Determination of tooth thickness in the processing

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Determination of tooth thickness in cylindrical gear processing

Abstract: in the gear processing process of automobile transmission, the hobbing shaving (or gear shaping) process adopted by our company at present needs to control the gear tooth thickness parameters in each process to ensure the gear backlash required by the final product

key words: center distance normal direction base pitch base circle helix angle base circular arc tooth thickness indexing circular arc tooth thickness common normal line length m value r value

1 the train of thought for deriving process detection tooth thickness is determined according to the parameters given in the product drawing:

since the product drawings of DPCA are provided by French PAS group at present, the gear parameters given in the product drawing are slightly different from the common parameters in China, See the following table for details:

when we get the part drawing and start to prepare the gear processing process, we should convert the parameters given in the product drawing into the parameters required in the process, such as gear module, graduation circle helix angle, displacement coefficient, etc., and determine the tooth thickness value for the final inspection after heat that is convenient for line edge detection. However, we can usually select any of the following methods to detect tooth thickness:

1 Fixed chord tooth thickness

2. Indexing arc tooth thickness

3. Length of common normal line

4. Measuring ball (rod) span: m value

5. Center distance between ball bottom and measured gear: R value

the tooth thickness measurement method commonly used by our company at present is R-value detection method. The advantages of this method are: high detection accuracy, small error, simple and rapid operation, suitable for mass production. The disadvantages are: special R-value detection device is required, the one-time input cost of the inspection tool is high, and it is not economical for single piece and small batch processing

after determining the final inspection r value of a part, we should track the heat treatment deformation through trial cutting and pre batch, and measure it several times to take the average value; Before shaving, the recommended margin value in the process manual should be used as a reference, and the gear hobbing process should determine how much shaving margin should be left for the shaving process through tests. The smaller the value is, the more economical it is. On the one hand, it can improve the service life of the shaving cutter and obtain better tooth surface roughness. Process tests are tracked by R-value data

2 key steps in the conversion process:

2.1 determine the normal modulus of the gear according to the normal base section:

pbn= π *mn*cos( α n)

2.2 according to the helix angle of the base circle, convert the helix angle of the component circle:

sin( β b)=sin( β)* cos( α n)

2.3 according to the maximum and minimum values of base arc tooth thickness, the maximum and minimum values of indexing arc tooth thickness are derived respectively:

sbt=s*rb/(r*cos( β))+ db*inv( α t)

2.4 calculate the maximum and minimum values of radial displacement coefficient from the tooth thickness of indexing circle (or base circle):

sn= π *mn/2+2*x*mn*tan( α n)

2.5 by combining the above calculated parameters with the known parameters given in the product drawing and taking the indexing circle (or base circle) spiral tooth thickness as the main line, we can easily calculate the tooth thickness required by our process: common normal length, fixed chord tooth thickness, m value and R value. These can be measured with corresponding detection tools on the production line, so as to monitor and adjust the production status at any time and ensure the conformity with the product drawings

2.6 calculation of common normal length:

2.6.1 calculation of equivalent number of teeth:

zn=z*inv α t/INV α N or zn=z/cos3( β)

2.6.2 calculate the number of cross teeth and round it to an integer:

k= (zn/180 °) *arccos (zn*cos( α n)/(zn+2*xn)) +0.5

2.6.3 calculate the standard common normal line length:

wk*=cos α n*[π*(k-0.5)+z'*inv α n]

2.6.4 calculation of displacement increment and decrement value:

△ w*=2*xn*sin α n. Replace the displacement coefficient xn with the maximum and minimum values respectively

2.6.5 calculate the actual common normal length value:

wk=mn* (wk*+ △ w*), and obtain the maximum and minimum values of the actual common normal length

2.7 calculation of fixed chord tooth thickness:

2.7.1 Calculation of fixed chord tooth thickness:

sc=mn* (COS α n) ^2* (our company officially goes to work today π/2 +2*x*tan α n)

2.7.2 calculate the fixed chord tooth height:

hc=ha-0.5*sc*tan α N

2.8 m value (measuring ball span) and R value (ball bottom radius value) calculation:

2.8.1 measuring rod (ball) center pressure angle involute function:

inv α Mt=inv α t+dp/(mn*z*cos α n) +2*xn*tan α N/z- π/(2*z)

2.8.2 initial value of spherical pressure angle radian (according to empirical formula):

α Mt0=(inv α Mt)^(1/3)-3*inv α/7.9

2.8.3 ball center pressure angle value (according to empirical formula):

α Mt=(inv α Mt+ α Mt0-tan( α Mt0)/tan( α Mt0))^2+ α Mt0

2.8.4 RM value (ball center distance):

rm=d*cos α/(2*cos α MT)

2.8.5 r value (ball bottom) odd and even teeth are the same:

the greater the deviation between the conditional stress and the real stress on the specimen; After "necking", re=rm dp

2.8.6 even tooth m value:


2.8.7 odd tooth m value:

mj=2*rm*cos (π/(2*z) +dp

2.8.8 calculate the inverse involute function method 2: when the involute function of the pressure angle at the center of the measuring ball is calculated in 2.8.1, use Newton iterative formula: xk+1=xk-f (XK)/f '(XK), where k=0, 1, 2,..., deduce: α k+1= α k-(tan α k- α k-inv α k/(tan α k) ^2, use Excel to compile a small program to substitute the value calculated in 2.8.1 into α K can get a more accurate angle value of the ball center pressure angle. See the reverse involute program

3 to calculate the R value required by the process:

the above calculated values are the corresponding values of tooth thickness required by the product drawing. Input the heat treatment deformation and shaving allowance in the self-made EXCEL program, and we can get the R value required by the hobbing and shaving process. See attached table I of Excel for the calculation steps of the original program (the instrument automatically enters the experimental program starting from the original platform on 3 pages): tooth thickness calculation program

the tooth thickness process control range of Ma5 driving gear can be determined by the tooth thickness calculation program. See the following table:


1 gear manual editorial board [gear manual] Volume I, first edition, published by China Machine Press, November, 1990, page to of Chongqing first edition

2 compilation group of small module gear measurement manual [small module gear measurement manual] The first edition was published by the National Defense Industry Press in november1972, page 54-66 of the first edition; Pages 184-365

Author: gongchangjun

unit: transmission process room of Xiangfan field support division of DPCA Technology Center

contact:; Fax:

email:gongchangjun@; Chgzs4338@

postal code: 441004 address: Hubei Xiangfan Transmission process room (end) of DPCA in high tech Development Zone

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