Page 273 - Modular design for machine tools

232 Engineering Design for Machine Tool Joints

Surface roughness. Notwithstanding the machining method of the joint
surface, the higher joint stiffness can be realized when the joint surface
is smoother, provided that the joint surface has no waviness and/or flat-
ness deviation.
Oil and grease as interfacial layer. In the actual machine tool joint, it is
difficult to realize the pure dried condition of the joint surface, but the
oil and grease exist always between the joint surfaces. In the flat joint
under static loading, however, these interfacial layers have no effect on
the joint deflection except for the lapped joint.

Hardness of joint surface. In general, Young’s modulus of the material
is independent of the hardness, and then the joint stiffness after first
loading appears not to have the influence of hardness. In accordance
with the measured results for the shaped joint made of EN 9 steel,
where the hardness of the joint surface was varied using direct hard-
ening and tempering or direct hardening and annealing, as reported by
Thornley and coworkers, the joint stiffness corresponding to unloading
is, contrary to the suggestion stated elsewhere, somewhat dependent on
the hardness of the joint surface. In short, it is very interesting that the
joint stiffness increases with hardening of the joint surface, simultane-
ously showing less residual deflection.

6.3 Design Formulas for Tangential Joint
Stiffness, Related Researches, and
Peculiar Behavior of Microslip

6.3.1 Expressions for static tangential
joint stiffness
The machine tool joint is often subjected to tangential loading together
with the normal preload, resulting in the occurrence of shear at the
interface. This shear deteriorates, for instance, the positioning accuracy
of the carriage of the engine lathe, where the positive stopper can be
used. In contrast, the shear induces duly the residual displacement or
microslip, by which the damping capacity at the jointed surface can be
determined. The joint under tangential loading can be represented with
a model that is a simple flat joint under the normal preload and tan-
gential loading and, in due course, is worth investigating as well as
that under only normal loading to understand deeply the characteris-
tics of the machine tool joint (see Fig. 5-17).
Importantly, Kirsanova [19] is credited to the first researcher for the tan-
gential joint stiffness in 1967. In due course, Kirsanova represented the
tangential joint deflection with an empirical expression to assist the design
procedure of the slideway. Table 6-8 summarizes the expressions for the