高速滚珠轴承—外转子系统静动态特性研究
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摘要
本文结合国家“十一五”军品配套研制项目的子项目“陀螺电机轴承单元动态性能仿真技术的研究”和国家自然科学基金项目(50575155)对高速滚珠轴承—外转子系统静动态特性进行了理论和试验研究。
首先确定了滚珠轴承高速特性方程组的基本变量,提出了基于接触角迭代的计算方法,优化了高速滚珠轴承动态特性求解方法。将钢球高速运转时内外接触变形与接触角的变化关系简化为首尾相接的两个虚拟非均匀杆,推导了虚拟非均匀杆系模型的刚度矩阵,形成了基于非均匀杆系有限元法的高速滚珠轴承动态特性计算方法。考虑陀螺力矩影响时,引入了根据滚珠瞬态平衡方程推导的滚珠姿态角公式,该计算方法完全克服了沟(滚)道控制假设的不足。引入了滚珠与沟道摩擦系数的半经验公式,形成了高速滚珠轴承三向受载的拟动力学模型。分别对外圈旋转时的滚珠离心力、陀螺力矩和旋滚比与内圈旋转的工况作了计算对比。确定了外圈旋转时的滚珠球心与沟道曲率中心相对位置,建立了适于外圈高速旋转的高速滚珠轴承拟动力学模型,为外转子(如微机械式陀螺马达)的动力特性分析与故障检测提供了理论基础。以某航空微机械式陀螺马达高速滚珠轴承—外转子为例进行了计算,结果表明在大约基频的1 2处存在亚谐振。对作为计算对象的陀螺马达进行了动态测试,验证了计算模型和计算结果的正确性。本论文的研究结果为高速滚珠轴承—外转子系统动力学研究提供了依据。
The works in this paper are supported by the national natural sciencefoundation (50575155), and the military supporting research of national“eleventh five-year plan”-“The research of simulation of dynamic characteristics of baering unit on gyro motor”.
The high-speed ball bearing-outer rotor system is applied spreadly in the field such as high-speed machine tool, fans and mechnical gyro motor.The research of it’s dynamic characteristics is the foundation of life span and reliability. But it’s calculation is very complex, and no special model for the outer ring rotation ball bearing, so the deeply research is restricted.
This paper proceeded in the basic calculation method of ball bearing, a new method is put forward, and a special model for outer ring rotation ball bearing and it’s outer rotor is established.The research from this paper laid the foundation for the dynamic analysis of high-speed ball bearing-outer rotor system.
The main research works can be described as follows:
(1)Based on the dynamic change of contact angle on hing-speeded angular-contact ball bearing,a system analysis of equations group of dynamic character and variable deliver of the adjunct equations is given respectively . Based above analysis , a rule is found that every adjunct equation is the founction of internal and external factual contact angular. And then a method based on the analysis of contact angular range is put forward which avoid the complexity and convergence of conventional Newton-Raphson method used in solving the dynamic equations group. The method of solving equations changdes into a method of proving equations. Furtherly a criterion which differentiates the optimum contact angular is given. At last, an example is given to indicate that the result of new method is very anastomotic to that obtained from traditional method. A chart about coupled variables is obtained which shows that the contact angle are the ultimate variables.Based on analysis above, an algorithom according to the feature of the bearing under axial load is put forward, which takes the contact angle as the iterate variables. An anlysis according to the present calculation results is given, which shows that the increment of internal contact angle is larger than that of external contact angle, this analysis would be helpful to define the contact angle field. So, the search field of contact angle is cut to one half, the calculation is simplified obviously.
(2)A new calculation method is put forward which simplifies the rolling ball under load at 3 direction into two hinge short bar according to the change features of the contact angle under high speed and the deformation of rolling ball and raceway. The specific form of stiffness matrix is given and the solving process by setting initial value of the load at three direction is discussesd. The congervence property is improved by this method. An example indicates that the method in this paper is feasible, and can replace the conventional quasi statics method.
(3)According to the analysis of equilibrium equation of inner ring,a rule is discoveried that the finite element method calculation model includes separate and known variables. So, the finite element method calculation model could be reduced into 4-order. Then, the calculation process of load distribution is simplified in a greater extent, and the simplified model is suitable for the calculation method based on Matlab, the stability of calculation is improved. An example indicates that the method in this paper is feasible, and can replace the conventional quasi statics method.
At the same time, the equation for determining the rollaway control parameter which decides the ratio of rollaway friction was deduced, so the determining process of the rollaway control parameter could be completed with the process of solving finite element model, and the rollaway control parameter could be more precise. The complexity of the variables'coupling in the conventional calculation method and the deficiency of the rollaway control assumption could be avoided.
(4)Based on the analysis of ratio of revolution and rolling on high-speed ball bearing , the shortage of raceway control theory is put forward. Then a precise relationship between inner and outer raceway control parameter is established according to the equilibriation of frictional force and gyro moment on rolling ball.The semi-empirical formula about friction factor between rolling element and raceway is introduced into the calculation process of linkage finite element method model. To avoid the shortage of raceway control theory, the attitude angle of rolling ball decided by raceway control theory is substituted by the one obtained from the analysis of D’Alembert princicle. So the friction factor and atitude angle of rolling ball are depended on normal load of rolling ball, and then in an accurate form and could be solved with dynamic equations group of high-speed ball bearing. At the same time,the quasi dynamics model of gyro motor ball bearing under axial load is established. A system analysis about the kinetic and dynamics characteristic of outer ring revolution high-speed ball bearing is given.Firstly,according to the variable deliver relationship,the kinetic parameters such as centrifugal force,gyro moment and revolution-rolling ratio of ball are simplified,so the coupling kinetic parameters are effectively segregated;furtherly,the three parameters are compared with the ones under inner ring revolution high-speed ball bearing,and some regulars are found such as the rollaway control assumption is not fit for the work condition of inner ring revolution.
(5)The lelative position of the rolling ball and rollaway center of curvature is restablished, and the explanation of the mechanics of the axial and radial deformation and moment rake angle is supplied, the lelative position relation of the rolling ball and rollaway center of curvature which is fit for the outer ring revolution high-speed ball bearing is set up.The linkage finite element model for outer ring revolution is completed, at the same time the method of solving is discussed.
Based on the above work,the specific calculation process based on the differences for bearing stiffness is given.Then a dynamic model for high-speed ball bearing and outer rotor came into being.
(6)According to the calculation method from above, a calculation example against a certain of air gyro motor and high speed ball bearing system is given, and the calculation about the unbalance quality of outer rotor is given too, through the spectrum transform based on the time history, the sub-resonant occuring at the 1 2 fundamental frequency is found.
(7)In order to verify the calculation model and results,a test experiment is made,and the sub-resonant is found too from the test signals,through analysis, the sub-resonant occurs between the 0.55-0.7 fundamental frequency,evne at the 1 4 fundamental frequency(axial test).
At last, a summery and prospect is given, the job project made for the future is put forward. The word in this full text is a whole research including the calculation method of static and dynamic characteristics, dynamic test method, detection and analysis of high-speed ball bearing-outer rotor system. The research supplied a foundation and gist for the design and fault detection of high-speed ball bearing-outer rotor system, and is significative for the advance of reliability and operation performance of the high-speed ball bearing-outer rotor system.At the same time, it is helpful for mastery of this key technology.
首先确定了滚珠轴承高速特性方程组的基本变量,提出了基于接触角迭代的计算方法,优化了高速滚珠轴承动态特性求解方法。将钢球高速运转时内外接触变形与接触角的变化关系简化为首尾相接的两个虚拟非均匀杆,推导了虚拟非均匀杆系模型的刚度矩阵,形成了基于非均匀杆系有限元法的高速滚珠轴承动态特性计算方法。考虑陀螺力矩影响时,引入了根据滚珠瞬态平衡方程推导的滚珠姿态角公式,该计算方法完全克服了沟(滚)道控制假设的不足。引入了滚珠与沟道摩擦系数的半经验公式,形成了高速滚珠轴承三向受载的拟动力学模型。分别对外圈旋转时的滚珠离心力、陀螺力矩和旋滚比与内圈旋转的工况作了计算对比。确定了外圈旋转时的滚珠球心与沟道曲率中心相对位置,建立了适于外圈高速旋转的高速滚珠轴承拟动力学模型,为外转子(如微机械式陀螺马达)的动力特性分析与故障检测提供了理论基础。以某航空微机械式陀螺马达高速滚珠轴承—外转子为例进行了计算,结果表明在大约基频的1 2处存在亚谐振。对作为计算对象的陀螺马达进行了动态测试,验证了计算模型和计算结果的正确性。本论文的研究结果为高速滚珠轴承—外转子系统动力学研究提供了依据。
The works in this paper are supported by the national natural sciencefoundation (50575155), and the military supporting research of national“eleventh five-year plan”-“The research of simulation of dynamic characteristics of baering unit on gyro motor”.
The high-speed ball bearing-outer rotor system is applied spreadly in the field such as high-speed machine tool, fans and mechnical gyro motor.The research of it’s dynamic characteristics is the foundation of life span and reliability. But it’s calculation is very complex, and no special model for the outer ring rotation ball bearing, so the deeply research is restricted.
This paper proceeded in the basic calculation method of ball bearing, a new method is put forward, and a special model for outer ring rotation ball bearing and it’s outer rotor is established.The research from this paper laid the foundation for the dynamic analysis of high-speed ball bearing-outer rotor system.
The main research works can be described as follows:
(1)Based on the dynamic change of contact angle on hing-speeded angular-contact ball bearing,a system analysis of equations group of dynamic character and variable deliver of the adjunct equations is given respectively . Based above analysis , a rule is found that every adjunct equation is the founction of internal and external factual contact angular. And then a method based on the analysis of contact angular range is put forward which avoid the complexity and convergence of conventional Newton-Raphson method used in solving the dynamic equations group. The method of solving equations changdes into a method of proving equations. Furtherly a criterion which differentiates the optimum contact angular is given. At last, an example is given to indicate that the result of new method is very anastomotic to that obtained from traditional method. A chart about coupled variables is obtained which shows that the contact angle are the ultimate variables.Based on analysis above, an algorithom according to the feature of the bearing under axial load is put forward, which takes the contact angle as the iterate variables. An anlysis according to the present calculation results is given, which shows that the increment of internal contact angle is larger than that of external contact angle, this analysis would be helpful to define the contact angle field. So, the search field of contact angle is cut to one half, the calculation is simplified obviously.
(2)A new calculation method is put forward which simplifies the rolling ball under load at 3 direction into two hinge short bar according to the change features of the contact angle under high speed and the deformation of rolling ball and raceway. The specific form of stiffness matrix is given and the solving process by setting initial value of the load at three direction is discussesd. The congervence property is improved by this method. An example indicates that the method in this paper is feasible, and can replace the conventional quasi statics method.
(3)According to the analysis of equilibrium equation of inner ring,a rule is discoveried that the finite element method calculation model includes separate and known variables. So, the finite element method calculation model could be reduced into 4-order. Then, the calculation process of load distribution is simplified in a greater extent, and the simplified model is suitable for the calculation method based on Matlab, the stability of calculation is improved. An example indicates that the method in this paper is feasible, and can replace the conventional quasi statics method.
At the same time, the equation for determining the rollaway control parameter which decides the ratio of rollaway friction was deduced, so the determining process of the rollaway control parameter could be completed with the process of solving finite element model, and the rollaway control parameter could be more precise. The complexity of the variables'coupling in the conventional calculation method and the deficiency of the rollaway control assumption could be avoided.
(4)Based on the analysis of ratio of revolution and rolling on high-speed ball bearing , the shortage of raceway control theory is put forward. Then a precise relationship between inner and outer raceway control parameter is established according to the equilibriation of frictional force and gyro moment on rolling ball.The semi-empirical formula about friction factor between rolling element and raceway is introduced into the calculation process of linkage finite element method model. To avoid the shortage of raceway control theory, the attitude angle of rolling ball decided by raceway control theory is substituted by the one obtained from the analysis of D’Alembert princicle. So the friction factor and atitude angle of rolling ball are depended on normal load of rolling ball, and then in an accurate form and could be solved with dynamic equations group of high-speed ball bearing. At the same time,the quasi dynamics model of gyro motor ball bearing under axial load is established. A system analysis about the kinetic and dynamics characteristic of outer ring revolution high-speed ball bearing is given.Firstly,according to the variable deliver relationship,the kinetic parameters such as centrifugal force,gyro moment and revolution-rolling ratio of ball are simplified,so the coupling kinetic parameters are effectively segregated;furtherly,the three parameters are compared with the ones under inner ring revolution high-speed ball bearing,and some regulars are found such as the rollaway control assumption is not fit for the work condition of inner ring revolution.
(5)The lelative position of the rolling ball and rollaway center of curvature is restablished, and the explanation of the mechanics of the axial and radial deformation and moment rake angle is supplied, the lelative position relation of the rolling ball and rollaway center of curvature which is fit for the outer ring revolution high-speed ball bearing is set up.The linkage finite element model for outer ring revolution is completed, at the same time the method of solving is discussed.
Based on the above work,the specific calculation process based on the differences for bearing stiffness is given.Then a dynamic model for high-speed ball bearing and outer rotor came into being.
(6)According to the calculation method from above, a calculation example against a certain of air gyro motor and high speed ball bearing system is given, and the calculation about the unbalance quality of outer rotor is given too, through the spectrum transform based on the time history, the sub-resonant occuring at the 1 2 fundamental frequency is found.
(7)In order to verify the calculation model and results,a test experiment is made,and the sub-resonant is found too from the test signals,through analysis, the sub-resonant occurs between the 0.55-0.7 fundamental frequency,evne at the 1 4 fundamental frequency(axial test).
At last, a summery and prospect is given, the job project made for the future is put forward. The word in this full text is a whole research including the calculation method of static and dynamic characteristics, dynamic test method, detection and analysis of high-speed ball bearing-outer rotor system. The research supplied a foundation and gist for the design and fault detection of high-speed ball bearing-outer rotor system, and is significative for the advance of reliability and operation performance of the high-speed ball bearing-outer rotor system.At the same time, it is helpful for mastery of this key technology.
引文
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