Joint and Cardan Shafts

176 177 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 6.8 Critical speeds As shown in 5.1, the center part of the an- gled driveline, when transmitting torque, is stressed periodically in bending by additional moment M ZII . This incites the center part to vibrate. If the frequency of this bending vibra- tion approaches the natural frequency of the driveline, maximum stress in all components, buckling of the shaft and development of noi- se will result. To avoid this, long and fast running drivelines must be checked for critical bending vibration speeds. The critical, first order bending vibra- tion speed of a driveline employing tubing can be roughly calculated as follows: 6.7 RPM and deflection angle As shown in 2.3 by taking certain precautions, a constant output can be obtained on a uni- versal driveline. The center part, however, still retains a non-uniform motion; it is subjected twice per revolution to an acceleration and deceleration. The resulting acceleration tor- que caused this way is a function of the mass moment of inertia of the driveline‘s center part as well as of rpm and deflection angle. When regarding smoothness of opera- tion and wear, the product of rpm and deflec- tion angle should not be too high. For use in general mechanical engineering, appropriate guide values can be taken from the diagram below, which is designed for universal driveli- nes having a standard tubing of up to 1500 mm length. For vehicle drive trains, these guide values must often be exceeded. Here, at most, up to 1.5 times the diagram value can be permitted. Speed, RPMn (min -1 )  Joint size   Max. deflection angle ß (°) n kr  1,21 . 10 8  D 2 + d 2 [min -1 ] L 2 D = Tubing-outside diameter [mm] d = Tubing-inside diameter [mm] L = Center part length in [mm] Drivelines are used in the subcritical zone only. For reasons of safety, it must be ensu- red that the maximum operating speed is far enough away from its system‘s resonance (critical) speed. Therefore, the following applies: Max. Operating Speedn max  0,65 . n cr [RPM] 6.9 Larger tubing diameters The critical bending vibration speed of a dri- veline is, as can be seen from the critical rpm formula, a function of tubing diameters and length of center part. By going to larger tubing diameters, the critical speed of a driveline can be increased. However, the diameter increase must remain within defined limits since a cer- tain relationship between tubing dimensions and joint size must be adhered to. The dimension sheets of the different driveli- ne models list the possible tubing dimensions for each size. In all the cases where a single driveline is insufficient, multiple arrangements with intermediate bearings must be used. It must be noted that larger tubing diameters are feasible only above a certain shaft length. The following minimum lengths can be used as an angle line. Flange diameter [mm] Up to 65 75 to 100 120 to 180 Min. length S [mm] 650 950 1250 6.10 Tubing diagram For determining the required tubing diameter when maximum operating speed n max and center part length L are given. Max. operating speed n max (rpm)   Tubing diameter D (mm)  Center shaft length L (mm) Example: Center shaft length L = 1600 mm Max. operating speed n max = 3000 RPM Obtained: Tubing diameter 70 mm } 