COMPUTER SIMULATION OF INVOLUTE GEARS 

 

Dr.Cuneyt FETVACI (Assoc.Prof. of  Mechanical Engineering)

 

e-mail : fetvacic@istanbul.edu.tr

 

Generating with pinion-type cutter  

Theory :  F.Litvin

Application : S.L.Chang and C.B.Tsay

Chang and Tsay proposed the mathematical model of the involute-shaped shaper cutter.

 

DEVELOPED METHOD FOR SIMULATION

 

The mathematical model of the generating cutter is adopted from Chang and Tsay. Trochoidal paths of the cutter tip are investigated. Asymmetric involute teeth is also considered. Relative positions of the cutter during internal and external gear generations are obtained. Animation files are developed by using APDL- Ansys Parametric Design Language.

 

RELATIVE POSITIONS OF THE CUTTER

***Click the images for video files***

       

 

References :

 

PINION-TYPE

 

·        E. Buckingham, “Analytical Mechanics of Gears” (1949)

·        J.R.  Colbourne, “The Geometry of Involute Gears” (1987)

·        F.L. Litvin, “Gear Geometry and Applied Theory”, (1994)

·        S.L. Chang and C.B. Tsay, “Computerized Tooth Profile Generation and Undercut Analysis of Noncircular Gears Manufactured With Shaper Cutters”,1998.

·        G.Figlioini and J. Angeles, “The Synthesis of Elliptical Gears Generated by Shaper-Cutters”, 2003.

 

RACK-TYPE

 

·        E. Buckingham, “Analytical Mechanics of Gears” (1949)

·        J.R.  Colbourne, “The Geometry of Involute Gears” (1987)

·        F.L. Litvin, “Gear Geometry and Applied Theory”, (1994)

·        C.B.Tsay, “Helical gears with involute shaped teeth: Geometry, computer simulation, tooth contact analysis, and stress analysis,1988

·        S.C.Yang, “Mathematical model of a helical gear with asymmetric involute teeth and its analysis”, 2005

  1. Computer Simulation of Involute Tooth Generation, C.FETVACI, Mechanical Engineering, Dr. Murat Gokcek (Ed.), ISBN: 978-953-51-0505-3, InTech,

Available from: http://www.intechopen.com/books/mechanical-engineering/computer-simulation-of-involute-tooth-generation

  1. Computer Simulation of Helical Gears Generated by Rack-Type Cutters, Arabian Journal for Science and Engineering,  C.FETVACI, Vol. 36, No 7, 1321-1332, 2011  DOI: 10.1007/s13369-011-0116-y
  2. Generation Simulation of Involute Spur Gears Machined by Pinion-Type Shaper Cutters, C.FETVACI, Strojniški vestnik - Journal of Mechanical Engineering, 56(2010)10, 644-652, UDC 621.833.1:004.94
  3. Computer Simulation of Helical Gears with Asymmetric Involute Teeth, (Asimetrik Evolvent Helisel Dişli Çarkların Bilgisayar Simülasyonu), C.FETVACI, Journal of The Faculty of Engineering and Architecture of Gazi University, Cilt 25, No. 3, s. 441-447, Eylül 2010, 
  4. Definition of Involute Spur Gear Profiles Generated by Gear-type Shaper Cutters", C.FETVACI, Mechanics Based Design of Structures and Machines, Vol. 38, No. 4, p. 481-492, 2010,
  5. Mathematical Model of a Spur Gear with Asymmetric Involute Teeth and Its Cutting Simulation”, C. FETVACI ve E. IMRAK,  Mechanics Based Design of Structures and Machines, 36:1, 34 – 46, 2008. 

 

Generating with rack-type cutter  

Theory :  F.Litvin

Application : C.B.Tsay , S.C. Yang

Tsay proposed the mathematical model of the rack-type cutter for generating helical gear with symmetric involute teeth. Yang proposed the equations for generating helical gear with asymmetric involute teeth.

 

DEVELOPED METHOD FOR SIMULATION

 

The mathematical model of the generating rack cutter is adopted from Yang. Trochoidal paths of the cutter tip are investigated. The geometric varieties of the cutter tip are investigated. Relative positions of the cutter during external gear generations are obtained. Animation files are developed by using APDL- Ansys Parametric Design Language.

 

 

 

RELATIVE POSITIONS OF THE CUTTER

 

  Video File