混合式陶瓷轴承沟道结构参数的简化算法

以目前钢轴承的结构参数合理正确和轴承滚动体与内外圈滚道在相同的接触应力及接触面积作用下具有相近的接触疲劳寿命及发热为前提 ,以相同负荷作用下 ,混合式陶瓷球轴承与相应钢轴承的接触应力和接触面积相等为依据 ,给出了混合式陶瓷球轴承内外圈沟道结构参数的简化计算方法。以 6 2 0 9深沟球轴承为例 ,对相应的混合式陶瓷球轴承的沟道曲率半径进行了计算 ,以计算结果制造的混合式陶瓷球轴承的运转性能完全能够满足使用要求     

Spindle deflections in high-speed machine tools — Modelling and simulation

This research attempts to develop spindle deflection error models for high-speed machining systems. A model for determining total spindle deflection at the tool-end is presented. The model incorporates spindle bearing characteristics, shifts in ball contact angles, and centrifugal force and gyroscopic moment effects at high speeds. It uses the transfer matrix method to determine the total deflections at the tool-end based upon the point contact deformations at the individual balls of an angular contact ball-bearing assembly. A simulator is also developed for simulating spindle end deflections for various spindle rotational speeds. The results of the simulation show contact angle variations and peak deflections at particular spindle rotational speeds. Important research issues are also presented.Nomenclature AF final position, inner raceway groove centre - RF initial position, inner raceway groove centre - W final position of ball centre - V initial position of ball centre - D ball diameter, mm - r _o inner raceway groove radius, mm - r _i inner raceway groove radius, mm - M gyroscopic moment, N-mm - FO r _o/D - FI r _i/D - P bearing pitch diameter, mm - K _o outer race load-deflection constant, N/mm^1.5 - K _i inner race load-deflection constant, N/mm^1.5 - CF centrifugal force, N - J mass moment of inertia, N.mm² - l length of spindle, mm - E modulus of elasticity, N/mm² - I moment of inertia of spindle, mm⁴ - Y deflection of spindle alongy-direction, mm - z deflection of spindle alongz-direction, mm - M moment at spindle end, N.mm - V shear force at spindle end, N - m spindle mass, kg - material density - _o outer race contact angle - _i inner race contact angle - nominal contact angle - _i inner race deformation - _o outer race deformation - angle between ball centre of rotation and the horizontal - mis-alignment (in degrees) of shaft assembly measured in a plane perpendicular to shaft axis (x-direction) - W1 ball and raceway angular raceway velocity ratio for outer raceway control - W2 ball orbital and angular raceway velocity ratio for rotating inner raceway and outer raceway control - circumferential ball position - raceway control parameter     

滚动直线导轨副的滚道中心距误差与承载性能的关系

静刚度和摩擦力作为导轨副关键承载性能指标,直接影响导轨副的运动精度及工作状态。基于赫兹接触理论,建立了滚道中心距误差与导轨副摩擦力和静刚度的模型,并结合理论计算模型与控制变量试验研究了导轨、滑块滚道中心距误差及滚珠过盈量对承载性能的影响规律,对比分析了滚道中心距不同误差情况下的摩擦力和静刚度。研究结果表明,静刚度相对误差为2.46%～8.20%,摩擦力相对误差为0.42%～11.33%。理论仿真值和试验实测值的一致性较好。     

High-precision radius measurement of ball indenter

To solve the problem of calibrating the radius of a ball indenter in a hardness tester, a laser confocal radius measurement and calibration method for the ball indenter is proposed without separating the ball from the body of the indenter. The laser confocal radius measurement and calibration method uses the maximum of the confocal axial intensity curve to precisely identify the cat’s eye and confocal position of the test ball indenter. The distance between these two positions is then measured to achieve high-precision radius measurement. The theoretical analyses and experimental results indicate that the radius measurement uncertainty of the ball indenter with a diameter of 1.5875 mm is within 0.12 μm.     

Kinematical analyses and transmission efficiency of a preloaded ball screw operating at high rotational speeds

High rotational speeds in ball screws (greater than 1000 rpm) cause more slip motion between balls and raceways than slower speeds. This increase in the slip motion increases the friction at the contact area, thus increasing the driving torque required for a high-speed ball screw. Theoretical analyses of the kinematics of a preloaded single-nut, double-cycle ball screw operating at high rotational speeds are presented in this study. The mechanical efficiency obtained from the theoretical driving torque, axial load and the orbital angular speeds of the ball was confirmed with experimental data. The slipping-rolling behaviour of each contact area was well developed from the distribution of stagnation lines consisting of pure-rolling points. Increasing the initial contact angle can significantly reduce the distance between the pure-rolling point and contact centre and decrease the driving torque, especially when the operating axial load approaches the applied preload. The mechanical efficiency can thus be increased, and wear may also be avoided by reducing the slip motion occurring at contact areas between balls and raceways.     

Rolling-Sliding Analysis in Ball Bearing Considering Thermal Effect

An analytical method is applied in the calculations of ball contact angles varying with the position angle of a ball bearing with a centrifugal force. This is further extended to investigate the thermal slipping behavior occurring at the contact surface of the inner raceway. The sliding velocities at the contact area are analyzed in the present study by the ball bearing contact mechanisms. The shear stress created at this contact surface is evaluated by considering the temperature-pressure dependence of the lubricant viscosity. The contact temperature of a ball and the inner raceway is obtained if the frictional heat created by the shear stress is available. Under the condition of controlling the outer raceway temperature, the thermal deformations of all components of a ball bearing are taken into account in the evaluation of bearing performance. Comparisons are made for several parameters, including the normal load, linear slip velocity, and linear traction force, between the results of considering the thermal effect or ignoring it. The friction torque evaluated by taking the thermal effect into account is higher than the torque evaluated when ignoring the thermal effect.     

几何误差和倾覆力矩对双螺母滚珠丝杠副载荷分布的影响#br#

建立了一种考虑几何误差（滚珠尺寸误差、丝杠导程误差和滚道齿形误差）和倾覆力矩的双螺母滚珠丝杠副载荷分布模型;通过试验测得4010型滚珠丝杠副的力与位移变形曲线,验证了理论模型的正确性;通过仿真分析研究了轴向外载荷、几何误差和倾覆力矩对双螺母滚珠丝杠副载荷分布的影响。研究结果表明：轴向外载荷一定时,倾覆力矩会导致双螺母滚珠丝杠副的载荷分布迅速变差;滚珠尺寸误差和滚道齿形误差会使双螺母滚珠丝杠副中滚珠的受载显著增大或减小;由于丝杠轴向误差累计的作用,导程误差会使双螺母滚珠丝杠副中一侧螺母受载增大,另一侧螺母受载减小;在误差大小一定的情况下,导程误差对载荷分布的影响程度大于尺寸误差和齿形误差,即双螺母滚珠丝杠副的载荷分布对导程误差的敏感度更高。     

全陶瓷球轴承套圈沟道精密磨削用砂轮修整试验

为提高金刚石圆弧砂轮外缘轮廓精度,减少全陶瓷球轴承套圈沟形误差,采用金刚石碟片对树脂基金刚石圆弧砂轮进行修整;对比修整前后砂轮的表面形貌及套圈沟形误差,验证砂轮的修整效果.修整后砂轮表面出现光泽,露出表面的金刚石磨粒明显增多,部分金刚石磨粒破碎,形成新切削刃或脱落,增大容屑空间;修整前沟形误差的平均值为5.823μm,...     

一种四点接触球轴承桃形沟参数测量方法

基于四点接触球轴承桃形沟沟道与球的位置关系,提出了一种沟道参数间接测量方法,解决了桃形沟沟曲率半径和沟曲率中心偏心距的测量问题,利用SolidWorks的尺寸驱动功能对上述方法进行了反向验算,结果具有较高的准确度.     

关于深沟球轴承沟曲率半径系数的选取

在不考虑轴承游隙的基础上,对深沟球轴承几何参数及接触应力分析,根据极限应力的计算方法,绘制了不同沟曲率半径系数时的Coe曲线图,并说明了如何根据该图选取沟曲率半径系数。     

丝杠支撑专用双列角接触球轴承外圈沟道精度检测方法

针对丝杠支撑专用双列角接触球轴承外圈沟道接近半沟型,现有测量技术无法准确测量沟道位置及两沟间距问题,应用轴承高度测量仪,通过制作标准样圈,分别测量轴承外圈两端单边装配高并控制在工艺设定范围内,间接实现轴承沟道位置、直径和沟心距形成的轴承成品组装综合影响因素良好控制,从而保证轴承总体装配精度。     

滚道曲面几何参数对球轴承性能影响的数值研究

为探讨深沟球轴承内外滚道与滚动体之间的配合曲面的几何形状对轴承性能的影响,采用数值模拟的方法研究了球与圆弧曲面接触的弹流润滑问题,并讨论了外滚道曲面的两种曲率半径对深沟球轴承有关摩擦学性能的影响。结果表明,在载荷不变的情况下,随着滚道横向曲率半径的增大,二次压力峰值逐渐减小,最小油膜厚度先是增加然后减小,存在最大值;而随着滚道圆周滚动方向曲率半径的增大,油膜厚度不断减小,说明滚道圆周滚动方向上的曲率半径小时具有更好的润滑状态。     

球笼式等速万向节三点接触沟道的设计分析

提出一种三点接触沟道截面形式的球笼式等速万向节,其钟形壳外沟道的沟道截面形式为圆弧沟道,星形套内沟道的沟道截面形式为椭圆沟道或双心弧沟道.对其内、外沟道结构进行设计,并利用Hertz接触理论进行接触应力的计算.结果表明,三点接触沟道能减小内、外沟道接触应力,改善其内部接触状况.     

深沟球轴承的载荷分布与刚度特征研究

采用有限元法计算了"奇压"与"偶压"两种受载形式下深沟球轴承的静力学响应。对比讨论了轴承内接触应力分布、轴承变形及刚度的变化特征。结果表明当外载荷达到某一值时,关键滚动体与外圈滚道接触中心的接触应力明显大于与内圈滚道接触中心的接触应力,并随着载荷的增加,这个趋势越发明显;两种受载形式下,轴承的位移与刚度表现出明显的差异,奇压形式下,轴承的径向位移小于偶压形式下的径向位移,而奇压形式下的轴承刚度则大于偶压形式下的刚度;相同载荷作用下,静力学方法计算的轴承径向位移小于有限元法计算结果。     

基于圆心约束最小二乘圆拟合的短圆弧测量方法

坐标测量中通常采用最小二乘法拟合几何元素。测量短圆弧时,由于特征点数少,受到的噪声干扰大,测量精度难以保证。本文针对基于机器视觉系统的短圆弧测量,分析了采用最小二乘法多点测圆时,圆弧中心角对圆心及半径测量误差的影响,提出了圆心约束最小二乘圆拟合方法。利用本文的方法测量理论半径10mm,中心角20°的短圆弧,测量误差小于0.01mm。对比实验表明,利用圆心约束最小二乘圆拟合法测量短圆弧能有效提高拟合精度。     

Quasi-static Analysis of Thrust-loaded Angular Contact Ball Bearings Part Ⅱ:Results and Discussion

Ball bearings are widely employed mechanical components characterized by high precision and quality,and usually play important roles in various rotary machines and mechanisms.Many advanced applications require a deep understanding of their various kinematic and tribological characteristics that are essential to predict the fatigue endurance,relieve the vibration and minimize the power dissipation of ball bearings in particular applications.An angular contact ball bearing under a specified operating condition is simulated with the quasi-static/creepage analytical model proposed in the preceding article.The results demonstrate that the ball bearing is a statically determinate system.That the balls spin on both inner and outer races means the ball is controlled by neither the inner nor the outer raceway.The friction between the ball and raceway renders the inner and outer contact angles unequal.The larger the coefficient of friction is,the larger the angle deviation.The tangential traction perpendicular to the rolling direction due to the spin induces a gyro-like rotation of the ball with respect to the raceway even if no inertial effects are considered.The tangential elastic compliance of contacting surfaces gives rise to locked areas within the contact patch and transforms the sliding lines from circles into spirals.The differential slip due to the close conformity of the ball and raceway makes the sliding and traction distributions asymmetric,which will influence the location of the spinning center of the ball with respect to the raceway.The quasi-static/creepage model can be used to reveal the operating behaviors of ball bearings running under steady conditions and to optimize the design of ball bearings for specific applications.     

Simulating angular ball bearing lubricated elliptical contacts Film thickness and traction measurements

A high performance barrel and plate apparatus was built to study film formation and traction by simulating the real situation of a lubricated elliptical contact in an angular ball bearing under general kinematic conditions. Simultaneous measurements of load, speed of each surface, traction, and film thickness by optical interferometry can be performed. The sapphire disc plate and the steel barrel are driven independently at constant controlled speeds. Small relative sliding, lateral sliding and spinning near pure rolling conditions can be imposed by controlling barrel shaft angle contact location. Tests were performed at ambient temperature for a small barrel whose principal radii are 1.34 mm and 9.7 mm, for applied loads which generate Hertzian pressures up to 2 × 10⁹ N/m², and for a low viscosity mineral oil. Typical experimental results show that under elasto-hydrodynamic conditions, the centre film thickness is slightly below the values calculated from classical elastohydrodynamic theories and that oil starvation occurs at high speeds. Traction curves versus slide/roll ratio are presented for different loads and under spinning and lateral sliding conditions.     

A new method for determining the preload in a wire race ball bearing

This paper explores a numerical method to calculate the frictionless three-dimensional non-conforming contact problem associated with a wire race ball bearing used in a certain aircraft simulating rotary table, for challenging the conventional method on the determination of the preload magnitude. A computer program based on the Hertz elastic contact theory and a mathematical model of two critical loading conditions was performed in MATLAB^® by using an example of a wire race ball bearing having an approximately 900 mm diameter. The normal contact forces, the contact deformation, the maximum contact pressure, the semi-major axes and the semi-minor axes of contact ellipses of the ball-wire race were computed. The analytic results show that the overturning moment, the pitting corrosion and the shear failure due to combined stresses can be avoided by controlling preload values in the range 11.3–169.9 μm. The experimental results are closely in agreement with the theoretical results, and verify the availability of the numerical method. The research provides theoretical support for the development and further application of wire race ball bearings with large diameters.     

Rolling contact fatigue using solid thin film lubrication

This paper addresses rolling contact fatigue (RCF) testing in ultra high vacuum (UHV) under high speed conditions. A ball–rod RCF test platform has been adapted for testing in UHV conditions that allows rapid accumulation of stress cycles, over 10 million cycles within 5 h of testing at 130 Hz rotation. The UHV environment and solid lubrication enables good vibration detection for the onset of spall. In this paper, approximately 0.2 μm of silver is applied to the balls and provides sufficient lubrication for up to 25 h of testing, or 50 million stress cycles in high vacuum at 130 Hz. Seventy-nine RCF tests using thin-film silver lubrication have been completed covering two ball sizes, and two rod and ball materials. 9.53 mm diameter Rex 20 steel and silicon-nitride (Si₃N₄) rods were tested against 7.94 mm diameter Rex 20 and 12.7 mm diameter M50 steel balls. It was found that ball size and material hardness did not affect the stress cycle life over a Hertzian contact stress range of 2.1–4.2 GPa and Rockwell C hardness range of 62–77. Rather, the key limiter to test length is lubrication depletion based on 79 tests and an average silver thickness of 0.2 μm. One of the two failure modes were observed for all tests: (i) early life spall of the silver coating, and (ii) depletion of silver lubrication followed by spall failure of both the ball and rod surfaces. A third-body storage model along with the Control Volume Fraction Coverage (CVFC) assumption and analysis was used to predict lubrication availability between asperities on the third body. There is good agreement between calculated and measured post-test lubrication thickness using the third-body storage model.     

高速角接触球轴承中的冲击滑动研究

高速角接触球轴承中,球与保持架的碰撞会导致球与滚道的冲击滑动,从而引起滚道划伤和轴承早期失效。为探究球与保持架的冲击碰撞导致的瞬时滑动,以某高速角接触球轴承为研究对象,通过对联合载荷下角接触球轴承的动力学仿真,分析了变速工况及保持架结构参数对球与保持架的冲击碰撞、球与滚道的冲击滑动以及零件磨损率的影响。结果发现,加减速及恒定转速下,球与保持架的运动呈现周期性变化;由于球进入和离开径向载荷区域时公转角速度的变化,球与保持架碰撞并导致球相对内、外圈滚道发生冲击滑动;为适应球公转角速度的变化,适当增大兜孔间隙,可以减小球与保持架兜孔碰撞力的大小和频率,从而减小球与滚道的冲击滑动以及保持架的磨损率。