Calculating Gear CTT Max/Min Actual from Span Measurement 1

[SplineD]

thread406-252168

Hi, I am looking for Direct formula to calculate Gear Circular tooth thickness Max/Min Actual from Given Span Measurement.

I have done some research on internet, but they show only formula to calculate theoretical Span from theoretical (pi/2) CTT. Calculating CTT Max/Min Act is not given anywhere.

Following spline details I have:

N = 27
Module= 2.0
Pressure Angle= 20 Deg
Addendum Mod. Coeff.= 0.8
Root Dia= 53.2

Span Over 4 teeth= 22.43/22.37

In the drawing it shows:

CTT Max/Min Actual = 4.215/4.151. I would appreciate if anyone tell how to calculate this value.

Thanks in Advance.

 

[gearguru]

The span calculation is in any good gear textbook. It is pretty easy,
if one understands what it actually is and how the math covering the involute curves (creating the tooth profile) is applied.
To rely on some formula without knowing what and why it calculates is dangerous.

 

[israelkk]

You can not find a direct formula because you need the inverse of the involute function. It can only be calculated numerically by iterations.

 

[israelkk]

You can write a computer program to calculate the tooth thickness given the measured span or use a program like Mathcad that has a built in iteration function (Find function).

 

[israelkk]

Sorry, but I take back my previous two posts. If you know the pressure angle you know the involute too. Therefore, just use high school math to extract the tooth thickness from the span measurement equation.