Shaft Couplings — validation & limitations

What it calculates

Engineering estimate — this tool uses an accepted simplified model rather than one citable governing standard. Use it for preliminary sizing and verify the final design against manufacturer data or a qualified engineer.

• Design torque from nominal torque and a coupling-selection service factor
• Torque safety factor against catalog capacity for jaw, disc, Oldham, gear and universal-joint coupling types
• Misalignment tolerance check — radial, angular and axial — against per-type catalogue-representative limits
• Torsional vibration natural frequency and dynamic magnification factor (two-mass model)
• Universal joint (Cardan/Hooke) output-speed fluctuation and peak/minimum speed
• Shaft critical speed estimate for the coupled shaft span
• Suitability ranking of five coupling types for the entered operating conditions

Related standards — reference only, not implemented

• AGMA 9002reference only — Checks the shaft bore fits within the coupling's rated bore range — this is not a full AGMA 9002-B04 keyway/tolerance conformance check. Design torque, service factor, misalignment checks and torsional vibration follow general coupling-selection practice, not AGMA 9002, for jaw, disc, Oldham, gear and rigid coupling types.

Validation evidence — independent reference cases (2)

Each case runs the tool's engine on a worked example whose values come from a published source or a hand derivation from the cited equations, and an automated regression test asserts the engine against those values within the stated tolerance. "Conservative" means the engine is known to sit on the safe side of the reference and the test asserts that side. Sources are cited; their text is not reproduced.

• Shaft bending critical speed and speed-ratio verdict

  Agrees

  Source: Blevins, Formulas for Natural Frequency and Mode Shape (1979), Table 8-1, pinned-pinned lambda_1 = pi; Den Hartog, Mechanical Vibrations

  Inputs: Steel shaft d 50 mm, span 1.2 m, E 210 GPa, rho 7850 kg/m3; 1500, 3200, 3900 rpm

  Quantity	Reference value	Tolerance
  N_crit	4231.49 rpm	1e-6 relative
  Speed ratio at 3200 rpm	75.62 % (CHECK)	1e-5 relative
  Speed ratio at 3900 rpm	92.17 % (FAIL)	1e-5 relative

  Conservative simplification: A stepped shaft line is judged on the smaller diameter.

  tests/golden/REF-couplings-critical-speed.golden.test.ts

• Design torque, torque safety factor and shaft torsion

  Agrees

  Source: Shigley's Mechanical Engineering Design, 10th ed., Ch. 3 (T = P/omega, tau = 16T/(pi d^3)); KTR ROTEX / Lovejoy selection by torque times service factor

  Inputs: 30 kW at 1470 rpm, K_A 1.75, jaw coupling 2000 N·m, shafts d 38 mm; Oldham 500 N·m, T 300 N·m, K_A 1.5

  Quantity	Reference value	Tolerance
  Design torque	341.05 N·m	1e-6 relative
  Torque safety factor (jaw)	5.8643	1e-5 relative
  Shaft torsion, d 38 mm	31.654 MPa	1e-5 relative
  Torque SF, Oldham 300 N·m	1.1111 (FAIL)	1e-6 relative

  tests/golden/REF-couplings-torque-sf.golden.test.ts

Limitations

Conservative simplifications

• Shaft bending critical speed and speed-ratio verdict — A stepped shaft line is judged on the smaller diameter.

Not checked by this tool

• The specific coupling model's rating for the actual bore — A family catalogue rating is used; confirm the selected model's rated torque and bore chart
• Peak, start-up and short-circuit torque against the coupling's maximum torque — The service factor covers the duty; compare peak torques with the maker's maximum torque rating
• Key / shaft-hub connection (key shear, hub pressure, clamping) — Check with /keys or /pressfit
• Multi-mass torsional vibration analysis of the drive train — The torsional panel is a two-inertia estimate; for engines, inverters or reciprocating loads run a full torsional analysis
• Coupling balance quality for the operating speed — Check the maker's balance class against ISO 21940-11 (/dynamics for the rotor)
• Elastic element rating under vibratory torque and damping heat — Only the spider temperature range is screened; check the maker's vibratory torque and damping power ratings