Page 254 - Modular design for machine tools

214 Engineering Design for Machine Tool Joints

In the following, thus, first the quick notes for the single flat joint will
be stated, and then the design formula and some characteristic fea-
tures for each variant of the single flat joint will be summarized. In addi-
tion, the thermal behavior of the single flat joint will be touched on.

6.1 Quick Notes for Single Flat Joint,
Determination of Mathematical Model,
and Fundamental Knowledge about
Engineering Design Formulas
Although the flat joint appears to be very simple, the amount of related
knowledge is huge, even when we limit our discussion of the formula-
tion of the structural design data in terms of the static and dynamic stiff-
ness also including thermal deformation. In addition, the single flat
joint has, in principle, myriad influencing factors in relation to the joint
stiffness, e.g., magnitude and direction of the external and internal
loads, finished condition of joint surfaces, and the relative dimensional
difference between the upper and lower joint surroundings.
Importantly, the systematic classification of the single flat joint can
be, in principle, made by using the following three dominant facets,
which have been clarified through the long-standing experience in the
research and engineering development.
1. In consideration of larger effects of the direction of external load on
the joint behavior, the flat joint is required to branch into those
(a) under normal loading, (b) under tangential loading with normal
preload, and (c) under moment with normal preload.
2. The joint can be, in principle, classified into the two types depend-
ing on the magnitude of the interface pressure. The flat joint under
lower interface pressure corresponds with the slideway, whereas the
flat joint under higher interface pressure is an idealized model of
bolted joint. In fact, the bolted joint is prone to present a slight local
deformation, resulting in the nonuniform interface pressure distri-
bution. In other words, the bolted joint in the structural body shows,
in nearly all cases, bedding-in and warping of clamped component,
flairlike deformation at the bay-type flange, and so on (see Chap. 7).
3. More specifically, at issue is the relative stiffness of joint surround-
ings to the joint stiffness itself, resulting in the apparent difference
in joint deformation. As can be readily seen, the joint deformation is
subject to the magnitude and distribution of the interface pressure.
a. In the case of K > K , where K and K are the stiffnesses of joint
j
0
j
0
surroundings and of the joint itself, respectively, the joint surface
does not separate from itself and may deform uniformly across the
whole joint surface, when the normal load is applied. Consequently,
the interface pressure is in uniform or linear distribution, and we
can observe this kind at the slideway.