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Engineering Design Fundamentals and Single Flat Joint Characteristics 233

TABLE 6-8 Expressions for Tangential Joint Deflection
and Stiffness K s
Conditions obtained expressions Examples of
joints to be
Expression Relationships Shape and
p kgf/cm 2 p or t between K j size of joint applicable
t
and K 0 surface expressions
Rectangular type
0.9–3.6
Kirsanova < 2.0 — Area: 225 cm 2 Slideways
[19] d = K t kgf/cm 2
t
1.8–15 Circular type
Area: 51 cm 2
> K
K 0 j Annular ring
Koizumi d = C (t/p) 0–100 < 20 kgf – type Bolted joint
et al. [20] 2
K < K j Area: 2–26 cm
0
< 7.0
Back et al. <60 2
K s = (1/R) p S kgf/cm — — —
[21] (presumed)
(presumed)
p : tangential load, t: shear stress, p: normal interface pressure, C, K , R and S: constants.
t
t
Note: For the constant in the expression of Koizumi, please refer to Table 6-9.
tangential joint deflection so far proposed, although not guaranteeing
their reliabilities as well as that for damping, because no other investi-
gations were carried out after then by other researchers and engineers. In
short, the expression of Kirsanova can be written as

K P (6-3)

where
elastic tangential deflection, m
2
K coefficient of contact shear compliance, m cm /kgf

P tangential load, kgf/cm 2

The coefficient K is a function, in which the normal preload and surface

finish of the joint are variables, as shown in Fig. 6-11. For those of
Koizumi et al. and Back et al., the values for the constants are, in due
course, given as shown in Tables 6-9 and 6-10, respectively. It is very
interesting that the constant S in the expression of Back et al. is 0.5,
the same as that in the expression of Ostrovskii.

6.3.2 Representative researches into
behavior of the static tangential joint
stiffness and the microslip
Owing to the complexity of the characteristic features, the tangential
stiffness of the flat joint is not fully clarified yet, although interesting
behavior was already observed and reported elsewhere. More specifically,