When I graduated as a mechanical engineer in 1978, I landed a job in the “cold section” at Pratt & Whitney Canada (PWC) in Montreal. In those d...

Beginning with our June Issue, Gear Technology is pleased to present a series of full-length chapters excerpted from Dr. Hermann J. Stadtfeld’s latest scholarly — yet practical — contribution to the gear industry — Gleason Bevel Gear Technology. Released in March, 2014 the book boasts 365 figures intended to add graphic support of a better understanding and easier recollection of the covered material.

At the dawn of the Industrial Revolution, so-called mechanics were tasked with devising the precise methods that would make mass production possible. The result was the first generation of machine tools, which in turn required improved tooling and production methods.

The hobbing and generation grinding production processes are complex due to tool geometry and kinematics. Expert knowledge and extensive testing are required for a clear attribution of cause to work piece deviations. A newly developed software tool now makes it possible to simulate the cutting procedure of the tool and superimpose systematic deviations on it. The performance of the simulation software is illustrated here with practical examples. The new simulation tool allows the user to accurately predict the effect of errors. With this knowledge, the user can design and operate optimal, robust gearing processes.

Fig. 1 shows the effects of positive and negative rake on finished gear teeth. Incorrect positive rake (A) increase the depth and decreases the pressure angle on the hob tooth. The resulting gear tooth is thick at the top and thin at the bottom. Incorrect negative rake (B) decreases the depth and increases the pressure angle. This results in a cutting drag and makes the gear tooth thin at the top and thick at the bottom.

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.

Our research group has been engaged in the study of gear noise for some nine years and has succeeded in cutting the noise from an average level to some 81-83 dB to 76-78 dB by both experimental and theoretical research. Experimental research centered on the investigation into the relation between the gear error and noise. Theoretical research centered on the geometry and kinematics of the meshing process of gears with geometric error. A phenomenon called "out-of-bound meshing of gears" was discovered and mathematically proven, and an in-depth analysis of the change-over process from the meshing of one pair of teeth to the next is followed, which leads to the conclusion we are using to solve the gear noise problem. The authors also suggest some optimized profiles to ensure silent transmission, and a new definition of profile error is suggested.

Circular arc helical gears have been proposed by Wildhaber and Novikov (Wildhaber-Novikov gears). These types of gears became very popular in the sixties, and many authors in Russia, Germany, Japan and the People's Republic of China made valuable contributions to this area. The history of their researches can be the subject of a special investigation, and the authors understand that their references cover only a very small part of the bibliography on this topic.

In robot configurations it is desirable to be able to obtain an arbitrary orientation of the output element or end-effector. This implies a minimum of two independent rotations about two (generally perpendicular) intersecting axes. If, in addition, the out element performs a mechanical task such as in manufacturing or assembly (e.g., drilling, turning, boring, etc.) it may be necessary for the end-effector to rotate about its axis. If such a motion is to be realized with gearing, this necessitates a three-degree-of-freedom, three-dimensional gear train, which provides a mechanical drive of gyroscopic complexity; i.e., a drive with independently controlled inputs about three axes corresponding to azimuth, nutation, and spin.