Casting: solidification and defects
Chvorinov's rule gives solidification time: t = B(V/A)², where V is casting volume, A is surface area, and B is a mold constant. Thicker sections solidify last. Risers must solidify after the casting; design using (V/A)_riser > (V/A)_casting. Common defects: shrinkage cavities, porosity, hot tears, and cold shuts.
Check yourself: Does the riser have a larger V/A ratio than the section it feeds?
Forming: force estimation
In ideal open-die forging of a cylinder (no friction), force F = σ_y x A, where A is the instantaneous contact area. With friction, F increases. In rolling, draft = reduction in thickness; maximum draft Δh_max = μ²R, where μ is friction coefficient and R is roll radius. Volume constancy applies to plastic deformation.
Check yourself: Have you used the instantaneous area, not the original area, after deformation?
Machining: cutting forces and MRR
In orthogonal cutting, the material removal rate MRR = v x f x d (cutting speed x feed x depth of cut). Merchant's theory relates shear angle φ to rake angle α and friction angle β: 2φ + β - α = 90° (Merchant's equation). Cutting force F_c = τ_s A_s / (cos(β - α) cos φ), where A_s is shear area.
Check yourself: Are cutting speed, feed, and depth in consistent units for MRR?
Tool life and machining economics
Taylor's tool life equation: VT^n = C, where V is cutting speed, T is tool life, and n, C are constants. Higher speed reduces tool life. The economical cutting speed minimizes cost per piece; the speed for maximum production minimizes time per piece. These two optima are different.
Check yourself: Are you optimizing for minimum cost or maximum production rate?
Welding: heat input and joint design
Arc welding heat input H = ηVI/v, where η is efficiency, V is voltage, I is current, and v is welding speed. Higher heat input increases the heat-affected zone width. Joint types include butt, lap, fillet, and corner. Weld defects include porosity, lack of fusion, undercut, and distortion from residual stresses.
Check yourself: Have you included the process efficiency factor η in the heat input calculation?