Hypoid Gear Set Research Articles

An Ease-Off Based Method for Loaded Tooth Contact Analysis of Hypoid Gears Having Local and Global Surface Deviations

Actual hypoid gear tooth surfaces do deviate from the theoretical ones either globally due to manufacturing errors or locally due to reasons such as tooth surface wear. A practical methodology based on ease-off topography is proposed here for loaded tooth contact analysis of hypoid gears having both local and global deviations. This methodology defines the theoretical pinion and gear tooth surfaces from the machine settings and cutter parameters, and constructs the surfaces of the theoretical ease-off and roll angle to compute for the unloaded contact analysis. This theoretical ease-off topography is modified based on tooth surface deviations and is used to perform a loaded tooth contact analysis according to a semi-analytical method proposed earlier. At the end, two examples, a face-milled hypoid gear set having local deviations and a face-hobbed one having global deviations, are analyzed to demonstrate the effectiveness of the proposed methodology in quantifying the effect of such deviations on the load distribution and the loaded motion transmission error.

Effect of tooth mesh stiffness asymmetric nonlinearity for drive and coast sides on hypoid gear dynamics

A nonlinear time-varying dynamic model of a hypoid gear pair system with time-dependent nonlinear mesh stiffness, mesh damping and backlash properties is formulated to study the effect of mesh stiffness asymmetry for drive and coast sides on dynamic response. The asymmetric characteristic is the result of the inherent curvilinear tooth form and pinion offset in hypoid set. Using the proposed nonlinear time-varying dynamic model, effects of asymmetric mesh stiffness parameters that include mean mesh stiffness ratio, mesh stiffness variation and mesh stiffness phase angle on the dynamic mesh force response and tooth impact regions are examined systematically. Specifically, the dynamic models with only asymmetric mesh stiffness nonlinearity, with only backlash nonlinearity and with both asymmetric mesh stiffness and backlash nonlinearities are analyzed and compared. Using the parameters of a typical hypoid gear set, the extent of the effect of asymmetry in the mesh coupling on gear pair dynamics is quantified numerically. The results show that the increase in the mean mesh stiffness ratio tends to worsen the dynamic response amplitude, and the mesh stiffness parameters for drive side have more effect on dynamic response than those of the coast side one.

Computerized Modeling and Simulation of Spiral Bevel and Hypoid Gears Manufactured by Gleason Face Hobbing Process

The Gleason face hobbing process has been widely applied by the gear industry. But so far, few papers have been found regarding exact modeling and simulation of the tooth surface generations and tooth contact analysis (TCA) of face hobbed spiral bevel and hypoid gear sets. This paper presents the generalized theory of the face hobbing generation method, mathematic models of tooth surface generations, and the simulation of meshing of face hobbed spiral bevel and hypoid gears. The face hobbing indexing motion is described and visualized. A generalized description of the cutting blades is introduced by considering four sections of the blade edge geometry. A kinematical model is developed and analyzed by breaking down the machine tool settings and the relative motions of the machine elemental units and applying coordinate transformations of the elemental motions. The developed face hobbing generation model is directly related to a physical bevel gear generator. A generalized and enhanced TCA algorithm is proposed. The face hobbing process has two categories, non-generated (Formate®) and generated methods, applied to the tooth surface generation of the gear. In both categories, the pinion is always finished with the generated method. The developed tooth surface generation model covers both categories with left-hand and right-hand members. Based upon the developed theory, an advanced tooth surface generation and TCA program is developed and integrated into Gleason CAGE™for Windows Software. Two numerical examples are provided to illustrate the implementation of the developed mathematic models.

GM-15 DETERMINATION OF LAPPING MACHINE SETTINGS FOR HYPOID GEARS USING ARTIFICIAL INTELLIGENCE(GEAR MANUFACTURING)

The present paper deals with the determination of lapping machine settings for hypoid gear sets. Using an artificial intelligence, neural net, a developed system enables lapping machine settings to be automatically determined from a tooth contact patterns after tooth cutting and a target one. In order to improve the determination performance of the system, the method of selecting teacher signals, which are used for training the system, was discussed. As a result, it was revealed that the teacher signals should be selected under consideration of the frequency of the value for each machine setting parameter.

Simulation and Experimental Measurement of the Transmission Error of Real Hypoid Gears Under Load

The Transmission Error and Bearing Pattern of a gear set are fundamental aspects of its meshing behavior. To assess the validity of gear simulation models, the Transmission Error and Bearing Pattern of a Formate Hypoid gear set are measured under a variety of operating positions and applied loads. Measurement data are compared to simulation results of Tooth Contact Analysis and Loaded Tooth Contact Analysis models, and show excellent agreement for the considered test gear set. [S1050-0472(00)00901-6]

Prediction of Performance of Hypoid Gears by Observation of Tooth Contact Pattern. 2nd Report. Contact Pattern, Transmission Error and Stresses in Gear.

A practical algorithm to generate the composite error surface of mating tooth flank forms as a function of tooth contact pattern of hypoid gear set was proposed in the first report of this investigation. In this report, it is shown that the algorithm successfully reconstructs the composite error surface to bring a tooth contact pattern that matches well with the target pattern. Using this simulation program, the reliability of the predicted stress values and vibrational excitation as a function of tooth contact pattern was examined. The results estimated by this method showed good agreement with those values induced in the same gear set with the target composite error surface. The initial figure for the estimation of composite error surface has some influence on the accuracy of the prediction, but the proposed procedure for building initial composite error surface showed tolerable capability for the job.

A mathematical model for the tooth geometry of hypoid gears

A mathematical model of the circular-cut hypoid gear set has been developed herein to represent the tooth surface geometry of hypoid gears. It can be applied to simulate the tooth profiles manufactured by the Duplex Method, Helical Duplex Method, and Formate Method. By applying the computer graphics and the proposed mathematical model, the profile of the hypoid gear and the precision coordinates of any tooth surface point can be obtained. The coordinates of the tooth surface can be considered as the standard for checking the profile precision of the actual products. The proposed mathematical model of the hypoid gear can also be applied to the computer numerical controlled (CNC) machining, tooth contact analysis (TCA), and finite element stress analysis.

Lubrication at Elliptical Contacts

The classical hydrodynamic theory for point contacts is extended to cover the general case where the resolved hydrodynamic velocity is not directed along either of the axes of the ellipse of contact. Isobar plots of deduced values of the non-dimensional reduced pressure, q, are shown for some of these cases. A first approximation to an elastohydrodynamic film thickness equation is derived, for this general case, by equating the maximum reduced pressure generated between undeformed bodies to the inverse of the pressure coefficient of viscosity, α. The theory is applicable to the contact conditions that exist between the teeth of hypoid gears, and the variation of lubricant film thickness with pinion offset and gear ratio for a range of hypoid gear sets has been deduced. Experiments have been performed on a crossed cylinders machine, the results of which demonstrate the general validity of the theory.