Design Method of System Tolerances in Cylindrical Gearboxes for Cost-Efficient Optimization of the Excitation Behavior

<p style="text-align: center;"><img src="/ueditor/php/upload/image/20260123/1769179225109972.png" title="1769179225109972.png" alt="1.png"/></p><p style="text-align: justify;"><span style="font-family: arial, helvetica, sans-serif; font-size: 12px;">The design of cylindrical gears is currently often carried out separately from the development of surrounding gear components. This applies in particular to the procedure for defining the tolerance limits to be adhered to. In most cases, empirical design experience is used when the tolerance limits are defined on the drawings for housing components, gear shafts, roller bearings or gear bodies. The specification of the tolerance limits to be adhered to determines in detail the manufacturing processes for each individual component that are suitable for achieving the tolerance requirements. This has a major influence on the overall production costs. Due to the accumulating effect of the system tolerance chain, various types of deviations in surrounding gear components with an influence on the gear kinematics affect the tooth contact ratios to varying degrees. This means that not only profile and tooth flank deviations of the gear have a detrimental effect on the various components of the noise excitation, but also deviations on the housing, shafts and bearings as they have an impact on the gears’ positions. At the same time, the specific costs per unit of deviation for the components used in a series gearbox are different. State of the Art The state of the art first discusses the methods available for determining manufacturing process costs. Existing models for mapping the deviation-cost relationship are then presented. Finally, methodical approaches to tolerance design on mechanical systems are presented. Determining the Manufacturing Process Costs for Conventional Processes in Gearbox Production Beckers has developed an evaluation model for the economic efficiency of production process sequences. Economic efficiency, which is defined as the quotient of yield per input of resources, is the result of the calculations. The use of resources (costs) can be classified into direct costs Cin, which can be directly allocated to the component, and overheads Coverall (e.g., development costs or patenting costs). The overheads Coverall are not further subdivided here in detail, as they are incurred independently of the selected process chain (Ref. 1). The individual costs Cin can be further broken down into the costs of the raw part CRH minus the income from returned material ERM (chips or workpiece remnants). Other direct costs CSE and the sum of all costs of the individual processes CF,j. Other direct costs include transport, storage, etc. (Ref. 1). For the comparison of different manufacturing processes within the conventional process chain for gear production according to Klocke et al. the same values are assumed for ERM and CSE across processes, since, for example, transport scopes do not vary to any significant extent and the machined volume is identical (Ref. 2). This means that the processes used in a conventional process chain hardly differ in this respect. For the manufacturing costs of the individual process CF,j per component, a further breakdown can be made into labor costs CL,j, machine costs CM,j, tool costs CW,j and other items that are negligible for the following process chain comparisons (Ref. 1, 3). The expression formulated by Beckers for the individual costs Kein is also proposed in a generalized form by Yu et al. for process sequences (Ref. 4). He uses the description to train a genetic algorithm to minimize the total costs. However, this approach is not further detailed. The labor, machine and tool costs depend on the machining time of the individual part tE,j and the time of contact tPA,j,k of the tool. Changing the time of contact tPA,j,k by adjusting cutting parameters such as the feed rate or the number of strokes in turn has a major influence on the expected tool life tSZ,j,k and the quality parameters of the component. The time tE,j can be further broken down into basic time tG,j, distribution time tV,j, recovery time tEr,j and any waiting times tW,j (Ref. 1). According to Klocke et al., the basic time tG,j can be determined by dividing it into primary machining and idle time th,j and tn,j. While the primary machining time th,j includes all direct progress in the sense of process progress, the idle time tn,j includes supporting processes such as clamping, measuring, aligning the raw part in the machine or dressing the grinding tool (Ref. 3).</span></p><p style="text-align: justify;"><span style="font-family: arial, helvetica, sans-serif; font-size: 12px;">Consideration of the formulaic relationships shows that the cost variance is strongly influenced by the time per component. This time is subject, among other things, to the choice of cutting parameters and machining tactics (influence on primary machining time th,j) as well as additional expenses for calibrating the raw part in the machining position or changing to another tool (influence on idle time tn,j), which are decisive for the quality parameters. The manufacturable component qualities of an individual process, therefore, correlate directly with the time per component in the process tE,j, insofar as this is based on the basic time of the process tG,j.</span></p>