# Tooth thickness measurement with pins or balls

This measuring method is similar to that used for the control of screw threads. The diameter of the pin is chosen in such a way that this is in contact with the tooth flanks at the pitch diameter and, on the other hand, is larger than the tip circle located in tooth spaces that are diametrically opposed towards each other. The pin diameter can be calculated in function of the module of the gear parameters, namely: the module – pressure angle – correction – number of teeth. The calculated diameter does not always give a practical diameter as a result, therefore is then chosen for a standard pin diameter which is available. For gears with normal teeth without correction one uses usually standard pins whose diameters are located approximately on the following values:

• 1.75 m for external gears with a pressure angle of a = 20°
• 1.7. m for external gears with a pressure angle of a = 14°30′
• 1.65 m for internal gears with a pressure angle of a = 20°
• 1.6. m for internal gears with a pressure angle of a = 14°30′

In order not to repeat details, we give only the main formulas for the different gear types.

## Formula for the ideal pin diameter:
dp = z.m.cosa.(invφ + )

The formula for calculating the diameter Md for an even number of teeth:
Md = The formula for calculating the diameter Md for an odd number of teeth:
Md ## 2 Helical teeth

Formula for the ideal pin diameter:
dp = zv.mn.cosan.(invφv + )
The formula for calculating the diameter Md for an even number of teeth:
Md = The formula for calculating the diameter Md for an odd number of teeth:
Md ## 3 Internal gear Formula for the ideal pin diameter:
dp = z.m.cosa.( – invφ)

The formula for calculating the diameter Md for an even number of teeth:
Md = The formula for calculating the diameter Md for an odd number of teeth:
Md ## 4 Gear racks with a straight or helical teeth Straight teeth:

Formula for the ideal pin diameter:
dp = The formula for the calculation of the size Md:
Md Helical teeth:

Formula for the ideal pin diameter:
dp = The formula for the calculation of the size Md:
Md ## 5 Measurement of worms with 3 pins Formula for the ideal pin diameter:
dp = The formula for the calculation of the size Md:
Md 