Tolerance Stack-Up With Polycarbonate: Where Thermal Expansion Bites is the governing analysis for PC assemblies when a rigid mounting loop spans a temperature delta. The coefficient of linear thermal expansion of unfilled polycarbonate is 65 × 10⁻⁶ K⁻¹ to 70 × 10⁻⁶ K⁻¹ over 23 °C to 100 °C when measured per ISO 11359-2:2021. The linear expansion expression ΔL = α × L₀ × ΔT applied to a 100 mm PC carrier at ΔT = 40 K yields 0.260 mm to 0.280 mm. An equivalent cold-rolled steel carrier at 11.7 × 10⁻⁶ K⁻¹ yields 0.047 mm. The 0.213 mm to 0.233 mm difference can exceed the ±0.2 mm clearance allocated for snap-fit or gasket compression; thermal expansion, not the ±0.1 mm molding tolerance, drives the stack-up.

Under equilibrium at 23 °C and 50 % RH per ISO 291, unfilled PC acquires 0.15 % water uptake after 24 h and up to 0.35 % at saturation per ISO 62. Hygroscopic expansion adds a separate reversible dimensional term that is frequently omitted in thermal tolerance stack-ups. Because PC is amorphous, mold shrinkage is isotropic at 0.005 mm/mm to 0.007 mm/mm per ISO 294-4, but local density gradients in thick sections introduce non-uniform post-mold expansion. When the rib-to-wall ratio exceeds 0.6:1, mold-flow simulation should be coupled with CLTE data; published data for this specific configuration is limited, and laboratory measurement per ASTM E831-19 is required before final tolerance release.

When a 150 mm Polycarbonate Enclosure Is Toleranced Without CLTE Compensation

Worst-case and root-sum-square stacks diverge because thermal expansion is a deterministic mean shift rather than a random variable. A 150 mm PC enclosure mounted to a steel frame at 23 °C and operated at 80 °C experiences ΔT = 57 K. The PC growth is 0.556 mm at 65 × 10⁻⁶ K⁻¹ and 0.599 mm at 70 × 10⁻⁶ K⁻¹, while the steel frame grows 0.100 mm at 11.7 × 10⁻⁶ K⁻¹. The net length mismatch is 0.456 mm to 0.499 mm. If the design gap is 0.80 mm ± 0.25 mm, the lower bound of the as-designed gap is 0.55 mm, leaving only 0.051 mm to 0.094 mm margin before screw-hole clearance, paint thickness, and elastomer compression are added. Substituting an RSS calculation with a 1.5 process capability factor on the same inputs produces ±0.289 mm at the 3σ boundary, but this treatment is invalid for the thermal term unless the operating temperature range is itself a measured distribution. Thermal growth should be entered as a bias with upper and lower limits derived from the actual vehicle or equipment thermal profile.

Replacing unfilled PC with 20 wt% glass-fiber reinforced PC reduces CLTE to approximately 30 × 10⁻⁶ K⁻¹ in flow direction and 45 × 10⁻⁶ K⁻¹ transverse, as published in resin suppliers’ technical bulletins. This anisotropy complicates the stack-up because flow direction and transverse direction must be treated as different materials in the tolerance loop. A 100 mm long structural PC frame rib at ΔT = 40 K expands 0.120 mm along flow and 0.180 mm across flow, while the same part in unfilled PC expands 0.260 mm to 0.280 mm. The reduced CLTE is accompanied by increased warpage from orientation gradients; published data for this specific configuration is limited.

Resin preparation also modifies tolerance stack-up because residual moisture affects both viscosity and part stability. PC must be dried to 0.02 % moisture at 120 °C for 3–4 h in a desiccant dryer with a dew point below −30 °C. Processing above 0.03 % moisture produces splay and hydrolysis, and the molecular weight drop shifts long-term dimensional stability. On the injection molding line, melt temperature is maintained at 280–320 °C and mold temperature at 70–100 °C. A mold temperature below 70 °C increases frozen-in orientation, which creates anisotropic thermal expansion and warpage after demolding. The cavity is dimensionally corrected for 0.005–0.007 mm/mm shrink per ISO 294-4, but the correction is valid only for a defined packing pressure and gate geometry. Variations in packing pressure alter local shrink; mold-flow simulation is required before the tolerance sheet is released.

Automotive forward-lighting lenses demonstrate that part-level dimensional conformance at room temperature does not guarantee assembly-level clearance. A 300 mm wide PC headlamp lens moulded with 0.006 mm/mm shrink compensation in a 2800 kN clamp force machine at melt temperature 300 °C and mold temperature 85 °C measures within ±0.15 mm at 23 °C. After the lens is hot-plate welded to a PC housing and exposed to 85 °C under solar load, the lens width grows 1.17 mm at 65 × 10⁻⁶ K⁻¹; the steel radiator support behind the housing moves only 0.21 mm over the same 300 mm span. The 0.96 mm differential displacement must be absorbed by slotted mounts, elastomeric seals, or a deliberate flexure zone. In production, slot length is not a packaging convenience; it is calculated from the worst-case thermal mismatch plus seal recovery tolerance and screw-head clearance.

Snap-fit beam deflection tolerances also interact with thermal expansion. A PC cantilever snap beam with length 12 mm, width 2 mm, and thickness 0.8 mm is deflected 0.30 mm to engage a steel housing. At 70 °C, the beam length grows 0.037 mm at 65 × 10⁻⁶ K⁻¹; the steel catch point grows only 0.007 mm. The differential thermal movement is 0.030 mm. If the minimum engagement depth is 0.20 mm, the available margin is 0.10 mm. Thermal movement consumes 30 % of that margin. In the field, this appears as intermittent disengagement when the assembly is hot and vibration is present.

What Happens When a PC Hub Is Pressed Onto a Steel Shaft?

A 20 mm bore PC hub with an initial 0.050 mm radial interference on a steel shaft at 23 °C loses grip as temperature increases. At 70 °C, ΔT = 47 K, the diametral differential expansion is ΔD = D × (α_PC − α_steel) × ΔT = 20 mm × (65−11.7) × 10⁻⁶ K⁻¹ × 47 K = 0.050 mm. The 0.050 mm interference is therefore wholly consumed at 70 °C, leaving a borderline zero grip condition. At 23 °C, the elastic hoop strain is 0.0025, corresponding to a hoop stress of approximately 6.0 MPa at 2400 MPa tensile modulus, which is below the short-term yield stress of 60 MPa per ISO 527-2. Nevertheless, PC creeps under continuous load; after 24 h at 60 °C the effective interference loss may be further increased by viscoelastic relaxation, and published data for this specific configuration is limited.

Optical Encoder Disks and Radial Runout at ΔT = 55 K

In optical position sensing, radial centration of a PC code wheel is typically specified at ±0.020 mm, giving a total radial band of 0.040 mm. A PC encoder disk with a 12.5 mm radius bonded to a steel hub expands radially 0.045 mm when the assembly rises from 23 °C to 78 °C at 65 × 10⁻⁶ K⁻¹. The steel hub expands only 0.008 mm over the same radius and ΔT. The differential radial growth of 0.037 mm consumes 92 % of the total centration band before considering adhesive creep, anisotropic filler distribution, or vibration. If the adhesive bond line is 0.100 mm thick, the thermal mismatch is partitioned between shear strain in the adhesive and radial runout at the disk edge; the transmitted runout depends on adhesive modulus, cure shrinkage, and joint geometry.

Thermal expansion also reduces axial preload in clamped joints. A PC flange with a 10 mm stack height under a steel M6 screw and brass insert is compressed to 0.15 mm at 23 °C. At 85 °C, ΔT = 62 K, the PC stack height increases 0.040 mm while the steel screw increases 0.007 mm, leaving 0.033 mm of relaxation. The retained clamp load falls in proportion to the displacement divided by the effective joint stiffness; measurement on the production joint is required because creep modulus and polymer stress relaxation alter the apparent stiffness over time. The operational boundary is a continuous service temperature below 85 °C for unfilled PC when a metal compression limiter is not present.

A gear pump cartridge of unfilled PC for a diagnostic instrument is moulded with a 0.004 mm/mm cavity shrink allowance because wall thickness is 1.8 mm and melt temperature is 290 °C. The cartridge is assembled with a steel drive gear. Moist-heat sterilisation at 121 °C for 30 min pushes the polymer toward its 147 °C glass transition temperature. At ΔT = 98 K, the center distance between 40 mm spaced gear bores expands 0.255 mm to 0.274 mm. The steel gear center distance grows 0.046 mm. The differential of 0.209 mm to 0.228 mm exceeds the normal gear backlash band of 0.05 mm to 0.15 mm, leading to interference and potential cracking unless the gear mesh is designed with wider thermal backlash compensation or the cartridge is replaced by a glass-filled grade with a lower CLTE. Creep and stress relaxation at 121 °C further reduce preload and centerline dimensional stability over repeated cycles; published data for this specific cartridge configuration is limited.