Jonny Harianto

Robust Optimization of Cylindrical Gear Tooth Surface Modifications Within Ranges of Torque and Misalignments

Tooth surface modifications are small, micron-level intentional deviations from perfect involute geometries of spur and helical gears. Such modifications are aimed at improving contact pressure distribution, while minimizing the motion transmission error to reduce noise excitations. In actual practice, optimal modification requirements vary with the operating torque level, misalignments, and manufacturing variance. However, most gear literature has been concerned with determining optimal flank form modifications at a single design point, represented by fixed, single load and misalignment values. A new approach to the design of tooth surface modifications is proposed to handle such conditions. The problem is formulated as a robust design optimization problem, and it is solved, in conjunction with an efficient gear contact solver (Load Distribution Program (LDP)), by a direct search, global optimization algorithm aimed at guaranteeing global optimality of the obtained microgeometry solutions. Several tooth surface modifications can be used as microgeometry design variables, including profile, lead, and bias modifications. Depending on the contact solver capabilities, multiple performance metrics can be considered. The proposed method includes the capability of simultaneously and robustly handling several conflicting design objectives. In the present paper, peak contact stress and loaded transmission error amplitude are used as objective functions (to be minimized). At the end, two example optimizations are presented to demonstrate the effectiveness of the proposed method.

A Methodology for Obtaining Optimum Gear Tooth Micro-Topographies for Noise and Stress Minimization Over a Broad Operating Torque Range

This paper presents a method of evaluating the effect of micro-geometric or micro-topographic variation on various gear performance parameters, such as noise excitations, gear contact and root stresses, film thickness, and surface temperature under loaded conditions. Micro geometries that are considered are profile crown, profile slope, lead crown, lead slope, and bias modifications variations. Various combinations of these micro geometries are considered in analytical simulations in which respective gear design metrics are evaluated based on the calculated load distributions. This paper will provide a walk through analysis for a helical gear design in order to describe the procedure.Copyright

Tooth Flank Corrections of Wide Face Width Helical Gears that Account for Shaft Deflections

The tooth flank correction of power transmission helical gears with wide face width is studied by using a finite element based shaft deflection analysis program in conjunction with a numerical load distribution analysis procedure. The load distributions along the line of action, the elastic deflections and transmission errors of gear pairs are obtained by solving the equations of compatibility of displacement and equilibrium of forces. This paper discusses the influences of tooth flank corrections (tip relief, root relief, lead modification, end relief and their combinations) on gear stresses and transmission errors due to shaft deflections. The technique used in the paper has the capability of modeling all significant geometric and elastic contributions due to tooth contact of the pair being analyzed as well as other gears mounted on the same shafts. The results show that it is possible to optimize at the design stage the gear micro-geometry for minimum stresses and transmission errors without changing the gear macro-geometry.Copyright

An Experimental Investigation of the Effect of Tooth Asymmetry and Tooth Root Shape on Root Stresses and Single Tooth Bending Fatigue Life of Gear Teeth

In this paper, effects of root fillet geometry and tooth asymmetry on tooth bending stresses and fatigue lives of spur gears are investigated. For this purpose, an existing gear analysis model, the Load Distribution Program (LDP), is employed to define four basic tooth geometry variations. These four variations are (i) symmetric tooth profiles (i.e. identical loaded and unloaded flanks) with full circular root geometry (at the maximum radius possible), (ii) symmetric tooth profiles with an elliptical root geometry, (iii) asymmetric tooth profiles (i.e. loaded and unloaded flanks at different pressure angles) with full circular root geometries, and (iv) asymmetric tooth profiles with an elliptical root geometry on the right (loaded) flank and a circular root geometry on the left flank. Under these conditions, variations (ii), (iii), and (iv) are predicted to have maximum root stresses that are 7.6%, 22.4%, and 24.3% less than that of the baseline case (i). Actual test articles representing these four variations were qualified through dimensional measurements of the profiles and the root fillet regions. The roots of several of the teeth of each gear type were instrumented and strain measurements under various tooth load levels are compared with the predictions. Single tooth bending fatigue tests were also performed to obtain fatigue data for each variation of the test gears. The resultant tooth bending fatigue performance of each gear variation is shown to correlate with the level of root stress reduction achieved. Experiments indicate that the most significant life increases compared to the baseline conditions are achieved with the last variation (asymmetric tooth profiles and an elliptical root shape), where the mean life is increased by more than 30 times. It is also shown through examination of the broken teeth that the critical locations where the cracks initiated agree well with the predicted locations of the maximum root stresses.Copyright

Prediction and Minimization of Mechanical Power Loss of Gear Pair via Analytical Approach

A highly efficient parallel-axis gear train is widely used in automobile transmissions. Power losses in a parallel-axis gear train are mainly generated by gears and bearings. In this study, an analytical methodology is introduced to predict the friction-related mechanical power loss of a gear pair in a parallel-axis gear train. The mechanical power loss of a gear under typical operating and lubrication conditions is estimated through a gear contact analysis model and a friction coefficient formulation. A design parameter study is performed to identify the effect of the parameters on gear mechanical power loss. Design optimization is also conducted to minimize the mechanical power loss of the gear pair.

Robust optimization of cylindrical gear tooth surface modifications within ranges of torque and misalignments

Tooth surface modifications are small, micron-level intentional deviations from perfect involute geometries of spur and helical gears. Such modifications are aimed at improving contact pressure distribution, while minimizing the motion transmission error to reduce noise excitations. In actual practice, optimal modification requirements vary with the operating torque level, misalignments, and manufacturing variance. However, most gear literature has been concerned with determining optimal flank form modifications at a single design point, represented by fixed, single load and misalignment values. A new approach to the design of tooth surface modifications is proposed to handle such conditions. The problem is formulated as a robust design optimization problem, and it is solved, in conjunction with an efficient gear contact solver (LDP), by a direct search, global optimization algorithm aimed at guaranteeing global optimality of the obtained micro-geometry solutions. Several tooth surface modifications can be used as micro-geometry design variables, including profile, lead, and bias modifications. Depending on the contact solver capabilities, multiple performance metrics can be considered. The proposed method includes the capability of simultaneously and robustly handling several conflicting design objectives. In the present paper, peak contact stress and loaded transmission error amplitude are used as objective functions (to be minimized). At the end, two example optimizations are presented to demonstrate the effectiveness of the proposed method.Copyright