Coupling Selection (Service Factor)
Size a shaft coupling from nominal torque and service factor: from power and speed (or a directly given nominal torque) plus drive and load characteristics, starts per hour and ambient temperature, get the required coupling torque - optionally with a traffic-light check against the nominal and maximum torque of the selected coupling.
Calculation
The temperature factor applies to torsionally flexible (elastomer) couplings; for all-metal couplings use S_T = 1.0.
Characteristic values
- Nominal torque M_nenn
- 19.76 Nm
- Application factor S_A
- 1.8
- Starting factor S_Z
- 1.2
- Temperature factor S_T
- 1
- Overall factor S_A·S_Z·S_T
- 2.16
- Required coupling torque M_erf
- 42.68 Nm
Selection recommendation: choose the next larger catalogue coupling with M_KN >= M_erf.
Sketch: shaft coupling (hubs with an indicated elastomer gear ring)
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Formulas and fundamentals
Nominal Torque
From power P and speed n, the shaft's nominal torque follows from the well-known shorthand formula:
Alternatively, the nominal torque is given directly, for example from a gearbox datasheet or as a result of the drive sizing calculator.
Application Factor S_A
The application factor accounts for the combination of drive characteristic and load characteristic (guideline values per Roloff/Matek): uniform electric motor 1.0/1.5/2.0, electric motor with increased starting torque (direct-on-line) 1.2/1.8/2.4, internal combustion engine with 4 to 6 cylinders 1.5/2.0/2.5, and internal combustion engine with 1 to 3 cylinders 2.0/2.5/3.0 - each for the load classes uniform, moderate shocks and heavy shocks.
Starting and Temperature Factor
Frequent starts place additional load on the coupling: the starting factor S_Z rises from 1.0 (up to 10 starts per hour) through 1.2 (up to 60) and 1.3 (up to 120) to 1.5 (above 120 starts per hour). For elastomer torsionally flexible couplings, the permissible load capacity decreases as the ambient temperature rises; the temperature factor S_T is 1.0 up to 40 °C, 1.2 up to 60 °C and 1.4 up to 80 °C. For torsionally rigid all-metal couplings this effect does not apply, S_T = 1.0.
Required Coupling Torque
The three factors multiply to give the required coupling torque:
Select the next larger catalogue coupling with M_KN >= M_erf. The calculator shows the utilization M_erf/M_KN as a traffic light (up to 80 % pass, up to 100 % warning, above that fail).
Peak Torque and Further Checks
For jerky load peaks - especially with servo drives with high acceleration torque - the peak torque M_spitze (e.g. taken from the drive sizing calculator) must additionally be checked against the coupling's maximum torque M_Kmax: M_spitze <= M_Kmax. Misalignment values (radial, axial, angular) between the shaft ends and the permissible speed limit must also be checked against the catalogue; they are not part of this calculation.
Worked example
Reference example: An electric motor with increased starting torque (direct-on-line) drives a machine with moderate shocks at P = 3 kW and n = 1450 rpm, with up to 60 starts per hour and an ambient temperature up to 40 °C. The nominal torque is M_nenn = 9550·3/1450 = 19.76 Nm.
The application factor for direct-on-line starting with moderate shocks is S_A = 1.8, the starting factor for up to 60 starts per hour is S_Z = 1.2, and the temperature factor up to 40 °C is S_T = 1.0. The overall factor is therefore S_A·S_Z·S_T = 1.8·1.2·1.0 = 2.16, and the required coupling torque is M_erf = 19.76·2.16 ≈ 42.7 Nm.
A catalogue coupling with M_KN = 60 Nm thus has a utilization of 42.7/60 = 71 % (green, pass). If a smaller coupling with M_KN = 35 Nm is chosen instead, the utilization is 122 % (red, fail) - here the next larger size must be selected.
Frequently asked questions
Which service factor should I use for my application?
The application factor S_A results from the combination of drive characteristic (uniform or direct-on-line electric motor, internal combustion engine with 4 to 6 or 1 to 3 cylinders) and load characteristic (uniform, moderate shocks, heavy shocks). Added to this are the starting factor S_Z depending on starts per hour and - for torsionally flexible couplings - the temperature factor S_T. When in doubt, use the next higher value of the respective class; for critical applications the coupling manufacturer provides application-specific factors.
Torsionally flexible or torsionally rigid coupling - what is the difference?
Torsionally flexible couplings (e.g. with an elastomer spider or gear ring) absorb shocks, torsional vibration and part of the misalignment between the shafts, but require the temperature-dependent check (factor S_T). Torsionally rigid couplings (all-metal, e.g. gear or disc couplings) transmit the torque virtually backlash-free and without damping, but are more sensitive to shocks and misalignment. Compensating couplings (bellows, Oldham couplings) are designed purely to compensate for misalignment, are torsionally stiff and provide no significant damping.
What needs to be considered for servo drives regarding peak torque?
Servo drives reach a multiple of the nominal torque when accelerating and braking. If the nominal torque alone is not sufficient for coupling selection, the peak torque M_spitze - usually directly available from the drive sizing calculator - must additionally be checked against the coupling's short-term permissible maximum torque M_Kmax. If this is exceeded, cracks in the elastomer or blocking/slipping of the coupling can occur.
Which misalignment values do I also need to check?
In addition to torque, every coupling limits the permissible misalignment between the shaft ends: radial (parallel offset), axial (length compensation, e.g. due to thermal expansion) and angular (misalignment). These values are given in the coupling catalogue and must be observed independently of the torque calculated here - exceeding them significantly reduces the service life of the flexible elements or the bearings.
Why does ambient temperature affect the coupling torque?
For torsionally flexible couplings with an elastomer gear ring, the permissible load capacity of the material decreases as temperature rises - the ring softens and wears faster. The temperature factor S_T therefore increases the calculated required torque so that sufficient margin remains at elevated operating temperature (e.g. near heat sources). This effect does not apply to all-metal couplings (S_T = 1.0).
Is a larger coupling always the better choice?
Not necessarily: a significantly oversized coupling is heavier, larger, more expensive and, for torsionally flexible designs, can even damp more softly than intended, worsening the torsional vibration behaviour of the drivetrain. The sensible choice is the next larger size with M_KN just above M_erf (utilization ideally in the green range up to 80 %), not the largest available coupling.
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