Contact Stress Reliability Analysis Model for Cylindrical Gear with Circular Arc Tooth Trace Based on an Improved Metamodel

Although there is currently no unified standard theoretical formula for calculating the contact stress of cylindrical gears with a circular arc tooth trace(referred to as CATT gear),a mathematical model for determining the contact stress of CATT gear is essential for studying how parameters affect its contact stress and building the contact stress limit state equation for contact stress reliability analysis.In this study,a mathematical relationship between design parameters and contact stress is formulated using the KrigingMetamodel.To enhance the model’s accuracy,we propose a new hybrid algorithm that merges the genetic algorithm with the Quantum Particle Swarm optimization algorithm,leveraging the strengths of each.Additionally,the“parental inheritance+self-learning”optimization model is used to fine-tune the KrigingMetamodel’s parameters.Following this,amathematicalmodel for calculating the contact stress of Variable Hyperbolic Circular-Arc-Tooth-Trace(VH-CATT)gears using the optimized Kriging model was developed.We then examined how different gear parameters affect the VH-CATT gears’contact stress.Our simulation results show:(1)Improvements in R2,RMSE,and RMAE.R2 rose from0.9852 to 0.9974(a 1.22%increase),nearing 1,suggesting the optimized Kriging Metamodel’s global error is minimized.Meanwhile,RMSE dropped from3.9210 to 1.6492,a decline of 57.94%.The global error of the GA-IQPSO-Kriging algorithm was also reduced,with RMAE decreasing by 58.69%from 0.1823 to 0.0753,showing the algorithm’s enhanced precision.In a comparison of ten experimental groups selected randomly,the GA-IQPSO-Kriging and FEM-based contact analysis methods were used to measure contact stress.Results revealed a maximum error of 12.11667 MPA,which represents 2.85%of the real value.(2)Several factors,including the pressure angle,tooth width,modulus,and tooth line radius,are inversely related to contact stress.The descending order of their impact on the contact stress is:tooth line radius>modulus>pressure angle>tooth width.(3)Complex interactions are noted among various parameters.Specifically,when the tooth line radius interacts with parameters such as pressure angle,tooth width,and modulus,the resulting stress contour is nonlinear,showcasing amultifaceted contour plane.However,when tooth width,modulus,and pressure angle interact,the stress contour is nearly linear,and the contour plane is simpler,indicating a weaker coupling among these factors.

Advancing high-speed train gearbox durability:enhanced bearing load and contact stress through transition from helical to herringbone gears

High-speed trains typically utilize helical gear transmissions,which significantly impact the bearing load capacity and fatigue service performance of the gearbox bearings.This paper focuses on the gearbox bearings,establishing dynamic models for both helical gear and herringbone gear transmissions in high-speed trains.The modeling particularly emphasizes the precision of the bearings at the gearbox's pinion and gear wheels.Using this model,a comparative analysis is conducted on the bearing loads and contact stresses of the gearbox bearings under uniform-speed operation between the two gear transmissions.The findings reveal that the helical gear transmission generates axial forces leading to severe load imbalance on the bearings at both sides of the large gear,and this imbalance intensifies with the increase in train speed.Consequently,this results in a significant increase in contact stress on the bearings on one side.The adoption of herringbone gear transmission effectively suppresses axial forces,resolving the load imbalance issue and substantially reducing the contact stress on the originally biased side of the bearings.The study demonstrates that employing herringbone gear transmission can significantly enhance the service performance of high-speed train gearbox bearings,thereby extending their service life.

Loaded multi-tooth contact analysis and calculation for contact stress of face-gear drive with spur involute pinion

The analytical method based on "Hertz theory on normal contact of elastic solids" and the numerical method based on finite element method (FEM) calculating the contact stress of face-gear drive with spur involute pinion were introduced, and their relative errors are below 10%, except edge contact, which turns out that these two methods can compute contact stress of face-gear drive correctly and effectively. An agreement of the localized bearing contact stress is gotten for these two methods, making sure that the calculation results of FEM are reliable. The loaded meshing simulations of multi-tooth FEM model were developed, and the determination of the transmission error and the maximal load distribution factor of face-gear drive under torques were given. A formula for the maximal load distribution factor was proposed. By introducing the maximal load distribution factor in multi-tooth contact zone, a method for calculating the maximal contact stress in multi-tooth contact can be given. Compared to FEM, the results of these formulae are proved to be reliable, and the relative errors are below 10%.

Contact Stress Distribution of a Pear Cam Profile with Roller Follower Mechanism

The problem of this paper is the high contact stress at the point of contact between the cam and the follower.A pear cam and roller follower mechanism were studied and analyzed for different position of the follower and different contact compression load.The objective of this paper is to study the effect of contact compression load on the contact stress distribution of the cam profile at the point of contact.Four different positions of the follower with the cam was considered(0°,90°,180°,and 270°).The theory of circular plate was applied to derive the analytic solution of the contact stress.The numerical simulation had been done using ANSYS Ver.19.2 package to determine the contact stress,while SolidWorks software was used to investigate follower displacement,velocity,and acceleration.Four distinct values of the compression contact load,such as 3.121 N,6.242 N,9.364 N,and 12.485 N,were used in the numerical simulation.In the experiment setup,a photo-elastic technique was carried out in the field of polarized light to exhibit the stress distribution on the cam specimen.The annealed PSM-4 backalate material was used in the experiment setup.The experimental value of contact stress was checked and verified analytically and numerically at the point of contact.The innovation in this paper the use of spring-damper system which reduce the value of contact stress at the point of contact.The contact stress was maximum 2.136 MPa when the follower located at 270°with the cam,while the contact stress was minimum 1.802 MPa when the follower located at 180°at compression load 12.485 N.

Hybrid Method to Analyze Contact Stress Distribution on Dry Friction Interfaces

A hybrid method is established by combining photoelastic experiment and finite element analysis.The method is used to evaluate contact stress distribution on dry friction interfaces,such as the contact interfaces between shrouds of fan blades and turbine blades.The photoelastic stress frozen experiment method is used to decide the displacement boundary conditions of numerical calculation.Higher accuracy and efficiency of solving problems are improved by the method.Technical difficulty and high cost of experiment are also avoided by the method.Good agreement of the stress distribution by using the hybrid method and experiment is obtained.

Effect of flank angle and friction coefficient on contact stress of turbine rotor

In order to simulate the stress of turbine rotor in aeroengine, based on the ANSYS, the simplification model of the turbine rotor was built up. By applying the simplification model, the contact stress of turbine rotor was computed. The maximum contact stress appears at the chamfer below the flank, which agrees with experiment result. At the same time, the contact stress changing with the flank angle and friction coefficient was calculated, The results show that the contact stress in the flank increases slowly with the increase of flank angle; with the friction coefficient increasing, the contact stress in flank length decreases; the contact stress will not change when the friction coefficient is over 0.25.

CALCULATION OF CONTACT STRESS OF PLASTIC GEARS

A calculation method of contact problem of plastic gears based on three parameter model of viscoelasticity material is presented. In this calculation method, the influence of temperature upon the property of plastics is considered and an iteration process of temperature-elasticity module-friction coefficient is proposed. From the rolling contact problem of two viscoelastic cylinders with parallel axis, a set of normal-tangential contact coupled integral equations is obtained. Through numerical treatment and normal-tangential iteration, the normal contact stress,tangential stress and contact width of plastic gears are acquired.

A MIXED METHOD OF SOLUTION FOR CONTACT STRESSES ON ROLLER

A mixed method of solution for contact stresses on rollers was suggested by the combina- tion of similitude principle.photoelastic method,Hertz's contact theory and numerical calculation.Thus,not only the distribution regularity of axial contact pressure on roller of limited length,but also the three-dimensional solution of stresses in the contact po- sitions may be obtained.An actual example is presented in the paper.It shows that the practical damaged phenomenon in real roller is in agreement with the result of the analysis

Calculating method of contact stress for non-circular gears

According to Hertz theory, the difference of contact stress for non-circular gears and equivalent gears is compared in the paper, a calculating method of contact stress for non-circular gears by using equivalent gears is researched, and computing formulas of power and rotation speed for equivalent gears are deduced. A numerical simulation of contact stress for non-circular gears has also been conducted based on the finite element method. By the comparison of fitting curves, the feasibility of using equivalent gears instead of non-circular gears to calculate the contact stress is testified.

The Influence of the Supporting Wheel Deflection of Large-scale Rotary Kiln on Maximum Contact Stress

The relation between the maximum contact stress ratio and deflection angle is derived from Hertz contact theory when the deflection of rotary kiln supporting wheel happens. According to the analysis of practical example, the maximum contact stress ratio within the deflection range of rotary kiln supporting wheel is listed. The contact stress will increase largely when rotary kiln supporting wheel deflects with little angle, which probably will result in accidents correlating to safety. This will provide theory conference for the design, the operating condition analysis and adjusting of the rotary kiln.

Piezoelectric sensing method for segmental joint contact stress during shield tunnel construction

The emergence of curved shield tunnels poses a significant construction challenge.If the quality of the segment assembly is not guaranteed,many segment cracks and damage will result from the stress concentration.Sensing the contact stresses between segmental joints is necessary to improve the quality of segments assembled for shield tunnel construction.Polyvinylidene difluoride(PVDF)piezoelectric material was chosen for the sensor because it can convert contact stresses into electrical signals,allowing the state of the segmental joints to be effectively sensed.It matches the working environment between the segmental joints of the shield tunnel,where flexible structures such as rubber gaskets and force transfer pads are present.This study proposes a piezoelectric sensing method for segmental joints in shield tunnels and conducts laboratory tests,numerical analyses,and field tests to validate the feasibility of the method.The results indicate that the PVDF film sensor can effectively sense the entire compression process of the gasket with different amounts of compression.The piezoelectric cable sensor can effectively sense the joint offset direction of the gasket.For differently shaped sections,the variation in the force sensed by the piezoelectric cable sensors was different,as verified by numerical simulation.Through the field test,it was found that the average contact stress between the segmental joints was in the range of 1.2–1.8 MPa during construction of the curved shield tunnels.The location of the segmental joints and the type of segment affect the contact stress value.The field monitoring results show that piezoelectric sensing technology can be successfully applied during assembly of the segments for effective sensing of the contact stress.

Investigation into the analysis method for assessing contact stress in joint prosthesis

Contact stress is the important cause of wear and failure of knee joint prostheses implanted in the human body during movement.The calculation of contact stress on joint prostheses is often inaccurate due to the deviation of joint position during activity.This paper proposes a correction method for contact stress based on finite element results.Firstly,the contact stress and contact radius between femoral and tibial prostheses of knee joint were calculated and analyzed by Hertz contact theory.Then,individualized finite element models based on the individualized geometry of the joint prosthesis and individualized loading were constructed,and the finite element contact stress was analyzed.The finite element results were calibrated utilizing the Hertz contact theory.Additionally,this study investigated the impact of three gait patterns(normal gait,medial thrust gait,and bouncing gait)on the contact stress experienced by the tibial insert.The research methods and results can provide ideas for theoretical analysis and finite element simulation of prosthetic joint contact,as well as offer theoretical support and analysis methods for evaluating the lifespan of prosthetic joints.

Contact stress non-uniformity of wafer surface for multi-zone chemical mechanical polishing process

A finite element analysis(FEA)model is developed for the chemical-mechanical polishing(CMP)process on the basis of a 12-in five-zone polishing head.The proposed FEA model shows that the contact stress non-uniformity is less dependent on the material property of the membrane and the geometry of the retaining ring.The larger the elastic modulus of the pad,the larger contact stress non-uniformity of the wafer.The applied loads on retaining ring and zone of the polishing head significantly affect the contact stress distribution.The stress adjustment ability of a zone depends on its position.In particular,the inner-side zone has a high stress adjustment ability,whereas the outer-side zone has a low stress adjustment ability.The predicted results by the model are shown to be consistent with the experimental data.Analysis results have revealed some insights regarding the performance of the multi-zone CMP.

Effect of friction on the contact stress of a coated polymer gear

Polymer gears are used extensively in various applications.However,durability issues have been emerging because of friction at gear tooth contact areas.To extend the lifetime of polymer gears,a low-frictional coating has been considered as a possible strategy.In this study,a finite element simulation method was performed to investigate the contact stress between a pair of coated polymer gears.The simulation included various friction coefficients(COFs)for studying the effects of friction during the operation.Numerical results revealed that the friction causes the contact stress to shift over the roll angle,which is attributed to the direction of the sliding friction based on a free-body diagram.We also investigated the effects of coating and found that a thin coating has little effect on the bulk deformation behavior of the gear.Moreover,the stress distribution in the coating at the pitch point was investigated as the COF increased.Under zero friction,three notable stress regions were observed:1)the center of the surface,2)the end of the contact,and 3)the overall contact area.As COF was increased in the micro-slip region of the contact interface,both tensile and compressive stresses in the coating increased.This study provides significant aid to engineers for understanding the stress response of the coating applied to polymer gears to achieve an optimal design.

Subloading-friction model with saturation of tangential contact stress

The incorporation of the saturation of the tangential contact stress with the increase of the normal contact stress is required for the analysis of the friction phenomenon of solids and structures subjected to a high normal contact stress,which cannot be described by the Coulomb friction condition,in which the tangential contact stress increases linearly with the increase of the normal contact stress.In this article,the subloading-friction model,which is capable of describing the smooth elastic-plastic transition,the static-kinetic transition,and the recovery of the static friction during the cease of sliding,is extended to describe this property.Further,some numerical examples are shown,and the validity of the present model will be verified by the simulation of the test data on the linear sliding of metals.

STUDY ON LOADS AND CONTACT STRESSES FOR TOROIDAL DRIVE

The load distribution and calculating formulae of the contact stresses in the rotor worm and stator helical surface for toroidal drive are given. The effecting factors on contact stresses and their effects are analyzed. The results is useful for reference purposes in manufacture and design of the drive.

CONTACT FRICTION ANALYSIS AND STRESS OSCILLATION SUPPRESSION WITH A SIMPLE INTERFACE ELEMENT

A simple interface element for analyzing contact friction problems is developed. Taking nodal displacements and contact stresses as unknowns, this element can simulate frictional slippage, decoupling and re-bonding of two bodies initially mating or having gaps at a common interface. The method is based on the Finite Element Method and load incremental theory. The geometric and static constraint conditions on contact surfaces are treated as additional conditions and are included in stiffness equations. This simple element has the advantages of easy implementation into standard finite element programs and fast speed for convergence as well as high accuracy for stress distribution in interface. Undesirable stress oscillations are also investigated whenever large stress gradients exist over the contact surfaces. Exact integration or the conventional Gauss integration scheme used to evaluate the interpolation function matrix of the interface element is found to be the source of the oscillations. Eigenmode analysis demonstrates that the stress behavior of an interface element can be improved by using the Newton-Cotes integration scheme. Finally, the test example of a strip footing problem is presented.

Analysis and Numerical Simulation of Rolling Contact between Sphere and Cone

In non-conforming rolling contact, the contact stress is highly concentrated in the contact area. However, there are some limitations of the special contact model and stress model used for the theoretical study of the phenomenon, and this has prevented in-depth analysis of the associated friction, wear, and failure. This paper is particularly aimed at investigating the area of rolling contact between a sphere and a cone, for which purpose the boundary is determined by the Hertz theory and the geometries of the non-conforming surfaces. The phenomenon of stick-slip contact is observed to occur in the contact area under the condition of no-full-slip（Q 〈 μ·P）. Using the two-dimensional rolling contact theory developed by CARTER, the relative positions of the stick and slip regions and the distribution of the tangential force over the contact area are analyzed. Furthermore, each stress component is calculated based on the Mc Ewen theory and the idea of narrow band. The stress equations for the three-dimensional rolling contact between the sphere and the cone are obtained by the principle of superposition, and are used to perform some numerical simulations. The results show that the stress components have a large gradient along the boundary between the stick and slip regions, and that the maximum stress is inversely proportional to the contact coefficient and proportional to the friction coefficient. A new method for investigating the stress during non-classical three-dimensional rolling contact is proposed as a theoretical foundation for the analysis of the associated friction, wear, and failure.

Effects of Service Condition on Rolling Contact Fatigue Failure Mechanism and Lifetime of Thermal Spray Coatings——A Review

The service condition determines the Roiling Contact Fatigue（RCF） failure mechanism and lifetime under ascertain material structure integrity parameter of thermal spray coating. The available literature on the RCF testing of thermal spray coatings under various condition services is considerable; it is generally difficult to synthesize all of the result to obtain a comprehensive understanding of the parameters which has a great effect on a thermal spray coating＇s resistance of RCF. The effects of service conditions（lubrication states, contact stresses, revolve speed, and slip ratio） on the changing of thermal spray coatings＇ contact fatigue lifetime is introduced systematically. The effects of different service condition on RCF failure mechanism of thermal spray coating from the change of material structure integrity are also summarized. Moreover, In order to enhance the RCF performance, the parameter optimal design formula of service condition and material structure integrity is proposed based on the effect of service condition on thermal spray coatings＇ contact fatigue lifetime and RCF failure mechanism. The shortage of available literature and the forecast focus in future researches are discussed based on available research. The explicit result of RCF lifetime law and parameter optimal design formula in term of lubrication states, contact stresses, revolve speed, and slip ratio, is significant to improve the RCF performance on the engineering application.

Stress-deformed state of cylindrical specimens during indirect tensile strength testing

In this study, the interaction between cylindrical specimen made ofhomogeneous, isotropic, and linearlyelastic material and loading jaws of any curvature is considered in the Brazilian test. It is assumed thatthe specimen is diametrically compressed by elliptic normal contact stresses. The frictional contactstresses between the specimen and platens are neglected. The analytical solution starts from the contactproblem of the loading jaws of any curvature and cylindrical specimen. The contact width, correspondingloading angle （2 ^0）, and elliptical stresses obtained through solution of the contact problems are used asboundary conditions for a cylindrical specimen. The problem of the theory of elasticity for a cylinder issolved using Muskhelishvili＇s method. In this method, the displacements and stresses are represented interms of two analytical functions of a complex variable. In the main approaches, the nonlinear interactionbetween the loading bearing blocks and the specimen as well as the curvature of their surfacesand the elastic parameters of their materials are taken into account. Numerical examples are solved usingMATLAB to demonstrate the influence of deformability, curvature of the specimen and platens on thedistribution of the normal contact stresses as well as on the tensile and compressive stresses actingacross the loaded diameter. Derived equations also allow calculating the modulus of elasticity, totaldeformation modulus and creep parameters of the specimen material based on the experimental data ofradial contraction of the specimen.