Gears are industrial components with a precise geometry. Identification of their basic parameters plays an important role in their reverse design and quality control process. This article describes a new approach for the calculation of helical gear's basic parameters using optical data acquired by 3D digitizer. This approach is implemented by acquiring cloud-ofpoints data (COP-data) from the bearing seats and gear tooth surface. Cylinder surface fitting through COP-data acquired from bearing seats is performed for the determination of gear axis of rotation. In a final step, involute helicoid surface fitting through COP-data acquired from gear tooth surface determines the helical gear's primary features. Particle swarm optimization algorithm as an efficient method is applied to perform the surface fitting process in this article.

A procedure for calculating and optimizing hypoid gear surface performance characteristics in the presence of the most typical errors associated with machining errors of the differential housing and assembly of gears is presented. Such errors that result in mounting or position errors of hypoid gears positioning are considered in optimization procedures and basic settings of Gleason machine. The goal of this paper is to consider machining and assembling errors of differential housing unique to a given typical manufacturing line so that conditions of optimized match between gears and the differential housing of that particular manufacturing line can be achieved. During this optimization, the condition of a predetermined contact situation up to the second-order, with optimization of third-order contact situation is considered. In order to check this calculation with other methods, the results were compared to the Gleason TCA program [1]. Moreover, practical experiments of contact pattern positioning errors on hypoid tooth surfaces with a Gleason 17A Hypoid Gear Tester are done and presented.

Hypoid gears are widely used in rear drive and 4WD vehicle axles. Investigation of their sensitivity to misalignments is one of the most important aspects of their design and optimization procedures. Because of unavoidable mounting deflections under working load, the values for mounting distances and angle deviate from the designed (desired) values (due to elastic deformation of differential housing and gear shafts). As a result the performance characteristics will be changed. This study provides a calculation procedure to design "optimized vehicle differential housing side elastic coefficients" that maintains primary performance characteristics during load variations (caused by both the road and engines). The calculation is based on third order contact surface parameters for combined mismatched tooth surfaces. Calculations will be done in four separate groups to maintain four primary groups of performance characteristics, including: i) the amount of transmission error ii) contact pattern shape (by controlling bias angle) iii) backlash and iv) contact pattern size; in all mentioned cases theoretical contact pattern position during differential housing deflections is kept unchanged. Moreover, an experimental analysis was performed on a hypoid gear pair, the results of which were in close relation to theoretical results of sensitivity of contact pattern location. The method used in this study gives insight to effects of differential housing and gear shaft deflections (as misalignments) on hypoid gear performance. Considering this information in differential housing and gear shaft design will provide more correlations between hypoid gear pair and their housing and shafts in order to optimize performance characteristics under actual load.