Casting, Forming, Welding and Powder Processing

Metal forming mechanics

Metal forming changes the shape of a workpiece by plastic deformation, so the forces and power depend on the mean flow strength \bar{\sigma} of the material and on the geometry of the deformation zone. For wire drawing through a conical die, neglecting friction and redundant work, the drawing stress is \sigma_d = \bar{\sigma}\ln\frac{1}{1-r}, where r is the fractional reduction in cross-sectional area. The drawing force is F = \sigma_d A_1 with A_1 the exit area, and the drawing power is P = F\,v_1, where v_1 is the exit speed of the wire and not the entry speed. When front and back tensions act on a perfectly plastic material with no friction, the ideal relation is \sigma_f - \sigma_b = \bar{\sigma}\ln(A_0/A_1), so the achievable area ratio is set by the difference between the tensions divided by the flow stress.

In rolling, the strip is drawn into the roll gap only if friction is large enough. The bite condition is \mu \ge \tan\alpha, where \alpha is the bite angle and \cos\alpha = 1 - \Delta h/D for roll diameter D. For small angles the maximum single-pass draft is \Delta h_{max} = \mu^2 R, so the minimum exit thickness is h_f = h_0 - \Delta h_{max}. Roll speed and flow strength do not enter this limit, which depends only on friction and geometry. Without front and back tensions, the minimum friction coefficient needed to bite is \tan\alpha, and it grows with draft and falls with roll diameter. When choosing a lubricant, the coefficient of friction must reach the required threshold for the given draft and roll radius, otherwise the strip will not be drawn in. The thickness at a point located by the angle \theta measured from the line of centres is h = h_f + 2R(1-\cos\theta), which is the geometry used to locate the neutral point.

In open-die forging with no friction, the die pressure equals the flow stress Y, so the load is F = Y A_f, where A_f is the cross-sectional area at the final height. The area follows from constant volume, A_0 h_0 = A_f h_f. For extrusion, the extrusion ratio is R_e = A_0/A_f, the ratio of initial to final cross-sectional area. For round stock it equals the square of the diameter ratio, and the billet length does not change it.

Sheet-metal drawing gives characteristic defects with specific causes. Orange peel is a coarse surface texture produced by large grains that deform unevenly during stretching. Flange wrinkling results from insufficient or absent blank holding force. Tearing at the cup bottom corner is caused by a very small punch corner radius, which concentrates thinning. Earing at the cup rim is caused by planar anisotropy of the sheet. Feasibility of a draw is checked with the reduction ratio r = (D_b - d)/D_b and the thickness-to-blank-diameter ratio t/D_b. Both limits must be met, so the blank must be small enough to keep the reduction low but large enough for the sheet thickness to be adequate.

Casting and molding processes

Each casting and molding process is selected by the shape and scale of the part it can make. Continuous casting draws metal from a water-cooled mould to produce semi-finished sections of constant cross-section, such as slabs and strips. Investment (lost-wax) casting uses a wax pattern and ceramic shell to reproduce thin walls and intricate shapes. Centrifugal casting rotates the mould so that the melt is pressed against the outer wall, which suits hollow axisymmetric parts such as pipes.

In true centrifugal casting, the free inner surface of the casting is always circular and concentric with the axis of rotation, because it is the free surface of a liquid under centrifugal force. The outer surface takes the shape of the mould cavity and may be polygonal. A cross-section with a non-circular inner boundary therefore cannot be produced by this process.

In injection blow molding, a hollow preform is first formed by injection molding over a core rod. Compressed air fed through the core rod then expands the still-warm preform against the mould cavity to form a bottle, so air, not a liquid, is the blowing medium. Injection molding forces molten thermoplastic into a closed mould cavity under pressure, which makes solid, three-dimensional parts with complex shapes and good dimensional control at high production rates.

In sand casting, the sprue feeds metal into the mould. Applying Bernoulli's equation from the free surface of the pouring basin to a sprue section at atmospheric pressure gives v = \sqrt{2gh}, where h is the head above that section. For a constant volumetric flow Q = A v, the sprue area must therefore shrink toward the bottom in proportion to the velocity, so that A_{lower}/A_{upper} = v_{upper}/v_{lower}. Gauge pressure at a point in the sprue is kept at zero as the limiting case that prevents aspiration.

Arc welding power and heat

In arc welding, the power source sets the arc voltage and current. For a linear (drooping) DC source with open-circuit voltage V_{oc} and short-circuit current I_{sc}, the voltage is V = V_{oc}(1 - I/I_{sc}). The arc power VI is largest at V = V_{oc}/2 and I = I_{sc}/2, which gives P_{max} = V_{oc}I_{sc}/4.

Not all electrical power reaches the metal. Some is lost in forming the arc and some is lost from the workpiece by convection and radiation, so the effective power is the input power VI minus these losses. Losses are applied to the input power once, not compounded. For example, if a stated fraction of input power is lost during arc formation, the remaining power is reduced further by any fixed loss from the workpiece.

The heat input per unit weld length is H = \eta V I / v, where \eta is the heat transfer efficiency, V the arc voltage, I the current and v the travel speed. Two welds have equal heat input when their products of voltage, current and efficiency divided by speed are equal.

The welding speed follows from the energy balance. The energy needed to melt metal per unit volume is the specific melting energy U, so the energy per unit length of weld is UA, where A is the weld cross-section. Setting the melted power equal to UAv gives v = \eta_t \eta_m P/(UA) when the heat transfer and melting efficiencies are \eta_t and \eta_m.

Chvorinov's rule solidification time

Chvorinov's rule states that the solidification time of a casting is t = C\,(V/A)^n, where V/A is the volume-to-surface-area ratio, called the modulus, and C is the mould constant that depends on the mould material, the metal and the pouring conditions. The exponent is usually n = 2. Because the rule depends on the modulus, scaling every linear dimension by a factor k scales V/A by k and the solidification time by k^2.

The mould constant can be found from a measured solidification time. Once the volume is known, V = m/\rho, and the surface area of a cylinder of given diameter and height follows from its geometry. Then C = t/(V/A)^2 for n = 2. Be careful to use consistent units, usually min and cm.

Two castings of different shape but the same metal and mould have equal solidification time only when their moduli are equal. For a cube of side a, V/A = a/6. For a cylinder of radius r and length L, V/A = \frac{r^2 L}{2rL + 2r^2}, which simplifies for the given proportions. Equating the two moduli gives the required size ratio.

The centre-line feeding resistance in this context compares the time taken for the centre of the casting to solidify with the total solidification time measured from the start at the surface. The centre-line solidification interval is the difference between the end time and the start time at the centre, and the ratio of that interval to the total time, expressed as a percentage, gives the feeding resistance.

Polymer processing methods

Each polymer process suits a particular class of product. Extrusion forces molten polymer through a die, so it makes long parts with a uniform cross-section such as pipes and profiles. Injection molding makes complex parts with close dimensional tolerances from thermoplastics. Blow molding inflates a hollow preform to produce closed hollow shapes such as bottles. Compression molding is the common route for thermosetting components, which are pressed and cured in a heated mould.

Injection molding of polymer composites injects melt that already contains the reinforcements into a closed mould cavity, where it solidifies on cooling. Melt temperature, injection speed and screw speed are important process parameters because they govern viscosity, filling and plasticizing. Common reinforcements are particles, whiskers and short fibers. The polymer does not deform plastically as a solid; it takes the mould shape by viscous flow of a melt and then solidifies.

In extrusion, the emerging polymer swells beyond the die opening because the stretched melt recovers elastically when it leaves the die, so the section is larger than the opening. A circular opening produces a circular section. A square opening gives a swollen section with rounded corners, while a square opening with concave sides compensates for swell and relaxes to a sharp square.

Component–manufacturing process matching

Matching a component to its process requires knowing which process gives the required shape, material and volume at acceptable cost. Deep drawing is used for thin sheet metal cups and shells, such as an oil pan. Powder metallurgy is used for hard materials that are hard to cast or machine, such as cemented carbide tool inserts. Blow molding produces hollow plastic bottles. Sand casting produces complex metal shapes in low to medium volumes.

Several metal working processes are matched to products by their deformation pattern. A beverage can is formed from sheet by drawing a cup. A connecting rod is forged, because forging aligns the grain flow with the shape of the part and gives good strength. A seamless pipe is produced by hot extrusion of a billet over a mandrel. Steel balls for bearings are formed by skew rolling between inclined rolls.