Page 235 - Modular design for machine tools

Basic Knowledge of Machine Tool Joints 195

K , K = P/δ, kgf/µm
sh
sn
P
Q

δ
P
δ

Normal joint stiffness K sn Tangential joint stiffness K sh
Figure 5-17 Stiffness expressions for flat joints under normal and
tangential loading.

In fact, Eisele and Corbach [16] and Andrew [17] proposed this
expression and verified its validity to a large extent. Assuming that the
j( t )
joint deflection is a a e when the flat joint is subjected to the load
0
j t
P dyn P e , both the in-phase and quadrature stiffnesses yield to
0
K k and K c (5-2)
b
a
In the dry metal joint, the damping capacity in the direction normal to
the joint surface is likely to be nil, i.e., K 0, and thus the dynamic
b
joint stiffness yields K itself.
a
Within an engineering context, the dynamic behavior of the joint is very
complicated compared with the static behavior, and consequently it is not
possible to express perfectly the dynamic behavior of the joint using only
the dynamic stiffness. In fact, such frequency response and transmitting

= P e jωt
P dyn 0
a = a · e j(ωt – ξ)
0

k c

K dyn = K + jk = k + jωc Figure 5-18 Expression for dynamic
a
b
joint stiffness (by Eisele and
P dyn : Exciting force Corbach).
a: Vibration amplitude
ξ: Phase difference between P dyn and a