Casting, Forming and Joining

Casting and rolling processes

Two forming processes are covered here: centrifugal casting and rolling. In true centrifugal casting, the molten metal is spun against the outer mould wall, so the outer radius of the casting sets the centrifugal acceleration. The G-factor is the ratio of centrifugal acceleration to gravity, G = \omega^2 r/g, and the rotational speed follows from N = 60\omega/(2\pi) rpm.

In rolling, friction draws the workpiece into the roll gap. With Coulomb friction coefficient \mu and roll radius R, the maximum possible draft is \Delta h_{max} = \mu^2 R. A pass is feasible only if the required draft does not exceed this bite limit.

• Roll-workpiece contact length — L = \sqrt{R\,\Delta h}, the projected arc of contact for a draft \Delta h.
• Volume constancy — t_0 w_0 L_0 = t_1 w_1 L_1, used to find the exit length or width after a change in thickness.
• Average flow stress and roll force — for a power-law material Y_f = K\varepsilon^n, the average over the pass is Y_{avg} = K\varepsilon^n/(1+n), and the roll separating force is F = Y_{avg}\,w\,L.

Example: a 40 mm thick plate reduced by 4 mm in a pass with roll radius 200 mm has L = \sqrt{200 \times 4} \approx 28.3 mm.

Additive manufacturing processes

Additive manufacturing builds parts layer by layer, and each process is defined by the form of its feedstock and by how a layer is created. Filament, wire, liquid resin, powder and sheet are the common feedstock forms, so matching a process to its input is a standard exam task.

• Thermoplastic filament — the filament is melted in a heated nozzle and extruded as beads. Fused deposition modelling (FDM) uses this route, with ABS as a typical material.
• Wire — a continuous metal wire is fed into a melt pool created by an arc, laser or electron beam. Directed energy deposition processes use wire feedstock.
• Liquid photopolymer resin — each layer is cured by light in a resin vat. Stereolithography works this way, and the resin is typically of the epoxy or acrylate type.
• Heat-fusible powder — a laser fuses powder particles locally in a powder bed, as in selective laser sintering.
• Sheet — layers of paper, thermoplastic or green compacted metal sheet are bonded and cut to profile, as in laminated object manufacturing.
• Powder stream — laser-engineered net shaping injects metal powder into a melt pool, and titanium is a common material.

The STL file format describes a surface as triangular facets, so its errors are geometric. Missing facets leave holes, non-manifold topology occurs when an edge is shared by more than two facets, and degenerate facets have zero area or collinear vertices. The staircase effect, which comes from layer slicing and faceting of curved surfaces, is a resolution limit rather than a file error.

Pattern and mould in sand casting

A pattern is a replica of the part around which mould material is packed to form the mould cavity. Patterns are often themselves produced from moulds or dies, for example wax patterns injected into metal dies.

In terms of boundaries, the mould walls enclose the region that the molten metal will occupy, while the pattern surfaces mark the regions into which mould material must not enter.

Pattern allowances compensate for the behaviour of the metal and the moulding process.

• Shrinkage allowance — compensates for contraction during solidification and cooling.
• Machining (finishing) allowance — extra stock left for subsequent machining.
• Draft — a taper that eases withdrawal from the sand.
• Distortion allowance — counters warping caused by uneven cooling.
• Shake allowance — the pattern is made slightly smaller because rapping it to loosen it enlarges the mould cavity.

The main mould elements have distinct functions.

• Blind riser — a reservoir of molten metal that feeds the casting during solidification.
• Chill — removes heat faster from a section, so it solidifies sooner.
• Skim bob — removes slag and other impurities from the melt surface.
• Core — forms an internal cavity in the casting.
• Insulating sleeve — slows heat loss from the riser, so it increases the riser's solidification time.
• Inoculant — acts as a nucleating agent that refines grain structure.

Arc welding heat input

Heat input per unit length of weld is H = \eta_h VI/v, where \eta_h is the heat transfer efficiency of the arc, V the voltage, I the current and v the travel speed. Multiplying by the melting efficiency \eta_m and dividing by the specific energy to melt U (in J/mm^3) gives the volume of metal melted per unit weld length, \eta_m H/U.

When filler wire of diameter d is fed at speed f, the wire supplies a volume \pi d^2 f/4 per second. Setting the filler fraction of the bead volume equal to this supply rate gives the required feed rate.

For a heat source with a circular heated area, the power absorbed is given as a cumulative fraction within concentric radii. The power absorbed in an annulus equals the difference between the cumulative powers at the outer and inner radii, and the power density is that power divided by the annular area \pi(r_2^2 - r_1^2).

Chvorinov's rule solidification time

Chvorinov's rule states t_s = B\,(V/A)^n, where V/A is the casting modulus (volume divided by cooling surface area), B depends on the mould material and the metal, and n is usually taken as 2. Castings poured under identical conditions can therefore be compared by modulus alone, and the ratio of solidification times is (M_1/M_2)^2.

Modulus values for common shapes are useful. A cube of side a has M = a/6, and a cylinder whose diameter equals its height has M = D/6. Among shapes of equal volume, a sphere has the smallest surface area and therefore the largest modulus, so it solidifies most slowly.

When the cross-section changes, the new time is t_{new} = t_{old}\,(M_{new}/M_{old})^2.

Example: a cube and a cylinder of equal volume give a modulus ratio of about 0.92, so with n = 2 the cube solidifies in about 0.92^2 \approx 0.85 of the cylinder's time.

Powder metallurgy particle size analysis

The size distribution of metal powder particles is measured by laser scattering, also called laser diffraction. The method analyses the angular intensity pattern of light scattered by the particles, and larger particles scatter light at smaller angles. The size distribution is calculated from this pattern.

Laser reflection, laser absorption and laser penetration are not measurement principles for this purpose, so the exam term to remember is laser scattering.

Resistance spot welding heat

In resistance spot welding, heat is generated by Joule heating, H = I^2 R t, where R includes the contact resistance at the faying interface. Because the interface resistance is the dominant source of heat, the nugget forms at the sheet interface.

The nugget is a cylinder of diameter d and sheet thickness t, with volume V = \pi d^2 t/4. The energy needed to melt it is the melting energy per unit volume multiplied by V.