Dynamic Analysis and Design of Steel-Ball Grinding Machines Based on No-Slip Cases
Based on no-slip cases between steel balls and lapping discs while a horizontal grinding machine is working, the motion equations of the ball lapping are established and the law of motion is revealed by the MATLAB software. This paper shows that the difference of the trace spacing is reduced by increasing the disc diameter, which can make the trace distribution of the steel ball surface more uniform. In order that balls do not slip when rotary disc drives them to rotate, the ranges of the lapping pressure and lapping disc speed is deduced by using the dynamics analysis considering from the vertical trench surface and along the groove surface, respectively. Finally, this paper takes the selected material as an example to analyze the process parameters that affect the lapping curves, and explains the selection principles of alpha and beta when the trench has some bias, which can provide a reference to improve the quality of the steel balls surface.
Variations of instability in a rotating spindle system with various bearings
Abstract To drive the speed of spindle faster and faster, especially for micro-via-drilling, the gas bearing–spindle is a must. However, most investigations of the dynamic characteristics of the spindle system are limited to the ball bearing type of spindle. This work examines the dynamic instability of a rotating spindle system with various bearings to elucidate the difference between the ball and gas bearing–spindle systems. A round Euler–Bernoulli beam is used to approximate the spindle. The Hamilton principle is applied to derive the equation of motion for the spindle system, and the multiple scales perturbation method is employed to solve the instability solution of the system. The effects of bearing types and speeds of rotation on the dynamic characteristics and instability of a rotating spindle system are further studied.
Analytical Stability Analysis of Variable Spindle Speed Machining
A new analytical model to predict the chatter stability of variable spindle speed machining is presented. This model is based on transforming the linear differential equations with time varying delay to the solution of an infinite order characteristic equation. The model has been validated using the results of numerical time domain simulations and through experimentation. The analytical model employs normalized parameters which permits its use in studying the stability of variable spindle speed machining systems with a wide range of parameters without having to solve the complex system of differential equations. The analytical model is also used to design optimal variable spindle speed machining parameters in the presence of known fixed or varying machining dynamics.