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

  • Cheng Wang
  • Shouren Wang
  • Gaoqi Wang
Technical Paper
First Online:
Received:
Accepted:

Abstract

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.

Keywords

Gear Tooth profile modification TCA Machining Coordinate transformation 

List of symbols

LM

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

MN

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

PXY

Fixed coordinate system (in Fig. 5)

P

Pitch point (in Fig. 5)

PX

Coincident with the pitch line (in Fig. 5)

PY

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

O1X1Y1

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

O2X2Y2

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

ObXbYb

Cutting edge coordinate system

OtXtYt

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

si

Distance between O1Y1 and PY

mn

Normal modulus

ξn

Normal modification coefficient

α0n

Normal pressure angle of rack cutter

B1PB2

Line of action

φ

Rotation angle of gear

am

Half normal tooth thickness of rack cutter pitch line

rp

Radius of pitch circle

rb

Radius of basic circle

rf

Radius of dedendum circle

dp

Distance between ObXb and O1XI along ObYb axis direction

PT

Straight line through cutting point and pitch point P

MT

Tangent of cutting edge through cutting point T

β

Helix angle

L

Gear profile modification along radial direction in transverse plane

u

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

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Notes

Acknowledgements

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.

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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.School of Mechanical EngineeringUniversity of JinanJinanChina

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