Wildhaber-Novikov Gears Research Articles

Relieving the teeth of hobs for cutting the Wildhaber-Novikov gears

Screw and relieved surfaces with a profile of substantial and variable curvature are often used in machine parts and cutting tools. Among them, a special place is occupied by worm hobs for cutting the teeth of Wildhaber-Novikov gears with the profile of the generating worm, variable not only in radius, but also in sign of curvature. A technique for forming the tooth flanks of these hobs by a disk grinding wheel is developed, which allows the grinding and ground profiles in the axial section of the generating worm to be brought together as close as possible. The method for calculating the settings-up and profile coordinates of the grinding wheel is given for its performance in real production conditions.

Concept of Gear Synthesis Based on Assignment of Instant Contact Areas for Loaded Teeth

Objects of investigation are gears with point system of meshing, that is, with localized tooth contact. The purpose of investigation is the development of scientific fundamentals for a new method of optimization synthesis of plane and spatial gearing; the method basing on assignment of the shape, dimensions and location of instant areas of tooth contact along assigned and synthesized meshing lines. The purpose of synthesis is to determine parameters of contact point motion along the meshing line, parameters of contact areas and tooth surfaces for which the circumferential load becomes maximal. The synthesis is started with revealing the areas (within a fixed coordinate system) with good, acceptable and inacceptable conditions for tooth contact. This work is considered to be the continuation of M. L. Novikov method for generation of conjugate meshing. The manuscript involves the review of publications on methods for synthesis of meshing; statement of laws of mechanics and scientific knowledge applied when developing the concept of synthesis. It is shown that in Wildhaber-Novikov gears two convex solids are contacting with each other rather than a convex solid with the concave one. Fundamentals of the proposed concept are stated; the plan on implementation of the proposed concept of synthesis and design is presented; basic problems of initial stages of work are listed; and approaches to their solution are stated.

Computerized simulation of generation, meshing and contact of double circular-arc helical gears

The authors have investigated the generation, geometry, meshing and contact of double circular-arc helical gears. Such gears have been proposed in extension of the idea of single-arc Wildhaber-Novikov gears with the purpose: (i) to obtain two zones of meshing and reduce the bending stresses, and (ii) keep the advantage of reduced contact stresses of W.-N. gears. The proposed methods and developed computer programs cover the solution to the following problems: 1. Determination of the paths of contact on the gear tooth surfaces. 2. Determination of the bearing contact as the set of instantaneous contact ellipses. 3. Determination of transmission errors caused by gear misalignment. The investigation is illustrated with numerical examples.

The mathematical model of Wildhaber-Novikov gears applicable to finite element stress analysis

The mathematical model and results of tooth contact analysis (TCA) of the Wildhaber-Novikov (W-N) gear are given in Ref. [1] [F.L. Livtin and C.-B. Tsay, Trans. ASME, J. mech. Trans. Auto. Des. 556-564 (December 1985)]. A finite element method (FEM), using the SAP IV package, is employed to the W-N gear stress analysis. An automatic nodal points and meshes generating (AMG) computer program has been developed. By utilizing the mathematical model of the W-N gear and the AMG computer program, nodal points and meshes for finite elements analysis can be obtained automatically. By applying the results of TCA, the location and direction of applied loading on gear teeth can be defined. Root bending stresses of pinion and gear with different loading positions have been analyzed. Effects on root stresses due to variations of fillet radius and normal pressure angle of pinion have also been investigated.

Three-dimensional photoelastic study of the load-carrying capacity/face width ratio of Wildhaber-Novikov gears for automotive applications

Wildhaber-Novikov gears are becoming more and more popular for heavy load applications. They have been tried as speed-reducing gears, in spite of heavy noise generation, in aircraft jet engines, marine engines and agricultural machinery. These circular-arc gears, though stronger than involute geras, have the disadvantage of needing larger face width. Axial face width required can be minimized only at the expense of load-carrying capacity. This is not a serious disadvantage with stationary engines. But in the case of automotive applications, this fact limits the load-carrying capacity of Wildhaber-Novikov gears, since space problem is very critical in these applications and large face widths, therefore, cannot be used for such gear-reduction units. The face width is determined by the helix angle and, therefore, a thorough investigation of the dependence of the load-carrying capacity on helix angle is necessary, if these special types of gears have to make headway into the automotive field.

Photoelastic optimization of the profiles of Wildhaber-Novikov gears

Wildhaber-Novikov gears having circular flanks hold out a very promising future in the field of gearing for power transmission in very heavily loaded machineries. In order to optimize the profile parameters of these gears, a photoelastic investigation was carried out.

Gear Conformity and Load Capacity

A measure, M, of the conformity or closeness of fit of gears is proposed and it is shown that there is a limit on its value; this limit is a function of the material properties and is about 2.5 times the value for involutes for gears of case hardened steel. It is shown that no very large improvement in M can be had above that obtainable in known non-involute forms, specifically Wildhaber-Novikov gears.