scholarly journals Mathematical description of tooth flank surface of globoidal worm gear with straight axial tooth profile

2017 ◽  
Vol 7 (1) ◽  
pp. 407-415 ◽  
Author(s):  
Piotr Połowniak ◽  
Mariusz Sobolak
Keyword(s):  
Mathematical Description ◽  
Worm Gear ◽  
Tooth Surface ◽  
Contact Pattern ◽  
Contact Lines ◽  
Kinematic System ◽  
Worm Wheel ◽  
Axial Profile ◽  
Tooth Flank ◽  
Flank Surface

AbstractIn this article, a mathematical description of tooth flank surface of the globoidal worm and worm wheel generated by the hourglass worm hob with straight tooth axial profile is presented. The kinematic system of globoidal worm gear is shown. The equation of globoid helix and tooth axial profile of worm is derived to determine worm tooth surface. Based on the equation of meshing the contact lines are obtained. The mathematical description of globoidal worm wheel tooth flank is performed on the basis of contact lines and generating the tooth side by the extreme cutting edge of worm hob. The presented mathematical model of tooth flank of TA worm and worm wheel can be used e.g. to analyse the contact pattern of the gear.

scholarly journals Mathematical model of tooth flank of worm wheel in globoid worm gear

Mechanik ◽  
2017 ◽  
Vol 90 (1) ◽  
pp. 8-10
Author(s):  
Piotr Połowniak ◽  
Mariusz Sobolak
Keyword(s):  
Mathematical Model ◽  
Mathematical Description ◽  
Worm Gear ◽  
Tooth Formation ◽  
Kinematic System ◽  
Worm Wheel ◽  
Tooth Flank ◽  
Flank Surface

Presented is a mathematical description of tooth flank surface of the wormwheel in globoid worm gear. The kinematic system of tooth formation was performed. The mathematical description of tooth flank of globoid worm was used.

Analysis of Contact Lines on Corrected Planar Double-Enveloping Worm Wheel

2011 ◽  
Vol 341-342 ◽  
pp. 124-127
Author(s):  
Yue Min Zhang ◽  
Xiao Lin Wang ◽  
Xiao Ru Hao
Keyword(s):  
Contact Line ◽  
Worm Gear ◽  
New Method ◽  
Tooth Surface ◽  
Contact Lines ◽  
Matlab Software ◽  
Worm Wheel ◽  
Tooth Surfaces

The tooth-surfaces of corrected planar double-enveloping worm wheel were established by programming in MATLAB with the theory of spatial engagement. The contact lines were analyzed, and the contact styles were classified with given parameters. A new method of judging the types of contact lines was brought out. Based on the theory of spatial engagement, the re-machined planar double-enveloping worm gear is established by programming with MATLAB software. The contact lines on the worm wheel tooth-surface are analyzed and given the method of the contact line kind judgment.

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.

scholarly journals Mathematical model of the worm wheel tooth flank of a double-enveloping worm gear

2021 ◽  
Vol 60 (3) ◽  
pp. 3037-3046
Author(s):  
Piotr Polowniak ◽  
Mariusz Sobolak ◽  
Adam Marciniec
Keyword(s):  
Mathematical Model ◽  
Worm Gear ◽  
Worm Wheel ◽  
Tooth Flank

A General Method for Computing Worm Gear Conjugate Mesh Property: Part 1—The Generating Surface

1989 ◽  
Vol 111 (1) ◽  
pp. 143-147 ◽  
Author(s):  
Changqi Zheng ◽  
Jirong Lei ◽  
Michael Savage
Keyword(s):  
Mathematical Description ◽  
Gear Tooth ◽  
Mathematic Model ◽  
Worm Gear ◽  
Tooth Surface ◽  
Initial Curve ◽  
Parametric Description ◽  
General Method

This article is a two-part one: (1) the generating surface; (2) the mathematic model of the worm gear tooth surface. In this paper, a general method is presented for the description of generating surface enveloping any kind of worm tooth surface. This method is laid on the parametric description of the dresser curve as an initial curve. The initial curves of four common dressers are presented. By using these descriptions, the mathematical description and properties of any kind of worm gear tooth surface can also be obtained.

The Influence of Flank Deviations on the Vibration of a Helical Gear Pair Transmitting Light Load

1992 ◽  
Author(s):  
Kiyohiko Umezawa ◽  
Haruo Houjoh ◽  
Shigeki Matsumura
Keyword(s):  
Design Method ◽  
Load Condition ◽  
Helical Gear ◽  
Tooth Surface ◽  
Calculation Error ◽  
Single Pair ◽  
Contact Pattern ◽  
Light Load ◽  
Rotational Vibration ◽  
Tooth Flank

Abstract This paper introduces a simulator which can depict the rotational vibration of a helical pair having any kind of deviations transmitting light load. Under light load condition the contact pattern does not extend to full length of ideal contact tooth surface. Under this condition, the determination of the contact pattern sometimes become very sensitive to the numerical calculation error. In the worst cases, calculation leap into endless loop. The developed simulator was improved robuster. This paper firstly derives how we can obtain the relationship between the deflection and the load distribution of single pair of mating teeth. Secondary, the determination method of multi tooth pair load sharing is introduced. Afterwards, the simulation is experimentally verified with various kinds of tooth flank deviations. Through this study, an easy design method to realize a low vibration helical gear is suggested.

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.

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.

Characteristics of a Modified Double Enveloping Worm Gear Drive

1992 ◽  
Author(s):  
Vilmos Simon
Keyword(s):  
Gear Tooth ◽  
Worm Gear ◽  
Performance Characteristics ◽  
Tooth Surface ◽  
Gear Teeth ◽  
Gear Drive ◽  
Load Distributions ◽  
Worm Gearing ◽  
Axial Profile ◽  
New Type

Abstract A modified new type of double enveloping worm gearing is developed. The gear tooth surface is generated by a flying tool whose cutting edge has the modified profile of the entering edge of the worm, and the worm surface has a straight-lined axial profile and circular lead changed to the established rule. The same rule governs the motion of the flying tool in processing the gear teeth. To compare the performance characteristics of the classical and the modified new type of double enveloping worm gearings, the load distributions are calculated and the elastohydrodynamic analysis of lubrication is carried out for both types of worm gearings. The obtained results show the advantages of the new type of double enveloping worm gear drive.

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