On the Dynamic Accuracy of Machine-Tool Hydraulic Copying Systems

Abstract

The mathematical model of a hydraulic copying system, utilizing a fourway, critical centered spool valve and a symmetrical volume power cylinder under the action of dynamic cutting forces is developed. The model takes into account the following features: (a) dynamic behavior of the control valve and the action of the flow forces, (b) dry-friction between the copying system and its mountings, (c) dynamic behavior of the stylus, (d) time domain model of the kinematic input due to the template configuration, and (e) dynamic input that accounts for the cutting force fluctuations and its interaction with the velocity response of the system. A dynamic accuracy criterion which includes static, kinematic, and transient errors is formulated. The dynamic accuracy criterion is a function of the specified manufacturing tolerance of the produced workpiece and can be directly evaluated from the system analysis. Analog computer simulations are carried out to study the effects of various influencing parameters on the dynamic accuracy of copying systems. Plots are developed to be used as a guide for the design and operation of hydraulic copying systems. The dynamic accuracy is calculated for commercial copying systems using the methods developed and found that the results are in close agreement with the data supplied by the manufacturers.