Fuzzy Reliability Design of Machine Tool Spindle

1 Introduction The performance of the spindle components has a direct impact on the overall performance and processing quality as well as the machine productivity. A good performance spindle component must have sufficient stiffness. The traditional stiffness check is to control the deflection of the end of the spindle!

Not greater than the allowable value = 0.005, as practical! At =0.0049, we cannot simply assume that the spindle is absolutely reliable; as practical! At =0.0051, we should not simply assume that the spindle is absolutely unreliable. Due to the randomness and ambiguity of the manufacturing process such as load, material and machining, it is necessary to use the fuzzy reliability theory to design, and because the structural parameters of the machine tool spindle are the most important factors determining the stiffness of the spindle component, comprehensive consideration is required for stiffness. Fuzzy reliability design of the machine tool spindle is necessary.

2 Machine tool spindle fuzzy reliability prediction model Fuzzy reliability design According to the function function "=-% (+% is the generalized strength and generalized stress of the part respectively), the mechanical parts are divided into three kinds and "the absolute value is small" And the failure state ("<0, and the absolute value of" is larger), where the fuzzy state is a transition process describing the part from the safe state to the failed state. To this end, the safe state of the part is actually a fuzzy event, using the membership function! (") to describe. As shown in (b).

(!) is the membership function.

The membership function and the probability density function determine the safety and fuzzy random events of the machine tool spindle as 0. For the permissible deflection, yes! The maximum degree of membership is 1.

when-! "0, the stiffness of the part meets the requirements, the part is safe, and the membership in the fuzzy event is 1, ie!

(!) 21; if -! ! 0, and the absolute value is large, the rigidity of the spindle component does not meet the requirements, the spindle is unsafe, and the membership degree in the fuzzy event is 0; if -! ! 0, but the absolute value is small, the stiffness of the spindle components is somewhat safe. According to the above analysis, the membership function of the spindle stiffness fuzzy event can be represented by a trapezoidal distribution (as shown). The mathematical expression is in the conventional spindle deflection design, i can be slightly larger than (generally not more than 5) 21.05 The allowable deflection of the machine tool spindle and the deflection at the shaft end are generally normal distribution, and the probability density function is generally two bearings for the machine tool spindle structure support, as shown in the two-bearing spindle mechanical model. The spindle will be displaced at the end C under the action of +1++2, and the mean value of the deflection can be obtained by the linear superposition principle of material mechanics!

y is: the stiffness of the machine tool spindle is regarded as a fuzzy event, = 1 -! "0丨, and fuzzy events, not only its occurrence or not is uncertain, and its meaning is not very clear, that is, while expressing randomness, it also shows ambiguity. According to the probability measure of fuzzy events, the probability of fuzzy reliability of machine tool spindle '2)() is: the use of the deflection membership function: from the point of view of fuzzy mathematics, it is difficult to obtain the deflection accurately, and m2) other variables are usually in a certain range, that is, random Variables, the more random variables, the more accurate the calculation results, the author takes 1,%,%, are random variables, then consider the standard deviation of each of the above random variables T according to the Taylor series method to find the table *" (2.62)" 0.995604. This is the result of conventional reliability calculation.

It can be seen that the fuzzy reliability design of the machine tool spindle can reflect the actual situation, and the reliability calculation is more reasonable than the conventional calculation.

5 machine tool spindle reliability calculation formula machine tool spindle workload deformation T is generally a normal distribution, subordinate function (2) and probability density function (3) substituting (i) can be proved, when Ti (T0, there is *"(ht) is the case for conventional reliability design.

6 Calculation example A spindle on a machine tool is designed according to the mechanical factor of the machine tool spindle C"C"0.005, the elastic modulus of the shaft material is also a random variable, 7 conclusions (1) Introducing fuzzy reliability design in the design of the machine spindle structure Overcome the blindness of traditional design methods and improve the rationality of the design.

(2) The modeling process of the machine tool spindle fuzzy reliability design is universal, and other similar drive shafts with the same stiffness requirements are also applicable.

(3) Conventional reliability design is a special case of ignoring fuzzy reliability when ambiguity. Fuzzy reliability is general and versatile. It provides theoretical possibility and basis for solving the ambiguity problem in spindle reliability design.

Dong Yuge. Mechanical fuzzy reliability design. Beijing: Mechanical Industry Press, Xie Qingsheng, et al. Mechanical engineering fuzzy optimization method. Beijing: Mechanical Industry Publishing Liu Puzhen, Wu Yuda. Fuzzy theory and its applications. Beijing: National University of Defense Technology Press, 2000. Chen Weigong. Engineering Mechanics; M. Beijing: Higher Education Press, 2001. (Editor Ming Tao) Mechanical fuzzy reliability optimization and mechanical manufacturing.

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