High-performance tooth flank collaborative optimization model for spiral bevel and hypoid gears

Mathematical model of spiral bevel and hypoid gears manufactured by the modified roll method

Adaptive data-driven collaborative optimization of both geometric and loaded contact mechanical performances of non-orthogonal duplex helical face-milling spiral bevel and hypoid gears

Spiral bevel and hypoid gears are key components widely used for transmitting significant power in various types of vehicles and engineering machineries. In reality, these gear surfaces are quite rough with three-dimensional (3D) topography that may significantly influence the lubrication formation and breakdown as well as components failures. Previous spiral bevel and hypoid gears lubrication studies, however, were limited mostly to cases under the full-film lubrication condition with smooth surfaces. In the present study, a comprehensive analysis for gearing geometry, kinematics, mixed lubrication performance, and friction and interfacial flash temperature in spiral bevel and hypoid gears is developed based on a recently developed mixed elastohydrodynamic lubrication (EHL) model that is capable of handling practical cases with 3D machined roughness under severe operating conditions and considering the effect of arbitrary entrainment angle. Obtained results from sample cases show that the simulation model developed can be used as an engineering tool for spiral bevel and hypoid gears design optimization and strength prediction.

New methodology for determining basic machine settings of spiral bevel and hypoid gears manufactured by duplex helical method

Contact pattern and transmission error were compared for two different methods of simulating tooth generation and power transmission characteristics of hypoid gears. One method incorporates pinion and gear tooth flanks that are generated individually as a function of the parameters of the tooth cutting machine, and the other method uses the same gear tooth flank, but a different pinion tooth flank. The reference pinion tooth flank is a virtual one generated mathematically by a computer and it is conjugate to the gear tooth flank. The latter method uses the composite error surface of mating tooth flanks in the analysis. The calculated results were also compared with measured results obtained for four hypoid gear with four different kinds of tooth contact patterns. These investigations show the validity of the latter method for simulating the performance of hypoid gears. With this method, a gear engineer can apply knowledge of cylindrical involute gears to hypoid or bevel gears in predicting their performance.

Collaborative machine tool settings compensation considering both tooth flank geometrical and physical performances for spiral bevel and hypoid gears

The increasing demand for low noise and high strength leads to higher quality requirements in manufacturing spiral bevel and hypoid gears. Due to heat treatment distortions, machine tolerances, variation of cutting forces, and other unpredictable factors, the real tooth flank form geometry may deviate from the theoretical or master target geometry. This will cause unfavorable displacement of tooth contact and increased transmission errors, resulting in noisy operation and premature failure due to edge contact and highly concentrated stresses. In the hypoid gear development process, a corrective machine setting technique is usually employed to modify the machine settings, compensating for the tooth flank form errors. Existing published works described the corrective machine setting technique based on the use of mechanical hypoid gear generators, and the second-order approximation of error surfaces. Today, computer numerically controlled (CNC) hypoid gear generators have been widely employed by the gear industry. The universal motion concept has been implemented on most CNC hypoid generators, providing additional freedoms for the corrections of tooth flank form errors. Higher-order components of the error surfaces may be corrected by using the higher-order universal motions. This paper describes a new method of tooth flank form error correction utilizing the universal motions for spiral bevel and hypoid gears produced by the face-milling process. The sensitivity of the changes of tooth flank form geometry to the changes of universal motion coefficients is investigated. The corrective universal motion coefficients are determined through an optimization process with the target of minimization of the tooth flank form errors. A numerical example of a face-mill completing process is presented. The developed new approach has been implemented with computer software. The new approach can also be applied to the face-hobbing process.

The increasing demand for low noise and high strength leads to higher quality requirements in manufacturing spiral bevel and hypoid gears. Due to heat treatment distortions, machine tolerances, variation of cutting forces and other unpredictable factors, the real tooth flank form geometry may deviate from the theoretical or master target geometry. This will cause unfavorable displacement of tooth contact and increased transmission errors, resulting in noisy operation and premature failure due to edge contact and highly concentrated stresses. In the hypoid gear development process, a corrective machine setting technique is usually employed to modify the machine settings, compensating for the tooth flank form errors. Existing published works described the corrective machine setting technique based on the use of mechanical hypoid gear generators, and the second order approximation of error surfaces. Today, Computer Numerically Controlled (CNC) hypoid gear generators have been widely employed by the gear industry. The Universal Motion Concept (UMC) has been implemented on most CNC hypoid generators, providing additional freedoms for the corrections of tooth flank form errors. Higher order components of the error surfaces may be corrected by using the higher order universal motions. This paper describes a new method of tooth flank form error correction utilizing the universal motions for spiral bevel and hypoid gears produced by the face-milling process. The sensitivity of the changes of tooth flank form geometry to the changes of universal motion coefficients is investigated. The corrective universal motion coefficients are determined through an optimization process with the target of minimization of the tooth flank form errors. A numerical example of a face-mill completing process is presented. The developed new approach has been implemented with computer software. The new approach can also be applied to the face-hobbing process.

A general formulation for the calculation of the load sharing and transmission error under load of spiral bevel and hypoid gears

Data-driven operation and compensation approaches to tooth flank form error measurement for spiral bevel and hypoid gears

Contact fatigue life forecasting model considering micro-scale subsurface stress for aerospace spiral bevel gears

Data-driven process control considering both geometric and loaded contact performance evaluations has been an increasingly important stage in field of spiral bevel and hypoid gears. A new data-driven manufacturing process control strategy is proposed for a high performance spiral bevel and hypoid gears. Here, to distinguish with the conventional simulated loaded tooth contact analysis (SLTCA) using economical finite element software package, the numerical loaded tooth contact analysis (NLTCA) is of more flexibility and practicality. In light of the advantages of the improved design for six sigma (DFSS), it is integrated with NLTCA for establishing a novel data-driven process control of gear manufacturing. Firstly, in improved DFSS framework, quality function deployment (QFD) is used to determine four sub-objective high-performance evaluation items. Then, their data-driven relationships between machine settings are respectively determined by using NLTCA. In particular, the manufacturing process control is further converted into multi-objective optimization (MOO) modification of the hypoid generator settings. Finally, an interactive preference point approach is applied for data-driven control of its iterative step and it can obtain a robust solution from Pareto optimal front. A case study is provided to verify the proposed methodology.

In the blank design of spiral bevel and hypoid gears, the face cone is defined as an imaginary cone tangent to the tops of the teeth. Traditionally, the face cone element or generatrix is a straight line. On the other hand, the tooth root lines which are traced by the blade tips are normally not straight lines. As a result, the tooth top geometry generally does not fit the mating member’s real root shape, providing an uneven tooth root-tip clearance; additionally, in some cases root-tip interference between the tooth tip and the root tooth surfaces of the mating gear members may be observed. To address this issue, this paper describes a method of determining an optimized face cone element for spiral bevel and hypoid gears. The method is based on the incorporation of calculation of tooth surface and root geometries, the conjugate relationship of the mating gear members, the ease-off topography, and the tooth contact analysis. The resulting face cone element may not be a straight line but generally an optimized curve that, in addition to avoidance of the interference, offers maximized contact ratio and even tooth root-tip clearance. Manufacturing of bevel gear blanks with a curved face cone element can be implemented by using computer numerically controlled (CNC) machines.

In the blank design of spiral bevel and hypoid gears, the face cone is defined as an imaginary cone tangent to the tops of the teeth. Traditionally, the face cone element or generatrix is a straight line. On the other hand, the tooth root lines, which are traced by the blade tips, are normally not straight lines. As a result, the tooth top geometry generally does not fit the mating member’s real root shape, providing an uneven tooth root-tip clearance; additionally, in some cases root-tip interference between the tooth tip and the root tooth surfaces of the mating gear members may be observed. To address this issue, this paper describes a method of determining an optimized face cone element for spiral bevel and hypoid gears. The method is based on the incorporation of calculation of tooth surface and root geometries, the conjugate relationship of the mating gear members, the ease-off topography, and the tooth contact analysis. The resulting face cone element may not be a straight line but generally an optimized curve that, in addition, to avoidance of the interference, offers maximized contact ratio and even tooth root-tip clearance. Manufacturing of bevel gear blanks with a curved face cone element can be implemented by using computer numerically controlled machines.

On micro flank geometric topography design for spiral bevel and hypoid gears