Determining an analytical criterion for the effective speed of a spindle unit for the automatic machining of long workpieces

Abstract

This study considers a long bar workpiece fixed in the spindle assembly of a bar lathe according to the “clamping chuck-intermediate radial support” scheme. The task addressed relates to the limitation in the effective spindle speed because of the operating speed approaching the first critical frequency of transverse vibrations of the bar.

A distinctive feature of the results is the representation of the critical speed as a function of three controlled parameters: the diameter of the bar, the length of the calculated span, and the stiffness of the intermediate radial support of the bar. That makes it possible to obtain an engineering criterion for the effective speed of the spindle assembly when machining a long bar workpiece.

Practically significant results are attributed to the features of the adopted model in which the clamping chuck is represented as an equivalent clamping, the intermediate support is considered to be a rigid or elastic-flexible radial support and the dimensionless parameter of relative stiffness μ is used. That has made it possible to reflect the transition from virtually no support to perfectly rigid support and to establish a nonlinear saturable effect of the support stiffness on the critical frequency.

For a solid round steel bar, a compact dependence nkp = Kcm · d/L2 was obtained, where Kcm ≈ 1.86 · 105 rev m/min. It was established that the span length has a quadratic effect on the critical frequency, the diameter has a linear effect, and an increase in the support stiffness is effective only up to the saturation zone. Based on the resulting relations, the limiting dependences of the effective operation of the system on the frequency load coefficient were constructed.

The results are suitable for the preliminary selection of the inter-support distance, the bar diameter, as well as the conditions of its support when designing, modernizing, and adjusting bar automatic lathes