#interference

Interference (press and shrink) fit engineering maths as an API, computed locally and deterministically from the Lamé thick-wall equations — the contact-pressure, holding-capacity and assembly-temperature numbers a mechanical designer or machinist sizes a shaft-and-hub joint with. The pressure endpoint gives the contact pressure that builds at the interface from the diametral interference, the shaft and hub diameters and the elastic modulus, plus the tensile hoop stress at the hub bore — the highest stress in the joint, which a thin hub can split if it exceeds the yield: a 50 mm solid steel shaft in a 100 mm hub with 0.05 mm interference makes about 75 MPa of contact pressure and 125 MPa of bore hoop stress, and doubling the interference doubles the pressure. The holding endpoint turns that pressure into the axial push-out force and the transmissible torque through the friction at the interface (force = pressure × contact area × friction, torque = force × shaft radius), the figures that decide whether the joint slips under load. The assembly-temperature endpoint gives the heating (hub) or cooling (shaft) temperature change for a shrink fit — ΔT = (interference + clearance) ÷ (α × diameter) — so the part slides on freely and grips as it returns to temperature. Everything is computed locally and deterministically, so it is instant and private. Ideal for mechanical-design and machine-building tools, manufacturing and CAD utilities, and engineering calculators. Pure local computation — no key, no third-party service, instant. Same-material Lamé estimates — verify against the material yield with a safety factor. 3 compute endpoints. For thin-wall pressure-vessel stress use a pressure-vessel API.

api.oanor.com/pressfit-api

Wave-optics diffraction and interference as an API, computed locally and deterministically. The double-slit endpoint applies Young's two-slit interference, d·sinθ = m·λ: from a wavelength and the slit separation it returns the angle of the m-th bright fringe and, given the screen distance, the fringe spacing Δy = λ·L/d and the position of any maximum — the classic experiment that proved light is a wave. The grating endpoint handles a diffraction grating, d·sinθ = m·λ with d = 1/lines: from a wavelength and the grating density (lines per millimetre) it gives the diffraction angle of each order and the maximum observable order ⌊d/λ⌋, flagging orders that do not exist. The single-slit endpoint computes single-slit diffraction, a·sinθ = m·λ for the dark fringes (minima), and, given the screen distance, the width of the bright central maximum 2·λ·L/a. Wavelengths may be entered in metres, nanometres or micrometres. Everything is computed locally and deterministically, so it is instant and private. Ideal for physics and optics-education tools, spectroscopy and grating design, laser and photonics apps, and laboratory software. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is wave-optics diffraction; for thin-lens imaging use a lens API and for Snell's-law refraction use a Snell API.

api.oanor.com/diffraction-api