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 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.

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.

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.

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.

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.

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.

超高压压裂管汇由壬接头预紧特性分析

针对超高压压裂管汇由壬接头安装预紧力不当导致结构破坏或密封泄漏的问题,以某公司研制的175 MPa超高压由壬接头为研究对象,利用ABAQUS建立由壬接触模型,采用有限单元法对该接头进行应力分析与强度评定以及密封性能判定。结果表明:预紧力大小对母由壬应力几乎没有影响,对公由壬、翼型螺母和三瓣挡圈应力有显著影响,且都呈现正相关性,影响程度从高到低依次为公由壬、翼型螺母、三瓣挡圈和母由壬;额定工况下预紧力超过250 kN时,公由壬轴肩圆角处应力超过其材料许用应力,结构静强度不满足要求可能会发生结构破坏;预紧力小于150 kN时,不足以抵抗内压作用,公由壬和母由壬球头锥面密封结构分离;在能够确保球头锥面密封性和结构安全性的150~250 kN预紧力范围内,氢化丁腈橡胶(HNBR)密封圈表面接触应力始终大于实时流体工作压力,密封圈密封性能良好。推荐安装预紧力范围为150~250 kN,在该范围内密封圈结构的静强度以及密封性均能满足要求。

接触问题的三角形载荷离散FFT加速算法

接触问题控制方程的有效求解,往往涉及到复杂的数学理论知识,而在实际工程应用中,接触应力分布又具有高度随机性。为高效快速求解任意载荷分布下固体的接触响应,基于三角形载荷离散单元,嵌入离散卷积快速傅里叶变换(DC-FFT)算法,提供了一种高精度、高可靠度的计算方法。相比于通常采用的分段均布载荷离散方法,三角形单元的解析求解略显复杂,但能更好地模拟接触载荷任意分布的特性,对于接触边缘处载荷由零递增或递减为零的情况,也可以予以充分考虑。为优化三角形载荷离散单元的求解方法,根据接触影响系数矩阵的“激励-响应”特性,推导了三角形载荷单元和均布载荷单元作用下的应力分量解析解。通过构造包含影响系数矩阵的离散卷积形式应力解,将某一目标节点在所有载荷单元作用下,重复度极高的矩阵运算叠加过程,采用DC-FFT算法来简化加速计算。通过程序编程计算,分析验证了所提出算法的精确度和高效性。

基于分形理论的变齿厚齿轮接触应力分析

为了更准确地反应变齿厚齿轮齿面真实接触应力,构建了变齿厚齿轮的齿面接触系数,并对其合理性进行了验证。基于分形接触理论和Hertz接触理论建立了综合考虑齿轮齿面粗糙形貌、接触点弹性变形、材料特性等参数的变齿厚齿轮接触模型,计算变齿厚齿轮的接触强度,并与有限元计算结果进行比较,验证了方法的有效性。通过分形理论得出齿轮啮合时载荷与面积的关系,并对4个基本参数进行仿真,分析分形接触模型的效果。结果表明,通过数值模拟和分析实际接触面积与载荷的关系图,验证了分形接触模型的准确性。基于有限元理论、Hertz接触理论和分形理论,对变齿厚齿轮的齿面接触强度进行了比较和分析,验证了分形接触模型计算变齿厚齿轮接触应力的正确性,该模型的建立为变齿厚齿轮的设计与强度校核提供了一定的理论依据。

具有圆度误差的径向金属密封接触应力研究

由于加工圆度误差的影响,井下流量控制阀径向金属密封接触应力分布不均匀,从而影响密封性能。利用有限元方法研究具有圆度误差的径向金属密封唇部接触应力分布,并分析圆度误差对径向金属密封接触应力的影响;基于有限元分析结果提出径向金属密封接触应力分布的理论解析式,并进行误差分析。具有圆度误差的径向金属密封唇部接触应力分布的理论解与数值解相符,各参数引起的最大接触应力的平均相对误差约为10%。根据具有圆度误差的径向金属密封副接触应力的分布规律,提出合理的过盈量函数,修正了径向金属密封轴对称结构的悬臂梁模型的接触应力理论关系式,得出了圆度误差下的径向金属密封接触应力分布规律。研究结果为井下流量控制阀径向金属密封的设计提供了理论指导。

埋头弹步枪导轨曲线槽的设计分析

为研究不同导轨曲线槽形状对埋头弹步枪导轨-弹膛机构运动特性以及弹膛突耳与导轨曲线槽接触力的影响,以某中口径埋头弹步枪为对象,基于一次函数、二次函数、三次函数和五次多项式函数设计了4种导轨曲线槽,建立了相应的导轨-弹膛机构的三维模型,采用Adams建立了导轨-弹膛机构的虚拟样机模型,利用Abaqus建立了导轨-弹膛机构有限元模型,并进行了仿真研究与分析。仿真结果表明:选用不同导轨曲线槽时,活动弹膛升降速度、导轨曲线槽与突耳间的接触力、以及导轨曲线槽的接触应力明显不同,最大接触应力主要分布在导轨曲线槽起始位置和终止位置;选择五次多项式函数作为导轨轮廓曲线时,导轨曲线槽起始位置和终止位置的接触应力较其他导轨曲线槽的接触应力小。

深水测试密闭环空压力变化下的封隔器胶筒性能分析

为探讨深水测试双封隔器由密闭环空压力变化引起的变形与强度问题,建立双封隔器胶筒结构的力学分析模型。根据工作过程中封隔器间密闭环空压力的变化,对胶筒的密封性能进行分析,得到各胶筒的应变量、等效应力以及接触应力的变化情况。分析采用胶筒不同圆形倒角参数时封隔器胶筒与套管的接触特性,研究胶筒倒角参数对封隔器密封性能的影响,得出封隔器的优化结构参数。结果显示:各胶筒的应变量、等效应力以及接触应力均随密闭环空压力的增大而增大,其中下胶筒的增大幅度最明显;各胶筒变形量随着胶筒倒角的增大无明显变化,但等效应力随着胶筒倒角的增大均减小,而随着胶筒倒角的增大上胶筒和中胶筒的接触应力均增大,下胶筒的接触应力先增大后减小。因此,一定程度上增大胶筒倒角有利于提升封隔器的密封性能,倒角半径为0.75 mm时为最优结构。

平行轴变齿厚齿轮接触应力解析计算

变齿厚齿轮作为一种新型齿轮,目前尚无成熟的接触应力理论和计算方法。为了从理论上计算变齿厚齿轮齿面上的最大接触应力,了解变齿厚齿轮在不同参数下接触应力的变化情况。文中在赫兹公式的基础上,考虑变齿厚齿轮的几何结构,确定了变齿厚齿轮重合度、曲率半径、法向载荷、接触线长、重合度系数和齿形角系数的计算方法。研究了不同节锥角、齿数、模数和压力角对变齿厚齿轮接触应力的影响,通过有限元分析验证了变齿厚齿轮接触应力理论计算公式的正确性。研究结果表明:推导出的变齿厚齿轮接触应力计算公式具有较高的精度,能够准确地反映齿面的真实接触应力值,为变齿厚齿轮的结构设计、强度校核等提供了一定的依据。

圆柱面结合部接触应力的三维分形模型

为了对机械结构中圆柱结合部的承载能力进行研究,基于Hertz接触理论,并结合修正的三维分形理论,应用三维分形曲面来模拟实际工程中的结合面,在综合考虑宏观特性因素与微观形貌因素的情况下,建立了圆柱结合部接触应力的三维分形模型,并与Hertz接触模型进行了对比分析,证明了所建立模型的合理性。通过Matlab仿真分析得到,从宏观特性因素上,可以选用内接触圆柱结合部,或增大小圆柱体的半径来降低接触应力,提高承载能力;从微观形貌因素上,可以减小分形尺度参数,或减小材料特性参数来降低接触应力。分形维数对接触应力的影响比较复杂:当2.1≤D≤2.5时,增大分形维数,可以降低接触应力;当2.5≤D≤2.9时,减小分形维数,可以降低接触应力。