Research Of Static And Dynamic Characteristics Of High-Speed Ball Bearing-Outer Rotor System

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.