scholarly journals Kinematic Precision of Gear Trains

1983 ◽  
Vol 105 (3) ◽  
pp. 317-326 ◽  
Author(s):  
F. L. Litvin ◽  
R. N. Goldrich ◽  
J. J. Coy ◽  
E. V. Zaretsky
Keyword(s):  
Gear Tooth ◽  
Contact Point ◽  
Approximate Methods ◽  
Gear Noise ◽  
Bevel Gears ◽  
Tooth Surfaces ◽  
Noise Measurements ◽  
Gear Trains ◽  
Helicopter Transmission ◽  
General Method

Kinematic precision is affected by errors which are the result of either intentional adjustments or accidental defects in manufacturing and assembly of gear trains. This paper explains a general method for the determination of kinematic precision of gear trains. The general method is based on the exact kinematic relations for the contact point motions of the gear tooth surfaces under the influence of errors. An approximate method is also explained. Example applications of the general and approximate methods are demonstrated for gear trains consisting of involute (spur and helical) gears, circular-arc (Wildhaber-Novikov) gears, and spiral-bevel gears. Gear noise measurements from a helicopter transmission are presented and discussed with relation to the kinematic precision theory.

Method for Generation of Spiral Bevel Gears With Conjugate Gear Tooth Surfaces

1987 ◽  
Vol 109 (2) ◽  
pp. 163-170 ◽  
Author(s):  
F. L. Litvin ◽  
Wei-Jiung Tsung ◽  
J. J. Coy ◽  
C. Heine
Keyword(s):  
Gear Tooth ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Straight Line ◽  
Parallel Motion ◽  
Tooth Surfaces ◽  
Spiral Bevel

The authors proposed a method for generation of spiral bevel gears that provides conjugate gear tooth surfaces. This method is based on a new principle for the performance of parallel motion of a straight line that slides along two mating ellispses with related dimensions and parameters of orientation. The parallel motion of the straight line, that is the contact normal, is performed parallel to the line which passes through the foci of symmetry of the related ellipses. The manufacturing of gears can be performed with the existing Gleason’s equipment.

Advanced Design and Manufacture of Face-Hobbed Spiral Bevel Gears

2009 ◽  
Author(s):  
V. Simon
Keyword(s):  
Gear Tooth ◽  
Numerical Control ◽  
Mutual Position ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Pinion Gear ◽  
Tooth Surfaces ◽  
Spiral Bevel ◽  
Tooth Flank ◽  
Crown Gear

The design and advanced manufacture of face-hobbed spiral bevel gears on computer numerical control (CNC) hypoid generating machines is presented. The concept of face-hobbed bevel gear generation by an imaginary generating crown gear is established. In order to reduce the sensitivity of the gear pair to errors in tooth-surfaces and to the mutual position of the mating members, modifications are introduced into the teeth of both members. The lengthwise crowning of teeth is achieved by applying a slightly bigger lengthwise tooth flank curvature of the crown gear generating the concave side of pinion/gear tooth-surfaces, and/or by using tilt angle of the head-cutter in the manufacture of pinion/gear teeth. The tooth profile modification is introduced by the circular profile of the cutting edge of head-cutter blades. An algorithm is developed for the execution of motions on the CNC hypoid generating machine using the relations on the cradle-type machine. The algorithm is based on the condition that since the tool is a rotary surface and the pinion/gear blank is also related to a rotary surface, it is necessary to ensure the same relative position of the head cutter and the pinion on both machines.

The Undercutting of Circular-Cut Spiral Bevel Gears

1992 ◽  
Vol 114 (2) ◽  
pp. 317-325 ◽  
Author(s):  
Zhang-Hua Fong ◽  
Chung-Biau Tsay
Keyword(s):  
Gear Tooth ◽  
Sufficient Conditions ◽  
Bevel Gear ◽  
Tooth Surface ◽  
Spiral Bevel Gear ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Tooth Surfaces ◽  
Sufficient And Necessary Conditions ◽  
Spiral Bevel

Undercutting is a serious problem in designing spiral bevel gears with small numbers of teeth. Conditions of undercutting for spiral bevel gears vary with the manufacturing methods. Based on the theory of gearing [1], the tooth geometry of the Gleason type circular-cut spiral bevel gear is mathematically modeled. The sufficient and necessary conditions for the existence and regularity of the generated gear tooth surfaces are investigated. The conditions of undercutting for a circular-cut spiral bevel gear are defined by the sufficient conditions of the regular gear tooth surface. The derived undercutting equations can be applicable for checking the undercutting conditions of spiral bevel gears manufactured by the Gleason Duplex Method, Helical Duplex Method, Fixed Setting Method, and Modified Roll Method. An example is included to illustrate the application of the proposed undercut checking equations.

scholarly journals Ideal Spiral Bevel Gears—A New Approach to Surface Geometry

1981 ◽  
Vol 103 (1) ◽  
pp. 127-132 ◽  
Author(s):  
R. L. Huston ◽  
J. J. Coy
Keyword(s):  
Differential Geometry ◽  
Gear Tooth ◽  
Parametric Representation ◽  
Spiral Bevel Gear ◽  
Surface Geometry ◽  
New Approach ◽  
Bevel Gears ◽  
Geometrical Characteristics ◽  
Tooth Surfaces ◽  
Spiral Bevel

This paper discusses the fundamental geometrical characteristics of spiral bevel gear tooth surfaces. The parametric representation of an ideal spiral bevel tooth is developed. The development is based on the elements of involute geometry, differential geometry, and fundamental gearing kinematics. A foundation is provided for the study of nonideal gears and the effects of deviations from ideal geometry on the contact stresses, lubrication, wear, fatigue life, and gearing kinematics.

Designing and Manufacturing Spiral Bevel Gears Using 5-Axis CNC Milling Machines

2011 ◽  
Author(s):  
Joe¨l Teixeira Alves ◽  
Miche`le Guingand ◽  
Jean-Pierre de Vaujany
Keyword(s):  
Manufacturing Process ◽  
Gear Tooth ◽  
Bevel Gear ◽  
Spiral Bevel Gear ◽  
Milling Machine ◽  
Cnc Milling ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Tooth Surfaces ◽  
Spiral Bevel

The design of spiral bevel gears still remains complex since tooth geometry and the resulting kinematics performance stem directly from the manufacturing process. Spiral bevel gear manufacture owes most to the works of Gleason and Klingelnberg. However, recent advances in milling machine technology and CAM (Computer Aided Manufacturing) make it possible to manufacture good quality spiral bevel gears on a standard 5-axis milling machine. This paper describes the CAD definition and manufacturing of spiral bevel gear tooth surfaces. Process performance is assessed by comparing the resulting surfaces after machining with the pre-defined CAD surfaces. Using this manufacturing process allows to propose new type of geometry. This one is more theoretical and, in some respects, easier to design than the standard spiral bevel gear as it enables simpler mesh optimization. The latter can be achieved by using the model of meshing under load recalled in this paper.

scholarly journals Kinematic Analysis of Spatial Geared Mechanisms

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Julie Penaud ◽  
Daniel Alazard ◽  
Alexandre Amiez
Keyword(s):  
Adjacency Matrix ◽  
Kinematic Analysis ◽  
Polar Coordinates ◽  
Constraint Matrix ◽  
New Approach ◽  
Bevel Gears ◽  
Gear Trains ◽  
Complex Coefficients ◽  
Two Degree Of Freedom ◽  
General Method

In this paper, a general method for kinematic analysis of complex gear mechanisms, including bevel gear trains and noncollinear input and output axes, is presented. This new approach is based on the nullspace of the kinematic constraint matrix computed from the mechanism graph or its adjacency matrix. The novelty is that the elements of the adjacency matrix are weighted with complex coefficients allowing bevel gears to be taken into account and the angular velocity of each link to be directly expressed using polar coordinates. This approach is illustrated on a two-degree-of-freedom car differential and applied to a helicopter main gear box. A MATLAB open source software was developed to implement this method.

Kinematic and Geometric Models of Gear Drives

1996 ◽  
Vol 118 (4) ◽  
pp. 544-550 ◽  
Author(s):  
F. L. Litvin ◽  
I. H. Seol ◽  
D. Kim ◽  
J. Lu ◽  
A. G. Wang ◽  
...  
Keyword(s):  
Gear Tooth ◽  
Helical Gears ◽  
Transmission Errors ◽  
Bevel Gears ◽  
Bearing Contact ◽  
Tooth Surfaces ◽  
Involute Gears ◽  
Computerized Simulation ◽  
Gear Drives ◽  
The Impact

A methodology is proposed for the modification of gear tooth surfaces that reduces the impact of gear drive misalignment, the shift of the bearing contact (accompanied in some cases with edge contact), and the occurrence of discontinuous functions of transmission errors. The proposed approach is tested by computerized simulation of meshing and contact for unloaded and loaded gear drives. Applications of geometry modifications to the design of spur and helical involute gears, double-circular helical gears, face-gear drives, face-milled spiral bevel gears with constant tooth height and worm-gear drives are represented.

Investigation of Noise Features of Planetary Gear Trains Based on Human Aural Characteristic

2017 ◽  
Author(s):  
Masao Nakagawa ◽  
Dai Nishida ◽  
Deepak Sah ◽  
Toshiki Hirogaki ◽  
Eiichi Aoyama
Keyword(s):  
Gear Tooth ◽  
Structural Complexity ◽  
Planetary Gear ◽  
Transmission Error ◽  
Sound Level ◽  
Tooth Surface ◽  
Surface Error ◽  
Planetary Gear Trains ◽  
Tooth Stiffness ◽  
Gear Trains

Planetary gear trains (PGTs) are widely used in various machines owing to their many advantages. However, they suffer from problems of noise and vibration due to the structural complexity and giving rise to substantial noise, vibration, and harshness with respect to both structures and human users. In this report, the sound level from PGTs is measured in an anechoic chamber based on human aural characteristic, and basic features of sound are investigated. Gear noise is generated by the vibration force due to varying gear tooth stiffness and the vibration force due to tooth surface error, or transmission error (TE). Dynamic TE is considered to be increased because of internal and external meshing. The vibration force due to tooth surface error can be ignored owing to almost perfect tooth surface. A vibration force due to varying tooth stiffness could be a major factor.

scholarly journals Computerized Design and Generation of Low-Noise Helical Gears with Modified Surface Topology

1995 ◽  
Vol 117 (2A) ◽  
pp. 254-261 ◽  
Author(s):  
F. L. Litvin ◽  
N. X. Chen ◽  
J. Lu ◽  
R. F. Handschuh
Keyword(s):  
Gear Tooth ◽  
Error Function ◽  
Transmission Error ◽  
Low Noise ◽  
Surface Topology ◽  
Helical Gears ◽  
Transmission Errors ◽  
Bearing Contact ◽  
Pinion Gear ◽  
Tooth Surfaces

An approach for the design and generation of low-noise helical gears with localized bearing contact is proposed. The approach is applied to double circular arc helical gears and modified involute helical gears. The reduction of noise and vibration is achieved by application of a predesigned parabolic function of transmission errors that is able to absorb a discontinuous linear function of transmission errors caused by misalignment. The localization of the bearing contact is achieved by the mismatch of pinion-gear tooth surfaces. Computerized simulation of meshing and contact of the designed gears demonstrated that the proposed approach will produce a pair of gears that has a parabolic transmission error function even when misalignment is present. Numerical examples for illustration of the developed approach are given.

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