Page 232 - Modular design for machine tools

192 Engineering Design for Machine Tool Joints

At present, each region cannot be exactly and quantitatively deter-
mined; however, the idea described here is considered reasonable and
applicable to the analysis, design, and research of the joint. To define the
region of the joint and to research the joint, thus, it is of great importance
to grasp the magnitude of the interface pressure being acted on the joint.
In consideration of some data already reported elsewhere, the magni-
tudes of the interface pressure can be roughly estimated as follows.

• For the sliding joint without local deformation: from 1 to 50 MPa
2
(about 0.1 to 5 kgf/cm )
• For the sliding joint with local deformation: from 50 to 250 MPa (about
2
5 to 25 kgf/cm )
2
• For the bolted joint: from 500 to 2000 MPa (about 50 to 200 kgf/cm )
Although the exact definition of joint itself has not been determined
yet, it is, at the least, necessary to represent clearly the leading joint
characteristics. Based on long-standing experience, there are two rep-
resentative expressions of the static and dynamic behavior of the struc-
tural body component in machine tools, such as in the bolted joint in
Fig. 5-15. The expressions for bending stiffness K SB and torsional stiff-
ness K ST are suitable for the engineering design, whereas another
expression is aimed at describing directly the joint characteristic itself.
The joint characteristic can be defined by using, e.g., the inclination
angle created by the existence of the joint. This inclination angle is
very sensitive to change in the essential features of the joint, showing
obviously the joint characteristics, and thus the expression using the
inclination angle is available for detailed research. Obviously, these
two expressions can be converted to one another, as already shown in
Fig. 5-15, provided that the flange behaves as a stiff body, resulting in
the linear distribution of the interface pressure.
Admitting the validity of the conversion shown in Fig. 5-15, at issue in
the machine tool structure is the complex loading condition, and often the
flange is prone to show local deformation. Within an engineering design,
the stiffnesses K and K ST are in fact useful and applicable; however, the
SB
equivalent stiffness, which is given by the column without any joints, is
required to have the fully quantified evaluation or to carry out an absolute
assessment. Figure 5-16 shows such a correlation together with the com-
plex loading condition in the machine tool, for the sake of the ease of under-
standing. In short, the joint stiffness can be evaluated by comparing, for
instance, K SB with K , resulting in the expression of relative stiffness.
OB
To enhance the sophisticated knowledge, the emphasis now is on the
flat joint, where two characteristics are at issue: one is the normal joint
stiffness K and the other is the tangential joint stiffness K sh, as shown
sn
in Fig. 5-17. In not only flat but also bolted joints, we should furthermore