Analytical and Experimental Tooth Contact Pattern of Large-Sized Spiral Bevel Gears in Cyclo-Palloid System

2009 ◽  
Author(s):  
Kazumasa Kawasaki ◽  
Isamu Tsuji
Keyword(s):  
Coordinate Measuring Machine ◽  
Tooth Surface ◽  
Contact Pattern ◽  
Tooth Contact ◽  
Spiral Bevel Gears ◽  
Form Errors ◽  
Bevel Gears ◽  
Measuring Machine ◽  
Spiral Bevel ◽  
Tooth Flank

The demand of large-sized spiral bevel gears has increased in recent years and hereafter the demand may increase more and more. The large-sized spiral bevel gears with equi-depth teeth are usually manufactured based on Klingelnberg cyclo-palloid system. In this paper, the tooth contact pattern of large-sized spiral bevel gears in this system are investigated analytically and experimentally. First, the tooth contact pattern and transmission errors of such gears are analyzed. The analysis method is based on simultaneous generations of tooth surface and simulations of meshing and contact. Next, the large-sized spiral bevel gears are manufactured and the tooth contact pattern of these gears is investigated experimentally. Moreover, the real tooth surfaces are measured using a coordinate measuring machine and the tooth flank form errors are detected using the measured coordinates. It is possible to analyze the tooth contact patterns of the spiral bevel gears with consideration of the tooth flank form errors expressing the errors as polynomial equations. Finally, the influence of alignment errors due to assembly on the tooth contact pattern is also investigated analytically and experimentally. These analyzed results were compared with experimental ones. As a result, two results showed a good agreement.

Analytical and Experimental Tooth Contact Pattern of Large-Sized Spiral Bevel Gears in Cyclo-palloid System

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Kazumasa Kawasaki ◽  
Isamu Tsuji
Keyword(s):  
Coordinate Measuring Machine ◽  
Tooth Surface ◽  
Contact Pattern ◽  
Tooth Contact ◽  
Spiral Bevel Gears ◽  
Form Errors ◽  
Bevel Gears ◽  
Measuring Machine ◽  
Spiral Bevel ◽  
Tooth Flank

Demand for large-sized spiral bevel gears has increased in recent years and a trend expected to continue. The large-sized spiral bevel gears with equi-depth teeth are usually manufactured based on Klingelnberg cyclo-palloid system. In this paper, the tooth contact pattern of large-sized spiral bevel gears in this system are investigated analytically and experimentally. First, the tooth contact pattern and transmission errors of such gears are analyzed. The analysis method is based on simultaneous generations of tooth surface and simulations of meshing and contact. Next, the large-sized spiral bevel gears are manufactured and the tooth contact pattern of these gears is investigated experimentally. Moreover, the real tooth surfaces are measured using a coordinate measuring machine and the tooth flank form errors are detected using the measured coordinates. It is possible to analyze the tooth contact pattern of the spiral bevel gears with consideration of the tooth flank form errors expressing the errors as polynomial equations. Finally, the influence of alignment errors due to assembly on the tooth contact pattern is also investigated analytically and experimentally. These analyzed results were compared with experimental ones. As a result, the two results showed a good agreement.

Tooth Contact Analysis and Manufacture on Multitasking Machine of Large-Sized Straight Bevel Gears With Equi-Depth Teeth

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Isamu Tsuji ◽  
Kazumasa Kawasaki ◽  
Hiroshi Gunbara ◽  
Haruo Houjoh ◽  
Shigeki Matsumura
Keyword(s):  
Contact Analysis ◽  
Tooth Surface ◽  
Contact Pattern ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Form Errors ◽  
Bevel Gears ◽  
Computer Aided ◽  
Tooth Surfaces ◽  
Tooth Flank

Straight bevel gears are widely used in the plant of large-sized power generation when the gears have large size. The purpose of this study is to manufacture the large-sized straight bevel gears with equi-depth teeth on a multitasking machine. The manufacturing method has the advantages of arbitrary modification of the tooth surface and machining of the part without the tooth surface. For this study, first, the mathematical model of straight bevel gears by complementary crown gears considering manufacture on multitasking machine is proposed, and the tooth contact pattern and transmission errors of these straight bevel gears with modified tooth surfaces are analyzed in order to clarify the meshing and contact of these gears. Next, the numerical coordinates on the tooth surfaces of the bevel gears are calculated and the tooth profiles are modeled using a 3D-Computer-Aided Design (CAD) system. Five-axis control machines were utilized. The gear-work was machined by a swarf cutting using a coated carbide end mill. After rough cutting, the gear-work was heat-treated, and it was finished based on a Computer-Aided Manufacturing (CAM) process through the calculated numerical coordinates. The pinion was also machined similarly. The real tooth surfaces were measured using a coordinate measuring machine and the tooth flank form errors were detected using the measured coordinates. As a result, the obtained tooth flank form errors were small. In addition, the tooth contact pattern of the manufactured large-sized straight bevel gears was compared with those of tooth contact analysis. The data showed good agreement.

Tooth Contact Analysis and Manufacture on Multi-Tasking Machine of Large-Sized Straight Bevel Gears

2011 ◽  
Author(s):  
Kazumasa Kawasaki ◽  
Isamu Tsuji ◽  
Hiroshi Gunbara
Keyword(s):  
Contact Analysis ◽  
Tooth Surface ◽  
Contact Pattern ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Form Errors ◽  
Bevel Gears ◽  
Tooth Surfaces ◽  
Tooth Flank ◽  
Coated Carbide

Straight bevel gears are widely used in the plant of large-sized power generation when the gears have large size. The purpose of this study is to manufacture the large-sized straight bevel gears with equi-depth on multi-tasking machine. The manufacturing method has the advantages of arbitrary modification of the tooth surface and machining of the part without the tooth surface. For this study, first the mathematical model of straight bevel gears by complementary crown gears considering manufacture on multi-tasking machine is proposed, and the tooth contact pattern and transmission errors of these straight bevel gears with modified tooth surfaces are analyzed in order to clarify the meshing and contact of these gears. Next, the numerical coordinates on the tooth surfaces of the bevel gears are calculated and the tooth profiles are modeled using a 3D-CAD system. 5-axis control machines were utilized. The gear-work was machining by a swarf cutting using a coated carbide end mill. After rough cutting, the gear-work was heat-treated, and it was finished based on a CAM process through the calculated numerical coordinates. The pinion was also machined similarly. The real tooth surfaces were measured using a coordinate measuring machine and the tooth flank form errors were detected using the measured coordinates. As a result, the obtained tooth flank form errors were small. In addition, the tooth contact pattern of the manufactured large-sized straight bevel gears was compared with those of tooth contact analysis. As a result, there was good agreement.

Kinematical Optimization of Spiral Bevel Gears

1992 ◽  
Author(s):  
Zhang-Hua Fong ◽  
Chung-Biau Tsay
Keyword(s):  
Mathematical Model ◽  
Bevel Gear ◽  
Tooth Surface ◽  
Spiral Bevel Gear ◽  
Tooth Contact ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Contact Patterns ◽  
Spiral Bevel ◽  
Kinematic Errors

Abstract Kinematical optimization and sensitivity analysis of circular-cut spiral bevel gears are investigated in this paper. Based on the Gleason spiral bevel gear generator and EPG test machine, a mathematical model is proposed to simulate the tooth contact conditions of the spiral bevel gear set. All the machine settings and assembly data are simulated by simplified parameters. The tooth contact patterns and kinematic errors are obtained by the proposed mathematical model and the tooth contact analysis techniques. Loaded tooth contact patterns are obtained by the differential geometry and the Hertz contact formulas. Tooth surface sensitivity due to the variation of machine settings is studied. The corrective machine settings can be calculated by the sensitive matrix and the linear regression method. An optimization algorithm is also developed to minimize the kinematic errors and the discontinuity of tooth meshing. According to the proposed studies, an improved procedure for development of spiral bevel gears is suggested. The results of this paper can be applied to determine the sensitivity and precision requirements in manufacturing, and improve the running quality of the spiral bevel gears. Two examples are presented to demonstrate the applications of the optimization model.

Kinematical Optimization of Spiral Bevel Gears

1992 ◽  
Vol 114 (3) ◽  
pp. 498-506 ◽  
Author(s):  
Zhang-Hua Fong ◽  
Chung-Biau Tsay
Keyword(s):  
Mathematical Model ◽  
Bevel Gear ◽  
Tooth Surface ◽  
Spiral Bevel Gear ◽  
Tooth Contact ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Contact Patterns ◽  
Spiral Bevel ◽  
Kinematic Errors

Kinematical optimization and sensitivity analysis of circular-cut spiral bevel gears are investigated in this paper. Based on the Gleason spiral bevel gear generator and EPG test machine, a mathematical model is proposed to simulate the tooth contact conditions of the spiral bevel gear set. All the machine settings and assembly data are simulated by simplified parameters. The tooth contact patterns and kinematic errors are obtained by the proposed mathematical model and the tooth contact analysis techniques. Loaded tooth contact patterns are obtained by the differential geometry and the Hertz contact formulas. Tooth surface sensitivity due to the variation of machine settings is studied. The corrective machine settings can be calculated by the sensitive matrix and the linear regression method. An optimization algorithm is also developed to minimize the kinematic errors and the discontinuity of tooth meshing. According to the proposed studies, an improved procedure for development of spiral bevel gears is suggested. The results of this paper can be applied to determine the sensitivity and precision requirements in manufacturing, and improve the running quality of the spiral bevel gears. Two examples are presented to demonstrate the applications of the optimization model.

Manufacture of Optimized Face-Hobbed Spiral Bevel Gears on Computer Numerical Control Hypoid Generator

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Machine Tool ◽  
Angular Displacement ◽  
Transmission Error ◽  
Numerical Control ◽  
Tooth Surface ◽  
Surface Geometry ◽  
Tooth Contact ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Spiral Bevel

In this study, a method is proposed for the advanced manufacture of face-hobbed spiral bevel gears on CNC hypoid generators with optimized tooth surface geometry. An optimization methodology is applied to systematically define optimal head-cutter geometry and machine tool settings to introduce optimal tooth modifications. The goal of the optimization is to simultaneously minimize tooth contact pressures and angular displacement error of the driven gear (the transmission error). The optimization is based on machine tool setting variation on the cradle-type generator conducted by optimal polynomial functions. An algorithm is developed for the execution of motions on the CNC hypoid generator using the relations on the cradle-type machine. Effectiveness of the method was demonstrated by using a face-hobbed spiral bevel gear example. Significant reductions in the maximum tooth contact pressure and in the transmission errors were obtained.

Computerized Investigation of Real Tooth Contact Analysis of Face-milled Spiral Bevel Gears

2021 ◽  
Author(s):  
GuangLei Liu ◽  
Weidong Yan ◽  
Yao Liu
Keyword(s):  
Contact Analysis ◽  
Tooth Surface ◽  
Surface Boundary ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Gear Drive ◽  
Spiral Bevel ◽  
Manufacturing Parameters

Abstract Real tooth contact analysis of spiral bevel gears is based on the original tooth surface grids (OTSG) formed by coordinate measuring machine (CMM). Since the size of OTSG is smaller than the tooth surface, it is sometimes impossible to get full meshing information. Reverse engineering is a way to solve the problem. The basic idea is to expand OTSG to the tooth surface boundary by reversing the manufacturing parameters of the spiral bevel gear drive. Thus a generalized reversing objective is set up for both of the gear and the pinion, which is the summation of deviations of all nodes between OTSG and corresponding computational tooth surface grids (CTSG) expressed by manufacturing parameters. The gear manufacturing parameters are reversed by observing duplex method. The pinionmanufacturing parameters are reversed by attempting the meshing behavior taken as input to local synthesis with modified roll motion. The initial meshing behavior is approximately ascertained by discrete tooth contact analysis based on OTSG, and meshing behavior at the mean contact point is figured out by interpolation method for function of transmission errors and contact path. Having reversed the manufacturing parameters, OTSG is expanded to the tooth surface boundary and real tooth contact analysis is conducted. A zero bevel gear drive of an aviation engine was employed to demonstrate the validity of the proposed methodology. The proposed method makes the real tooth contact analysis practical and provides prospect to improve meshing behavior more precisely.

Quantitative Analysis of the Influence of Installation Errors on the Contact Pattern of Spiral Bevel Gears

2011 ◽  
Vol 86 ◽  
pp. 278-282
Author(s):  
Guang Lei Liu ◽  
Rui Ting Zhang ◽  
Ning Zhao
Keyword(s):  
Quantitative Analysis ◽  
Tooth Surface ◽  
Test Machine ◽  
Contact Pattern ◽  
Tooth Contact Analysis ◽  
Local Synthesis ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Contact Patterns ◽  
Spiral Bevel

A method—characteristic parameters analysis (CPA) is put forward, which is used for quantitative analysis of contact pattern of spiral bevel gears with installation errors. For forming the tooth surface of spiral bevel gears, local synthesis is used. To imitate rolling test machine, the pinion drive torque is calculated under the indentation depth 0.00635mm. Driven by this torque, the size, shape, location and variation of contact pattern are obtained by loaded tooth contact analysis (LTCA). A pair of aviation spiral bevel gears was taken to quantitatively analyze the various contact patterns under different installation errors. The results indicate that the contact pattern is more sensitive to pinion axis installation error.

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