A calculation method of tooth profile modification for tooth contact analysis technology

  • Cheng WangEmail author
  • Shouren Wang
  • Gaoqi Wang
Technical Paper


Tooth contact analysis (TCA) technology is an approach for computerized simulation of meshing of aligned and misaligned gear, which has been widely used in the design of gears. In TCA technology, the gear modification is completed by first modifying the cutter and then using the cutter to cut the gear blank. The obtained results are the modification parameters of cutter rather than those of gear. With the rapid development of numerical control technology, directly modifying tooth profile becomes more convenient than modifying cutter to the complete tooth profile modification. However, at present, there is no bridge between TCA technology and tooth profile direct modification. Therefore, a calculation method of tooth profile modification for TCA technology is proposed in this paper. Firstly, the simulation process of machining gear by standard rack cutter is introduced. The profile equation and coordinates for standard gear tooth profile are given. Secondly, the simulation process of machining gear by modified rack cutter is introduced. The profile equation and coordinates for modified gear tooth profile are derived. Finally, by comparing the standard tooth profile with the modified tooth profile, the modification of tooth profile is calculated. Thus, the modification parameters of rack cutter obtained by TCA technology can be converted into the modification of tooth profile. An experiment which verified the accuracy of method is provided by the comparison between measuring curve of tooth profile of actual modification and theoretical curve of modified tooth profile.


Gear Tooth profile modification TCA Machining Coordinate transformation 

List of symbols


Straight line part of rack cutting edge (in Fig. 5)


Arc part of rack cutting edge (in Fig. 5)


Fixed coordinate system (in Fig. 5)


Pitch point (in Fig. 5)


Coincident with the pitch line (in Fig. 5)


The line through the center of machined gear (in Fig. 5)


Coordinate system built on the rack cutter which moves together with rack cutter


Coordinate system built on the machined gear which moves together with gear


Cutting edge coordinate system


Transverse coordinate system built on the machined gear

x1, y1

Cutting point coordinate in the rack cutter coordinate system

x2, y2

Cutting point coordinate in machined gear coordinate system

xb, yb

Cutting point coordinate in cutting edge coordinate system

xt, yt

Coordinate in transverse coordinate system

xt1, yt1

Coordinate in transverse coordinate system of standard gear tooth profile

xt2, yt2

Coordinate in transverse coordinate system of modified gear tooth profile


Distance between O1Y1 and PY


Normal modulus


Normal modification coefficient


Normal pressure angle of rack cutter


Line of action


Rotation angle of gear


Half normal tooth thickness of rack cutter pitch line


Radius of pitch circle


Radius of basic circle


Radius of dedendum circle


Distance between ObXb and O1XI along ObYb axis direction


Straight line through cutting point and pitch point P


Tangent of cutting edge through cutting point T


Helix angle


Gear profile modification along radial direction in transverse plane


Distance between the point of rack cutter profile and parabola pole

u1, u2

Position of three segment parabolas in the normal profile of rack cutter

u0, u3

Determined according to the actual working tooth profile length of rack cutter

di (i = 1,2,3)

The biggest modifications of each segment parabola



The authors wish to acknowledge the financial support of National Natural Science Foundation of China (Grant No. 51475210), A Project of Shandong Province Higher Educational Science and Technology Program (Grant No. J17KA027) and major research project of Shandong province (Grant No. 2018GGX103035) during the course of this investigation. The authors would also like to thank the editor and anonymous reviewers for their suggestions for improving the paper.


  1. 1.
    Chen Z, Shao Y (2013) Mesh stiffness calculation of a spur gear pair with tooth profile modification and tooth root crack. Mech Mach Theory 62:63–74CrossRefGoogle Scholar
  2. 2.
    Bahk C-J, Parker RG (2013) Analytical investigation of tooth profile modification effects on planetary gear dynamics. Mech Mach Theory 70:298–319CrossRefGoogle Scholar
  3. 3.
    Baglioni S, Cianetti F, Landi L (2012) Influence of the addendum modification on spur gear efficiency. Mech Mach Theory 49(3):216–233CrossRefGoogle Scholar
  4. 4.
    Simon VV (2011) Influence of tooth modifications on tooth contact in face-hobbed spiral bevel gears. Mech Mach Theory 46(12):1980–1998CrossRefGoogle Scholar
  5. 5.
    Hsu R-H, Hsien-Hsiu S (2014) Tooth contact analysis for helical gear pairs generated by a modified hob with variable tooth thickness. Mech Mach Theory 71:40–51CrossRefGoogle Scholar
  6. 6.
    Litvin FL, Jian L, Townsend DO et al (1999) Computerized simulation of meshing of conventional helical involute gears and modification of geometry. Mech Mach Theory 34:123–147CrossRefzbMATHGoogle Scholar
  7. 7.
    Litvin FL, Gonzalez-Perez I, Yukishima K, Fuentes A, Hayasaka K (2007) Design, simulation of meshing, and contact stresses for an improved worm gear drive. Mech Mach Theory 42(8):940–959CrossRefzbMATHGoogle Scholar
  8. 8.
    Zong-de FANG (1997) Tooth contact analysis of helical gears with modification. J Aerosp Power 12(3):247–250Google Scholar
  9. 9.
    Wang C, Cui HY, Zhang QP, Wang WM (2015) Contact model and tooth contact analysis of double helical gears with parallel-axis, crossed-axis and modification. Aust J Mech Eng 13(1):1–8CrossRefGoogle Scholar
  10. 10.
    Wang C, Cui HY, Zhang QP, Wang WM (2016) Modified optimization and experimental investigation of transmission error, vibration and noise for double helical gears. J Vib Control 22(1):108–120CrossRefGoogle Scholar
  11. 11.
    Simon V. Optional tooth modification for spur and helical gears.Trans. ASME J. Mech. Transm. Autom. Design, 1989,111(4): 611-615Google Scholar
  12. 12.
    Weck M (1987) 3-D tooth flank corrections-improving the bearing and running behavior of gears. Ind-Anz 109(11):30–31Google Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.School of Mechanical EngineeringUniversity of JinanJinanChina

Personalised recommendations