Анотація:

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.

Received:

Sunday, May 15, 2016

Accepted:

Wednesday, August 24, 2016