Page 260 - Modular design for machine tools

Engineering Design Fundamentals and Single Flat Joint Characteristics 219

As can be readily seen, the joint deflection is in exponential pro-
portion to the interface pressure p. In addition, C and m are the con-
stants depending mainly on the joint material, machining method and
roughness of joint surface, machined lay orientation, flatness deviation,
and size of joint area. The joint stiffness per unit area is thus given by

dp/d [1/(Cm)] p (1 m) (6-2)

In the engineering design, it is necessary to first determine the values
C and m in consideration of the dimensional and performance specifi-
cations of the objective joint. In general, the constant C is to be the
lower value for the joint made of high tensile strength material, having
small mating area, with high stiffness of joint surroundings, and with
mating surface of higher quality.
Table 6-2 shows some representative values for C and m available for
2
the joint, where the joint of 16 cm contact area is made of cast iron and
2
the interface pressure is less than 25 kgf/cm . These values were shown
by Back et al. [6], after arrangement of the experimental data reported
by Levina [3, 7], and Ostrovskii [4]. Although it has some limitations,
the expression can obviously unveil the essential feature of the joint,
clearly showing that m is, in general cases, equal to 0.5. In addition, it
is obvious from Eq. (6-2) that the joint stiffness is dependent upon the
interface pressure, simultaneously showing nonlinearity.

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TABLE 6-2 Values of C and m (Available up to p = 25 kgf/cm ) (Arranged by and
courtesy of Back)
Finishing methods Constants
Points in any Depth of scraping or
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l in of bearing area surface roughness, (mm) C m
3–5 0.3 0.5
20–25
6–8 0.5 0.5
Hand-scraped/ 15–18 0.8–1.0 0.5
hand-scraped
10–12 1.3–1.5 0.5
5–12 1.5–2.0 0.5
Hand-
scraped/ 15–18 1.0 R CLA 0.8–1.0 0.4
ground
Peripheral
ground/
peripheral 1.0 R CLA 0.6–0.7 0.4–0.5
ground
Finish planning/ 0.6 0.5
finish planning
Cast iron joint
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Note: Values of C and m are available when l and p are in mm and kgf/cm , respectively.