Page 258 - Modular design for machine tools

Engineering Design Fundamentals and Single Flat Joint Characteristics 217

stiffness and the stiffness of the joint surroundings. In fact, the proposed
classification system is very convenient when we apply the design data-
base for the spring constant and damping capacity of the single flat joint
to the practical structural design. In addition, it is notable that nearly
all the machine tool joints belong to one of these joint types, as mentioned
already in Chap. 5. Conceptually, Fig. 6-2 may assist the understanding
of the analytical procedure in the engineering calculation with special
respect to what a mathematical model is, although nowadays the com-
putation method is dominant. In the computation method, the FEM
model has been employed without exception, and the joint can be also
replaced with the model consisting of the spring-dashpot couple. 1,2
Given that the joint can be represented with the spring-dashpot model
and characterized by the state of interface pressure distribution as men-
tioned above, a primary concern is first how to determine the spring con-
stant and damping capacity within the engineering design formula. As
will be shown later, there have been a considerable number of expressions
relating to the normal and tangential joint stiffness under static loading,
3
and also to the damping capacity. In due course, another crucial issue is
the applicability of these expressions to the engineering design. Within
the expression context, only the expression for the normal joint stiffness
proposed by Ostrovskii has, in the wider scope of engineering calculation,
proved its validity without revealing any serious problems by
4
Kaminskaya, Back, Nakahara, and PERA to a large extent. In other
words, we can, under satisfactory conditions, conduct the engineering
design of the structure with the joint, e.g., slideways of flat and dovetail
types, taper connection, and bolted joint under static normal loading.
Reportedly, the model theory is can be applied to the structure with the
joint, provided that certain prerequisites are satisfied (refer to App. 2) [2],
and thus these expressions facilitate, in principle, the engineering design
of the joint. It is furthermore recommended that the constants in the
expression be varied, if possible, in consideration of the actual condition
of the joint to be designed.

1
Engineers benefit by the analytical method. Typically, the influencing factors govern-
ing the machine tool performance and rates of their effects can be grasped without any
difficulties by investigating only the final expression of the analytical solution.
2
The mathematical model can be determined in full consideration of the (1) structural
configuration, (2) capability of available program, and (3) ability of engineer who may
determine the mathematical model.
3
Hijink and van der Wolf reported once a firsthand view of the joint stiffness and damp-
ing in the beginning of 1970s.
Hijink, J. A. W., and A. C. H. van der Wolf, “Survey on Stiffness and Damping of Machine
Tool Elements,” Annals of CIRP, 1972, 22(1): 123–124.
4
PERA (Production Engineering Research Association of Great Britain) Report
Nos. 180 and 198, “Machine Tool Joints, Part 1 and Part 2,” late 1960s.