Page 259 - Modular design for machine tools

218 Engineering Design for Machine Tool Joints

6.2 Design Formulas for Normal Joint
Stiffness and Related Research
6.2.1 Expressions for static normal
joint stiffness
The single flat joint under normal loading can be characterized by the
following two facets.

1. The joint deflection is in nonlinear relation to the applied load.
2. The load-deflection curve shows, in general, the hysteresis behavior.
>K shows the uniform interface
In addition, the single flat joint of K 0 j
pressure across the whole joint surface.

In full consideration of these characteristic features, the expressions for
the normal joint deflection have been proposed as shown in Table 6-1. Of
these, the expression of Ostrovskii, as widely accepted in the engineer-
ing sphere, can be considered to be applicable to the engineering design
to a large extent.
More specifically, the expression of Ostrovskii can be written as
m
Cp (6-1)
where joint deflection in normal direction
p interface pressure
C, m constants

TABLE 6-1 Expressions for Normal Joint Deflection

Conditions Obtained Expressions Examples of
joints to be
Expression Relationships Shape and applicable
p, kgf/cm 2 between K j size of joint expressions
and K 0 surface
Slideways Slideway (including
Levina [3] l = C p < 4 K >> K j of machines locally deformed
0
0
in full-size condition)
K > K j Slideway (including
0
Ostrovskii [4] l = Cp m 0–25 – Circular type locally deformed
2
K < K j Area: 16 cm condition)
0
Annular ring
K > K j
0
Connolly & b 8–500 – type Bolted joint
Thornley [5] p = ae * l Area:
K < K j
0
around 13 cm 2
l: Normal joint deflection p: Interface pressure
a, b , C , C and m: Constants
*
0
Note: Numbers in brackets indicate references