滚珠丝杠副直线导轨进给单元动态性能研究
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摘要
数控机床的高速、高精、高效以及高自动化的发展对机床动态特性的要求越来越高,其中最主要的就是机床的振动性能,即机床的加工质量在很大程度上取决于机床所产生的振动。作为数控机床进给系统中的关键功能部件,滚珠丝杠副是一种细长的低刚度零件,在外界交变力的作用下极易产生振动和噪声。尤其在加长型数控机床中,由于工作台行程较长,丝杠也相应变长,导致进给系统的稳定性,刚性和抗振性等动态性能的下降,特别是在强力切削过程中振动比较严重,既影响了机床的加工精度和加工表面质量,又加速了刀具的磨损和损坏。直线滚动导轨副作为进给单元的支承导向装置,加工过程中的振动会增大导轨副的动态载荷,从而降低其寿命和精度的保持性。因此,研究滚珠丝杠副直线导轨进给单元动态性能具有很重要的理论和现实意义。
本文采用理论分析与试验研究相结合的方法,依据动力学理论,Hertz接触理论、振动理论及试验模态分析理论,研究了滚珠丝杠副直线导轨进给单元的动态特性,研究内容主要包括：
1)考虑进给单元中滚珠丝杠副、直线导轨副及支承轴承等结合面的影响,对滚珠丝杠副直线导轨进给单元进行了动力学建模,并根据拉格朗日方程推导了进给单元的振动微分方程,获得了进给单元的质量矩阵、刚度矩阵及阻尼矩阵。
2)考虑两端支承轴承的影响,应用Hertz接触理论,分析了在外加工作载荷作用下滚珠丝杠进给系统的接触变形及刚度,得出了单、双螺母滚珠丝杠副轴向接触刚度的影响因素并进行了对比分析。
3)建立了直线滚动导轨副接触刚度模型。该模型充分考虑了外加载荷,滚珠个数,滚珠预变形量等因素对接触刚度的影响。在此基础上,以LSA-45G型号的直线滚动导轨副为例,计算得到了直线滚动导轨副的Y向和Z向的接触刚度值。
4)采用试验模态分析技术,对滚珠丝杠副直线导轨进给单元试验台进行了模态试验研究。通过力锤激励试验,获得了进给单元的主要模态参数,包括模态质量、模态刚度、模态阻尼及相关振型。
5)根据振动理论,考虑丝杠两端轴承的弹性支承作用,建立了丝杠在两端弹性支承条件下的频率方程,推导了其振型函数,并将振型函数进行了正则化。结合模态试验获得的模态参数,研究了滚珠丝杠副直线导轨进给单元的振动模型,进行了考虑直线滚动导轨副的滚珠丝杠进给单元和不考虑直线滚动导轨副的滚珠丝杠进给单元的有限元模态分析,并与试验结果进行了对比,分析了进给单元的薄弱环节,并提出了改进意见。
理论分析与试验研究结果表明：
1)滚珠丝杠副中,滚珠与丝杠、螺母滚道结合面的轴向接触变形及刚度对滚珠丝杠副直线导轨进给单元的轴向动态特性有直接的影响。滚珠与丝杠、螺母滚道结合面的轴向接触变形及刚度受到轴向载荷、接触角、螺旋升角、滚珠个数、曲率比等设计参数的影响。
2)合理设计滚珠丝杠副的结构参数可以提高滚珠丝杠副的轴向接触刚度。增大接触角可以使单螺母滚珠丝杠副的轴向接触刚度有明显的降低,而且呈非线性变化。滚珠个数与单螺母滚珠丝杠副轴向接触刚度的关系接近线性,随着滚珠个数的增加,轴向接触刚度也增加。螺旋升角对单螺母滚珠丝杠副的轴向接触刚度影响不显著。单螺母滚珠丝杠副的轴向接触刚度对曲率比的变化比较敏感,随着曲率比的增加而明显降低。轴向载荷的增加使单螺母滚珠丝杠副轴向接触刚度呈非线性增大。
3)双螺母滚珠丝杠副的轴向接触刚度随着轴向载荷的增大而增大,而且随轴向载荷的变化近似线性。随着预紧力的增大,双螺母滚珠丝杠副的轴向接触刚度刚度明显增大,呈非线性变化。接触角、滚珠个数、螺旋升角以及曲率比的变化对双螺母滚珠丝杠副接触刚度的影响与其对单螺母滚珠丝杠副接触刚度的影响类似,只是相同条件下在数值上双螺母滚珠丝杠副接触刚度明显高于单螺母滚珠丝杠副接触刚度。因此在设计时需要寻找最优接触角,适当减小曲率比,增加滚珠数目,选择合适的预紧力,有利于提高滚珠丝杠螺母副的接触刚度。
4)直线滚动导轨副的接触刚度受到其工作载荷、滚珠预变形量及滚珠个数等设计参数的影响。工作载荷的增加会使直线滚动导轨副的Y向接触刚度增大,Z向接触刚度减小；滚珠预变形量的增加,会使直线滚动导轨副的Y向接触刚度增大,Z向接触刚度降低；滚珠个数的增多,会使直线滚动导轨副的Y向接触刚度降低,Z向接触刚度提高。
5)滚珠丝杠副直线导轨进给单元的主要振型为弯曲振动和扭转振动。滚珠丝杠副直线导轨进给单元的薄弱环节主要发生在丝杠螺母副及其与连接板的结合部位。滚珠丝杠副直线导轨进给单元的固有频率受到支承方式的影响：两端固定时其各阶固有频率明显高于一端固定一端简支的各阶固有频率。滚珠丝杠副直线导轨进给单元的固有频率受到螺母位置的影响：螺母位于丝杠固定端时的各阶固有频率比螺母位于丝杠简支端时的各阶固有频率要高,螺母位于丝杠两端时的各阶固有频率明显低于螺母位于丝杠中间位置时的各阶固有频率。考虑直线导轨副的滚珠丝杠进给单元的各阶固有频率要比不考虑直线导轨的滚珠丝杠进给单元的各阶固有频率更接近于试验结果,更加符合进给单元的实际真实情况。
研究结果为减小滚珠丝杠副直线导轨进给单元的动态变形,提高进给单元的抗振性指明了努力方向,对滚珠丝杠副直线导轨进给单元的结构设计、制造和工程应用具有重要的理论和实际指导意义。
The development of high-speed, high-precision, high-efficiency and high-automation NC machine tools has a demand in higher and higher processing performance and dynamic characteristics. And among all the dynamic characteristics, vibration performance is the most important, that is to say, processing quality of machine tools depends mainly on the vibration of itself. Research shows that the process quality depends largely on the vibration of NC machine tools, especially to high-speed, high-precision NC machine tools. Therefore, vibration of machine tools is an important problem in the study of dynamic characteristics of machine tool.
As a key functional part of NC machine tool feed system, ball screw, which is an elongated low rigidity component, easily produces vibration and noise in the external alternating force. Especially in large CNC machine tools, ball screw become longer with the longer travel of worktable, which results in a decline in such dynamic characteristics of feed system as stability, rigidity and vibration resistance, and so on, especially during heavy cutting, vibration becomes more serious, which both affects the machining precision and process quality of the surface and easily causes the rapid wear and damage of the tool.
Linear rolling guide works as supporting and guiding device of the feed unit, large vibration may increase the dynamic load of the guide during the processing and thus reduce its life and accuracy retention. As a result, there is important theoretical and realistic value about research on the dynamic characteristics of Ball Screws Linear Guide Feed Unit.
In this paper, by means of theoretical analysis and experimental research, on the basis of Dynamics theory, the Hertz contact theory, vibration theory and experimental modal analysis, the dynamic characteristics of Ball Screws Linear Guide Feed Unit is researched. The study contents are as follows:
1) Considering the influence of ball screws, linear rolling guide and ball bearing joint interfaces of Ball Screws Linear Guide Feed Unit, the Dynamics model is built, and the vibration differential equation is derived on the base of Lagrange equation.
2) Considering the influence of ball bearing in the end and on the basis of the Hertz contact theory, the contact deformation and stiffness analysis of ball screw feeding system under the external force is analyzed, and the structural influence factors on contact stiffness of the single and double nut ball screws is obtained and contrasted.
3) The model of contact stiffness of linear rolling guide is built, which consider such influence factors as external force, the number and pre-deformation of balls, etc. on the contact stiffness. Taking linear rolling guide LSA-45G for example, contact stiffness value in Y and Z direction is calculated.
4) By means of experimental modal analysis technique, experimental modal research on Ball Screws Linear Guide Feed Unit Test is investigated. Through the impulse test, a system main modal parameters are obtained, including modal mass, modal stiffness, modal damping and vibration shape.
5) According to vibration theory and considering the elastic supporting of ball bearing at both ends of ball screw, frequency equation under this condition and the function of vibration shape is derived. Using the experimental modal parameters, vibration shape of Ball Screws Linear Guide Feed Unit is researched. The finite element modal analysis of Ball Screws Linear Guide Feed Unit and ball screw feed system unconsidering linear rolling guide are carried on and compared with the experimental result. The weak links of the system is obtained and some suggestions for improvement are put forward.
Theoretical analysis and experimental study results are as follows:
1) The axial contact stiffness and the deformation of ball and raceway contact area have the direct influence on the axial dynamic characteristics of Ball Screws Linear Guide Feed Unit.Such design parameters as axial force, contact angle, helix angle, ball number, principal curvature, and so on, have an important influence on the axial contact stiffness and deformation on the ball and raceway contact area.
2) Reasonable design of structure parameters of ball screw pair can improve the axial stiffness of ball screw pair.the increase of contact angle can result in the nonlinear decrease of the axial contact stiffness of the single nut ball screws. The increase of ball number can result in the linear decrease of the axial contact stiffness of the single nut ball screws. The change of helix angle has an unobvious influence on the axial contact stiffness of the single nut ball screws. But the axial contact stiffness of the single nut ball screws changes sensitively with principal curvature. The increase of axial force can result in the nonlinear increase of the axial contact stiffness of the single nut ball screws.
3) Comparatively, the increase of axial force can result in the linear increase of the axial contact stiffness of the double nut ball screws, the increase of preload can result in the nonlinear increase of the axial contact stiffness of the double nut ball screws. Contact angle, ball number, helix angle and principal curvature have a similar influence on the axial contact stiffness of the double nut ball screws to the single nut ball screw, but under the same condition, the axial contact stiffness of the double nut ball screws is obviously higher than that of the single nut ball screws. Therefore, finding optimal contact angle, reducing the curvature ratio, increasing the number of balls and selecting the appropriate preload during the design of ball screw is conducive to improve the contact stiffness of the ball screw nut pair.
4) Such design parameters as external force, pre-deformation and the number of balls,etc have influence on the contact stiffness of linear rolling guide. The increase of external force can result in the increase of contact stiffness in Y direction and the decrease of contact stiffness in Z direction of linear rolling guide. The increase of pre-deformation can increase the contact stiffness in Y direction and decrease the contact stiffness in Z direction of linear rolling guide.The increase of the number of balls can decrease the contact stiffness in Y direction and increase the contact stiffness in Z direction of linear rolling guide.
The vibration shape of Ball Screws Linear Guide Feed Unit is mainly bending and twist motion.The weak links occurs mainly in the ball screw and the connection part of the connecting plate and ball screw.The natural frequencies of Ball Screws Linear Guide Feed Unit are affected by the support form of itself:natural frequencies of Ball Screws Linear Guide Feed Unit fixed at two ends are obviously higher than those of Ball Screws Linear Guide Feed Unit fixed at one end and simply supported. The natural frequencies of Ball Screws Linear Guide Feed Unit are affected by the location of the nut:The natural frequencies when the nut locates at two ends are higher than those when the nut locates at simply supported end, The natural frequencies when the nut locates at two ends are higher than those when the nut locates at middle.The natural frequencies of Ball Screws Linear Guide Feed Unit are more close to the experimental results than those of feed unit without linear rolling guide.
Research results provide research direction for the decline of dynamic deformation and the increase of vibration resistance of Ball Screws Linear Guide Feed Unit, and have an important theoretical and realistic guiding value for the structure design, manufacturing and engineering application of Ball Screws Linear Guide Feed Unit.
本文采用理论分析与试验研究相结合的方法,依据动力学理论,Hertz接触理论、振动理论及试验模态分析理论,研究了滚珠丝杠副直线导轨进给单元的动态特性,研究内容主要包括：
1)考虑进给单元中滚珠丝杠副、直线导轨副及支承轴承等结合面的影响,对滚珠丝杠副直线导轨进给单元进行了动力学建模,并根据拉格朗日方程推导了进给单元的振动微分方程,获得了进给单元的质量矩阵、刚度矩阵及阻尼矩阵。
2)考虑两端支承轴承的影响,应用Hertz接触理论,分析了在外加工作载荷作用下滚珠丝杠进给系统的接触变形及刚度,得出了单、双螺母滚珠丝杠副轴向接触刚度的影响因素并进行了对比分析。
3)建立了直线滚动导轨副接触刚度模型。该模型充分考虑了外加载荷,滚珠个数,滚珠预变形量等因素对接触刚度的影响。在此基础上,以LSA-45G型号的直线滚动导轨副为例,计算得到了直线滚动导轨副的Y向和Z向的接触刚度值。
4)采用试验模态分析技术,对滚珠丝杠副直线导轨进给单元试验台进行了模态试验研究。通过力锤激励试验,获得了进给单元的主要模态参数,包括模态质量、模态刚度、模态阻尼及相关振型。
5)根据振动理论,考虑丝杠两端轴承的弹性支承作用,建立了丝杠在两端弹性支承条件下的频率方程,推导了其振型函数,并将振型函数进行了正则化。结合模态试验获得的模态参数,研究了滚珠丝杠副直线导轨进给单元的振动模型,进行了考虑直线滚动导轨副的滚珠丝杠进给单元和不考虑直线滚动导轨副的滚珠丝杠进给单元的有限元模态分析,并与试验结果进行了对比,分析了进给单元的薄弱环节,并提出了改进意见。
理论分析与试验研究结果表明：
1)滚珠丝杠副中,滚珠与丝杠、螺母滚道结合面的轴向接触变形及刚度对滚珠丝杠副直线导轨进给单元的轴向动态特性有直接的影响。滚珠与丝杠、螺母滚道结合面的轴向接触变形及刚度受到轴向载荷、接触角、螺旋升角、滚珠个数、曲率比等设计参数的影响。
2)合理设计滚珠丝杠副的结构参数可以提高滚珠丝杠副的轴向接触刚度。增大接触角可以使单螺母滚珠丝杠副的轴向接触刚度有明显的降低,而且呈非线性变化。滚珠个数与单螺母滚珠丝杠副轴向接触刚度的关系接近线性,随着滚珠个数的增加,轴向接触刚度也增加。螺旋升角对单螺母滚珠丝杠副的轴向接触刚度影响不显著。单螺母滚珠丝杠副的轴向接触刚度对曲率比的变化比较敏感,随着曲率比的增加而明显降低。轴向载荷的增加使单螺母滚珠丝杠副轴向接触刚度呈非线性增大。
3)双螺母滚珠丝杠副的轴向接触刚度随着轴向载荷的增大而增大,而且随轴向载荷的变化近似线性。随着预紧力的增大,双螺母滚珠丝杠副的轴向接触刚度刚度明显增大,呈非线性变化。接触角、滚珠个数、螺旋升角以及曲率比的变化对双螺母滚珠丝杠副接触刚度的影响与其对单螺母滚珠丝杠副接触刚度的影响类似,只是相同条件下在数值上双螺母滚珠丝杠副接触刚度明显高于单螺母滚珠丝杠副接触刚度。因此在设计时需要寻找最优接触角,适当减小曲率比,增加滚珠数目,选择合适的预紧力,有利于提高滚珠丝杠螺母副的接触刚度。
4)直线滚动导轨副的接触刚度受到其工作载荷、滚珠预变形量及滚珠个数等设计参数的影响。工作载荷的增加会使直线滚动导轨副的Y向接触刚度增大,Z向接触刚度减小；滚珠预变形量的增加,会使直线滚动导轨副的Y向接触刚度增大,Z向接触刚度降低；滚珠个数的增多,会使直线滚动导轨副的Y向接触刚度降低,Z向接触刚度提高。
5)滚珠丝杠副直线导轨进给单元的主要振型为弯曲振动和扭转振动。滚珠丝杠副直线导轨进给单元的薄弱环节主要发生在丝杠螺母副及其与连接板的结合部位。滚珠丝杠副直线导轨进给单元的固有频率受到支承方式的影响：两端固定时其各阶固有频率明显高于一端固定一端简支的各阶固有频率。滚珠丝杠副直线导轨进给单元的固有频率受到螺母位置的影响：螺母位于丝杠固定端时的各阶固有频率比螺母位于丝杠简支端时的各阶固有频率要高,螺母位于丝杠两端时的各阶固有频率明显低于螺母位于丝杠中间位置时的各阶固有频率。考虑直线导轨副的滚珠丝杠进给单元的各阶固有频率要比不考虑直线导轨的滚珠丝杠进给单元的各阶固有频率更接近于试验结果,更加符合进给单元的实际真实情况。
研究结果为减小滚珠丝杠副直线导轨进给单元的动态变形,提高进给单元的抗振性指明了努力方向,对滚珠丝杠副直线导轨进给单元的结构设计、制造和工程应用具有重要的理论和实际指导意义。
The development of high-speed, high-precision, high-efficiency and high-automation NC machine tools has a demand in higher and higher processing performance and dynamic characteristics. And among all the dynamic characteristics, vibration performance is the most important, that is to say, processing quality of machine tools depends mainly on the vibration of itself. Research shows that the process quality depends largely on the vibration of NC machine tools, especially to high-speed, high-precision NC machine tools. Therefore, vibration of machine tools is an important problem in the study of dynamic characteristics of machine tool.
As a key functional part of NC machine tool feed system, ball screw, which is an elongated low rigidity component, easily produces vibration and noise in the external alternating force. Especially in large CNC machine tools, ball screw become longer with the longer travel of worktable, which results in a decline in such dynamic characteristics of feed system as stability, rigidity and vibration resistance, and so on, especially during heavy cutting, vibration becomes more serious, which both affects the machining precision and process quality of the surface and easily causes the rapid wear and damage of the tool.
Linear rolling guide works as supporting and guiding device of the feed unit, large vibration may increase the dynamic load of the guide during the processing and thus reduce its life and accuracy retention. As a result, there is important theoretical and realistic value about research on the dynamic characteristics of Ball Screws Linear Guide Feed Unit.
In this paper, by means of theoretical analysis and experimental research, on the basis of Dynamics theory, the Hertz contact theory, vibration theory and experimental modal analysis, the dynamic characteristics of Ball Screws Linear Guide Feed Unit is researched. The study contents are as follows:
1) Considering the influence of ball screws, linear rolling guide and ball bearing joint interfaces of Ball Screws Linear Guide Feed Unit, the Dynamics model is built, and the vibration differential equation is derived on the base of Lagrange equation.
2) Considering the influence of ball bearing in the end and on the basis of the Hertz contact theory, the contact deformation and stiffness analysis of ball screw feeding system under the external force is analyzed, and the structural influence factors on contact stiffness of the single and double nut ball screws is obtained and contrasted.
3) The model of contact stiffness of linear rolling guide is built, which consider such influence factors as external force, the number and pre-deformation of balls, etc. on the contact stiffness. Taking linear rolling guide LSA-45G for example, contact stiffness value in Y and Z direction is calculated.
4) By means of experimental modal analysis technique, experimental modal research on Ball Screws Linear Guide Feed Unit Test is investigated. Through the impulse test, a system main modal parameters are obtained, including modal mass, modal stiffness, modal damping and vibration shape.
5) According to vibration theory and considering the elastic supporting of ball bearing at both ends of ball screw, frequency equation under this condition and the function of vibration shape is derived. Using the experimental modal parameters, vibration shape of Ball Screws Linear Guide Feed Unit is researched. The finite element modal analysis of Ball Screws Linear Guide Feed Unit and ball screw feed system unconsidering linear rolling guide are carried on and compared with the experimental result. The weak links of the system is obtained and some suggestions for improvement are put forward.
Theoretical analysis and experimental study results are as follows:
1) The axial contact stiffness and the deformation of ball and raceway contact area have the direct influence on the axial dynamic characteristics of Ball Screws Linear Guide Feed Unit.Such design parameters as axial force, contact angle, helix angle, ball number, principal curvature, and so on, have an important influence on the axial contact stiffness and deformation on the ball and raceway contact area.
2) Reasonable design of structure parameters of ball screw pair can improve the axial stiffness of ball screw pair.the increase of contact angle can result in the nonlinear decrease of the axial contact stiffness of the single nut ball screws. The increase of ball number can result in the linear decrease of the axial contact stiffness of the single nut ball screws. The change of helix angle has an unobvious influence on the axial contact stiffness of the single nut ball screws. But the axial contact stiffness of the single nut ball screws changes sensitively with principal curvature. The increase of axial force can result in the nonlinear increase of the axial contact stiffness of the single nut ball screws.
3) Comparatively, the increase of axial force can result in the linear increase of the axial contact stiffness of the double nut ball screws, the increase of preload can result in the nonlinear increase of the axial contact stiffness of the double nut ball screws. Contact angle, ball number, helix angle and principal curvature have a similar influence on the axial contact stiffness of the double nut ball screws to the single nut ball screw, but under the same condition, the axial contact stiffness of the double nut ball screws is obviously higher than that of the single nut ball screws. Therefore, finding optimal contact angle, reducing the curvature ratio, increasing the number of balls and selecting the appropriate preload during the design of ball screw is conducive to improve the contact stiffness of the ball screw nut pair.
4) Such design parameters as external force, pre-deformation and the number of balls,etc have influence on the contact stiffness of linear rolling guide. The increase of external force can result in the increase of contact stiffness in Y direction and the decrease of contact stiffness in Z direction of linear rolling guide. The increase of pre-deformation can increase the contact stiffness in Y direction and decrease the contact stiffness in Z direction of linear rolling guide.The increase of the number of balls can decrease the contact stiffness in Y direction and increase the contact stiffness in Z direction of linear rolling guide.
The vibration shape of Ball Screws Linear Guide Feed Unit is mainly bending and twist motion.The weak links occurs mainly in the ball screw and the connection part of the connecting plate and ball screw.The natural frequencies of Ball Screws Linear Guide Feed Unit are affected by the support form of itself:natural frequencies of Ball Screws Linear Guide Feed Unit fixed at two ends are obviously higher than those of Ball Screws Linear Guide Feed Unit fixed at one end and simply supported. The natural frequencies of Ball Screws Linear Guide Feed Unit are affected by the location of the nut:The natural frequencies when the nut locates at two ends are higher than those when the nut locates at simply supported end, The natural frequencies when the nut locates at two ends are higher than those when the nut locates at middle.The natural frequencies of Ball Screws Linear Guide Feed Unit are more close to the experimental results than those of feed unit without linear rolling guide.
Research results provide research direction for the decline of dynamic deformation and the increase of vibration resistance of Ball Screws Linear Guide Feed Unit, and have an important theoretical and realistic guiding value for the structure design, manufacturing and engineering application of Ball Screws Linear Guide Feed Unit.
引文
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