Joint and Cardan Shafts

178 179 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 7. Application principles for double joint shafts in steering axles The double joint shafts of series 0.400.5 and 0.500.3 are intended for use in powered stee- ring axles only. 7.1 Kinematic conditions As shown in the sketch below, when steering is activated, the axle system is rotated around pin center D . The double joint deflects at its two joint pivot points A and B . Since shaft II is fixed axially, shaft I must move in the direc- tion S . This causes unequal joint deflection angles ß 1 and ß 2 , and therefore, also a non- uniform (fluctuating) output motion. The fluc- tuation can be kept very small provided joint center C is offset toward the fixed side by the compensation value X. This way, at a certain deflection angle (= synchronous motion angle ß x ) completely uniform motion is obtained, i.e., the two joint deflection angles ß 1 and ß 2 are equal. ßx = 30° bis 35° would be an appropriate synchronous motion angle to select A = Joint pivot point B C = center of the double joint D = rotation pin center a = distance of a joint point from the center ot the double joint e = axial movement of floating shaft X = center offset on installation ß x = uniform motion angle (synchronous) ß = total deflection angle ß 1 = deflection angle of each ß 2 individual joint } } 7.2 Center offset value x and max. slide movement e The center offset X required for smooth output can be derived from distance a and synchro- nous motion angle ß: Series 0.500 , synchronous motion angle ß x = 32° Calculated center offset value X for individual joint sizes: Series 0.400 , synchronous motion angle ß x = 35° 7.3 Sizing of double joint shafts Max. possible torque should be used for de- termining the required joint size. This could be the input torque, calculated from prime mo- ver output, gear ratio and power distribution, or also the tire slippage torque, derived from allowable axle loading, static tire radius and coefficient of friction. The lower of the two va- lues represents the maximum operating tor- que which should be used for determining the proper joint size. The double joint shaft select- ed this way will have adequate life expectan- cy, since the time percentage of maximum loa- ding is usually low. 7.4 Loads on the shaft bearing Double joint shafts, when not centered, must have a bearing support at both shaft halves right next to the joint with one shaft half fixed axially and the other floating axially. When torque is being transmitted, additional forces occur which must be taken into account when sizing the bearings. Joint size 0.408 0.409 0.411 0.412 Deflection angle ß° 50 50 50 50 x [mm] 1,5 1,7 2,0 2,2 Joint size 0.509 0.510 0.511 0.512 0.513 0.515 0.516 0.518 Deflection angle ß° 42 | 47 | 50 42 | 47 42 | 47 42 | 47 42 | 47 42 | 47 42 | 47 x [mm] 1,3 | 1,3 | 1,6 1,5 | 1,6 1,6 | 1,7 1,7 | 1,8 1,9 | 2,0 2,1 | 2,2 2,2 | 2,3 Sliding motion e at deflection angle ß, and also as a function of distance a and uniform motion angle ß x , can be calculated as follows: Series 0.500 , uniform synchronous motion angle ß x = 32° Max. slide motion e for the individual joint sizes: Series 0.400 , synchronous motion angle ß x = 35° Joint size 0.408 0.409 0.411 0.412 Deflection angle ß° 50 50 50 50 e [mm] 6,5 7,2 8,3 9,2 Joint size 0.509 0.510 0.511 0.512 0.513 0.515 0.516 0.518 Deflection angle ß° 42 | 47 | 50 42 | 47 42 | 47 42 | 47 42 | 47 42 | 47 42 | 47 e [mm] 4,5 | 6,0 | 7,9 5,2 | 6,9 5,8 | 7,8 6,1 | 8,1 6,7 | 9,0 7,3 | 9,7 7,8 | 10,5 X = – a a cos ß x 2 ( ) ßx 2 e = 2 a ß 2 ß 2 ß 2 ßx 2 cos –1 sin 2  +  cos 2 – sin 2 · cos 2