Thermal Analysis — 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.

• Spindle heat balance: bearing friction + motor losses + preload friction vs cooling capacity
• Bearing friction heat (Q = M·ω with M = µ·P·d_m/2 + M₀ = f₀·10⁻⁷·(ν·n)^(2/3)·d_m³ — load and speed/viscosity halves)
• Equilibrium temperature floored at the sink-side rise — a spindle is never left sitting at its own sink temperature
• Thermal axial growth and diametral expansion with material-library CTE
• Constrained thermal stress (5 materials, free/partial/full constraint, tension and compression)
• Bimetallic strip deflection, curvature and contact force (Timoshenko formula)
• Pipe expansion loop sizing — guided-cantilever leg length and symmetric U-loop geometry

Related standards — reference only, not implemented

• DIN 732reference only — Adjacent, but NOT a DIN 732 implementation. It solves a spindle-assembly heat balance for a TEMPERATURE — bearing friction heat from a bearing-maker constant-coefficient load term plus the published load-independent term M₀ = f₀·10⁻⁷·(ν·n)^(2/3)·d_m³, plus motor losses and preload friction, against a cooling-circuit capacity — and returns the equilibrium temperature, axial growth and diametral expansion. It computes no thermally safe speed and uses none of DIN 732's coefficients. It is an engineering estimate and is labelled as one.

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.

• Axial and diametral thermal growth, delta L = alpha·dT·L

  Agrees

  Source: Linear thermal expansion dL = alpha·dT·L; Gere & Goodno, Mechanics of Materials, thermal effects; Shigley thermal strain

  Inputs: Air case L 300, D 40 mm, dT 26.1118 K, alpha 11.7e-6/K; water case L 400, D 50 mm, dT 3.2880 K, alpha 23 um/(m·K)

  Quantity	Reference value	Tolerance
  axial growth air case (um)	91.65250	1e-5 relative
  diametral growth air case (um)	12.22033	1e-5 relative
  axial growth water case (um)	30.24929	1e-5 relative
  diametral growth water case (um)	3.78116	1e-5 relative

  tests/golden/REF-thermal-growth.golden.test.ts

• Spindle bearing and motor heat balance and temperature

  Agrees

  Source: rolling-bearing maker lubrication publication (speed-dependent friction M0); bearing-maker catalogue frictional moment; ISO 281:2007 Annex B (nu1, kappa); hand derivation of P = M·omega and Q = m·cp·dT

  Inputs: Water case: 4 AC bearings, 6000 rpm, dm 60, P 2000 N, motor 10 kW at 90 %, 6 L/min. Air case: 2 bearings, 3000 rpm, dm 50, P 1500 N

  Quantity	Reference value	Tolerance
  Q_total water case (W)	1376.343	1e-4 relative
  temperature water case (C)	23.288	1e-4 relative
  Q_bearings air case (W)	104.4473	1e-4 relative
  temperature air case (C)	51.112	1e-4 relative

  tests/golden/REF-thermal-heat-balance.golden.test.ts

Limitations

Not checked by this tool

• Bearing thermally safe operating speed (DIN 732 / ISO 15312) — Not implemented; compare the speed with the bearing maker's thermal reference and limiting speeds
• Preload change of the spindle bearings from the computed growth — The temperature band is a proxy; check the preload change with the bearing maker
• Transient warm-up and thermal gradients (front-to-rear, shaft vs housing) — Single-node steady model; measure or model warm-up for precision work
• Calibrated housing heat path and cooling-circuit performance — The housing resistance and cooling capacities are uncalibrated; verify with the spindle maker's thermal data
• Load-dependent bearing friction term M1 — Needs the static rating C0, which is not asked; use the bearing maker's friction model