Centre Distance (a)
The centre distance a is the spacing between the axes of rotation of two meshing gears. For standard gearing without profile shift, a = m·(z1+z2)/2. It directly affects backlash and — when deviating from the nominal centre distance — the operating pressure angle.
Standard Center Distance Formula
a = Center distance in mm
m = Module in mm
z1 = Number of teeth, gear 1
z2 = Number of teeth, gear 2
Valid for standard gearing (x1 + x2 = 0, no modified center distance).
Effect on Backlash and Pressure Angle
An increased center distance (a > a_nom) increases backlash and raises the operating pressure angle above the reference value of 20°. A decreased center distance reduces backlash to the point of jamming. In practice, the center distance is determined by the housing tolerance; the tooth thickness tolerance (backlash class) must be chosen so that the resulting backlash falls within the permissible range. For gears with profile shift (x1 + x2 ≠ 0), the operating center distance is larger or smaller than the standard center distance, and the operating pitch circles deviate from the reference circles.
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