribution demonstrates the potential of machine learning (ML) algorithms in predicting elastohydrodynamic lubrication (EHL) film thickness in elliptical contact with varying direction of lubricant entrainment, ranging from wide to slender elliptical configurations. The input parameters pertain to worm gear contacts, which are characterized by slender-like elliptical contact between a steel and a soft metal component. The study encompasses generating a database using numerical Finite Element Method (FEM) simulations, training artificial neural network (ANN) models, and evaluating their performance in terms of bias and variance. Key outcomes include the successful training of the ANN models, detailed analysis of the impact of tailored architecture on the ANN models' performance, and the superiority of the ANN compared to other ML regression algorithms. The study further identifies key input parameters that influence prediction accuracy and introduces a strategic dataset augmentation procedure to increase local and overall prediction accuracy. This strategic dataset augmentation enhances model robustness and precision while providing insights for expanding databases collaboratively. It holds potential for broader applications of ML for performance prediction of tribological contacts, thus paving the way for advanced ML models that consider additional factors and collaborative databases refined by multiple research groups.

Force model of ultrasonic empowered minimum quantity lubrication grinding CFRP

As a weight-reducing material in aerospace applications, carbon fiber reinforced polymer (CFRP) requires precision grinding to ensure the accuracy and assembly of mating positioning surfaces. However, achieving low-damage machining of CFRPs remains challenging. Flood cooling reduces the mechanical properties, while dry grinding deteriorates the surface integrity, making minimum quantity lubrication (MQL) a viable alternative. However, nanolubricants struggle to penetrate the grinding area due to gas barrier obstruction. Consequently, a new CFRP grinding approach using multiangle 2D ultrasonic vibration-empowered nanolubricant MQL was proposed. An analytical force model is crucial for optimizing machining strategies and adjusting parameters. The aim is to reveal grinding mechanics and develop a force model under different ultrasonic and lubrication-cooling conditions. First, a uniform random fiber distribution model and a grinding wheel model were established, and the mechanical properties of the interface were predicted. Then, the intermittent grinding behavior and dynamic stiffnesses of the multiangle 2D ultrasonic vibration-assisted grinding (UVAG) system were investigated based on the geometric kinematics of the grains' trajectory. Furthermore, based on the deformation deflection curve, bending fracture force models for 45°, 90°, and 135° fibers were established with different contact and boundary conditions. The material removal mechanisms of shear and tension-compression buckling in 0° CFRP grinding were revealed, and an elliptical contact normal force model was established. The interlayer shear in 45° CFRPs was analyzed. The longitudinal compressive matrix cracking and fiber shear fracture in the 90° CFRPs were elucidated. Fiber microbuckling and fiber bundle removal of 135° CFRPs were investigated. Finally, grinding force models with different fiber orientation angles (FOAs) were interconnected and experimentally assessed. Experimental assessments demonstrated that the grinding force model has acceptable estimation error and effectively captures the mechanics of CFRPs with different FOAs.

A modified Hertzian-based wheel-rail contact model for vehicle system dynamics simulation

This paper develops a modified Hertzian-based wheel-rail contact model (MHM) to improve the robustness and accuracy of the traditional Hertzian contact model in vehicle-track coupling dynamics simulation. First, the wheel-rail non-Hertzian contact area is estimated based on the virtual penetration (VP) area, and an equivalent ellipse of the non-Hertzian contact area is calculated. Then, taking the equivalent elliptical contact patch as the input, the wheel-rail normal problem is solved by using Hertzian contact theory. Finally, considering the effect of the non-elliptical contact patch on Kalker’s linear coefficient, a modified Shen–Hedrick–Elkins model is proposed. The computation accuracy, robustness, and efficiency of the developed MHM are assessed by comparing it with a robust Kalker variational method (RKVM), a VP-based non-Hertzian contact model RNHM, and two traditional Hertzian-based models. The comparison results show that the MHM improves the computational robustness and accuracy of the traditional Hertzian-based contact models. MHM achieves almost the same computational accuracy as the RNHM, but its computational efficiency is 2.4 times faster than RNHM. The developed MHM is an ideal model for vehicle-track coupling dynamics simulation.

EFFECT OF ENTRAINMENT SLIDING DIRECTION TO THE TRACTION COEFFICIENT FOR EHL ELLIPTICAL CONTACTS IN THE LINEAR ISOTHERMAL REGION

Abstract In many mechanical systems, elastohydrodynamic lubrication (EHL) is apparent in the interfaces be-tween rolling/sliding parts. Even at small slide-to-roll ratios, detailed knowledge about the oil film thickness and the traction exerted by the highly pressurized lubricant is crucial for the efficiency and reliability of such systems. In this study, we explore the impact of surface velocity direction and contact ellipticity on traction characteristics within EHL through numerical simulations using an elliptical EHL contact solver based on a fully-coupled finite-element approach. We present a novel master curve that correlates the traction coefficient slope with the lubricant entrainment direction and ellipticity, for el-liptical EHL contacts in the piezo-viscous elastic (PE) regime. We demonstrate that the master curve, shows a maximum relative difference of less than 3.2% to the numerical simulation results, proving its efficacy. This curve is particularly beneficial for multibody dynamics models, providing a reliable tool for predicting frictional forces in systems where elliptical EHL contacts, operating within the PE regime at low SRR, are prevalent.

Study on the contact performance of the variable hyperbolic circular arc tooth trace cylindrical gear with installation errors

Abstract. Installation errors are important factor for the contact performance of the variable hyperbolic circular arc tooth trace (VH-CATT) cylindrical gear; the study of the relationship between installation errors and contact performances is beneficial for gear vibration and noise reduction. Firstly, based on the meshing theory, the tooth surface equation and contact ellipse of the VH-CATT cylindrical gear were deduced, and the tooth surface imprinting experiment was realized. Next, the tooth contact analysis model of the VH-CATT cylindrical gear was developed to investigate the influence of the installation errors on the elliptical contact area. Then, the calculation formulas of the tooth surface gap and contact point flexibility matrix were carried out to develop the load tooth contact analysis model of the VH-CATT cylindrical gear. Finally, the influence of the installation errors on the load distribution was investigated. Research shows that the elliptical contact area of the VH-CATT cylindrical gear is a line contact within a certain range and is located in the middle section of the tooth width. The elliptical contact area of the VH-CATT cylindrical gear increases or decreases rapidly when meshing in and out, and all the installation errors have a certain influence on the elliptical contact area, except for the center distance error. The single-tooth meshing area with the installation errors is greater than that of the ideal gear pair. The load distribution area with the installation errors deviates from the middle section, except for the center distance error. The installation rotation errors around the x and y axis have a certain influence on the maximum load of the single-tooth meshing area. The research results provide a basis for improving the bearing capacity of the VH-CATT cylindrical gear and optimizing the design.

Review and comparison of selected methods of calculating wheel-rail contact tangential forces on the example of riding stability analysis of a two-axle vehicle

This article presents methods currently used in railway vehicle dynamics simulations (MBS) for calculating wheel-rail contact forces. Simulation models of two-axle vehicle built in Simpack 2023 simulation environment were used to compare the selected methods. The paper focuses on the issue of riding stability of the mentioned group of vehicles. The developed research methodology consists in simulating the riding of a vehicle exhibiting instability (hunting movement) on an ideal straight track using the wheel-rail contact models available in the Simpack 2023 environment. Then the obtained results are input data for recalculation of contact forces with selected algorithms. The study is aimed at comparing the selected methods for calculating contact forces, so there is no interaction of the algorithms tested with the MBS simulation model. The results obtained were compared with Kalker's "exact theory" of contact (CONTACT) for the elliptical contact area.

Simplified Formulation for Bush, Gibson, and Thomas Model

Abstract The random process model, also known as the multi-asperity contact model or statistical model, is one of the dominant methodologies for analyzing the contact between nominally flat rough surfaces. In 1975, Bush, Gibson, and Thomas developed a complete random process model (known as the BGT model) assuming that solid–solid contacts occur on the summits of the asperities, which are semi-ellipsoids uniquely described by three random variables (the asperity height and two principal peak curvatures). The Hertzian elliptic contact theory states that the contact area and normal load are implicit functions of the random variables, which results in an original BGT model with a complex formulation. In this study, we used an adapted Hertzian elliptic contact theory to simplify the formulation of the BGT model. The relative contact area to normal load relation predicted by the simplified BGT model perfectly agrees with that of the original formulation. It is anticipated that rough surface contact models with complex asperity interactions can be effectively built under the framework of this simplified BGT model.

Applicability of an Hertzian-type contact model for wheel-rail pairings as seen by an improved post-processing scheme for ultrasonic data

The contact between wheel and rail crucially affects the management of railways, since the vehicle dynamics, safety, and performance, for example, are all dependent on this. Therefore, in this contribution the load-dependence of nominal contact area – a broadly not considered aspect of the wheel-rail contacts within the literature – is addressed. We are applying an ultrasonic technique for the detection of the contact zone and an improved post-processing scheme for the measured ultrasonic reflection data. Accordingly, we found that the nominal contact area shows a power-law dependence on load which only on average is predicted by the elliptical Hertzian contact theory.

Rolling pairs with shifting contact geometry: Design, development, and validation

This work introduces two innovative rolling pair concepts to minimize slippage and reduce mass in cam-roller systems of large-scale hydraulic drivetrains: The variable contact length and the Shifting Contact Geometry concepts. Both aim to improve traction in the low contact force phase in cyclically loaded rolling contacts. The shifting contact geometry concept was validated using three custom rolling contacts: a line contact, a double elliptical contact, and a combination of both (i.e., shifting contact geometry). The tests were conducted under synchronized cyclic loading to mimic the conditions in a hydraulic drivetrain. Furthermore, a model from previous work was implemented to make predictions and compare them against the experimental results. During preliminary tests, the double elliptical contact displayed superior tractive behavior than the line contact under the same load thanks to higher contact pressures. Under synchronized cyclic loading, the line contact displayed high sensitivity to applied resisting torques at low contact forces, leading to high slide-to-roll ratios and traction force peaks. In contrast, the rolling pair with shifting contact geometry exhibited minimum slippage even under high resisting torques, resulting in substantially lower (and in most cases negligible) slide-to-roll ratio and traction force peaks. The simulations also captured this behavior, proving the validity of the model for predicting and comparing the rolling-sliding dynamics of these two different rolling pairs. This study demonstrates that rolling pairs with shifting contact geometry can not only improve the tribological performance of cam-roller contacts in large-scale hydraulic drivetrains but also yield a more favorable dynamic behavior.

Characterization of Contact Pressure Distribution and Bruising Prediction of Apple under Compression Loading

The pressure distribution characteristics of an apple subjected to compressive loading were investigated using the pressure-sensitive film (PSF) technique combined with apple bruise measurements. Pressure was unevenly distributed in the elliptical contact region. The average pressure had no effect on bruising because it changed slightly in the range of 0.26–0.31 MPa with increasing load. Pressures of 0.20–0.40 MPa accounted for 72% of the total pressure area. Comparatively, the area where pressure over 0.50 MPa was distributed could be ignored and showed little contribution to the bruise area. The contact edge subjected to pressure below 0.10 MPa showed that no bruising occurred. As a result, the relationship between the ≥0.10 MPa pressure area strongly correlated with the bruise area according to a linear equation, with a correlation coefficient of ≥0.99. When this relationship was applied to determine the bruise area with FE, satisfactory predicted results were obtained with minor error rates of 0–7.89% for loads of 54–80 N. But larger prediction errors occurred when the load was above 90 N, suggesting that the linear elastic FE model may not be appropriate for accurately predicting apple bruising.

Pneumatically tunable adherence of elastomeric soft hollow pillars with non-circular contacts

Dynamically tunable interfacial dry adhesion plays a significant role in numerous biological functions and industrial applications. Among various strategies, pneumatics-activated adhesive devices draw much attention due to their distinct advantages such as fast speed, reliable performance, large adhesion tunability and easily accessible materials. To understand and predict adhesion strength of pneumatics-activated adhesives, it is necessary to examine their interfacial mechanics that is nonlinearly coupled with the large deformation of the devices under pressure. However, previous studies have only focused on axisymmetric cases in which the outline of the contact area is circular, whereas the tunable adherence of non-circular contact controlled by pneumatics remains elusive. In this work, through a combination of experiments and simulations, we study the effect of non-circular contact geometry on tunable dry adhesion of pressure-activated soft hollow pillars. Specifically, elliptical, square, and rectangular contact shapes are considered and their effects on tunable adhesion of the soft hollow pillars are compared to that of circular contact geometry thoroughly. The results show that soft hollow pillars with elliptical, square, and rectangular contact surfaces demonstrate rich interfacial delamination behaviors that depend on the contact outline geometry and internal pressure. Among all contact geometries, elliptical contact has the highest adhesion tunability yet requires lowest activating pressure owing to the non-uniform curvature distribution of the contact outline. However, when the eccentricity increases, the elliptical contact has reduced tunability of adhesion caused by the contact of opposing sides of the sidewall upon buckling. For square and rectangular contacts, they have the lowest adhesion tunability and need higher activating pressure than those of circular and elliptical contact since the 90-degree edges of the sidewall prohibit buckling instability. Our findings greatly broaden the design space of pneumatics-activated adhesive devices by adding the contact geometry of the soft hollow pillars as a new design parameter, which can provide valuable guidance for tunable adhesive design for various applications in manufacturing and robotics.

Experimental validation of elliptical contact tire model with friction coefficient deduced from viscoelasticity of tread rubber

Experimental validation of elliptical contact tire model with friction coefficient deduced from viscoelasticity of tread rubber

Tire mechanical model for cornering simulation with friction coefficient calculated from viscoelasticity of rubber by multiscale friction theory

A friction coefficient of tire model for cornering simulation is generally set inductively to be consistent with experimental results. However, the inductively set friction coefficients have no clear relationship with the viscoelasticity of the rubber, so they cannot be used in the design of rubber formulations to obtain the desired friction coefficient. In this study, we propose a new tire mechanical model for cornering simulation that includes a friction coefficient deductively derived from the viscoelasticity of rubber based on the Persson’s multiscale friction theory. In this model, the contact pressure, sliding velocity, and lateral stress distributions are calculated based on an elliptical contact patch. Because the proposed model analytically connects the lateral force with the viscoelasticity of rubber, it is applicable to rubber design for achieving the targeted cornering properties. The validity of the model was experimentally verified using an internal drum machine with quartz piezoelectric sensors on an aluminium road segment. With appropriate parameter settings, the friction coefficient distribution in the length direction calculated by the proposed model agreed well with the experimental results compared to the elliptical contact patch tire model.

Machine Learning for Film Thickness Prediction in Elastohydrodynamic Lubricated Elliptical Contacts

This study extends the use of Machine Learning (ML) approaches for lubricant film thickness predictions to the general case of elliptical elastohydrodynamic (EHD) contacts, by considering wide and narrow contacts over a wide range of ellipticity and operating conditions. Finite element (FEM) simulations are used to generate substantial training and testing datasets that are used within the proposed ML framework. The complete dataset entails 915 samples; split into an 823-sample training dataset and a 92-sample testing dataset, corresponding to 90% and 10% of the combined dataset samples, respectively. The proposed ML model consists of a pre-processing stage in which conventional EHD dimensionless groups are used to minimize the number of inputs into the model, reducing them to only three. The core of the model is based on Gaussian Process Regression (GPR), a powerful ML regression tool, well-suited for small-sized datasets, producing output central and minimum film thicknesses, also in dimensionless form. The last stage is a post-processing one, in which the output film thicknesses are retrieved in dimensional from. The results reveal the capabilities and potential of the proposed ML framework, producing quasi-instantaneous predictions that are far more accurate than conventional film thickness analytical formulae. In fact, the produced central and minimum film thickness predictions are on average within 0.3% and 1.0% of the FEM results, respectively.

Thermal lubrication characteristics of hypoid Gear with non-Newtonian fluids considering roughness

Based on Hertz contact theory and EHL, the model of elliptic contact elastohydrodynamic lubrication considering load, speed, roughness, thermal effect, and shear-thinning effect of non-Newtonian fluids is established. The variation trend of oil film pressure, thickness, and temperature with load, entrainment velocity, and the slide-roll ratio is analyzed. Then, several lubrication states considering roughness, the thermal effect, and the characteristics of non-Newtonian fluid are compared. Compared with the smooth surface, the roughness when RMS is 0.15 μm increases the maximum film pressure (P max) by 8.34%, increases the maximum film temperature (T max) by 7.18%, and reduces the minimum film thickness (H min)by 9.13%. The pressure and temperature are more sensitive to light load. The results are approximate to that of the smooth surface when the entrainment velocity is big enough. The pressure and thickness decrease with the increasing slide-roll ratio. The decreasing speed of the oil film thickness becomes faster as a result of the thermal effect. The roughness and the characteristics of non-Newtonian fluid have a significant impact on temperature.

Crowned spur gears for constant mesh stiffness: A conceptual approach

Flank line crowning is a gear surface geometry modification that can be applied as a measure to accommodate contact imperfections along the gear teeth facewidth, that are a consequence of misalignment from either geometric defects or elastic deflection. Due to flank line crowning, the contact stiffness between the teeth of an ideal spur gear changes, thus modifying the gear mesh stiffness. Gear mesh stiffness fluctuations are one of the main driving factors behind gear performance, such as transmission error, dynamic overload and overall system vibration. Regardless of manufacturing feasibility, a set of analytical equations, derived from the classical elliptical contact theory is presented aiming to find the flank line crowning values along the path of contact that eliminate gear mesh stiffness fluctuations. This is achieved by transforming the shape of single teeth pair mesh stiffness through the contact stiffness, making it similar to the shape of the load sharing. A direct method to find the load sharing of spur gears with flank line crowning is also presented.

On Boussinesq's Problem for a Power-Law Graded Elastic Half-Space on Elliptical and General Contact Domains.

The indentation of a power-law graded elastic half-space by a rigid counter body is considered in the framework of linear elasticity. Poisson's ratio is assumed to be constant over the half-space. For indenters with an ellipsoidal power-law shape, an exact contact solution is derived, based on the generalizations of Galin's theorem and Barber's extremal principle for the inhomogeneous half-space. As a special case, the elliptical Hertzian contact is revisited. Generally, elastic grading with a positive grading exponent reduces the contact eccentricity. Fabrikant's approximation for the pressure distribution under a flat punch of arbitrary planform is generalized for power-law graded elastic media and compared with rigorous numerical calculations based on the boundary element method (BEM). Very good agreement between the analytical asymptotic solution and the numerical simulation is obtained for the contact stiffness and the contact pressure distribution. A recently published approximate analytic solution for the indentation of a homogeneous half-space by a counter body, whose shape slightly deviates from axial symmetry but is otherwise arbitrary, is generalized for the power-law graded half-space. The approximate procedure for the elliptical Hertzian contact exhibits the same asymptotic behavior as the exact solution. The approximate analytic solution for the indentation by a pyramid with square planform is in very good agreement with a BEM-based numerical solution of the same problem.

Dual experimental-numerical study of oil film thickness and friction in a wide elliptical TEHL contact: From pure rolling to opposite sliding

This study presents a dual experimental-numerical approach to simultaneously investigate oil film thickness and friction in a wide elliptical thermo-elastohydrodynamic (TEHL) contact over sliding conditions ranging from pure rolling to opposite sliding (slide-to-roll ratio SRR between 0 and 4). Experiments are performed on a barrel-on-disk tribometer instrumented for friction and optical oil film thickness measurements. In addition, a TEHL numerical model based on the full system approach is used to predict film thickness and friction response variation with sliding. The trends of film thickness variation with SRR are different for SRR lower and higher than 2 because of the genesis of the thermal viscosity wedge effect at opposite sliding. The friction coefficient measured experimentally increases with increasing SRR and then stabilizes at high SRR. The numerical model can accurately predict the film thickness over a wide range of sliding conditions. Also, the model predicts friction with a good accuracy for SRR>2. In contrast, for SRR<2, numerical results overestimate friction coefficient. In addition, a numerical parametric investigation is realized to understand the effect of varying ambient temperature, normal load, and entrainment velocity on film thickness and friction over a wide range of sliding conditions. Numerical results are then used to create a simple formula for an accurate estimation of the minimum film thickness based on classical dimensionless parameters and SRR for a wide range of sliding conditions (0≤SRR≤4).

Effect of boundary slip on elastohydrodynamic lubrication with arbitrary entrainment angle in elliptical contacts

PurposeThe purpose of this study is to describe and observe the influence of boundary slip associated with an arbitrary entrainment angle on the contact lubrication properties of ellipses.Design/methodology/approachBased on the modified Reynolds equation, the boundary slip of any angle is considered in the elliptic contact, and numerical simulation is carried out. In the above calculation, the progressive mesh densification method is used, which greatly reduces the computation time.FindingsThe results indicate that the variation of film thickness corresponding to different entrainment angles is distinct from those without considering boundary slip. In addition, boundary slip reduces the central film thickness and minimum film thickness, which makes the hydrodynamic pressure distribution smoother.Originality/valueThe present study focuses on the specific condition with the arbitrary direction of rolling and sliding velocity found in hypoid gears and worm, and some other components. The influence of boundary slip associated with arbitrary entrainment angle on the lubrication film thickness in elliptical contacts is first revealed, which improves a good understanding of elastohydrodynamic lubrication characteristics.

Cargo transport properties are enhanced by cylindrical microtubule geometry and elliptical contact zone on cargo surface

Molecular motors are responsible for carrying cellular transport of various membranous vesicles or organelles along cytoskeletal tracks. Transport of cellular cargos require high forces that are generated by motors working in groups. Hence, the properties of cargo transport can be modulated by varying various parameters such as cargo size and shape, microtubule geometry, motor number and their arrangement on cargo surface. Only those motors which are present in the contact zone on cargo surface have potential to bind to microtubule. Although earlier studies revealed the importance of cargo size, total motors attached to microtubule and their arrangement on cargo transport, yet how the contact zone influences binding of motors to microtubule largely remains unexplored. Here, it has been shown that contact zone is elliptical in shape for a spherical cargo and increases with cargo size for Kinesin-1 motors. To further understand the combined effect of elliptical contact zone and microtubule geometry on cargo transport, 3D mean-field model with uniform and clustered arrangement of motors for different cargo sizes and motor number has been used. Our findings indicate that cylindrical microtubule geometry maximizes the microtubule-bound motors which enhances the runlength and velocity of cargo transport. Our results show that microtubule-bound motors decrease with cargo size for uniform arrangement of motors on cargo thus decreasing its runlength and velocity, whereas in clustered arrangement, the number of microtubule-bound motors increase with cargo size which leads to increase in runlength and velocity.