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%.

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.

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.

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.

Precise Design and Stress Analysis of Straight Conical Gear

Variable section sweeping with sphere involutes is used to generate the precise model of tooth profile. The contact and bending stress of a straight conical gear set with static bearing contact during a meshing cycle is studied using finite element method. Numerical results and comments are presented, revealing that the edge contact causes stress concentration and the gear tooth profile needs further modification.

Interfacial friction effects on sealing performances of elastomer packer

Elastomer sealing performance is of critical importance for downhole tools application including the use of fracturing(Frac)plugs during multi-stage hydraulic fracking.In practice sealing performances of such plugs are normally evaluated through pressure tests,and in numerical simulation studies,maximum contact stress,average contact stress and contact length data are used to determine sealing quality between a packer and casing.In previous studies,the impact of friction forces on sealing performance is often overlooked.This work aims to fill this knowledge gap in determining the influence of friction forces on elastomer packer sealing performances.We first determined the most appropriate constitutive hyperelastic model for the elastomers used in frac plug.Then we compared analytical calculation results with Finite Element Analysis simulation using a simplified tubular geometry and showed the significant influences on interfacial friction on elastomer packer stress distribution,deformation,and contact stress after setting.With the demonstration of validity of FEA method,we conducted systematic numerical simulation studies to show how the interfacial friction coefficients can affect the maximum contact stress,average contact stress,contact stress distribution,and maximum mises stress for an actual packer used in plug products.In addition,we also demonstrated how the groove in a packer can affect packer deformation and evolvement during setting with the consideration of interfacial stress.This study underscores the critical role that friction forces play in Frac plug performance and provides a new dimension for optimizing packer design by controlling interfacial interactions at the packer contact surfaces.

Study on Sealing Characteristics of Sliding Seal Assembly of Aircraft Hydraulic Actuator

The hydraulic actuator,known as the"muscle"of military aircraft,is responsible for flight attitude adjustment,trajectory control,braking turn,landing gear retracting and other actions,which directly affect its flight efficiency and safety.However,the sealing assembly often has the situation of over-aberrant aperture fit clearance or critical over-aberrant clearance,which increases the failure probability and degree of movable seal failure,and directly affects the flight efficiency and safety of military aircraft.In this paper,the simulation model of hydraulic actuator seal combination is established by ANSYS software,and the sealing principle is described.The change curve of contact width and contact pressure of combination seal under the action of high-pressure fluid is drawn.The effects of different oil pressure,fit clearance and other parameters on the sealing performance are analyzed.Finally,the accelerated life test of sliding seal components is carried out on the hydraulic actuator accelerated life test rig,and the surface morphology is compared and analyzed.The research shows that the O-ring is the main sealing element and the role of the check ring is to protect and support the O-ring to prevent damage caused by squeezing into the fit clearance,so the check ring bears a large load and is prone to shear failure.Excessive fit clearance is the main factor affecting the damage of the check ring,and the damage parts are mainly concentrated at the edge of the sealing surface.This paper provides a theoretical basis for the design of hydraulic actuator and the improvement of sealing performance.

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.

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.

Tooth surface geometry optimization of spiral bevel and hypoid gears generated by duplex helical method with circular profile blade

In order to effectively improve meshing performance of spiral bevel and hypoid gears generated by the duplex helical method, the effects of straight lined and circular cutting edges profile on meshing and contact of spiral bevel and hypoid gears were investigated analytically. Firstly, a mathematical model of spiral bevel and hypoid gears with circular blade profile was established according to the cutting characteristics of the duplex helical method. Based on a hypoid gear drive, the tooth bearings and the functions of transmission errors of four design cases were analyzed respectively by the use of the tooth contact analysis(TCA), and the contact stresses of the four design cases were analyzed and compared using simulation software. Finally, the curvature radius of the circular profile blade was optimized. The results show that the contact stresses are availably reduced, and the areas of edge contact and severe contact stresses can be avoided by selecting appropriate circular blade profile. In addition, the convex and concave sides are separately modified by the use of different curvature radii of inside and outside blades, which can increase the flexibility of the duplex helical method.

Optimal rotor wear design in hypotrochoidal gear pump using genetic algorithm

The wear rate between the rotors of a hypotrochoidal gear pump is characterized.Using the knowledge of shape design on the rotors,the contact stresses without hydrodynamic effect between the rotor teeth were evaluated through the calculation of the Hertzian contact stress.Based on the above results and the sliding velocity between the rotors,a genetic algorithm (GA) was used as an optimization technique forminimizing the wear rate proportional factor (WRPF).The result shows that the wear rate or the WRPF can be reduced considerably,e.g.approximately 12.8%,throughout the optimization using GA.

Contact Mechanism of Rail Grinding with Open-Structured Abrasive Belt Based on Pressure Grinding Plate

The current research of abrasive belt grinding rail mainly focuses on the contact mechanism and structural design.Compared with the closed structure abrasive belt grinding,open-structured abrasive belt grinding has excellent performance in dynamic stability,consistency of grinding quality,extension of grinding mileage and improvement of working efficiency.However,in the contact structure design,the open-structured abrasive belt grinding rail using a profiling pressure grinding plate and the closed structure abrasive belt using the contact wheel are different,and the contact mechanisms of the two are different.In this paper,based on the conformal contact and Hertz theory,the contact mechanism of the pressure grinding plate,abrasive belt and rail is analyzed.Through finite element simulation and static pressure experiment,the contact behavior of pressure grinding plate,abrasive belt and rail under single concentrated force,uniform force and multiple concentrated force was studied,and the distribution characteristics of contact stress on rail surface were observed.The results show that under the same external load,there are three contact areas under the three loading modes.The outer contour of the middle contact area is rectangular,and the inner contour is elliptical.In the contact area at both ends,the stress is extremely small under a single concentrated force,the internal stress is drop-shaped under a uniform force,and the internal stress under multiple concentration forces is elliptical.Compared with the three,the maximum stress is the smallest and the stress distribution is more uniform under multiple concentrated forces.Therefore,the multiple concentrated forces is the best grinding pressure loading mode.The research provides support for the application of rail grinding with open-structured abrasive belt based on pressure grinding plate,such as contact mechanism and grinding pressure mode selection.

Modeling and application of thermal contact resistance of ball screws

Aiming at determining the thermal contact resistance of ball screws,a new analytical method combining the minimum excess principle with the MB fractal theory is proposed to estimate thermal contact resistance of ball screws considering microscopic fractal characteristics of contact surfaces.The minimum excess principle is employed for normal stress analysis.Moreover,the MB fractal theory is adopted for thermal contact resistance.The effectiveness of the proposed method is validated by self-designed experiment.The comparison between theoretical and experimental results demonstrates that thermal contact resistance of ball screws can be obtained by the proposed method.On this basis,effects of fractal parameters on thermal contact resistance of ball screws are discussed.Moreover,effects of the axial load on thermal contact resistance of ball screws are also analyzed.The conclusion can be drawn that the thermal contact resistance decreases along with the fractal dimension D increase and it increases along with the scale parameter G increase,and thermal contact resistance of ball screws is retained almost constant along with axial load increase before the preload of the right nut turns into zero in value.The application of the proposed method is also conducted and validated by the temperature measurement on a self-designed test bed.