Face-Hobbed Spiral Bevel Gears Research Articles

A Novel Cutting Method for Face-Hobbed Spiral Bevel Gears Based on Tool Path Modification

A novel tooth surface design method of face-hobbed spiral bevel gears is proposed, which utilizes a solid cutter without axis tilting through tool path control combining with optimized cutter blade profile to control tooth contact patterns and realize tooth lengthwise chamfering. Firstly, a gear tooth surface generating plan of tool path controlling actively is developed, the mathematical model of the tool path is built, and the equations are given in detail, the determination method of all control parameters is also described. Next, the tooth surface functions of generating gear and machined gear are established based on a mathematic model of the traditional cradle machine tool. Then, the machine setting is also given in concise equations. Finally, the tooth contact analysis is also conducted for a specific gear pair to validate the validity and the reasonability of the new tooth modification method.

Tool path active design for tooth modification of face-hobbed spiral bevel gears

An advanced design and manufacturing method called tool path active design for face-hobbed spiral bevel gears is mainly discussed in this paper. The method bases on the forming mechanism of extended epicycloids and utilizes an integrated cutter head without tilting, meanwhile, all its controlled parameters can be directly calculated according to the given meshing performances and modified conditions. Starting with the cutting principle of face-hobbing method, a tooth flank mending plan of altering tool path is developed, which detailed expressions are also given in functions. Then, the meshing performances which are used to determine the modification parameters are introduced and their formulas are also derived. Finally, the proposed method is validated by a numerical example of tooth contact analysis for a face-bobbed hypoid gear pair. As a further explanation, a numerical example of tooth contact analysis is done to validate the feasibility of the proposed method.

Conjugated action and methods for crowning in face-hobbed spiral bevel and hypoid gear drives through the spirac system

An analytical method for derivation of basic machine-tool settings that allows the conjugated action in face-hobbed spiral bevel and hypoid gear drives wherein the gear is not generated is proposed. This approach is used as starting point for investigation of further methods of crowning as the one where crowning is achieved through application of a tilt angle. A new approach where crowning is achieved through the application of modified roll between the rotations of the head-cutter and the pinion is proposed. It is based on the application of a two-term Fourier series of a parabolic function to provide a continuous and periodic function that is required in a continuous non-indexing process as face-hobbing. The existing and proposed approaches for crowning have been tested by the application of tooth contact analysis and geometry comparison. The results show that the proposed approach does not yield unloaded transmission errors and allows independent crowning at both tooth sides to get acceptable formations of the bearing contact for both rotational directions. Two numerical examples of design corresponding to a spiral bevel gear drive and a hypoid gear drive are presented as well starting from their basic data.

Optimization of cutter blade profile for face-hobbed spiral bevel gears

To eliminate the tooth edge contact and improve the distribution of the tooth contact stress for face-hobbed spiral bevel gears in the case of heavy load and misalignment considered, optimizing the cutter blade profile is one of the most effective solutions. Generally, a segment of circle arc is used to substitute the straight line to get a desired theoretical tooth contact pattern, however, which is not sufficient for a heavy-loaded gear pair. A multi-segment cutter blade profile with Toprem, Flankrem, and cutter tip is introduced to obtain the ideal load and contact stress distribution. First, the structure of cutter head is described geometrically, the mathematical model of new cutter blade profile is built, and the equation for each section is given in detail. Then, the calculations of all design parameters are represented step by step. Finally, a contrast experiment between the original cutter and new optimal cutter, including tooth contact analysis, finite element analysis, and practical rolling check, is carried out for Oerlikon hypoid gears to verify effectiveness.

Optimal Machine-Tool Settings for the Manufacture of Face-Hobbed Spiral Bevel Gears

In this study, an optimization methodology is proposed to systematically define the optimal head-cutter geometry and machine-tool settings to simultaneously minimize the tooth contact pressure and angular displacement error of the driven gear (the transmission error), and to reduce the sensitivity of face-hobbed spiral bevel gears to the misalignments. The proposed optimization procedure relies heavily on the loaded tooth contact analysis for the prediction of tooth contact pressure distribution and transmission errors influenced by the misalignments inherent in the gear pair. The load distribution and transmission error calculation method employed in this study were developed by the author of this paper. The targeted optimization problem is a nonlinear constrained optimization problem, belonging to the framework of nonlinear programming. In addition, the objective function and the constraints are not available analytically, but they are computable, i.e., they exist numerically through the loaded tooth contact analysis. For these reasons, a nonderivative method is selected to solve this particular optimization problem. That is the reason that the core algorithm of the proposed nonlinear programming procedure is based on a direct search method. The Hooke and Jeeves pattern search method is applied. The effectiveness of this optimization was demonstrated on a face-hobbed spiral bevel gear example. Drastic reductions in the maximum tooth contact pressure (62%) and in the transmission errors (70%) were obtained.

Optimal Tooth Modifications in Face-Hobbed Spiral Bevel Gears to Reduce the Influence of Misalignments on Elastohydrodynamic Lubrication

In this study, an optimization methodology is proposed to systematically define the optimal tooth modifications introduced by head-cutter geometry and machine-tool settings to minimize the influence of misalignments on the elastohydrodynamic (EHD) lubrication characteristics in face-hobbed spiral bevel gears. The goal is to simultaneously maximize the EHD load-carrying capacity of the oil film and to minimize power losses in the oil film when different misalignments are inherent in the gear pair. The proposed optimization procedure relies heavily on the EHD lubrication analysis developed in this paper. The core algorithm of the proposed nonlinear programming procedure is based on a direct search method. Effectiveness of this optimization was demonstrated on a face-hobbed spiral bevel gear example. A drastic increase in the EHD load-carrying capacity of the oil film and a reduction in the power losses in the oil film were obtained.

Manufacture of Optimized Face-Hobbed Spiral Bevel Gears on Computer Numerical Control Hypoid Generator

In this study, a method is proposed for the advanced manufacture of face-hobbed spiral bevel gears on CNC hypoid generators with optimized tooth surface geometry. An optimization methodology is applied to systematically define optimal head-cutter geometry and machine tool settings to introduce optimal tooth modifications. The goal of the optimization is to simultaneously minimize tooth contact pressures and angular displacement error of the driven gear (the transmission error). The optimization is based on machine tool setting variation on the cradle-type generator conducted by optimal polynomial functions. An algorithm is developed for the execution of motions on the CNC hypoid generator using the relations on the cradle-type machine. Effectiveness of the method was demonstrated by using a face-hobbed spiral bevel gear example. Significant reductions in the maximum tooth contact pressure and in the transmission errors were obtained.

Design of face-hobbed spiral bevel gears with reduced maximum tooth contact pressure and transmission errors

The aim of this study is to define optimal tooth modifications, introduced by appropriately chosen head-cutter geometry and machine tool setting, to simultaneously minimize tooth contact pressure and angular displacement error of the driven gear (transmission error) of face-hobbed spiral bevel gears. As a result of these modifications, the gear pair becomes mismatched, and a point contact replaces the theoretical line contact. In the applied loaded tooth contact analysis it is assumed that the point contact under load is spreading over a surface along the whole or part of the “potential” contact line. A computer program was developed to implement the formulation provided above. By using this program the influence of tooth modifications introduced by the variation in machine tool settings and in head cutter data on load and pressure distributions, transmission errors, and fillet stresses is investigated and discussed. The correlation between the ease-off obtained by pinion tooth modifications and the corresponding tooth contact pressure distribution is investigated and the obtained results are presented.

Influence of tooth modifications on tooth contact in face-hobbed spiral bevel gears

In this study the influence of tooth modifications induced by machine tool setting and head-cutter profile variations on tooth contact characteristics in face-hobbed spiral bevel gears is investigated. The concept of face-hobbed spiral bevel gear generation by an imaginary generating crown gear is applied. The modifications of tooth surfaces are introduced into the teeth of both members. The lengthwise crowning of teeth is achieved by applying a slightly bigger radius of lengthwise tooth flank curvature of the crown gear generating the concave side of pinion/gear tooth-surfaces, and by the variation of machine tool settings in the generation of pinion/gear teeth. The ease-off in the tooth height direction of meshing tooth surfaces is achieved by applying a head-cutter whose profile consists of two circular arcs, instead of a straight-line. The method of tooth contact analysis applied determines the path of contact, the potential contact lines, the separations along these lines, and the transmission errors. A computer program implements the method. By using this program the influence of the variation of machine tool settings and of head-cutter geometry on tooth contact is investigated and discussed.

A load distribution model for hypoid gears using ease-off topography and shell theory

A computationally efficient load distribution model is proposed for both face-milled and face-hobbed hypoid gears produced by Formate and generate processes. Tooth surfaces are defined directly from the cutter parameters and machine settings. A novel methodology based on the ease-off topography is used to determine the unloaded contact patterns. The proposed ease-off methodology finds the instantaneous contact curve through a surface of roll angles, allowing an accurate unloaded tooth contact analysis in a robust and accurate manner. Rayleigh-Ritz based shell models of teeth of the gear and pinion are developed to define the tooth compliances due to bending and shear effects efficiently in a semi-analytical manner. Base rotation and contact deformation effects are also included in the compliance formulations. With this, loaded contact patterns and transmission error of both face-milled and face-hobbed spiral bevel and hypoid gears are computed by enforcing the compatibility and equilibrium conditions of the gear mesh. The proposed model requires significantly less computational effort than finite elements (FE) based models, making its use possible for extensive parameter sensitivity and design optimization studies. At the end, comparisons to the predictions of a FE hypoid gear contact model are also provided to demonstrate the accuracy of the model under various load and misalignment conditions.