Computation of shaping errors for fine boring of smooth and stepped holes

On the basis of precision theory we propose the method of computation of static and dynamic errors of cross-sectional shapes of holes in fine boring of smooth and stepped holes. We consider particular cross-sectional shape errors caused by such factors: – Error of the tooled hole form caused by the axis hope displacement in the workpiece relative to the spindle axis; – Error of the tooled hole form caused by the hole out-of-roundness in the workpiece; – Error of the tooled hole form caused by unevenness of the cutter radial compliance at the angle of spindle rotation. According to time characteristics the errors can be divided into static with frequency substantially less than the lowest natural frequency of the process system, and dynamic, caused by vibrations. Static error rate is usually a multiple of the spindle speed. The computations of deviations from the roundness of the cross section caused by vibrations are determined by computing the amplitudes of forced vibrations. Computations of individual static errors based on the average values of compliance, the material being processed and the processing mode are reduced to construction of nomographs for various materials. Dynamic errors are determined by computation of forced vibrations amplitudes on the basis of systems of ordinary differential equations describing the vibrations of a machine closed dynamic system. These equations allow to compute the amplitude of the forced vibrations of smooth and stepped boring bars. A distinctive feature of the computations for multiple tooling is allowance for mutual influence of excitations arising at each step of a boring bar. It is assumed that at multiple tooling each of the working cutters creates its own errors, the values of which are found by the nomograms for single-cutter tooling. Full tooling error at each step caused by some source of error is determined as the sum of the errors: of both, own and additional, caused by all working cutters. Additional errors can be found through coefficients of influence through dividing by the respective cutter's own compliance and through multiplying by the appropriate factor of influence. We obtained results of computations and experiments of the dependence of the total error on the ratio of the boring bar steps lengths. Analysis of roundness charts of the bored holes shows that vibrations can be a factor largely determining the shape of the cross section of the hole. Experiments have shown that when the rotation speed changed the excitations of the spindle poles changed too. Under unfavorable excitation frequencies the tooling errors increase by 1,5–2 times. The study results allow us to compare the two most common ways to reduce the errors caused by elastic deformations: the use of the dynamic damper and the processing of holes in two runs. The experimental results confirm the non-monotonic dependence of the amplitudes of forced vibrations on the ratio of the boring bar steps lengths.