高速滚珠丝杠副动力学性能分析及其实验研究
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摘要
精密滚珠丝杠副是数控机床的关键功能部件,随着高速切削技术的发展,对滚珠丝杠副的线速度提出了越来越高的要求。滚珠丝杠副的高速化同时带来了振动、噪声和由于摩擦引起的温升等诸多问题,噪声和温升成为制约滚珠丝杠副高速化的关键因素。研究摩擦和噪声等高速滚珠丝杠副的动力学性能,分析影响滚珠丝杠副高速性能的关键因素,为高速滚珠丝杠副的设计和制造提供理论和技术支持,具有重要的理论价值和实际意义。
本文应用接触力学、碰撞力学、弹流动力润滑和结构噪声的理论,结合实验研究了滚珠丝杠副的摩擦力矩和高速下的噪声问题,研究内容主要包括:
1)应用Hertz接触理论,在考虑螺旋升角的情况下,分析了滚珠在工作滚道中的接触特性及各结构参数对接触特性的影响。
2)根据运动学理论,分析滚珠丝杠副中滚珠与丝杠轴之间的运动关系,探讨各结构参数对滚珠自旋和滑移运动的影响。
3)应用Hertz接触模型和牛顿第二定律,建立了滚珠与返向器碰撞的力学模型,设计了测量碰撞接触时间的试验装置。研究分析了碰撞角度、结构和材料参数对碰撞力的影响。分析了滚珠碰撞后的运动变化情况,以及在循环返向滚道中的运动流畅性。
4)根据滚珠丝杠副的结构特点,研究分析了滚珠丝杠副摩擦力矩的产生机理,建立了摩擦力矩的分析模型,分析讨论了滚道制造误差对摩擦力矩的影响。运用弹流动力润滑理论分析滚珠丝杠副的润滑状态,实验研究了导致滚珠丝杠副摩擦力矩低频波动的原因。
5)实验研究了端部偏转式返向结构滚珠丝杠副的噪声特性,分析了其主要噪声与振动之间的联系,通过对滚珠丝杠副径向振动激励频率的计算,确定了端部偏转式高速滚珠丝杠副的主要噪声机理。
理论分析和试验研究表明:
1)滚珠丝杠副中滚珠与丝杠滚道的接触压力和变形大于滚珠与螺母滚道的接触压力和变形。随着接触角的增大,接触压力和变形减小,螺旋升角对接触特性无显著影响,接触特性对曲率比的变化非常敏感,随着曲率比的增大,接触压力和变形显著上升。
2)滚珠丝杠副在正常转速下,滚珠中心的线速度不高,自转速度却相当高;滚珠直径大小对旋滚比影响不大,接触角的变化对旋滚比影响比较明显,在接触角为38°时,旋滚比最小;随着螺旋升角和滚珠直径的增大,滚珠的滑移率增大。
3)碰撞接触时间的测量结果表明,本文建立的滚珠与返向器的碰撞力学模型符合实际情况。碰撞角度越大,初始速度越高,则碰撞力越大,通过减小碰撞角度、采用小直径钢球或陶瓷球、或者采用弹性模量较低的工程塑料制作返向器,可以有效降低碰撞力。返向器的材料应选择弹性模量小、法向恢复系数小,而摩擦特性良好的材料。
4)滚珠丝杠副的滚道加工误差对摩擦力矩的影响具有“平均效应”,制造误差的存在从总体上增大了滚珠丝杠副的摩擦力矩。滚珠丝杠接触副中很难建立起完全弹流油膜,低速下,油膜润滑参数Λ小于1,处于边界润滑状态,润滑不良导致的摩擦系数过大可能是滚珠丝杠副摩擦力矩较大的主要原因。
5)低速下油润滑时,滚珠丝杠副的摩擦力矩较大,内循环和外循环插管式结构滚珠丝杠副的摩擦力矩常出现归一化频率为1Hz的波动,脂润滑时,摩擦力矩较小,而且非常平稳。分析表明,归一化频率为1Hz的波动是由润滑不良引起的滚珠的拥堵和散开所导致的。
6)端部偏转式结构滚珠丝杠副的噪声明显小于插管式丝杠副,且音质有显著改善。其噪声主要频率随丝杠转速的变化而改变,与螺母相连的工作台的振动与滚珠丝杠副的主要噪声无关,端部偏转式结构滚珠丝杠副的主要噪声机理为丝杠滚道波纹度激起的螺母强迫振动,滚珠与返向器的碰撞噪声已不是该结构滚珠丝杠副的主要噪声。脂润滑时,噪声频率特性不变,但噪声水平略有降低。
A ball screw driven mechanism is a key component of numerical control machine tools. With the development of high-speed cutting technology, the feed rate of the ball screw becomes faster and faster. However, with the development of ball screws tends towards high-speed, problems such as noise, high temperature resulted from fiction become more and more badly. Therefore the problem of the noise and friction becomes the key factor to increase the ball screw speed. Therefore, it is significant to study the dynamical performance of ball screw mechanism and research the pivotal influencing factors on the performance. The study provides effective guidance to increase the dynamic performance of high-speed ball screw mechanism.
The problems of friction torque and noise in high-speed of ball screw mechanism are studied by applying contact mechanics, impact mechanics, the theory of elastohydrodynamic lubrication (EHL) and structural noise, and combining the friction torque and noise test. The contents of this paper are as follows.
1) Considering helical angle, the contact characteristic between balls and grooves is studied based on the theory of Hertz. And the influences of structural parameters on the contact characteristic are investigated.
2) Based on kinematics theory, the kinematic relation between balls and screw shaft is analyzed and the influences of important structural parameters on spinning and slip of balls are investigated.
3) The mechanical model of impact between the ball and the returner is proposed based on the theory of Hertz contact and the Newton Second Law. A special device is designed to measure the time of impact-contact process. The influences of impact angle, structural parameters and material of ball screw mechanism on the impact force are investigated. Furthermore, the motion of the balls on the groove after impact and the fluency of the balls in returner groove are investigated.
4) According to the design features of ball screw mechanism, a model of friction torque is proposed to analyze the composition and generation of friction torque. The influence of manufacturing errors of grooves on friction torque is analyzed. And the lubrication state of the ball screw mechanism is investigated by applying the theory of elastohydrodynamic lubrication. Combining the test result and spectrum of friction torque, the reason of the fluctuation of friction torque of ball screw mechanism is investigated.
5) The noise characteristic of end-cap type ball screw mechanism is compared with return pipe type ball screw mechanism through spectrum analysis of noise. The relation between noise and vibration of end-cap type ball screw in high speed is investigated and the noise generating mechanism of this type ball screw is ascertained.
The conclusions of theoretical analysis and experimental study results are as follows:
1) The contact stress and deformation between balls and screw shaft groove are larger than the side between balls and nut groove. The contact stress and deformation decrease with increasing of the contact angle. And the variation of helical angle has no noticeable influence on contact characteristic of ball screw mechanism. However, the contact characteristic is very sensitive to the variation of the curvature ratio. The contact stress and deformation increases remarkably as the curvature ratio increases.
2) At normal rotational speed, although the motion speed of ball center is not high, the rotational speed is quite high. The size of a ball has no noticeable influence on the spin-to-roll ratio of a ball, but the contact angle is of remarkable influence on the spin-to-roll ratio. When the contact angle is equal to 38°, the spin-to-roll ratio reaches the minimum point. The slippage ratio of a ball is increased with the increase of helical angle and the size of a ball.
3) The test result proves that the model of impact behavior between ball and returner based on Hertz contact model and the Newton Second Law is reliable. The impact force increases greatly with the increase of impact angle and the incipient speed of the ball. The impact force can be decreased through using smaller steel balls or ceramic balls, decreasing impact angle, or making returner with engineering plastic whose elastic modulus is smaller than the steel. The small elastic modulus, small restitution coefficient and good friction characteristic material is the best selection to make returner.
4) The manufacturing errors of groove in ball screw mechanism affect the value of the friction torque averagely. The errors increase the total value of the friction torque. For the ball screw contact couple, it is difficult to built full elastohydrodynamic lubricating film. Usually, the parameter A of lubrication state is smaller than one, and the contact couple runs on conditions of boundary lubrication. Therefore the high friction coefficient resulted from poor lubrication may be the primary reason of the high friction torque.
5) When the ball screw mechanism runs at lower speed and is lubricated by oil, the friction torque of ball screw is higher than at high speed. And the friction torque of the inner-return type and bayonet-tube type ball screw mechanism often fluctuates at the normal frequency of 1Hz. When the ball screw mechanism is lubricated by grease, the friction torque is smaller and changes smoothly. Analysis indicates that the fluctuation of the friction torque at the normal frequency of 1Hz is resulted from the jam and fall off of balls because of poor lubrication.
6) The sound volume of the end-cap type ball screw mechanism is much smaller the bayonet-tube type, what's more the tone quality of the end-cap type is much better than the bayonet-tube type. The principal frequency of the noise varies with the rotational speed of the ball screw mechanism. The vibration of the table jointed with nut has nothing to do with the noise of ball screw mechanism. The noise of end-cap type ball screw mechanism is caused by the forced vibration of the nut which is inspired by the waviness of screw shaft groove, the noise caused by the impact between the ball and the returner is not the principle noise. When the ball screw mechanism is lubricated with grease, the spectral distribution remains the same, but the sound volume declinesslowly.
本文应用接触力学、碰撞力学、弹流动力润滑和结构噪声的理论,结合实验研究了滚珠丝杠副的摩擦力矩和高速下的噪声问题,研究内容主要包括:
1)应用Hertz接触理论,在考虑螺旋升角的情况下,分析了滚珠在工作滚道中的接触特性及各结构参数对接触特性的影响。
2)根据运动学理论,分析滚珠丝杠副中滚珠与丝杠轴之间的运动关系,探讨各结构参数对滚珠自旋和滑移运动的影响。
3)应用Hertz接触模型和牛顿第二定律,建立了滚珠与返向器碰撞的力学模型,设计了测量碰撞接触时间的试验装置。研究分析了碰撞角度、结构和材料参数对碰撞力的影响。分析了滚珠碰撞后的运动变化情况,以及在循环返向滚道中的运动流畅性。
4)根据滚珠丝杠副的结构特点,研究分析了滚珠丝杠副摩擦力矩的产生机理,建立了摩擦力矩的分析模型,分析讨论了滚道制造误差对摩擦力矩的影响。运用弹流动力润滑理论分析滚珠丝杠副的润滑状态,实验研究了导致滚珠丝杠副摩擦力矩低频波动的原因。
5)实验研究了端部偏转式返向结构滚珠丝杠副的噪声特性,分析了其主要噪声与振动之间的联系,通过对滚珠丝杠副径向振动激励频率的计算,确定了端部偏转式高速滚珠丝杠副的主要噪声机理。
理论分析和试验研究表明:
1)滚珠丝杠副中滚珠与丝杠滚道的接触压力和变形大于滚珠与螺母滚道的接触压力和变形。随着接触角的增大,接触压力和变形减小,螺旋升角对接触特性无显著影响,接触特性对曲率比的变化非常敏感,随着曲率比的增大,接触压力和变形显著上升。
2)滚珠丝杠副在正常转速下,滚珠中心的线速度不高,自转速度却相当高;滚珠直径大小对旋滚比影响不大,接触角的变化对旋滚比影响比较明显,在接触角为38°时,旋滚比最小;随着螺旋升角和滚珠直径的增大,滚珠的滑移率增大。
3)碰撞接触时间的测量结果表明,本文建立的滚珠与返向器的碰撞力学模型符合实际情况。碰撞角度越大,初始速度越高,则碰撞力越大,通过减小碰撞角度、采用小直径钢球或陶瓷球、或者采用弹性模量较低的工程塑料制作返向器,可以有效降低碰撞力。返向器的材料应选择弹性模量小、法向恢复系数小,而摩擦特性良好的材料。
4)滚珠丝杠副的滚道加工误差对摩擦力矩的影响具有“平均效应”,制造误差的存在从总体上增大了滚珠丝杠副的摩擦力矩。滚珠丝杠接触副中很难建立起完全弹流油膜,低速下,油膜润滑参数Λ小于1,处于边界润滑状态,润滑不良导致的摩擦系数过大可能是滚珠丝杠副摩擦力矩较大的主要原因。
5)低速下油润滑时,滚珠丝杠副的摩擦力矩较大,内循环和外循环插管式结构滚珠丝杠副的摩擦力矩常出现归一化频率为1Hz的波动,脂润滑时,摩擦力矩较小,而且非常平稳。分析表明,归一化频率为1Hz的波动是由润滑不良引起的滚珠的拥堵和散开所导致的。
6)端部偏转式结构滚珠丝杠副的噪声明显小于插管式丝杠副,且音质有显著改善。其噪声主要频率随丝杠转速的变化而改变,与螺母相连的工作台的振动与滚珠丝杠副的主要噪声无关,端部偏转式结构滚珠丝杠副的主要噪声机理为丝杠滚道波纹度激起的螺母强迫振动,滚珠与返向器的碰撞噪声已不是该结构滚珠丝杠副的主要噪声。脂润滑时,噪声频率特性不变,但噪声水平略有降低。
A ball screw driven mechanism is a key component of numerical control machine tools. With the development of high-speed cutting technology, the feed rate of the ball screw becomes faster and faster. However, with the development of ball screws tends towards high-speed, problems such as noise, high temperature resulted from fiction become more and more badly. Therefore the problem of the noise and friction becomes the key factor to increase the ball screw speed. Therefore, it is significant to study the dynamical performance of ball screw mechanism and research the pivotal influencing factors on the performance. The study provides effective guidance to increase the dynamic performance of high-speed ball screw mechanism.
The problems of friction torque and noise in high-speed of ball screw mechanism are studied by applying contact mechanics, impact mechanics, the theory of elastohydrodynamic lubrication (EHL) and structural noise, and combining the friction torque and noise test. The contents of this paper are as follows.
1) Considering helical angle, the contact characteristic between balls and grooves is studied based on the theory of Hertz. And the influences of structural parameters on the contact characteristic are investigated.
2) Based on kinematics theory, the kinematic relation between balls and screw shaft is analyzed and the influences of important structural parameters on spinning and slip of balls are investigated.
3) The mechanical model of impact between the ball and the returner is proposed based on the theory of Hertz contact and the Newton Second Law. A special device is designed to measure the time of impact-contact process. The influences of impact angle, structural parameters and material of ball screw mechanism on the impact force are investigated. Furthermore, the motion of the balls on the groove after impact and the fluency of the balls in returner groove are investigated.
4) According to the design features of ball screw mechanism, a model of friction torque is proposed to analyze the composition and generation of friction torque. The influence of manufacturing errors of grooves on friction torque is analyzed. And the lubrication state of the ball screw mechanism is investigated by applying the theory of elastohydrodynamic lubrication. Combining the test result and spectrum of friction torque, the reason of the fluctuation of friction torque of ball screw mechanism is investigated.
5) The noise characteristic of end-cap type ball screw mechanism is compared with return pipe type ball screw mechanism through spectrum analysis of noise. The relation between noise and vibration of end-cap type ball screw in high speed is investigated and the noise generating mechanism of this type ball screw is ascertained.
The conclusions of theoretical analysis and experimental study results are as follows:
1) The contact stress and deformation between balls and screw shaft groove are larger than the side between balls and nut groove. The contact stress and deformation decrease with increasing of the contact angle. And the variation of helical angle has no noticeable influence on contact characteristic of ball screw mechanism. However, the contact characteristic is very sensitive to the variation of the curvature ratio. The contact stress and deformation increases remarkably as the curvature ratio increases.
2) At normal rotational speed, although the motion speed of ball center is not high, the rotational speed is quite high. The size of a ball has no noticeable influence on the spin-to-roll ratio of a ball, but the contact angle is of remarkable influence on the spin-to-roll ratio. When the contact angle is equal to 38°, the spin-to-roll ratio reaches the minimum point. The slippage ratio of a ball is increased with the increase of helical angle and the size of a ball.
3) The test result proves that the model of impact behavior between ball and returner based on Hertz contact model and the Newton Second Law is reliable. The impact force increases greatly with the increase of impact angle and the incipient speed of the ball. The impact force can be decreased through using smaller steel balls or ceramic balls, decreasing impact angle, or making returner with engineering plastic whose elastic modulus is smaller than the steel. The small elastic modulus, small restitution coefficient and good friction characteristic material is the best selection to make returner.
4) The manufacturing errors of groove in ball screw mechanism affect the value of the friction torque averagely. The errors increase the total value of the friction torque. For the ball screw contact couple, it is difficult to built full elastohydrodynamic lubricating film. Usually, the parameter A of lubrication state is smaller than one, and the contact couple runs on conditions of boundary lubrication. Therefore the high friction coefficient resulted from poor lubrication may be the primary reason of the high friction torque.
5) When the ball screw mechanism runs at lower speed and is lubricated by oil, the friction torque of ball screw is higher than at high speed. And the friction torque of the inner-return type and bayonet-tube type ball screw mechanism often fluctuates at the normal frequency of 1Hz. When the ball screw mechanism is lubricated by grease, the friction torque is smaller and changes smoothly. Analysis indicates that the fluctuation of the friction torque at the normal frequency of 1Hz is resulted from the jam and fall off of balls because of poor lubrication.
6) The sound volume of the end-cap type ball screw mechanism is much smaller the bayonet-tube type, what's more the tone quality of the end-cap type is much better than the bayonet-tube type. The principal frequency of the noise varies with the rotational speed of the ball screw mechanism. The vibration of the table jointed with nut has nothing to do with the noise of ball screw mechanism. The noise of end-cap type ball screw mechanism is caused by the forced vibration of the nut which is inspired by the waviness of screw shaft groove, the noise caused by the impact between the ball and the returner is not the principle noise. When the ball screw mechanism is lubricated with grease, the spectral distribution remains the same, but the sound volume declinesslowly.
引文
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