Contact Analysis Model Research Articles

Dynamic characteristic analysis of spur gear system considering tooth contact state caused by shaft misalignment

The effect of gear contact state change due to shaft misalignment on meshing stiffness is usually neglected in the traditional stiffness calculation model with misalignment error, the further influence mechanism of shaft misalignment on gear dynamic characteristics is also unclear. To address these shortcomings, a new mesh stiffness calculation model with misaligned gear considering the effects of tooth contact state is proposed by combining the improved loaded tooth contact analysis (LTCA) model. Then the effects of tooth contact state changes aroused by shaft misalignment on the meshing stiffness excitation are investigated. Moreover, a dynamic model of the misaligned gear system with 8 degrees of freedom (DOF) is established, and based on which the dynamic characteristics of the gear system are investigated and verified by experiment. The study results indicate that the proposed model can be used to evaluate the stiffness excitation and dynamic characteristics of the misaligned gear system with the tooth contact state taken into consideration. This study can provide a theoretical method for evaluating and identifying shaft misalignment errors.

A two-way coupled FSI model for the rapid evaluation of accidental loads following ship hard grounding

The assessment of structural crashworthiness following ship grounding events should consider the influence of multi-physics on dynamic response. To date, this has been achieved by computationally expensive approaches combining explicit 3D FEA with hydrodynamic solvers (e.g. Conti et al. (2021); Kim et al. (2021)). To offer an alternative, this paper presents a rapid six degree of freedom (6-DoF) two-way coupled fluid–structure interaction (FSI) model that could be used for the rapid evaluation of ship dynamic response and structural crashworthiness during hard grounding events. The time domain solution is based on a simplified contact analysis model that combines the external dynamics idealization of Taimuri et al. (2020) with an extended version of the internal mechanics analytical formulation of Simonsen (1997a) and Sun et al. (2017). The plate cutting angle is calibrated based on the rock geometry and hull indentation. A ray-tracing algorithm that utilizes panels and the tip of a conical rock is implemented to idealize hull penetration. The model is numerically validated by comparing results against LS-DYNA simulations for a box-shaped barge of double bottom configuration and a passenger vessel. Parametric studies demonstrate that longitudinal and vertical forces produced by different models compare well. However, the lateral forces for the study case of a passenger ship progressing along a straight path are shown to be underestimated. This is because the proposed method (i) does not allow for the influence of lateral loading on longitudinal hull members and (ii) overestimates the forces in regions of extreme curvature (e.g. fore shoulder, bow and boundaries of the hull).

Research on the Method of Prediction for Fuzzy Tooth Surface of Involute Gear

Surface appearance of involute gear is the basis to research the dynamic performance of gear transmission system. The Delaunay triangulation method of layered local dynamic is proposed to construct the precise tooth surface of the known tooth surface appearances. The concave and convex region of the real tooth surface was extracted by isosurface subdivision. In order to smooth the surface, the energy method and the improved fractal method with minimum included angle are used to smooth the curve. On the basis of the loaded tooth contact analysis of involute gears, the loaded tooth contact analysis model of digital error tooth surface is constructed. The tooth surface appearances of fuzzy tooth surface were predicted by extracting contact patterns under various working parameters on the experimental platform. Through the analysis on actual examples, it is concluded that the method proposed in this manuscript can accurately predict the tooth surface morphology of fuzzy tooth surface and lay the foundation for the dynamic performance optimization of gear system with fuzzy tooth surface.

Influence of Misalignment on Beveloid Gear Tooth Contact and Dynamic Characteristics in Transfer Case Transmission of AWD Vehicle

Beveloid gears are usually employed to transfer motion of small shaft angle, but the assembly errors or misalignment can affect the gear tooth contact and dynamic performance. A dynamic model and tooth contact analysis model of the intersecting beveloid gear pair are established, the defects of the theoretical tooth surface in the meshing are analyzed, and a microgeometry modification method to improve the meshing performance is proposed. At the same time, the effects of system misalignment and manufacturing errors on its meshing characteristics are considered. By studying the sensitivity of the static and dynamic characteristics of beveloid gear on different misalignment components, the influence laws of misalignment on the contact pattern, transmission error, mesh stiffness, and dynamic excitation force are obtained, which give suggestions for tooth surface modification and support structural stiffness design of beveloid gear with a good NVH performance.

Cylindrical Roller Bearings with Optimized Profile Taking into Account the Material Structure and Operating Temperature

Abstract The present paper proposes a method for an almost uniform pressure distribution between the rolling elements, based on the modification of the roller’s initial straight profile and accounting for material parameters related to the operating temperature. The optimization process is analyzed by including the possible misalignment and/or tilting angles of the roller due to operating conditions. A computer program was developed in the Borland C++ programming language. The contact pressure distribution is evaluated by using a three-dimensional contact analysis model based on the Boussinesq force-displacement relations for a half-space combined with the flexibility approach. For a fast analysis, the algorithm uses a Conjugate Gradient Method in deriving the contact pressures and the real contact area.

A novel calculation method of long period pinion axial displacement and meshing impact force for double helical gear considering asymmetry error

The cumulative pitch errors of the left and right helical gears are the main source of the asymmetry error for the double helical gear. In this paper, a new three-dimensional loaded tooth contact analysis (3-DLTCA) model of double helical gear considering long period asymmetry error is proposed. The desired error (modification), undesired error (cumulative pitch error) and the change of normal clearance increment of left and right helical gear pairs caused by the axial shift of the driving pinion are considered in the model. Based on the new 3-DLTCA model, combined with the equivalent gap of the current meshing tooth pair, the meshing impact force (MIF) of the current meshing tooth pair in each meshing period is calculated. The results show that the proposed model can quickly and accurately calculate the long period end loaded transmission error (ELTE) and pinion axial displacement (PAD) of double helical gear with asymmetry error. Moreover, the long period asymmetry error of double helical gear has great effect on the MIF for left and right helical gears.

A multi-physics transient wear model for helical gear pairs

This study combines the use of a Tooth Contact Analysis (TCA) model for helical gear pair conjunctions with a multifaceted tribological model, implicitly coupled with a multi-body dynamic system. A reduced order 2-D Elastohydrodynamic Lubricant (EHL) film thickness prediction facilitates the estimation of viscous and boundary friction with a Greenwood-Tripp asperity model, as well as a lubricated wear methodology. An implicit approach is used to capture progressing wear upon gear teeth with consideration of gear microgeometry. The use of the numerical EHL model gives new insights to the coupled evolution of wear and dynamics on efficiency and NVH throughout the component’s life cycle.

A Calculation Method for Tooth Wear Depth Based on the Finite Element Method That Considers the Dynamic Mesh Force

Gear wear is a progressive material removal process that gradually changes the tooth profile shape and dynamic mesh force, where the dynamic mesh force affects the tooth surface wear. To describe this process, a spur gear dynamic model that includes the mesh stiffness and unloaded static transmission error (STE) of the worn tooth profile is proposed for calculating the dynamic mesh force. Then, based on the finite element method (FEM), a dynamic contact analysis model that considers the dynamic mesh force is proposed for calculating the time-varying contact stress and relative sliding distance of the tooth surface mesh point. Finally, combined with the Archard wear model, a tooth wear depth calculation method that considers the worn tooth profile and the dynamic mesh force is proposed. In addition, the wear depth and dynamic characteristics under different wear times are studied.

A fatigue model for spiral bevel gears under mixed elastohydrodynamic lubrication conditions

AbstractMany contributions have focused on the pitting analysis in gear transmissions. However, studies on pitting fatigue in spiral bevel gears are limited due to the complexity of tooth contact and lubrication analysis. This paper is to present a reasonable methodology to simulate the pitting crack nucleation of spiral bevel gears considering the real three‐dimensional (3D) rough surface contact where the intermittent asperity stress concentrations is prominent. The proposed model includes a loaded tooth contact analysis model, a mixed elastohydrodynamic lubrication model proposed previously, 3D stress filed formulation, and multi‐axial fatigue criterions. In order to determine an appropriate multi‐axial fatigue criterion for spiral bevel gear, a characteristic plane approach and a conventional critical plane approach are employed in this study. The predicted micro‐pitting lives are compared to published micro‐pitting investigations to assess the reliability of two fatigue criterions in simulation of the micro‐pitting failure. It is observed that the characteristic plane approach is better to reveal the failure mechanism in spiral bevel gears.

An optimal tangential contact model for wheel-rail non-Hertzian contact analysis and its application in railway vehicle dynamics simulation

Relative to the Hertzian theory, the non-Hertzian contact model (NHM) can better reflect the contact characteristic between wheel and rail in railway vehicle dynamics simulation. In this paper, an optimal wheel-rail tangential contact model is determined for vehicle dynamics simulation. First, based on i) the modified Kik–Piotrowski (MKP) contact model, ii) four different ellipse-equivalent methods, and iii) the modified FASTSIM model or modified FaStrip model, eight NHMs are proposed. Then, taking the Kalker's variational method (KVM) as a reference, the computational accuracies of the eight NHMs for calculating the linear creep coefficient and the tangential forces for the typical tangential contact scenarios are compared. NHM II, that is, the model coupled with the MKP model, the ellipse-equivalent method adopted in the Kik–Piotrowski (KP) model, and the modified FaStrip model, shows the best computational accuracy. Finally, the traditional Hertzian & FASTSIM model, the NHM II model, and KVM model are applied to the vehicle-track coupled dynamics simulations, and the dynamics response of a high-speed train running on a slab track is calculated by different contact models. The comparison results show that the NHM II model exhibits better agreement with the KVM compared with the Hertz & FASTSIM model.

A Fractal Model of Elastic–Plastic Contact Between Rough Surfaces for a Low-Velocity Impact Process

Under the low-velocity impact conditions, in order to study the contact load variation law of the ellipsoid elastic bodies, an elastic–plastic contact analysis model of rough ellipsoid surfaces is provided based on elastic–plastic fractal theory. A spherical elastic–plastic fractal model considering friction factors is established, and the spherical diameter density distribution function and elastic contact mechanics are used as the solution methods. The two contact surfaces are taken as the research object, and the influence of relevant variables on the contact intensity is analyzed. The analysis results show that the fractal dimension and roughness have a greater effect on contact performance, the contact load is positively related to the surface roughness, and the lower friction coefficient has a weaker effect on the contact load, and the correctness of the present model is verified by comparing finite element simulation results and other studies. The modified spherical contact load function provides a theoretical basis for the friction and wear of the microscopic surface, it can be applied for solving the sliding contact problems with different impact velocities and the surface bearing capacity of the impact parts can be improved.

Tooth Surface Modification for Helical Gear Pairs considering Mesh Misalignment Tolerance

Mesh misalignment in mating the gear tooth surface is common and difficult to be determined accurately because of system deformation and bearing clearances, as well as manufacturing and assembly errors. It is not appropriate to consider the mesh misalignment as a constant value or even completely ignore it in the tooth surface modification design. Aiming to minimize the expectation and variance of static transmission error (STE) fluctuations in consideration of mesh misalignment tolerance, a multiobjective optimization model of tooth surface modification parameters is proposed through coupling the NSGA-II algorithm and an efficient loaded tooth contact analysis (LTCA) model. The modified tooth flank of helical gear pairs is defined using 6 design variables which are related to profile modification, lead modification, and bias modification. The influences of mesh misalignment on time-dependent meshing stiffness (TDMS) and STE of unmodified and modified helical gear pairs are investigated. Then, the dynamic transmission error (DTE) of modified helical gears in consideration of mesh misalignment is discussed. The results indicate that the designed modified tooth surface shows good robustness to mesh misalignment.

A novel tooth surface modification methodology for wide-faced double-helical gear pairs

Aiming to improve the meshing quality of tooth surface and reduce the system vibration, a novel tooth surface modification methodology for the wide-faced double-helical gear pairs is developed in consideration of system flexibility. The quasi-static multi-point contact analysis model for double-helical gear system is established based on the new concept of axial multi-point contact and the substructure technique. The mesh misalignment caused by system flexibility and the compensated tooth surface modification parameters can be determined. Also, a multi-objective optimization mathematical model of tooth surface modification is established in order to reduce the fluctuation of vibration exciting force and improve the load distribution. The Pareto frontier solutions of tooth surface modification parameters are obtained by combining the loaded tooth contact analysis(LTCA) model and the NSGA-II algorithm. The final modified tooth surface for wide-faced double-helical gear pairs is obtained using the combination of compensated tooth surface modification and multi-objective optimization modification. The influences of system flexibility and tooth surface modification on quasi-static behaviors of the wide-faced double-helical gear pairs are discussed.

A Novel Loaded Tooth Contact Analysis Procedure With Application to Internal–External Straight Bevel Gear Mesh in a Pericyclic Drive

Abstract A comprehensive numerical loaded tooth contact analysis (LTCA) model is proposed for straight bevel gears that exhibit large number of teeth in contact, well beyond the involute line of action limits. This kind of contact is observed when the meshing gears have conformal surfaces, as in a pericyclic mechanical transmission, and is traditionally analyzed using finite element simulations. The pericyclic drive is kinematically similar to an epicyclic bevel gear train and is characterized by load sharing over large number of teeth in an internal–external bevel gear mesh, large shaft angles (175–178 deg), nutational gear motion, and high reduction ratio. The contact region spreads over a large area on the gear tooth flank due to high contacting surface conformity. Thus, a thick plate finite strip method (FSM) was utilized to accurately calculate the gear tooth bending deflection. Based on the tooth deformation calculation model and accounting for initial surface separation, a variational framework is developed to simultaneously solve for load distribution and gear tooth deformation. This is followed by calculation of contact stress, bending stress, mesh stiffness, and transmission error. The results demonstrate the high-power density capabilities of the pericyclic drive and potential for gear noise reduction. The model developed herein is applied with real gear tooth surfaces, as well.

Dynamic Simulation Analysis on Axle Spline of High‐Speed Train Gauge‐Change System

Spline couplings are widely used in transmission systems to transfer torque due to their higher load carrying capacity and better durability performance. Most researches are conducted under static and quasistatic loading cases; however, very little is known about their contact behavior and stress distribution under dynamic loading cases, especially as a key transmission component between wheel and axle. In this paper, a 3D dynamic contact and impact analysis model of the wheel‐axle spline of high‐speed train gauge‐change system is employed in order to investigate the effect of driving velocity and assembling error and vibration on spline couplings. Three categories of loading cases are considered: (i) 0.3 m/s2 driving rate representing quasistatic loading case; (ii) 0.5 m/s2 driving rate representing normal loading case, and (iii) 1 m/s2 driving rate representing exceptional loading case. Aside from this, influence of spline misalignment, including radial misalignment and circumferential misalignment, has been investigated under normal loading case. Numerical results for surface integral contact analysis conducted by LS‐DYNA and MATLAB were presented and compared for the verification of the results.

An elastic model for tooth contact analysis of spur gears using FEM simulation

Gears are a class of machine parts very often used in the most diverse industries due to their many advantages. In addition to the many benefits they provide, gears also have some disadvantages related to the noise and vibrations they can introduce into the system they are part of. The operating drawback which may occur is closely related to the geometry of contact and manufacturing and assembling errors. Investigation of the contact error effect on the operating condition should be first carried out through simulation approach. Gear efficiency can be investigated through the tooth contact analysis (TCA) method and stress analysis. The main target of TCA is to set up the contact path and to determine the transmission error function caused by clearance, gear misalignments or backlash. Generally, TCA is performed considering the elastic behaviour, which frequently implies to get data for different contact positions for full meshing analysis. Nevertheless, TCA outcome delivers noteworthy data about kinematic errors, contact ellipses and the estimation of the instantaneous contact point of the meshing gears. A numerical tool was developed in this work to obtain the contact path in spur gears, which allowed to compute the displacements, stress and strain fields in the contact regions. Furthermore, an analysis of the influence of manufacturing and assembling errors on the contact path and mesh quality was performed. Such an approach may provide an optimal design solution for spur gears.

A Computational Model for the Analysis of the Static Forced Performance of Self-Equalizing Tilting Pad Thrust Bearings

Abstract While failure analyses in the archival literature report thrust collar misalignment as a major cause of collapse in oil lubricated thrust bearings (TB), a self-equalizing tilting pad thrust bearing (TPTB) improves operation reliability by adjusting its pads to account for thrust collar tilt. This paper describes a kinematics model for the equalizing mechanism integrated into an existing thermo-elastohydrodynamic (TEHD) analysis tool to deliver load performance predictions for self-equalizing TPTBs. The analysis considers the actual leveling plates geometric model as obtained from a solids modeling commercial software and accounts for the sliding friction forces acting at the contact points of the leveling plates and the rolling friction at their pivots. Further, a Hertz contact analysis model uses the predicted forces to deliver a peak pressure and deformation over the contact area between the leveling plates. Next, this paper presents predictions for an example self-equalizing TPTB operating with a thrust collar static misalignment φ = 0.01 deg. The bearing 126 mm in outer diameter has six pads, operates at 4 krpm (26 m/s maximum surface speed) and under a specific load/pad ranging from 0.5 to 3.5 MPa. Compared to a nonequalizing TPTB, a self-equalizing TPTB operates with up to 50% larger minimum film thickness and about ½ largest elastic deformation. Friction forces acting at the contact points of the leveling plates show a significant effect on the performance of the pad leveling system as they reduce the film clearance and increase a pad peak pressure. Predictions from the Hertz contact analysis agree with those from a commercial finite element analysis tool and show a significantly large peak pressure at the contact points of the leveling plates (> 0.9 GPa) when the bearing supports a 3 MPa/pad specific load. This paper stresses the importance of conducting a comprehensive multiple-pad analysis to accurately evaluate the performance and reliable operation of self-equalizing TPTBs.

Collision in the expansion joint effects on the seismic behavior of large-scale aqueduct

ABSTRACT Under earthquake, two beams of the aqueduct’s expansion joint may collide; thus, this will endanger the safety of the structure and even lead to girder falling accident. Quite a few studies of this issue use the simple one-dimensional model, but little takes the collision phenomenon under the action of multi-dimensional earthquake into account. According to the Contact-Impact Problems of large-scale aqueduct under earthquake action between the adjacent beam segments, a three-dimensional contact analysis model has been used to simulate the collision phenomenon. And the response of aqueduct structure collision one-dimensional seismic and multidimensional earthquake is compared; the results reveal that the three-dimensional frictional contact impact finite element model can simulate the real aqueduct structure under seismic pounding effect.

Quasi-Static Characteristics and Vibration Responses Analysis of Helical Geared Rotor System with Random Cumulative Pitch Deviations

As one of the long period gear errors, the effects of random cumulative pitch deviations on mesh excitations and vibration responses of a helical geared rotor system (HGRS) are investigated. The long-period mesh stiffness (LPMS), static transmission error (STE), as well as composite mesh error (CMS), and load distributions of helical gears are calculated using an enhanced loaded tooth contact analysis (LTCA) model. A dynamic model with multi degrees of freedom (DOF) is employed to predict the vibration responses of HGRS. Mesh excitations and vibration responses analysis of unmodified HGRS are conducted in consideration of random cumulative pitch deviations. The results indicate that random cumulative pitch deviations have significant effects on mesh excitations and vibration responses of HGRS. The curve shapes of STE and CMS become irregular when the random characteristic of cumulative pitch deviations is considered, and the appearance of partial contact loss in some mesh cycles leads to decreased LPMS when load torque is relatively low. Vibration modulation phenomenon can be observed in dynamic responses of HGRS. In relatively light load conditions, the amplitudes of sideband frequencies become larger than that of mesh frequency and its harmonics (MFIHs) because of relatively high contact ratio. The influences of random cumulative pitch deviations on the vibration responses of modified HGRS are also discussed.

An efficient three-dimensional dynamic contact model for cylindrical gear pairs with distributed tooth flank errors

Coupled loaded tooth contact analysis (LTCA) model and lumped-parameters model, an efficient three-dimensional dynamic contact model for cylindrical gear pairs with distributed tooth flank errors is established. The solution scheme of the proposed model is constructed using a combination of the loaded tooth contact algorithm and the Newmark integration method. The dynamic load distributions at different input speeds can be determined, and the dynamic time-dependent mesh stiffness and dynamic composite mesh error are proposed and calculated. The proposed model is validated by comparing the obtained numerical results with the experimental results from the published works, and has much higher efficiency compared with three-dimensional dynamic contact finite element method. The effects of helix angle, mesh damping, distributed tooth flank errors and output torque on the vibration behaviors and dynamic load distributions of cylindrical gear pairs under different working conditions are investigated and discussed. The proposed model can also be used to predict the vibration behaviors and the instantaneous three-dimensional dynamic contact state of cylindrical gear pairs with different distribution forms of tooth flank errors and various tooth surface modifications.