scholarly journals Contact Ratios and Transmission Errors of a Helical Gear Set with Involute-Teeth Pinion and Modified-Circular-Arc-Teeth Gear.

2001 ◽  
Vol 44 (3) ◽  
pp. 867-874 ◽  
Author(s):  
Yi-Cheng CHEN ◽  
Chung-Biau TSAY
Keyword(s):  
Helical Gear ◽  
Circular Arc ◽  
Transmission Errors

Compensating analysis of a double circular-arc helical gear by computerized simulation of meshing

2001 ◽  
Vol 215 (7) ◽  
pp. 759-771 ◽  
Author(s):  
C-K Chen ◽  
C-Y Wang
Keyword(s):  
Mathematical Model ◽  
Helical Gear ◽  
Tooth Contact Analysis ◽  
Angular Misalignment ◽  
Circular Arc ◽  
Numerical Examples ◽  
Transmission Errors ◽  
Bearing Contact ◽  
Tooth Surfaces ◽  
Computerized Simulation

A mathematical model of a stepped double circular-arc helical tooth profile with two centre offsets is developed. The conditions of gear meshing that reflect manufacturing and assembly errors are simulated. The locations of bearing contact and the contact path pattern of mating tooth surfaces are determined by tooth contact analysis (TCA). By applying the proposed mathematical model and TCA, single error impact can be determined. To compensate for offset and angular misalignment, the authors propose an adjustable bearing whereby transmission errors can be minimized. The investigation is illustrated with several numerical examples.

Geometry Design and Contact Ratio Analysis for Circular Arc Parallel-Axis Helical Gears

2016 ◽  
Author(s):  
Z. Chen ◽  
B. Lei ◽  
Q. Zhao
Keyword(s):  
Rolling Process ◽  
Helical Gear ◽  
Space Curve ◽  
Impact Factors ◽  
Contact Ratio ◽  
Circular Arc ◽  
Practical Applications ◽  
Geometry Design ◽  
Gear Mechanism ◽  
The Impact

Based on space curve meshing theory, in this paper, we present a novel geometric design of a circular arc helical gear mechanism for parallel transmission with convex-concave circular arc profiles. The parameter equations describing the contact curves for both the driving gear and the driven gear were deduced from the space curve meshing equations, and parameter equations for calculating the convex-concave circular arc profiles were established both for internal meshing and external meshing. Furthermore, a formula for the contact ratio was deduced, and the impact factors influencing the contact ratio are discussed. Using the deduced equations, several numerical examples were considered to validate the contact ratio equation. The circular arc helical gear mechanism investigated in this study showed a high gear transmission performance when considering practical applications, such as a pure rolling process, a high contact ratio, and a large comprehensive strength.

scholarly journals Generation of a double-crowned involute helical gear with twist-free tooth flanks by a CNC hobbing machine with three synchronous axes

2017 ◽  
Vol 39 (2) ◽  
pp. 97-108
Author(s):  
Van-The Tran
Keyword(s):  
Computer Simulation ◽  
Rotation Angle ◽  
Computer Numerical Control ◽  
Helical Gear ◽  
Numerical Control ◽  
Production Costs ◽  
Parabolic Curve ◽  
Transmission Errors ◽  
Simulation Results ◽  
Center Distance

In the conventional hobbing process, a double-crowned involute helical gear is generated by the hob cutter with parabolic-curve tooth profiles for the cross-profile crowning and varied the center distance between the hob and work gear for the longitudinal crowning. Therefore, to cut a double-crowned helical gear not only requires at least four synchronous axes and hob cutter regrinding (which increases production costs) but also induces twisted tooth flanks on the generated work gear. In this paper, I propose a hobbing method by applying a modified work gear rotation angle that enables double-crowning of involute helical gear's tooth flanks using a standard hob cutter and a computer numerical control (CNC) hobbing machine with only three synchronous axes. The proposed method has also verified by using two computer simulation examples to compare the meshing-conditions, contact ellipses, and transmission errors of the double-crowned gear pairs with that produced by applying the conventional hobbing method. Computer simulation results reveal the advantages of the proposed novel hobbing method.

Tooth Contact Analysis of Longitudinal Cycloidal-Crowned Helical Gears With Circular Arc Teeth

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Wei-Shiang Wang ◽  
Zhang-Hua Fong
Keyword(s):  
Gear Tooth ◽  
Longitudinal Direction ◽  
Transmission Error ◽  
Helical Gear ◽  
Contact Analysis ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Circular Arc ◽  
Tooth Flank ◽  
Assembly Error

This paper proposes a new type of double-crowned helical gear that can be continuously cut on a modern Cartesian-type hypoid generator with two face-hobbing head cutters and circular-arc cutter blades. The gear tooth flank is double crowned with a cycloidal curve in the longitudinal direction and a circular arc in the profile direction. To gauge the sensitivity of the transmission errors and contact patterns resulting from various assembly errors, this paper applies a tooth contact analysis technique and presents several numerical examples that show the benefit of the proposed double-crowned helical gear set. In contrast to a conventional helical involute gear, the tooth bearing and transmission error of the proposed gear set are both controllable and insensitive to gear-set assembly error.

Kinematic errors on helical gear of triple circular-arc teeth

2014 ◽  
Vol 28 (8) ◽  
pp. 3137-3146 ◽  
Author(s):  
Xiao-Shun Xie ◽  
Hsueh-Cheng Yang
Keyword(s):  
Helical Gear ◽  
Circular Arc ◽  
Kinematic Errors

Design of Planetary Gear Reducer with Double Circular-Arc Helical Gear

2012 ◽  
Vol 152-154 ◽  
pp. 1595-1600 ◽  
Author(s):  
Chin Yu Wang
Keyword(s):  
Convex Combination ◽  
Planetary Gear ◽  
Gear Ratio ◽  
Helical Gear ◽  
Tooth Profile ◽  
National Standard ◽  
Reduction Gear ◽  
Circular Arc ◽  
Pressure Angle ◽  
Minimum Number

The two gears of the double circular-arc helical gear is a mesh of a concave/convex combination. Because the curvature is close to each other, the strength also increased and thus, it is often used in heavily-loaded workplaces. The national standard for double circular-arc helical gear (ex., GB12759-91) is based on the size of the gear module to design its tooth profile. This shows that tooth geometric-related designs are quite complicated. If the effect of the different pressure angle parameter is considered, we would be unable to conduct relevant studies for the original standard formula with a double circular-arc helical gear set at a pressure angle of 24°. Firstly, this paper would redefine a new double circular-arc helical gear according to the discontinuousness tooth profile molded line of the double circular-arc helical gear and unchangeable pressure angle and explain the improvements in the design and stress analysis of the tooth especially since the double circular-arc helical gear has no limitation in the minimum number of teeth. Thus, the decrease in the driving gears’ number of module and can further increase the reduction gear ratio. For heavily-loaded planetary gear reducer, it’s quite obvious in the miniaturizing and high torque superiority. This paper also used certain winch’s speed reducer as example to explain that the change of the pressure angle can reduce contact stress by 3%~40% and also enhances the torque ability by 3%~40%.

Bearing contact of a helical gear pair with involute teeth pinion and modified circular-arc teeth gear

2001 ◽  
Vol 215 (10) ◽  
pp. 1175-1187 ◽  
Author(s):  
Y-C Chen ◽  
C-B Tsay
Keyword(s):  
Point Contact ◽  
Transmission Error ◽  
Helical Gear ◽  
Circular Arc ◽  
Curvature Analysis ◽  
Bearing Contact ◽  
Tooth Surfaces ◽  
Principal Directions ◽  
Helical Gear Pair

This paper investigates the contact ellipse of a helical gear set, composed of an involute pinion and a modified circular-arc gear based on curvature analysis. This gear drive exhibits point contact and parabolic transmission error due to the double crowning effect of the gear, i.e. crowning in both profile and longitudinal directions. The principal directions and curvatures of the generating tool surfaces were derived by means of differential geometry and Rodrigues’ equation. The principal directions and curvatures of the pinion and gear surfaces were obtained directly from the generating surfaces. Finally, the determination of the contact ellipses of the mating tooth surfaces was achieved. Numerical examples are also provided to demonstrate the computational results.

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