Joint and Cardan Shafts

166 167 Application Guidelines Calculation data Technical Annex Technical Annex  Service Phone Europe  + 49 (0) 71 42 / 353-0  Service Phone North America  + 1 – 2 6 9 / 6 3 7 7 9 9 9  Catalog  Spare parts  Drive-Shaft Calculation  Installation and Maintenance  www.elbe-group.com 1.4 Arrangement configuration Z-Configuration: Input and output shaft are parallel to each other on one plane. Requirement: ß 1 = ß 2 W-Configuration: Input and output shaft intersect on one plane. Requirement: ß 1 = ß 2 Common deflection plane Common deflection plane no common deflection plane plane I plane II Three-dimensional configuration: (Combined Z and W configuration) Input and output shaft cross each other offset in space. No common plane exists. Therefore the inner forks must be offset by the angle  (See 1.1 „Exception“). Requirement: ß R1 = ß R2 The resultant three-dimensional deflection angle ß R derived from the vertical and horizon- tal angular deviation, is calculated as: ß R = arctan  tan 2 ß v + tan 2 ß h 2. Motion relationships and torques 2.2 Motion and torque characteristics of a sigle joint as a function of deflection angle ß M dI = Input torque M dII = Output torque  I = Input – angular velocity  Il = Output – angular velocity When analyzing the motion and torque charac- teristics of a singular joint, it is found that with a constant angular velocity- and torque input, a fluctuating motion and torque curve is obtai- ned at the output. The reason for this fluctua- tion can easily be illustrated by following the torque characteristics at the fork position  1 = 0° and  1 = 90° as shown at left. Since the torque can only be transmitted in the spider plane, the spider however, depending on the fork position, is always at a right angle to the input or output axis, output torque fluctuates twice per revolution between M dI · cos ß and M dI /cos ß. 2.1 Rotation angle of a single joint as a function of deflection angle ß  1 = Input – rotation angle  2 = Output – rotation angle If a single joint is deflected by angle ß and ro- tated in this condition, rotation angle  2 of the output shaft differs from rotation angle  1 of the input shaft. The relationship between the two rotation angles is as follows: tan  2 = tan  1 cos ß As can be seen from the adjacent diagram, maximum lead occurs at about 45 °, maximum lag at about 135°. Fork position  1 = 0° is then obtained, when the input fork is located in the deflection plane of the joint. Input Output fork position uniform uniform non-uniform fork position fork position