This paper presents theory, analysis, and results of
a novel spindle design (patent pending) with
application to bevel gear lapping and testing
machines. This spindle design includes a
rotationally compliant element that can substantially
reduce the dynamic forces induced between the
gear members while rolling under load. In lapping
machines, this technology has added stability to the
process and raised maximum speeds by 50% as
compared with conventional spindles. In testing
machines, it has reduced the influence of the
machine on the quality of the test results and
allowed them to retain their integrity at higher
speeds. Although, particularly advantageous in
direct-drive spindle designs, the compliant concept
can benefit belt-driven or geared spindles as well.
The rotationally compliant element, found in at least
one spindle in such machines, breaks the total
spindle inertia into two parts: a relatively free forward
part into which the workholding equipment and gear
is mounted, and a servo-controlled rearward portion
that contains the motor (or is driven by a motor),
motion transducer, and chuck/dechuck mechanism.
The inertia of the forward portion is minimized,
whereas the inertia of the rearward portion can
remain or be made large. When reduced inertia
lowers the dynamic forces between the gear teeth at
their point of generation, the motion transmission
error (MTE) becomes truer to the gearset geometry
and the excitation of the machine structure is
reduced.
The presence of a highly compliant rotational
element with spring-like properties also allows a
novel torque control technique to be applied in a
CNC machine. This technique reduces the burden
on the electronic servo system to actively maintain
torque in an environment of dynamic disturbances,
relying instead on the laws of physics on a simple
mechanism to reject these disturbances.
The theory of this highly compliant (HC) spindle
concept is presented using simplified models,
providing the explanation for the process benefits it
brings. Analysis and simulations give additional
insight into the dynamics of the system. Finally,
some examples of actual lapping results are
presented.