Three-Dimensional Analysis of Hypoid Gears

1971 ◽  
Vol 93 (4) ◽  
pp. 1275-1279
Author(s):  
I. M. Daniel
Keyword(s):  
Three Dimensional ◽  
Gear Pair ◽  
Stress Distributions ◽  
Hypoid Gear ◽  
Hypoid Gears ◽  
Load Distributions ◽  
Loading Device ◽  
Freezing Cycle ◽  
Photoelastic Analysis ◽  
Set Up

A three-dimensional photoelastic analysis using the stress-freezing and slicing techniques was conducted to obtain stress and load distributions in a hypoid gear pair. Precise full-scale plastic models of a gear and pinion were manufactured. A special mounting fixture was designed and built of the same photoelastic plastic as that used for the model. A set-up gage was also designed and manufactured for gaging the gear and pinion settings. Fine adjustments were made by means of shims. The desired contact, calculated to produce maximum fillet stresses, was checked with a marking compound and gaged with a stock-dividing gage. A loading device was used to apply pure torque to the pinion. The assembled model was loaded and taken through the stress-freezing cycle. Subsequently, the teeth under engagement were sliced and analyzed to obtain contact and fillet stress distributions.

Report 16: Photoelastic Analysis of Journal Bearings: Preliminary Investigations

1967 ◽  
Vol 182 (7) ◽  
pp. 90-94
Author(s):  
R. W. T. Preater
Keyword(s):  
Pressure Distribution ◽  
Three Dimensional ◽  
Stress Distributions ◽  
Freezing Cycle ◽  
Photoelastic Analysis ◽  
Loading Tests ◽  
Dynamic Loading Conditions ◽  
Time Of Presentation ◽  
The City

Determination of the stress distributions associated with composite shell bearings under static and dynamic loading conditions is discussed briefly. Experimental work recently started at The City University, using the three-dimensional ‘frozen stress’ photoelastic technique, is described. Preliminary static loading tests have been carried out over a range of low temperatures, prior to stress freezing, on a simple bearing and shaft assembly made in Araldite. One successful stress freezing cycle has been completed and the pressure distribution at the point of stress freezing is shown compared with low temperature distributions for a constant duty parameter. It is anticipated that, at the time of presentation of this report, the stress distribution at the lubrication surface, as determined by analysis, may be shown compared with the recorded pressure distribution.

Optimal Tooth Modifications in Hypoid Gears

2004 ◽  
Vol 127 (4) ◽  
pp. 646-655 ◽  
Author(s):  
Vilmos Simon
Keyword(s):  
Load Distribution ◽  
Angular Position ◽  
Point Contact ◽  
Tooth Surface ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Transmission Errors ◽  
Tool Profile

A method for the determination of optimal tooth modifications in hypoid gears based on improved load distribution and reduced transmission errors is presented. The modifications are introduced into the pinion tooth surface by using a cutter with bicircular profile and optimal diameter. In the optimization of tool parameters the influence of shaft misalignments of the mating members is included. As the result of these modifications a point contact of the meshed teeth surfaces appears instead of line contact; the hypoid gear pair becomes mismatched. By using the method presented in (Simon, V., 2000, “Load Distribution in Hypoid Gears,” ASME J. Mech. Des., 122, pp. 529–535) the influence of tooth modifications introduced on tooth contact and transmission errors is investigated. Based on the results that was obtained the radii and position of circular tool profile arcs and the diameter of the cutter for pinion teeth generation were optimized. By applying the optimal tool parameters, the maximum tooth contact pressure is reduced by 16.22% and the angular position error of the driven gear by 178.72%, in regard to the hypoid gear pair with a pinion manufactured by a cutter of straight-sided profile and of diameter determined by the commonly used methods.

Optimal Tooth Modifications in Hypoid Gears

2003 ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Angular Position ◽  
Point Contact ◽  
Tooth Surface ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Transmission Errors ◽  
Tool Profile

A method for the determination of optimal tooth modifications in hypoid gears based on improved load distribution and reduced transmission errors is presented. The modifications are introduced into the pinion tooth surface by using a cutter with bicircular profile and by changing the cutter diameter. In the optimization of tool parameters the influence of shaft misalignments of the mating members is included. As the result of these modifications a point contact of the meshed teeth surfaces appears instead of line contact; the hypoid gear pair becomes mismatched. By using the method presented in [1] the influence of tooth modifications introduced on tooth contact and transmission errors is investigated. Based on the results that was obtained the radii and position of circular tool profile arcs and the cutter diameter for pinion teeth generation were optimized. By applying the optimal tool parameters, the maximum tooth contact pressure is reduced by 16.22% and the angular position error of the driven gear by 178.72%, in regard to the hypoid gear pair with a pinion manufactured by a cutter of straight-sided profile and of diameter determined by the commonly used methods.

Optimization of Machine Tool Settings on Hypoid Gear Dynamics

2019 ◽  
Author(s):  
Chia-Ching Lin ◽  
Yawen Wang ◽  
Teik C. Lim ◽  
Weiqing Zhang
Keyword(s):  
Dynamic Response ◽  
Machine Tool ◽  
Rotor System ◽  
Design Parameters ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Hypoid Gears ◽  
Tool Setting ◽  
Setting Parameters ◽  
Optimal Machine

Abstract Hypoid gears are widely used to transmit torque on cross axis shafts in a vehicle rear axle system. The dynamic responses of these hypoid geared rotor system have a significant effect on the performance of noise, vibration, and harshness (NVH) for the vehicle design. From past studies, the main source of excitation for this vibration energy comes from hypoid gear transmission error (TE). Thus, the design of hypoid gear pair with minimization of TE is one way to control the dynamic behavior of the vehicle axle system. In this paper, an approach to obtain minimum TE and improved dynamic response with optimal machine tool setting parameters for manufacturing hypoid gears is discussed. A neural network, named Feed-Forward Back Propagation (FFBP), with Particle Swarm Optimization (PSO) and Gradient Descent (GD) training algorithms are used to predict the TE. With the optimal machine tool setting parameters, a 14 degrees of freedom geared rotor system analysis is performed to verify the improvement on dynamic response aiming at minimizing the TE. A case study of a hypoid gear pair with specified design parameters and working condition is presented to validate the proposed method. The results conclude that minimization of TE, the main excitation of vehicle axle gear whine noise and vibration, with optimal machine tool setting parameters can improve the overall dynamic response. The proposed approach provides a better understanding of an optimal design hypoid gear set to minimize TE and effect on vehicle axle system dynamics.

An Investigation of Root Stresses of Hypoid Gears with Misalignments

2011 ◽  
Vol 133 (7) ◽  
Author(s):  
M. A. Hotait ◽  
A. Kahraman ◽  
T. Nishino
Keyword(s):  
Gear Pair ◽  
Hypoid Gear ◽  
Computationally Efficient ◽  
Problem Model ◽  
Efficient Treatment ◽  
Position Errors ◽  
Set Up ◽  
Static Conditions ◽  
Hypoid Gear Pairs ◽  
The Impact

In this study, the impact of misalignments on root stresses of hypoid gear sets is investigated experimentally and theoretically. An experimental set-up designed to allow operation of a hypoid gear pair under loaded quasi-static conditions with various types of tightly controlled misalignments is introduced. These misalignments include the position errors (V and H) of the pinion along the vertical and horizontal directions, the position error (G) of the gear along its axis, and the angle error (γ) between the two gear axes. For example, face-hobbed hypoid gear pair from an automotive axle application is instrumented via a set of strain gauges positioned at the roots along the faces of multiple teeth to measure root strains within a range of input torque. These root strain measurements at different V, H, G, and γ values are presented. A computational model is also proposed to predict the root stresses of face-milled and face-hobbed hypoid gear pairs under various loading and misalignment conditions. The model employs an automated finite elements mesh generator based on a predefined template for a general and computationally efficient treatment of the problem. Model predictions are compared to measurements at the end to assess the accuracy of the model and describe the measured sensitivities.

Flank Modification Methodology for Face-Hobbing Hypoid Gears Based on Ease-Off Topography

2006 ◽  
Vol 129 (12) ◽  
pp. 1294-1302 ◽  
Author(s):  
Yi-Pei Shih ◽  
Zhang-Hua Fong
Keyword(s):  
Design Parameters ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Tooth Contact Analysis ◽  
General Technique ◽  
Local Synthesis ◽  
Hypoid Gears ◽  
Gear Drive ◽  
Polynomial Coefficients ◽  
Spiral Bevel

The fundamental design of spiral bevel and hypoid gears is usually based on a local synthesis and a tooth contact analysis of the gear drive. Recently, however, several flank modification methodologies have been developed to reduce running noise and avoid edge contact in gear making, including modulation of tooth surfaces under predesigned transmission errors. This paper proposes such a flank modification methodology for face-hobbing spiral bevel and hypoid gears based on the ease-off topography of the gear drive. First, the established mathematical model of a universal face-hobbing hypoid gear generator is applied to investigate the ease-off deviations of the design parameters—including cutter parameters, machine settings, and the polynomial coefficients of the auxiliary flank modification motion. Subsequently, linear regression is used to modify the tooth flanks of a gear pair to approximate the optimum ease-off topography suggested by experience. The proposed method is then illustrated using a numerical example of a face-hobbing hypoid gear pair from Oerlikon’s Spiroflex cutting system. This proposed flank modification methodology can be used as a basis for developing a general technique of flank modification for similar types of gears.

How to Obtain the Formal Tooth Bearing Pattern Between Hypoid Gear and the Conjugate Pinion

2000 ◽  
Author(s):  
Norio Ito ◽  
Koichi Takahashi
Keyword(s):  
Conventional Method ◽  
Analytical Method ◽  
Second Order ◽  
Tooth Surface ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Third Order ◽  
Hypoid Gears ◽  
Gear Cutting ◽  
Tooth Surfaces

Abstract In this paper, the relationships between the conjugate tooth surfaces of hypoid gears and the formal tooth bearing pattern are presented. First, we introduce the tooth surface elements necessary for the tooth bearing. Next, the tooth bearing pattern, which changes according to the generating condition of the pinion, is introduced. The hypoid gear pair is a formate gear and the pinion generated to run with such a gear. The conventional method for analyzing the tooth bearing pattern has been developed by the motion of generation between second-order tooth surfaces. In this paper, the tooth surface is expressed by the original third-order tooth surface, and the tooth bearing pattern is analyzed by the meshing motion of the tooth surface. The tooth bearing pattern obtained from such an analytical method becomes the formal tooth bearing. Therefore, the machine settings for accurate gear cutting become possible, and the desired tooth bearing pattern can be obtained beforehand without a trial cutting.

Generation of Hypoid Gears on CNC Hypoid Generator

2011 ◽  
Vol 133 (12) ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Gear Tooth ◽  
Velocity Ratio ◽  
Transmission Error ◽  
Tooth Surface ◽  
Polynomial Functions ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Kinematic Scheme ◽  
Hypoid Gears ◽  
Fifth Order

In this study, polynomial functions of orders up to five are applied to induce variations in the cradle radial setting and the velocity ratio in the kinematic scheme of the machine tool for the generation of the pinion tooth surfaces corresponding to reduced transmission error amplitudes of a hypoid gear pair. The new CNC hypoid generators have made it possible to perform this nonlinear correction motions for the cutting of the face-milled hypoid gears. An algorithm is developed for the execution of motions on the CNC hypoid generator for the generation of face-milled hypoid gear tooth surface, based on the machine tool setting variation on the cradle-type hypoid generator induced by the optimal polynomial functions up to fifth-order. By using the corresponding computer program, the motion graphs of the CNC hypoid generator are determined for the generation of hypoid gear tooth surface, based on the optimal variation in the velocity ratio in the kinematic scheme and on the variation in the cradle radial setting on a cradle-type generator. The results presented indicate that the variation of the velocity ratio in the kinematic scheme of the hypoid generator induced by a fifth-order polynomial function resulted in a 62% reduction of the maximum transmission error of the gear pair.

Hobbing of Bevel and Hypoid Gears

2013 ◽  
Author(s):  
David B. Dooner
Keyword(s):  
Helical Gear ◽  
Bevel Gear ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Hypoid Gears ◽  
Virtual Models ◽  
Spiral Angle

The paper presents a hyperboloidal hob cutter similar to a cylindrical hob cutter used to fabricate spur and helical gear elements today. This hyperboloidal cutter can be used to manufacture bevel and hypoid gear elements using an existing CNC hobbing machine. These bevel and hypoid gear elements can be either spur or spiral. This hyperboloidal hob cutter is entirely different from the circular face cutters today as part of face hobbing. A brief overview of the existing circular face cutting technology is presented along with some of its geometric limitations. Subsequently, concepts of the hyperboloidal hob cutter are presented. These concepts include crossed hyperboloidal gears, cutter spiral angle, invariant speed relations, and cutter coordinates. Two illustrative examples are presented to demonstrate the concept of the hyperboloidal hob cutter. The first example is a spur bevel gear pair and the second example is a spiral hypoid gear pair. Virtual models of the cutter in mesh with the gear elements are presented.

scholarly journals Comparison of Tooth- and Bone-Borne Appliances on the Stress Distributions and Displacement Patterns in the Facial Skeleton in Surgically Assisted Rapid Maxillary Expansion—A Finite Element Analysis (FEA) Study

Materials ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1152
Author(s):  
Rafał Nowak ◽  
Anna Olejnik ◽  
Hanna Gerber ◽  
Roman Frątczak ◽  
Ewa Zawiślak
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Three Dimensional ◽  
Element Model ◽  
Rapid Maxillary Expansion ◽  
Stress Distributions ◽  
Maxillary Expansion ◽  
Facial Skeleton ◽  
Element Analysis ◽  
Maxillary Constriction

The aim of this study was to compare the reduced stresses according to Huber’s hypothesis and the displacement pattern in the region of the facial skeleton using a tooth- or bone-borne appliance in surgically assisted rapid maxillary expansion (SARME). In the current literature, the lack of updated reports about biomechanical effects in bone-borne appliances used in SARME is noticeable. Finite element analysis (FEA) was used for this study. Six facial skeleton models were created, five with various variants of osteotomy and one without osteotomy. Two different appliances for maxillary expansion were used for each model. The three-dimensional (3D) model of the facial skeleton was created on the basis of spiral computed tomography (CT) scans of a 32-year-old patient with maxillary constriction. The finite element model was built using ANSYS 15.0 software, in which the computations were carried out. Stress distributions and displacement values along the 3D axes were found for each osteotomy variant with the expansion of the tooth- and the bone-borne devices at a level of 0.5 mm. The investigation showed that in the case of a full osteotomy of the maxilla, as described by Bell and Epker in 1976, the method of fixing the appliance for maxillary expansion had no impact on the distribution of the reduced stresses according to Huber’s hypothesis in the facial skeleton. In the case of the bone-borne appliance, the load on the teeth, which may lead to periodontal and orthodontic complications, was eliminated. In the case of a full osteotomy of the maxilla, displacements in the buccolingual direction for all the variables of the bone-borne appliance were slightly bigger than for the tooth-borne appliance.

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