Critical Speed Analysis And Structural Optimization Of Rotor-Ball Bearing Systems

Spindle technology has been developed along with the developments and demands ofmodern manufacturing technology such as high-speed grinding and high-speed CNCmachine tools. As the power and speed of spindles growing higher and higher, the spindleswith high speed are used more and more widely in many machine tools. The workingspeed of an spindle usually approximates its first critical speed, and most of the spindlebearings reached the limit speed allowed by their designs. so it is necessary to study thedynamic performance of an spindle such as natural frequency and critical speed.Based on the analysis of the dynamic states and the dynamic stiffness of ball bearingsrunning in high speed, the natural frequency and the critical speed of a rotor–ball bearingsystem is analyzed and the structure is optimized in this paper.Firstly, the contact between the rolling elements and raceways is analyzed by using ofHertzian contact theory, and the static analysis of ball bearings are finished then. Based onquasi-static model of the ball bearing which including the inertial effects of the centrifugalforce and the gyroscopic moment of the rolling elements, a numerical approach ispresented to calculate the dynamic characteristics parameters including dynamic stiffnessof a single spindle bearing or a spindle bearing group. Besides, the influences on thedynamic stiffness exerted by working speed and inner ring centrifugation are elaborated.What’s more, the effectiveness of both the model of the ball bearing and the Numericalcalculation programs are verified by analyzing specific examples.Combining with the effects of the nonlinear supporting characters of spindle bearings,the finite element model of the rotor-ball bearing system is built up as Timoshenko’s beam,where the shear effect and the gyroscopic effect of the spindle shaft are taken into account.Based on the model, a program is developed in Matlab to calculate dynamiccharacteristics parameters including the first critical speed. The effectiveness of both theNumerical calculation program and the model of the rotor–ball bearing system are verifiedby comparing the calculation results and experiment observations. Besides, taking thebearing distance and inner diameter of the shaft as design variables and the first critical speed as objective, a practical rotor–ball bearing system is optimized, the result shows thefirst nature frequency increases by6.68%after optimization.Through the dynamic analysis of the ball bearing and the rotor–ball bearing system,It is showed that the stiffness of spindle bearings is obviously influenced by the workingspeed and inner ring centrifugation, in order to get more realistic result, It is necessary totake this into consideration during analyzing the dynamic characteristics of a rotor–ballbearing system; The bearing distance is the main factor which influencing the criticalspeed of a rotor–ball bearing system, the dynamic performance of a rotor–ball bearingsystem can be improved by disposing the spindle bearings reasonably.