Evaluation of the Design of the Excitation Behavior

The design of the excitation behavior based on the total transmission error of a gear pair is often carried out by considering supposed worst-case scenarios in which the limit values of the geometric deviations are mapped. The main disadvantages of this approach are, on the one hand, that the maximum excitations do not necessarily have to occur at minimum or maximum deviation amounts, as different flank and form deviations have different effects on the course of the load-free transmission error and influence each other (Ref. 2). On the other hand, when assuming approximately normally distributed deviations, particularly high deviation amounts occur much less frequently, so that a worst-case consideration is often unsuitable. For the reasons mentioned, parameters from descriptive statistics are used here to evaluate the excitation. In addition to the mean value, standard deviation, median and RMS value, these are the 80 percent, 85 percent, 90 percent, 95 percent and 98 percent quantiles. The latter determine the maximum values of the total transmission error for the associated probability and can be important quality parameters. Weighting factors can be used to set the aforementioned statistical variables, which are determined per tolerance iteration on n = 200 variants, in a preferred relationship to each other. For the calculations carried out here, all statistical parameters are weighted equally. In detail, different orders of the total transmission error in the long-wave and short-wave range are analyzed. The rotational orders O = 1, 2, 4 of the pinion and wheel shaft are analyzed. In addition, the first to third gear mesh orders O = 23, 46, 69 (in relation to the pinion) and the neighboring sidebands of these (O = 22, 24, 45, 47, 68, 70 in relation to the pinion) are analyzed. On the one hand, the excitation orders can be set in relation to each other with a manual weighting in order to subsequently determine an overall score for the excitation of a tolerance design. Another option is to implement an automated determination of the weighting factors. This first determines the frequency of occurrence of the drive speed at the pinion using a time-speed curve, which is taken from the WLTP test cycle for motor vehicles as an example (Ref. 32). This is done in intervals of ΔnPinion = 100 rpm from nPinion = 100…18,000 rpm, which would correspond to the entire speed range up to the maximum speed of the car. The evaluation orders are converted into excitation frequencies along the speed segments with a step size of ΔnPinion = 100 rpm. Each excitation frequency per speed step is then weighted with the A-weighting curve according to ISO 226 (Ref. 33). The value obtained there is furthermore multiplied by the frequency of occurrence of the speed step under observation and then arithmetically averaged over all speed steps. In this way, weighting factors are obtained for each order of transmission error, which depend on the frequency of occurrence of the speed and the A-weighting of the human noise sensing. Finally, a grade is awarded. A linear evaluation is carried out in the range gA = 1…6 (good to bad). The acoustic grade gA = 1 corresponds to a reduction of the statistical parameter by p = 5 percent compared to a conventionally estimated reference design. The grade gA = 6 means a deterioration of p = +5 percent. Finally, the individual scores are arithmetically averaged to give the overall acoustic score. The reference thus achieves the overall grade gref = 3.5.