Using this method it is possible to give 45, 93, 173, 273 regularly distributed speeds of the variable shaft with a set of only 5, 6, 7, 8 reserved change gears respectively.

Many change gears are used in loom type 1511M and 1511 for varying weft set. It is possible to minimize the amount of these change gears by using optimization technique.

OPTIMIZATION OF THE METHOD OF SELECTING THE TOOTH NUMBER SERIES IN A SET OF CHANGE GEARS Part Ⅰ: The Differences between Logarithms (D. B. L.) of the Tooth Numbers in a Set of Change Gears and the Regularity of their Distribution

According to the construction and movement of gear-machine,this paper explores the inherent regularities of the machine movement of generating process oblique-gear of prime number,and introduces the calculating principles and methods of the drive chain. The general principles of optimization on rolling and differential movement,especially limmited natural resources of change gears are put forward.

On the basis of numerical model of speed change gears and considering the relative error of speed change system, the target function for optimization of transmission plan by means of a computer is achieved.

It is often the case that technology demands an accurate multi-step change of the speed ratio between various parts of machines, textile machines in particular. A great many change gears are, as a rule, necessary for this purpose. It is desirable to minimize the number of such gears. In this paper, a method for determining the optimal combinations of the tooth number series in a set of change gears is proposed, with which the number of gears is decreased to a minimum with the precision...

It is often the case that technology demands an accurate multi-step change of the speed ratio between various parts of machines, textile machines in particular. A great many change gears are, as a rule, necessary for this purpose. It is desirable to minimize the number of such gears. In this paper, a method for determining the optimal combinations of the tooth number series in a set of change gears is proposed, with which the number of gears is decreased to a minimum with the precision and number of steps of the speed ratio remaining unchanged. The proposed combinations are supported by mathematical proof.This is the first of a series of reports. It deals with the regularity of distribution of the speed ratio series when a definite number of change gears are used. A table illustrating optimal combinations of the D. B. L. of the tooth numbers with corresponding goars numbers up to 20 in a set is presented. (See table 5)Let z_i be the tooth number of the i-th gear in a set of n gears, z_1>z_2……>z_n. The speed ratio between certain machine parts is determined by the formula:I_(i,j)=z_i/z_jThe D. B. L. of the tooth numbers in a set of change gears is defined as:a_(i,j)=log_φI_(i,j)= log_φz_i-logφz_jWhere φ——the common ratio of each succesive pair of steps of the changeable speed ratios. There are 3 kinds of sets A with elements a_(i,j):1) Full sequenceA={1, 2, 3,……(?),M}Where M=n(n-1)/2.It is possible only when n≤4.2) Sequence with repetitionA={1,2,3……(?)d; h_1, h_2……h_d}Where h_i, h_2, h_a h_d<(?).If h_1, h_2,……h_d>(?), then set A is defined as3) Sequence with "broken tail" (interruption towards the end of the sequence).(Shown in Fig. 1)When n>4, repetition or "broken tail" in the sequence is inevitable. It is optimal to find proper combination of z_i of n-set to give maximum (?), or minimum repetition or interruption in the sequence.Some results for this purpose are given with examples. Data of comparison between this method and the method currently used in selecting the tooth number series are shown in table 6.

The problem in practice of determining the proper combination of z_i in a set of n change gears may be abstracted to the problem of finding the proper combination and permutation of the elements a_(i,i+1) of the set A_1 of the F. O. D. B. L. to give maximum M - d (Notations are the same as in Part Ⅰ). In part Ⅰ, we have given some results to find optimal combination of the elements of the Set A_1. In this part some rules for permuting these elements are introduced. 3 kinds of intercalated sets of the F....

The problem in practice of determining the proper combination of z_i in a set of n change gears may be abstracted to the problem of finding the proper combination and permutation of the elements a_(i,i+1) of the set A_1 of the F. O. D. B. L. to give maximum M - d (Notations are the same as in Part Ⅰ). In part Ⅰ, we have given some results to find optimal combination of the elements of the Set A_1. In this part some rules for permuting these elements are introduced. 3 kinds of intercalated sets of the F. O. D. B. L. have been found: 1. Set A_1 with even left wing (table 10); 2. Set A_1 with coincidence of both wings (table 12); 3. Set A_1 with circulated elements (table 13). In the given example, a set of 12_(+1) change gears (instead of 33 for current machines) are enough for ring spinning frames to give draft from 9.71 to 41.2 in 101 steps with step difference<2.2%, and another set of the same amount of change gears (instead of 19 for current machines) for the same machine to give twist from 190 t/m to 1314 t/m in 101 steps with step difference<3%. This method is practical and may be used for designing sets of change gears for any kind of machines (not merely confined to textile machinery). The analyses made in the paper may perhaps be useful in studying combinatorial mathematics.

In this paper optimum design of planetary mechanisms is worked out taking minimum volume as objective function, and the problem of choosing optimization parameters solved. Computer program used in this paper apply to standard gear teeth, as well as to teeth modified on the view point of equivalent strength, teeth modified on the view point of equivalent wear, and angular modification teeth. The mathmatical model and the method of solution mentioned are applicable to the optimum design of planetary transmissions...

In this paper optimum design of planetary mechanisms is worked out taking minimum volume as objective function, and the problem of choosing optimization parameters solved. Computer program used in this paper apply to standard gear teeth, as well as to teeth modified on the view point of equivalent strength, teeth modified on the view point of equivalent wear, and angular modification teeth. The mathmatical model and the method of solution mentioned are applicable to the optimum design of planetary transmissions of other varieties. It may be used in new designs and improved designs of products of planetary reducers, change gear boxes etc.