Berndt’s theory

The pitch diameter can be calculated based on the BerndtThe pitch diameter can be calculated based on the Berndt formula. This approach is an extension of the two balls method.
The accuracy of the pitch diameter resultdepends on the measurement accuracy of other parameterssuch as pitch, flank angle, and diameter of the balls

Formule 1

berndt formula1


d_{2},D_{2} = m cdot {cos%itheta -+d_{D} ·} {cos {%ibèta - %igamma} over 2} over {sin {%ibèta + %igamma} over 2} cdot sqrt{1-{m^2 cdot sin^2 %itheta} over {d_D^{2} cdot cos^2 left ( {%ibèta - %igamma} over 2 right )}} +- left (l over n - 2 cdot l cdot %itheta over %ipi right)·{cos %ibèta cdot cos %igamma} over {sin(%ibèta + %igamma)}

 

Formule 2
 berndt formula2
 
arcsin(%itheta_{k}) = {d_{D} cdot l} over {%ipi cdot m^2}·{cos %ibèta cdot cos %igamma cdot cos {%ibèta - %igamma} over 2} over {cos {%ibèta + %igamma} over 2}· {sqrt{1-{m^2 cdot sin^2 %itheta_{k-1}} over {d_D^{2} cdot cos^2 left ( {%ibèta - %igamma} over 2 right )}} over {cos %itheta_{k-1} +- {sin left ( {%ibèta + %igamma} over 2 right ) cdot cos left ({%ibèta - %igamma} over 2 right)}·{d_D} over {m} cdot {sqrt{1-{m^2 cdot sin^2 %itheta_{k-1}} over {d_D^{2} cdot cos^2 left ( {%ibèta - %igamma} over 2 right )}}}}} 

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