Rational axial shift of gear cutter

Abstract

The relation between the axial shift and n is not always unique. In milling a single blank with each adjustment of the cutter, decrease in axial shift is accompanied by corresponding increase in n , so long as the tooth wear of the cutter is within permissible limits. However, in milling two or three blanks with each cutter adjustment, n will be proportional to the product of the number of axial shifts and the number of gears machined in each cutter adjustment and will also depend on the nonuniform wear of the cutting teeth. We know that the teeth on the input section of the cutter are subject to more wear. The wear of each tooth in cutting is different. Accordingly, reducing the axial shift to some critical value may entail reduction in the number of gears machined per cutter adjustment so as not to exceed the permissible tooth wear. The number of gears machined over the cutter’s working life may be reduced (since the product of the number of axial shifts and the number of gears machined per cutter adjustment is reduced), even though the number of axial shifts may increase. Conversely, increasing the axial shift to some critical value may increase the number of gears machined per adjustment and hence increase the number of gears machined within the working life. Existing recommendations regarding the axial shift are obtained experimentally or taken from hobbing practice. Thus, recommended values were presented as a function of the tooth inclination and the number of number of gear teeth to be cut, for the standard series of modules (2‐26 mm), in [1]. It was shown that factors significantly affecting the axial shift include the module, the tooth inclination, and the number of tooth to be cut on the gear. However, the discrete values of these factors do not permit the use of these recommendations to determine the rational axial shift of the cutter in other machining conditions [1]. Accordingly, we need to determine the rational axial shift for specific values of the relevant factors. We may use 3D simulation to determine the rational axial shift. As we know, increasing the cutting path length of the cutter tooth or the total volume of metal removed by each tool will increase the cutter wear. Therefore, we have developed a 3D model of tooth cutting that permits accurate determination of both the cutting path length for each cutter tooth and the total metal volume removed by the tooth. On the basis of the simulation, we may sample possible axial shifts so as to determine the value best ensuring equal cutting path lengths for each cutter tooth or equal metal volume removed by each cutter tooth, for the maximum possible number of teeth. This approach to determining the rational axial shift is considered for the example of producing a straighttooth gear using a single-setting cutter. The gear parameters are as follows: height H = 20 mm; module m = 3 mm; number of teeth z 1 = 45. The parameters of the gear cutter are as follows: number of straight chip channels 14; external diameter d a 0 = 112 mm; length of mill’s working section L f = 90 mm; cutting speed v cu = 25 m/min; cutter speed n 0 = 71.05 rpm; axial supply of cutter s ax.c = 2 mm/turn. Each tooth of the cutter is assigned an index n z , which may increase or decrease relative to the symmetry axis of the cutter tooth’s axial profile (with index n z = 0). The symmetry axis of the cutter tooth’s axial profile (with n z = 0) lies in the plane of cutter rotation, passing through the intercenter distance of the cutter and blank.