高速螺母驱动型滚珠丝杠副动力学特性研究
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摘要
数控机床的大型化和高速化,不但要求机床主轴转速不断提高,而且进给速度也要求越来越快。常规的滚珠丝杠副,尤其是大型、重型高档数控机床用的大行程丝杠副,自身重量较螺母大得多,因此丝杠旋转惯性力很多,导致发热、变形和能耗严重,变形的丝杠在旋转过程中又会产生振动和噪声,降低了设备的工作精度。这是目前一个亟待解决的问题。因此本研究根据运动的相对性,提出新型“螺母驱动型滚珠丝杠副”,把传统的“丝杠驱动方式”改为“螺母驱动方式”。
本研究借助于数学建模、力学分析、计算分析软件和实验研究等方法,在构建滚动体运动学、接触模型及进给系统结构动力学模型基础上,对螺母驱动型滚珠丝杠副高速传动性能进行研究,研究内容主要包括：
1.根据运动学理论,对高速螺母驱动型滚珠丝杠副滚动体运动学进行分析。求解了滚珠滚动速度与驱动螺母轴转速之间的运动关系,推导出滚动体公转和自转角速度,求取双螺母内滚动体接触点位置及滑动速度。理论分析得出相同驱动速度时螺母驱动型滚珠丝杠副滚动体公转和自转角速度低于传统的丝杠驱动型滚珠丝杠副滚动体公转和自转角速度。
2.根据Hertz接触理论,对高速螺母驱动型滚珠丝杠副滚动体接触特性进行分析。建立了轴向载荷、惯性效应、位移约束联合作用下的高速螺母驱动型滚珠丝杠副接触分析模型,应用迭代法求解非线性方程组,分析了不同转速和轴向力等工况下滚珠丝杠副接触参数的变化规律。根据理论计算求取系统进给加速度。结果表明滚珠丝杠副高速运动时,螺母组件内接触角、法向载荷以及弹性变形随转速和轴向载荷的变化而变化。与丝杠驱动型相比采用相同额定转矩电机驱动,螺母驱动型滚珠丝杠副降低了传动系统转动惯量,进而降低系统驱动能耗,螺母驱动型滚珠丝杠副可获得更高进给加速度,更具有高速性。
3.对预紧力可调的双螺母驱动型滚珠丝杠副进给系统进行结构动力学分析,首先建立滚珠丝杠副结构动力学模型。分析了预紧力的变化对固有频率的影响规律,主要设计参数的变化对系统低阶固有频率的影响。结果表明,进给系统固有频率具有时变性。与传统的丝杠驱动型相比,采用螺母驱动型滚珠丝杠副,提高了进给系统低阶固有频率,可使系统具有更宽的通频带,提高系统的速度环增益和位置环增益,从而提高整个系统的快速响应能力和加工精度。
4.建立了摩擦力矩的分析模型,分析了滚珠丝杠副摩擦力矩的产生机理。研究轴向载荷、轨道制造误差等对摩擦力矩的影响,分析了摩擦力知低频波动的原因。运用弹流动力润滑理论分析滚珠丝杠副的润滑状态。结果表明轴向载荷、滚道波纹度是对摩擦力矩波动性影响很大。
7.研制了螺母驱动型滚珠丝杠副并实际应用,借助超长轴键槽铣削机床对螺母驱动型滚珠丝杠副和丝杠驱动型滚珠丝杠副进行了振动响应实验和温升测试实验。实验研究表明螺母驱动型滚珠丝杠副系统第一阶固有频率大于丝杠驱动型滚珠丝杠副第一阶固有频率,在相同工作环境下丝杠驱动型滚珠丝杠副传动机构丝杠温升总体大于螺母驱动情况下丝杠的温升。
本研究为高速精密滚珠丝杠副的设计、制造提供了理论和技术支持,为研制开发具有完全自主知识产权的高速精密滚珠丝杠副指出了一条切实可行的途径,对提高我国数控机床的制造水平有较大的理论意义和实际应用价值。
Numerical control machine tools of large-scale and high-speed require not only a continuous increase in rotating speed of spindle but also a more rapid feed speed. Conventional ball screw pair, especially the large stroke screw pair of large-scale, heavy-duty and high-end numerical control machine tools, is much heavier than the nut. Therefore, screw rotary inertia force can cause the rising of heat, deformation and severe energy consumption.The deformed screws will produce vibration and noise during the rotation reducing the operation accuracy of the equipment. This remains an open question in the field. Therefore, according to the relativity of movement, the study puts forward a new-type of "nut-driven ball screw pair" and changes the traditional "screw-driven mode" to "nut-driven mode".
With the aid of mathematical modeling, mechanical analysis, computational analysis software, experimental study and other methods, the high-speed transmission performance of nut-driven ball screw pair on the basis of establishing rolling body kinematics, contact model and feed system structural dynamics model was studied in this thesis. The contents of the study are as follows:
1. According to kinematical theory, the rolling body of high-speed but-driven ball screw pair was analyzed. The study has clarified the kinematical relationship between balls rolling speed and drive nut axis revolving speed, deduced the revolution and rotation angular speed of the rolling body and acquired the contact point position and sliding speed of the rolling body in double nut. A conclusion is drawn based on theoretical analysis that the speed and direction of rolling body in driving nut of nut-driven ball screw pair are different from those of rolling body in driving nut of screw-driven ball screw pair; at the same driving speed, the revolution and rotation angular speeds of rolling body of nut-driven ball screw pair are lower than those of rolling body of conventional screw-driven ball screw pair.
2. According to Hertz's contact theory, analysis on kinematics and dynamics rolling element contact characteristics of nut driven ball screw pair under high-speed was performed. In an effort to establish contact analysis model for high-speed nut-driven ball screw pair under joint action of axial load, inertial effect, displacement constraint and apply iteration method to solve non-linear simultaneous equations. At the same time, the change rule of ball screw pair contact parameters under different revolving speed and axial force has been analyzed as well. Feed acceleration was obtained on the basis of theoretical calculation. The results show that when ball screw pair is at a high speed, contact angle, axial load and elastic deformation in the nut assembly change with speed and axial load. Compared with screw-driven type, it is driven by the motor with the same torque; nut-driven ball screw reduces rotational inertia of drive system, thereby reducing energy consumption of system driver; nut-driven feed system can produce great feed acceleration and has high speed.
3. The dynamical analysis on feed system of double nut-driven ball screw pair with adjustable pre-tightening force was carried out; firstly, by establishing the structural dynamical model of ball screw pair, both the effects of changes in pre-tightening force on natural frequency and that of the changes in major design parameters on the low order natural frequency of the system have been analyzed. The results show that the natural frequency of feed system has time-varying characteristics. Compared with conventional screw-driven type, it adopts nut-driven ball screw pair, which improves the low order natural frequency of feed system, causes the system to have a wider bandwidth, improves the speed loop gain and position loop gain of the system, and thus enhances rapid response capacity and machining accuracy of the feed system.
4. The study established the analysis model of friction torque to analyze the generating mechanism of friction torque of the ball screw pair. The influences of manufacturing errors and the axial load on the friction torque were analyzed. The reasons of low-frequency fluctuations of friction torque were studied. It applies the elastic hydrodynamic lubrication theory to analyze the lubrication conditions of ball screw pair. The results show that the axial load and rolling path waviness have a significant impact on fluctuation of friction torque.
5. The nut-driven ball screw pair was designed and put into practical application, and relied on super long axis keyway milling machine to carry out vibration response test and temperature test on nut-driven ball screw pair and screw-driven ball screw pair. Experimental studies show the first-order natural frequency of nut-driven ball screw pair system is higher than that of screw-driven ball screw pair; under the same operating environment, the temperature rise of screw-driven ball screw pair is higher than that of nut-driven ball screw pair.
The study provides the theoretical and technical supports for design and manufacture of ball screw pairs with high speed and high precision, indicating a practical way to the research and development of high-speed and high-precision ball screw pair with completely independent intellectual property rights, which showed theoretical and practical significance to improve the manufacturing level of CNC machine tools in China.
本研究借助于数学建模、力学分析、计算分析软件和实验研究等方法,在构建滚动体运动学、接触模型及进给系统结构动力学模型基础上,对螺母驱动型滚珠丝杠副高速传动性能进行研究,研究内容主要包括：
1.根据运动学理论,对高速螺母驱动型滚珠丝杠副滚动体运动学进行分析。求解了滚珠滚动速度与驱动螺母轴转速之间的运动关系,推导出滚动体公转和自转角速度,求取双螺母内滚动体接触点位置及滑动速度。理论分析得出相同驱动速度时螺母驱动型滚珠丝杠副滚动体公转和自转角速度低于传统的丝杠驱动型滚珠丝杠副滚动体公转和自转角速度。
2.根据Hertz接触理论,对高速螺母驱动型滚珠丝杠副滚动体接触特性进行分析。建立了轴向载荷、惯性效应、位移约束联合作用下的高速螺母驱动型滚珠丝杠副接触分析模型,应用迭代法求解非线性方程组,分析了不同转速和轴向力等工况下滚珠丝杠副接触参数的变化规律。根据理论计算求取系统进给加速度。结果表明滚珠丝杠副高速运动时,螺母组件内接触角、法向载荷以及弹性变形随转速和轴向载荷的变化而变化。与丝杠驱动型相比采用相同额定转矩电机驱动,螺母驱动型滚珠丝杠副降低了传动系统转动惯量,进而降低系统驱动能耗,螺母驱动型滚珠丝杠副可获得更高进给加速度,更具有高速性。
3.对预紧力可调的双螺母驱动型滚珠丝杠副进给系统进行结构动力学分析,首先建立滚珠丝杠副结构动力学模型。分析了预紧力的变化对固有频率的影响规律,主要设计参数的变化对系统低阶固有频率的影响。结果表明,进给系统固有频率具有时变性。与传统的丝杠驱动型相比,采用螺母驱动型滚珠丝杠副,提高了进给系统低阶固有频率,可使系统具有更宽的通频带,提高系统的速度环增益和位置环增益,从而提高整个系统的快速响应能力和加工精度。
4.建立了摩擦力矩的分析模型,分析了滚珠丝杠副摩擦力矩的产生机理。研究轴向载荷、轨道制造误差等对摩擦力矩的影响,分析了摩擦力知低频波动的原因。运用弹流动力润滑理论分析滚珠丝杠副的润滑状态。结果表明轴向载荷、滚道波纹度是对摩擦力矩波动性影响很大。
7.研制了螺母驱动型滚珠丝杠副并实际应用,借助超长轴键槽铣削机床对螺母驱动型滚珠丝杠副和丝杠驱动型滚珠丝杠副进行了振动响应实验和温升测试实验。实验研究表明螺母驱动型滚珠丝杠副系统第一阶固有频率大于丝杠驱动型滚珠丝杠副第一阶固有频率,在相同工作环境下丝杠驱动型滚珠丝杠副传动机构丝杠温升总体大于螺母驱动情况下丝杠的温升。
本研究为高速精密滚珠丝杠副的设计、制造提供了理论和技术支持,为研制开发具有完全自主知识产权的高速精密滚珠丝杠副指出了一条切实可行的途径,对提高我国数控机床的制造水平有较大的理论意义和实际应用价值。
Numerical control machine tools of large-scale and high-speed require not only a continuous increase in rotating speed of spindle but also a more rapid feed speed. Conventional ball screw pair, especially the large stroke screw pair of large-scale, heavy-duty and high-end numerical control machine tools, is much heavier than the nut. Therefore, screw rotary inertia force can cause the rising of heat, deformation and severe energy consumption.The deformed screws will produce vibration and noise during the rotation reducing the operation accuracy of the equipment. This remains an open question in the field. Therefore, according to the relativity of movement, the study puts forward a new-type of "nut-driven ball screw pair" and changes the traditional "screw-driven mode" to "nut-driven mode".
With the aid of mathematical modeling, mechanical analysis, computational analysis software, experimental study and other methods, the high-speed transmission performance of nut-driven ball screw pair on the basis of establishing rolling body kinematics, contact model and feed system structural dynamics model was studied in this thesis. The contents of the study are as follows:
1. According to kinematical theory, the rolling body of high-speed but-driven ball screw pair was analyzed. The study has clarified the kinematical relationship between balls rolling speed and drive nut axis revolving speed, deduced the revolution and rotation angular speed of the rolling body and acquired the contact point position and sliding speed of the rolling body in double nut. A conclusion is drawn based on theoretical analysis that the speed and direction of rolling body in driving nut of nut-driven ball screw pair are different from those of rolling body in driving nut of screw-driven ball screw pair; at the same driving speed, the revolution and rotation angular speeds of rolling body of nut-driven ball screw pair are lower than those of rolling body of conventional screw-driven ball screw pair.
2. According to Hertz's contact theory, analysis on kinematics and dynamics rolling element contact characteristics of nut driven ball screw pair under high-speed was performed. In an effort to establish contact analysis model for high-speed nut-driven ball screw pair under joint action of axial load, inertial effect, displacement constraint and apply iteration method to solve non-linear simultaneous equations. At the same time, the change rule of ball screw pair contact parameters under different revolving speed and axial force has been analyzed as well. Feed acceleration was obtained on the basis of theoretical calculation. The results show that when ball screw pair is at a high speed, contact angle, axial load and elastic deformation in the nut assembly change with speed and axial load. Compared with screw-driven type, it is driven by the motor with the same torque; nut-driven ball screw reduces rotational inertia of drive system, thereby reducing energy consumption of system driver; nut-driven feed system can produce great feed acceleration and has high speed.
3. The dynamical analysis on feed system of double nut-driven ball screw pair with adjustable pre-tightening force was carried out; firstly, by establishing the structural dynamical model of ball screw pair, both the effects of changes in pre-tightening force on natural frequency and that of the changes in major design parameters on the low order natural frequency of the system have been analyzed. The results show that the natural frequency of feed system has time-varying characteristics. Compared with conventional screw-driven type, it adopts nut-driven ball screw pair, which improves the low order natural frequency of feed system, causes the system to have a wider bandwidth, improves the speed loop gain and position loop gain of the system, and thus enhances rapid response capacity and machining accuracy of the feed system.
4. The study established the analysis model of friction torque to analyze the generating mechanism of friction torque of the ball screw pair. The influences of manufacturing errors and the axial load on the friction torque were analyzed. The reasons of low-frequency fluctuations of friction torque were studied. It applies the elastic hydrodynamic lubrication theory to analyze the lubrication conditions of ball screw pair. The results show that the axial load and rolling path waviness have a significant impact on fluctuation of friction torque.
5. The nut-driven ball screw pair was designed and put into practical application, and relied on super long axis keyway milling machine to carry out vibration response test and temperature test on nut-driven ball screw pair and screw-driven ball screw pair. Experimental studies show the first-order natural frequency of nut-driven ball screw pair system is higher than that of screw-driven ball screw pair; under the same operating environment, the temperature rise of screw-driven ball screw pair is higher than that of nut-driven ball screw pair.
The study provides the theoretical and technical supports for design and manufacture of ball screw pairs with high speed and high precision, indicating a practical way to the research and development of high-speed and high-precision ball screw pair with completely independent intellectual property rights, which showed theoretical and practical significance to improve the manufacturing level of CNC machine tools in China.
引文
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