PE Mechanical Machine Design cheat sheet

Worst-case tolerance stack-up = sum of individual tolerances; statistical (RSS) stack-up = square root of the sum of squared tolerances for independent random dimensions.

Clearance fit requires hole minimum > shaft maximum; interference fit requires shaft minimum > hole maximum; transition fits lie between these conditions.

Basic hole system (H): the hole lower deviation is zero, so the minimum hole equals basic size and the shaft limits create the clearance or interference.

Bonus tolerance at MMC = |actual mating size - MMC size|, added to the stated geometric tolerance on the feature control frame.

Factor of safety n = strength / applied stress; for combined static loading compare von Mises stress against yield strength and maximum shear against 0.5 Sy.

Single-payment present worth P = F(1+i)^-n; capital recovery A = P[i(1+i)^n]/[(1+i)^n - 1]; series compound amount F = A[(1+i)^n - 1]/i.

Normal distribution: 68.3% of values within +/-1 sigma, 95.4% within +/-2 sigma, 99.7% within +/-3 sigma; coefficient of variation = sigma / mean.

Unit conversions: 1 psi = 6.895 kPa; 1 MPa = 145.0 psi; 1 in = 25.4 mm; 1 hp = 550 ft-lb/s = 0.7457 kW; 1 kgf = 9.807 N.

Nominal stress at a discontinuity is computed on the net section, then multiplied by the theoretical stress concentration factor Kt to obtain peak elastic stress.

Fatigue criteria: Goodman sigma_a/Se + sigma_m/Sut = 1/n; Soderberg sigma_a/Se + sigma_m/Sy = 1/n; Gerber sigma_a/Se + (sigma_m/Sut)^2 = 1/n.

Marin equation: Se = kakbkckdkekfSe', where Se' is about 0.5 Sut for wrought steel with Sut <= 1400 MPa (200 ksi), otherwise about 700 MPa.

Fatigue notch factor Kf = 1 + q(Kt - 1); notch sensitivity q approaches 1 for sharp notches in high-strength steel and approaches 0 for ductile low-strength metals.

Bearing rating life L10 = (C/P)^a in millions of revolutions, with a = 3 for ball bearings and a = 10/3 for roller bearings; hours = 10^6 L10 / (60 rpm).

Gear tooth bending by Lewis: sigma = Wt/(FmY), where Wt is tangential load, F face width, m module, and Y the Lewis form factor from tooth count.

Bolted joint: preload Fi = 0.75AtSp; joint stiffness constant C = kb/(kb + km); bolt stress sigma_b = Fi/At + C*P/At under external load P.

Euler column: Pcr = pi^2EI/(K*L)^2 with K = 1.0 pinned-pinned, 0.5 fixed-fixed, 0.7 fixed-pinned, 2.0 fixed-free; use the Johnson parabola when the slenderness ratio is below the transition value.

Fillet weld effective throat = 0.707 times the leg size, so weld area = 0.707leglength and shear stress = force / weld area.

A power screw is self-locking when the friction coefficient mu is greater than or equal to tan(lambda), where lambda is the helix (lead) angle.

SAE 1045 is a 0.45% carbon medium-carbon steel; 4140 is Cr-Mo; 4340 is Ni-Cr-Mo; 1020 is low-carbon and commonly carburized.

Heat-treat sequence: anneal or normalize, austenitize, quench to martensite, then temper; the tempering temperature sets the final strength-toughness balance.

Hardenability is measured by the Jominy end-quench test and depends on alloy content and austenitic grain size, not on carbon content alone.

Hardness scales: Rockwell C for hardened steel, Rockwell B for soft or low-carbon steel, Brinell for castings and coarse microstructures, Vickers for microhardness and thin cases.

Case hardening methods: carburizing (low-carbon steel, surface near 0.8-1.0% C), nitriding (alloy steel, no quench required), and induction or flame hardening (selective surface).

Carbon equivalent CE = C + Mn/6 + (Cr+Mo+V)/5 + (Ni+Cu)/15; CE above about 0.40 signals reduced weldability and requires preheat and low-hydrogen practice.

Gray cast iron has flake graphite that provides damping and machinability but low tensile ductility; ductile (nodular) iron has spheroidal graphite with useful strength and elongation.

Aluminum 6061-T6 properties: Sut about 310 MPa, Sy about 275 MPa, E about 69 GPa; 7075-T6 is stronger but less corrosion resistant.

Shot peening and cold rolling induce compressive surface residual stress and raise fatigue life, while decarburization, plating, and nicks reduce it.