1. LOAD DETERMINATION
In order to select the correct PTO Shaft, the torques acting on the shaft must be determined.
- Operating torque of the PTO Shaft
- Maximum torque of the PTO Shaft
When the power and rotational speed of the driven equipment are known, the torque (nominal torque) can be calculated using the following formula:
Tn = Nominal torque.
A more accurate load torque is obtained from the nominal torque by taking into account the service factor, which depends on the application of the shaft. The nominal torque of the shaft is multiplied by the service factor to determine the load torque used for comparison.
The resulting load torque must be lower than the load torque TK specified in the shaft tables.
Torques shown in the shaft tables:
TK = Load torque
The load torque is defined based on the capacity of the universal joint.
TCS = Functional limit torque
The maximum permissible torque that can be transmitted for a limited period of time without damage.
TDW = Operating torque
The continuously permissible torque under fluctuating loads.
TDSch = Pulsating torque
The continuously permissible torque under pulsating loads.
When selecting a PTO Shaft, both bearing service life and shaft strength must be considered separately. Depending on the type of load, operating torque TDW and pulsating torque TDSch must also be taken into account.
2. THEORETICAL SERVICE LIFE OF THE UNIVERSAL JOINT
The theoretical service life Lh of the PTO Shaft (universal joint) is based on the bearing LC factor and can be determined using the formula below:
If the required service life Lh is known, the correct joint size can be calculated based on the bearing factor LC.
LC values are obtained from the PTO Shaft dimension tables.
n = Shaft rotational speed (rpm)
β = Joint angle (°)
T = Torque (kNm)
If the duty cycle of the PTO Shaft (time/load) is known, the service life can be calculated based on this data. In such cases, please contact our technical service. In some applications, an internal combustion engine may cause overloads on the shaft, which must be taken into account using the shock factor K1.
| Engine type | Factor K1 |
|---|---|
| Electric motor | K1 = 1.00 |
| Petrol engine, 4 cylinders or more | K1 = 1.1555 |
| Diesel engine, 4 cylinders or more | K1 = 1.20 |
The values shown in the table are general reference values.
If flexible couplings are used, the shock factor is lower. The values specified by the engine and coupling manufacturers must always be verified.
SELECTION BASED ON OPERATIONAL STRENGTH
If the duty cycle is known, the operational strength can be determined.
The calculated service life of the PTO Shaft under normal operating conditions must be equal to or greater than the required service life.
If the duty cycle is not known, please contact us for assistance with the selection.
Our calculations are based on the operating torque T and the occurring maximum torque TSP.
The maximum operating torque is determined by the type of operation and the torque characteristics and must be lower than the corresponding TDSch or TDW values.
Typical torque values
The maximum torque TSP is determined based on the nominal torque of the driven machine and the service factor K of the application. This torque must not exceed the load torque TK of the shaft.
TSP = maximum torque (Nm)
TN = nominal torque (Nm)
TK = load torque (Nm)
K = service factor
3. OPERATING ANGLES
The most typical arrangements in applications are Z and W configurations. We initially assume that the shafts in the system are in the same plane.
When the joint angles β1 and β2 are equal, the shafts rotate uniformly.
In this case, the yokes must be aligned in the same plane.
Maximum permissible angular deviation
In applications involving high rotational speeds and/or high torques, the angular deviation should be limited to 1°–1.5°.
In applications with low rotational speeds, a larger angular deviation (3°–5°) can be allowed without significant effects.
If multiple PTO Shafts are used and/or they are not in the same plane, please contact us for consultation.
Maximum continuous operating angle
Depending on the PTO Shaft series and type, the maximum joint angle is 44°. Due to the kinematics of the joint, the maximum operating angle must be limited in relation to the rotational speed.
To ensure smooth system operation, the mass acceleration torque of the intermediate section must not be exceeded. This torque depends on
The product of speed and operating angle
= n × β
and on the mass moment of inertia of the intermediate shaft section.
The stated values apply only to the Z configuration.
For the W configuration, the values must be divided by two.
4. ROTATIONAL SPEED
Evaluation of the critical rotational speed
PTO Shafts are elastic components that can bend and deflect. Therefore, the first and, if applicable, second order critical rotational speeds are significant from both a safety and operational standpoint. For safety reasons, the maximum permissible rotational speed must be kept sufficiently below the critical rotational speed.
nsal.max. = Continuous maximum rotational speed
nkrit = Critical rotational speed
The critical rotational speed for a specific PTO Shaft type is determined by the length and diameter of the shaft tube (see Table 5.1, page 44). For greater lengths, the diameter of the shaft tube must be increased.
Since the tube diameter is proportional to each shaft size, a shaft can only be manufactured up to a certain maximum length. Installations requiring a greater length must be implemented using intermediate shafts with center bearings.
This table applies to applications where fixed support bearings are located close to the flanges. In other cases, such as installations with flexible bearing arrangements, the critical rotational speed is lower.
Depending on the application, exceeding the second order critical speed may cause vibrations. If the joint angle exceeds 3° or if greater shaft length is required, please contact us for assistance.
5. PTO SHAFT LENGTH
The operating length of the PTO Shaft is determined based on the distance between the driving and driven units and the allowable axial movement of the shaft.
Terms:
Lz = Compressed length
The shortest length of the PTO Shaft.
La = Axial travel (slip length)
The spline in the shaft allows the length to change by this amount. This value is fixed for each shaft type and must not be exceeded.
Lz + La = Maximum continuous operating length
During operation, this is the maximum length the shaft may reach.
The basic rule for defining the correct operating length is to add half of the axial travel to the minimum length of the PTO Shaft.
LB = Lz + ½ La [mm]
In applications requiring greater axial movement, the operating length must be selected so that the actual movement remains within the permissible axial travel limits.
