Ensuring accuracy of cylindrical toothed gear wheels at production design

Abstract

1 One of the efficient methods of ensuring the accuracy of machine element processing is design of processes of their production on the basis of regularities of stage-by-stage variation and forming of accuracy parameters (blank quality, element design, state of equipment and auxiliaries, and so on). Unfortunately, this approach is seldom applied at present in the practice of machine engineering. One of the reasons is the erroneous, although widely spread, opinion that element accuracy is formed mainly at the final processing. Moreover, mathematical models of many processes of machine element processing are lacking. For mathematical modeling of the variation and forming of accuracy parameters of cylindrical toothed gear wheels (CTGW) during their production, extensive experimental studies were carried out by us. The variation of the accuracy parameters of teeth and CTGW base surfaces at basic processing operations and the influence of the accuracy of base surfaces and cutting modes on tooth accuracy at gear milling and shaping were studied. In the framework of this problem, stage-by-stage variation of eleven accuracy factors of teeth and five accuracy factors of CTGW base surfaces of tractors, auto trucks, and metal-cutting machines (module m = 2‐5 mm; number of teeth 23‐51; material steels 45, 40Kh, 25KhGT, 20KhN3A, 18KhGT, and so on) after eight processing operations of tooth processing and eleven operations of base surface processing under industrial and laboratory conditions were studied experimentally. The following technological processes (TP) were studied: shaving on rigid and expanding mandrels and chemical‐thermal processing (CTP)—cementation and nitrocementation in muffleless aggregates, gear burnishing, gear honing, gear grinding by conical and worm wheels, bore processing (including drilling; core drilling; single- and double-broaching; honing; burnishing; grit blasting; CTP; and rough, half-rough, and finish turning), as well as CTP and ring gear grinding. 1 Based on Proceedings of the International Scientific-Technical Conference “Improvement of Machine Quality at Stages of Their Lifetime,” Bryansk, 2005. In the course of the studies, 65 batches of CTGW were processed and measured under production conditions and 15 batches under laboratory conditions; the size of each batch was N = 50‐100 pieces. About 90% of the CTGW dimension types manufactured in auto, tractor, and machine-tool construction in the Republic of Belarus were covered. The processing of the experimental data showed the appropriateness of the application of correlationregression analysis for modeling the stage-by-stage variation of the CTGW accuracy parameters on the basis of measurement of one sample of sufficient volume. For this purpose, among other things, the accuracy parameter distributions (192 distributions were studied) and the stationary character and ergodicity of the considered TP for the chosen parameters were analyzed. Moreover, phase analysis of the variation of the CTGW kinematical accuracy factors for different types of gear treatments was carried out. Some results of research characterizing the phenomenon of technological heredity at variation of CTGW accuracy parameters during their processing and the possibility of modeling stage-by-stage correlations of these parameters for the considered processing operations are given in Tables 1‐3 (the data on tooth accuracy parameters according to GOST 1643-81 are given in Table 1, the accuracy parameters of mounting bores are given in Table 2, and the accuracy parameters of ring gear ends are given in Table 3). It was established that, for most CTGW accuracy parameters and their processing operations, technological heredity takes place, since r xy > 0.273, B > 10%, where r xy is the pair correlation coefficient between the values of this parameter ( x ) before and ( y ) after the considered operation, and B is the variance of the value of y from the previous operation. The analysis of results obtained in the present studies and those carried out earlier provided the possibility of assuming that the dependences y = f ( x ) can be described by first or second order polynomials,