Thermal Analysis Calculator — Spindle Heat Balance, Thermal Expansion & Stress

None — and the tool says so on every panel. There is no governing standard for a spindle-assembly heat balance. The bearing friction heat is a bearing maker's published simplified constant-coefficient estimate (a manufacturer method, not a standard); the motor-loss split, the cooling capacities and the lumped thermal resistance are unsourced engineering heuristics; the thermal expansion relation ΔL = α·ΔT·L is elementary. Use the tool for preliminary sizing and verify a final precision-spindle design against measured data or thermal FEA/CFD.

DIN 732:2010 is 'Rolling bearings — Thermally safe operating speed — Calculation and correction values'. It solves a BEARING heat balance for the SPEED at which friction heat equals what the bearing can dissipate — n_θ = n_θr · f_n, from a thermal speed rating per DIN ISO 15312 plus a lubricant parameter and a load parameter. It applies to a bearing, not to a spindle assembly, and it contains no motor-loss term, no cooling jacket, no lumped spindle resistance and no thermal expansion. This calculator implements none of it, and it does not compute a thermally safe speed. Earlier versions of this page named DIN 732 as the governing standard; that claim has been removed.

Because it physically cannot, and the same is true of an air-cooled or uncooled spindle sitting at ambient. At steady state all the generated heat has to leave through some resistance, and a body cannot push heat into a sink it is exactly as warm as. For a water jacket or oil circuit the coolant itself warms by Q_total/(ṁ·c_p) on its way through, so the spindle that heated it is at least that warm; for forced air and uncooled spindles the model's own lumped resistance supplies the same floor. The calculator applies this on all four cooling options — an earlier version applied it only to the liquid ones, which left forced-air spindles still reporting a 0 K rise and zero thermal growth. Treat the floor as a low estimate rather than a hard bound: other heat paths reduce it, while the real film and wall resistance adds to it.

Four: no cooling (a flat 10 W of radiation), forced-air convection (a fixed 50 + 0.2 × spindle length, in watts), water-jacket cooling (ṁ·c_p·ΔT with water c_p = 4 186 J/kg·K and an assumed 10 K jacket rise), and recirculating oil cooling (oil c_p = 2 000 J/kg·K, density 0.85 kg/L, assumed 15 K rise). Every capacity is a fixed wattage independent of the spindle temperature, which is the model's biggest simplification. Note that the oil option models a RECIRCULATING oil circuit at the flow you enter — true oil-air (minimal-quantity) mist lubrication meters oil in millilitres per hour and removes only tens of watts, so select 'No cooling' for that. Water-jacket and oil results reference the coolant inlet temperature; forced-air and uncooled spindles reference ambient.

Axial growth = α · ΔT · L_spindle and diametral expansion = α · ΔT · d_shaft, where α is the material's coefficient of thermal expansion from the material library and ΔT is the rise above the coolant or ambient base. On a machine-tool spindle the axial growth shifts the Z-datum directly and the diametral expansion changes tool-tip runout and bearing fits; even 20 µm of axial shift can exceed tight machining tolerances, which is why thermal error compensation is standard on high-precision CNC.

Yes, and it assesses both on the stress magnitude. A member restrained against free movement goes into compression when heated and into TENSION when cooled — the sense that opens cracks in brittle material and welds — and the tension case is exactly as large as the equivalent heating case. The safety factor is Sy/|σ| and the yield banner fires on |σ|, so a cryogenic line, a chilled circuit or a shrink fit is checked as severely as a hot one.

It computes the tip deflection, curvature, sensitivity and contact force of a two-layer cantilever strip whose layers have different coefficients of thermal expansion — the classic thermostat and thermal-actuator geometry. The curvature uses Timoshenko's closed form, which is exact for a uniform bonded strip. The contact force uses the COMPOSITE transformed-section rigidity of both layers, and the strip width is an input; layer thicknesses, moduli, CTEs and the contact gap are all editable.

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