This article discusses the relationships among the fillet stress on a thin rim planet gear, the radial clearance between the gear rim and the gear shaft, the tooth load, the rim thickness, the radius of curvature of the center line of the rim, the face width and the module.

Most steel gear applications require appreciable loads to be applied that will result in high bending and compressive stresses. For the material (steel) to meet these performance criteria, the gear must be heat treated. Associated with this thermal processing is distortion. To control the distortion and achieve repeatable dimensional tolerances, the gear will be constrained during the quenching cycle of the heat treatment process. This type of fixture quenching is the function of gear quench pressing equipment.

Analysis of helical involute gears by tooth contact analysis shows that such gears are very sensitive to angular misalignment leading to edge contact and the potential for high vibration. A new topology of tooth surfaces of helical gears that enables a favorable bearing contact and a reduced level of vibration is described. Methods for grinding helical gears with the new topology are proposed. A TCA program simulating the meshing and contact of helical gears with the new topology has been developed. Numerical examples that illustrate the proposed ideas are discussed.

Gear hobbing is a generating process. The term generating refers to the fact that the gear tooth form cut is not the conjugate form of the cutting tool, the hob. During hobbing both the hob and the workpiece rotate in a continuous rotational relationship. During this rotation, the hob is typically fed axially with all the teeth being gradually formed as the tool traverses the work face (see Fig. 1a).

Complete calendar for January/February 1994

Because of the better thermal conductivity of CBN abrasives compared to that of conventional aluminum oxide wheels, CBN grinding process, which induces residual compressive stresses into the component, and possibly improves the subsequent stress behavior. This thesis is the subject of much discussion. In particular, recent Japanese publications claim great advantages for the process with regard to an increased component load capacity, but do not provide further details regarding the technology, test procedures or components investigated. This situation needs clarification, and for the this reason the effect of the CBN grinding material on the wear behavior and tooth face load capacity of continuously generated ground gears was further investigated.

This is Part II of a two-part series on the basics of gear hobbing. Part I discussed selection of the correct type of hobbing operation, the design features of hobs and hob accuracy. This part will cover sharpening errors and finish hob design considerations.

Optimization is applied to the design of a spiral bevel gear reduction for maximum life at a given size. A modified feasible directions search algorithm permits a wide variety of inequality constraints and exact design requirements to be met with low sensitivity to initial values. Gear tooth bending strength and minimum contact ration under load are included in the active constraints. The optimal design of the spiral bevel gear reduction includes the selection of bearing and shaft proportions in addition to gear mesh parameters. System life is maximized subject to a fixed back-cone distance of the spiral bevel gear set for a specified speed ratio, shaft angle, input torque and power. Significant parameters in the design are the spiral angle, the pressure angle, the numbers of teeth on the pinion and gear and the location and size of the four support bearings. Interpolated polynomials expand the discrete bearing properties and proportions into continuous variables for gradient optimization. After finding the continuous optimum, a designer can analyze near-optimal designs for comparison and selection. Design examples show the influence of the bearing lives on the gear parameters in the optimal configurations. For a fixed back-cone distance, optimal designs with larger shaft angles have larger service lives.

The Hobbing Process The hobbing process involves a hob which is threaded with a lead and is rotated in conjunction with the gear blank at a ratio dependent upon the number of teeth to be cut. A single thread hob cutting a 40-tooth gear will make 40 revolutions for each revolution of the gear. The cutting action in hobbing is continuous, and the teeth are formed in one passage of the hob through the blank. See Fig. 1 for a drawing of a typical hob with some common nomenclature.

The complete and accurate solution t the contact problem of three-dimensional gears has been, for the past several decades, one of the more sought after, albeit elusive goals in the engineering community. Even the arrival on the scene in the mid-seventies of finite element techniques failed to produce the solution to any but the most simple gear contact problems.