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A series of bench-top experiments was conducted to determine the effects of metallic debris being dragged through meshing gear teeth. A test rig that is typically used to conduct contact fatigue experiments was used for these tests. Several sizes of drill material, shim stock and pieces of gear teeth were introduced and then driven through the meshing region. The level of torque required to drive the “chip” through the gear mesh was measured. From the data gathered, chip size sufficient to jam the mechanism can be determined.
This article reviews mathematical models for individual components associated with power losses, such as windage, churning, sliding and rolling friction losses.
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.
A very important parameter when designing a gear pair is the maximum surface contact stress that exists between two gear teeth in mesh, as it affects surface fatigue (namely, pitting and wear) along with gear mesh losses. A lot of attention has been targeted to the determination of the maximum contact stress between gear teeth in mesh, resulting in many "different" formulas. Moreover, each of those formulas is applicable to a particular class of gears (e.g., hypoid, worm, spiroid, spiral bevel, or cylindrical - spur and helical). More recently, FEM (the finite element method) has been introduced to evaluate the contact stress between gear teeth. Presented below is a single methodology for evaluating the maximum contact stress that exists between gear teeth in mesh. The approach is independent of the gear tooth geometry (involute or cycloid) and valid for any gear type (i.e., hypoid, worm, spiroid, bevel and cylindrical).
How dynamic load affects the pitting fatigue life of external spur gears was predicted by using NASA computer program TELSGE. TELSGE was modified to include an improved gear tooth stiffness model, a stiffness-dynamic load iteration scheme and a pitting-fatigue-life prediction analysis for a gear mesh. The analysis used the NASA gear life model developed by Coy, methods of probability and statistics and gear tooth dynamic loads to predict life. In general, gear life predictions based on dynamic loads differed significantly from those based on static loads, with the predictions being strongly influenced by the maximum dynamic load during contact.
In most transmission systems, one of the main power loss sources is the loaded gear mesh. In this article, the influences of gear geometry parameters on gear efficiency, load capacity, and excitation are shown.
Point-surface-origin (PSO) macropitting occurs at sites of geometric stress concentration (GSC) such as discontinuities in the gear tooth profile caused by micropitting, cusps at the intersection of the involute profile and the trochoidal root fillet, and at edges of prior tooth damage, such as tip-to-root interference. When the profile modifications in the form of tip relief, root relief, or both, are inadequate to compensate for deflection of the gear mesh, tip-to-root interference occurs. The interference can occur at either end of the path of contact, but the damage is usually more severe near the start-of-active-profile (SAP) of the driving gear.
When designing a gear set, engineers usually want the teeth of the gear (Ng) and the pinion (Np) in a "hunting" mesh. Such a mesh or combination is defined as one in which the pinion and the gear do not have any common divisor by a prime number. If a mesh is "hunting," then the pinion must make Np x Ng revolutions before the same pinion tooth meshes with the same gear space. It is often easy to determine if a mesh is hunting by first determining if both the pinion and the gear teeth are divisible by 2,3,5,7,etc. (prime numbers). However, in this age of computerization, how does one program the computer to check for hunting teeth? A simple algorithm is shown below.