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O. Almen (1935) developed a new calculation formula derived from numerous cases of scuffing damage and preservation of operating arcuate-cut bevel gear rear-axis drives. He discovered that the product of the Hertzian contact stress and the sliding velocity is crucial. Later, in 1943, he added to this product the greatest distance of the contact point on the line of action from the pitch point (termed the PVT formula; refer to [6]). 2 Functions and Classification of Gears and Teeth F A ≤ F AGrenz 19 (1/17) pa Hertzian contact stress on the tooth tip /ga sliding velocity on tooth tip ga distance of point of tip contact from the pitch point; partial contact length The parameter FA was calculated at the head of the pinion and the gear.

Two tooth flanks meet at the point Py. The flank 1 rotates with 71 around the centre point 01 and flank 2 with 72 around 02. 3 Law of gears for cylindrical gearing / y1 = Ȧ1 r y1 , / y 2 = − Ȧ 2 r y 2 27 (1/24) In order to prevent any flank separation, both flanks must possess an equal velocity ȣn in the direction of the normals NN. With ȣy1 or ȣy2, this includes the angle Įy1 or Įy2: cos Į y1 = / n , cos Į = / n y2 / y1 / y2 (1/25) with Įy1, Įy2 expressed by the radii rb and ry. This then gives cos Į y1 = r b1 , cos Į y2 = r b 2 r y1 r y2 (1/26) From Equations (1/25) and (1/26), we then obtain / y1 r b1 = / y2 r b 2 r y1 with / y1 ry1 which results in = Ȧ1 , i= r y2 /2 ry1 Ȧ1 Ȧ2 = − Ȧ2 , =− rb1 rw2 = r =0 C rb2 rw1 , w1,2 1,2 rb2 r = − w2 r b1 rw1 (1/27) (1/28) The pitch circle radii rw1,2 are given by the position of the point C.

Here Mab acts in the sense of inhibiting the rotary motion. , generally speaking Mab  Man, then because ΣM = 0 (1/49) there must be a third torque at work. This is in fact the reaction torque acting from the baseplate, with which the fixing elements of the gear box are subject to load (Figure 1/37). Equation (1/49) in its full form then reads M an + M G + M ab = 0 (1/50) i = Ȧan Ȧab Pan + ( Pab + PV ) = 0 M an Ȧan = Pan > 0 ; M ab Ȧab = Pab < 0 Ș = − Pab Pan , M ab = −M an Ș Figure 1/37 External torques acting on the gear 38 1 Overview, General Principles Substituting Mab from Equation (1/48) into Equation (1/50), we now obtain for the reaction torque MG acting on the housing from the baseplate (1/51) M G = (Ș i - 1 )M an The sign of the gear ratio i is to be included in the equation.

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