# EHL center stress formula of line contact and design of cylindrical gear based on EHL stress

1.EHL center stress formula of line contact

The fitting formula of the central stress under EHL condition is proposed

Where PC is the Elastohydrodynamic center stress, MPa; α ‘is the visco compression index, m2 / N; η 0 is the dynamic viscosity, PA · s; u is the entrainment speed, M / s.

2.Design formula of spur gear based on EHL center stress

The equivalent radius of curvature of gear in node meshing is as follows:

Where, D1 driving wheel indexing circle diameter, mm.

Entrainment speed

Where α is the pressure angle; V is the linear speed, M / S; N1 is the driving wheel speed, R / min.

Calculated load per unit length along tooth width

Gear torque

Where P1 is the transmitted power, kW.

Substituting the expression of the above parameters into the formula, we can get the following results:

Using PC instead of σ h, the design criterion of tooth contact fatigue strength is established: PC ≤ [σ H], and the design formula of contact fatigue strength of spur gear tooth surface based on EHL central stress is obtained

Where DC is the diameter of gear indexing circle based on the central stress formula, mm.

3.Helical gear design formula based on EHL stress

Similarly, the helical gear design formula can be derived

The angle of helix base is the angle of helix.

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