# Hertz formula and design formula of cylindrical gear based on Hertz stress

1 Hertz formula

The formula of maximum Hertz contact stress is as follows:

Where, σ h is the maximum Hertz contact stress, MPa; W is the calculated load per unit length, N / mm; e ‘is the comprehensive elastic modulus, MPa; R is the comprehensive radius of curvature, mm.

2 design formula of spur gear based on Hertz formula

The design formula of spur gear based on Hertz formula is used in engineering

Where, DH is the diameter of gear indexing circle based on Hertz formula, mm; K is load factor; T1 is driving gear torque, NMM; φ D is gear width coefficient; μ is gear transmission ratio; Ze is material elastic influence coefficient; zh is area coefficient and [σ H] is allowable contact stress, MPa.

3 design formula of cylindrical helical gear based on Hertz formula

The design formula of cylindrical helical gear based on Hertz formula is used in engineering

Where, ε α is the coincidence degree of the end face.

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