Manufacturing Processes: Exam 2

Ch 8-12, including quizzes, exam study guide, and ch 10 lecture overview

Cutting Ratio ($r$)

In orthogonal machining, the ratio of the undeformed chip thickness ($t_o$) to the cut chip thickness ($t_c$), expressed as $r = \frac{t_o}{t_c}$.

Shear Angle ($\phi$)

The angle defining the orientation of the shear plane relative to the workpiece surface in orthogonal cutting, related to rake angle ($\alpha$) and cutting ratio ($r$) by $\tan(\phi) = \frac{r\cos(\alpha)}{1 - r\sin(\alpha)}$.

Merchant's Relation

An analytical relationship in orthogonal metal cutting predicting the shear angle via $\phi = 45^\circ + \frac{\alpha}{2} - \frac{\beta}{2}$, where $\alpha$ is the rake angle and $\beta$ is the friction angle; it typically over-predicts experimental shear angles by approximately $10^\circ$.

Taylor's Tool Life Equation

The fundamental empirical relationship $V T^n = C$ relating cutting speed ($V$) to tool life ($T$), where $n$ is the tool life exponent and $C$ is the cutting speed yielding a tool life of 1 minute.

High-Speed Steel Tool Life Exponent ($n$)

The empirical exponent in Taylor's equation for high-speed steel (HSS) tools, characterized by low values ranging between $0.08$ and $0.2$, causing tool life to decrease substantially with even modest increases in cutting speed.

Approach Length ($l_c$)

The additional travel distance required for a milling cutter of diameter $D$ to reach full engagement depth $d$ in slab milling, defined as $l_c = \sqrt{D \cdot d}$.

Surface Finish vs. Machining Cost Curve

A curve showing that manufacturing cost increases steeply once surface roughness specifications fall below approximately $R_a = 6.3\,\mu\text{m}$ ($250\,\mu\text{in.}$), requiring supplementary operations like finish turning, grinding, and honing.

Specific Grinding Energy ($u$)

The energy consumed per unit volume of material removed during abrasive grinding (e.g., $14\text{--}68\,\text{W}\cdot\text{s/mm}^3$ for low-carbon steel), which is significantly higher than in conventional turning or milling due to small chip sizes and high negative rake angles of abrasive grains.

Kerf Width ($b$) in Wire EDM

The total channel width cut by electrical discharge wire machining, equal to the wire diameter ($d_{wire}$) plus twice the spark gap ($b = d_{wire} + 2 \cdot \text{gap}$).

Degree of Polymerization (DP)

The number of repeating constitutional monomer units (mers) comprising a polymer chain, computed as $\text{DP} = \frac{\text{molecular weight}}{\text{mer weight}}$.

Polymer Stress Relaxation

The time-dependent reduction in mechanical stress under constant strain described by $\sigma(t) = \sigma_o e^{-t/\lambda}$, caused by viscous sliding of polymer chains past one another and responsible for clamping force loss in gaskets and snap fits.

Rule of Mixtures (Longitudinal Composite Modulus)

An analytical formulation predicting the elastic modulus of a unidirectional composite along the fiber direction as a volume-weighted average: $E_c = x E_f + (1 - x) E_m$.

Extruder Operating Point

The steady-state flow rate and head pressure established at the intersection of the linear extruder pumping characteristic curve ($Q = Q_d - \frac{\pi D H^3 \sin^2(\theta)}{12 \eta l} p$) and the die characteristic curve ($Q = K p$).

Cure Depth ($C_d$)

The depth of photopolymerization achieved during stereolithography (SLA) as given by the Beer-Lambert formulation $C_d = D_p \ln\left(\frac{E_o}{E_c}\right)$, which must exceed the layer thickness to ensure interlayer adhesion.

Powder Compaction Pressure Decay

The exponential attenuation of compaction pressure with depth ($x$) within a single-action powder pressing die caused by wall friction, given by $p_x = p_o e^{-4\mu k x / D}$.

Green Density ($\rho_{green}$)

The bulk density of an unsintered powder compact, which is related to the final sintered density and volumetric sintering shrinkage by $\rho_{green} = \rho_{sintered}\left(1 - \frac{\Delta L}{L_o}\right)^3$.

Sintering Neck Growth Mechanisms

The particle bonding mechanisms during sintering: solid-state diffusion (which draws particle centers together, causing volumetric shrinkage) versus liquid-phase material transport (which bridges particles without center distance shrinkage).

Feedstock Separation in MIM

A metal injection molding defect occurring at abrupt transitions or sharp section changes where binder and powder separate, leaving binder-rich zones that warp or distort during debinding and sintering.

Ceramic Porosity Degradation

The empirical decrease in ceramic strength and stiffness as volume fraction porosity ($P$) increases, described by $\text{UTS} = \text{UTS}_o e^{-n P}$ and $E = E_o(1 - 1.9P + 0.9P^2)$.

Interparticle Water vs. Pore Water

In ceramic drying, interparticle water separates the clay platelets and causes dimensional shrinkage upon removal; once particles contact, the remaining pore water evaporates without causing additional shrinkage.

Heat Input per Unit Length ($H/l$)

The thermal energy transferred to a welded workpiece per unit linear travel, defined as $\frac{H}{l} = \frac{e V I}{v}$, which balances the melting energy requirement ($u A$) of the bead cross section.

Resistance Spot Welding Nugget

The molten and solidified lenticular weld nugget joining overlapping sheet metals, formed between water-cooled copper electrodes by resistive Joule dissipation ($H = I^2 R t$) under clamping pressure.

Brazing Clearance Effect

The dependency of joint shear and tensile strength on joint gap, where an optimum gap between $0.025\,\text{mm}$ and $0.2\,\text{mm}$ promotes capillary draw, while excessive clearance markedly diminishes joint strength.

Inertia Friction Welding Cycle

A solid-state joining cycle where flywheel rotational kinetic energy ($E = \frac{I S^2}{C}$) supplies frictional heat between rotating and stationary interfaces, followed by an upset force step that creates plastic deformation and flash without bulk melting.

Fusion Weld Defects

Geometric and metallurgical flaws in fusion welded joints, including cracks, underfill, inclusions, undercut, overlap, porosity, and lack of penetration.

Incomplete Penetration

A fusion weld defect characterized by the weld bead failing to reach the root or penetrate the full joint thickness, typically caused by insufficient heat input per unit length relative to the required melting energy.

Weld Porosity

Gas-induced voids and spherical cavities trapped in solidified weld beads, caused by moisture, oil, contaminated flux, or hydrogen gas evolution during cooling.

True or False: Increasing the cutting speed tends to reduce or eliminate the built-up edge (BUE).

True

True or False: Crater wear occurs on the flank face of the tool, and flank wear occurs on the rake face.

False

Which of the following help reduce or eliminate a built-up edge?

Increasing the cutting speed

Increasing the rake angle

Using an effective cutting fluid

The Taylor tool-life equation, VTⁿ = C, describes the relationship between:

Cutting speed and tool life

True or False: Ultrasonic machining is a good choice for soft, ductile metals such as copper and aluminum.

False

Fig. 9.43 shows machining cost versus required surface finish. Why does over-specifying the surface finish on a drawing raise cost so much?

Finer finishes need extra operations such as grinding and honing, so cost jumps in steps rather than rising smoothly.

Wire EDM cuts a 20 mm thick copper plate at a wire feed rate of 0.015 m/s with a 0.4 mm kerf. Copper density is 8970 kg/m³ and the latent heat of fusion is 2.05×10⁵ J/kg. What power is needed to melt the removed material?

About 221 W

Why is diamond a poor abrasive for grinding steel, and what should be used instead?

Carbon from the diamond dissolves into the iron at grinding temperatures, so the grains wear quickly; use cBN or aluminum oxide instead.

Below its glass-transition temperature (Tg), an amorphous polymer is:

Hard, rigid and glassy (brittle)

Why can’t a thermoset be remelted and reshaped once it has cured?

Its chains are cross-linked into a rigid 3-D network

As the degree of polymerization (molecular weight) increases:

Strength and melt viscosity both increase

Vulcanization of rubber mainly involves:

Cross-linking the polymer chains, usually with sulfur

Which additive manufacturing process uses a UV laser to cure liquid photopolymer layer by layer?

Stereolithography (SLA)

What is the correct order of the basic steps in powder metallurgy (PM)?

Powder production → blending → compaction → sintering → finishing

Sintering temperatures for metal powders are usually within what range of the metal’s melting point?

70–90%

Which of the following is NOT a typical characteristic of ceramics?

High ductility and toughness

In thermal (physical) tempering of glass, the surfaces are cooled quickly while the bulk is still hot. Once the whole piece has cooled, what is the residual stress state?

Compression on the surfaces, tension in the interior

Which of the following are all continuous glass-processing methods?

Floating, drawing, and rolling

`"What is a mer?"

"The repeating chemical unit that makes up a polymer chain (poly = many

"What is the mer of polyethylene?"

"Two carbons and four hydrogens (C2H4)."

"What polymer results from replacing one hydrogen in polyethylene with chlorine?"

"PVC (polyvinyl chloride)."

"Why is PTFE (Teflon) non-stick?"

"All hydrogens are replaced by fluorine. Fluorine's high electron affinity gives PTFE its non-stick behavior."

"How does molecular weight affect polymer properties?"

"Longer chains increase entanglement

"What is the degree of polymerization (DP)?"

"DP = average molecular weight / molecular weight of one mer."

"What is a thermoplastic?"

"A polymer that can be melted and reprocessed."

"What is a thermoset?"

"A polymer that is permanently cross-linked and cannot be remelted."

"What is an elastomer?"

"A cross-linked polymer with highly elastic behavior

"How does branching affect crystallization?"

"Branching introduces disorder and disrupts crystallization."

"How does cross-linking affect a polymer?"

"Covalent bonds between chains prevent flow and produce elastic behavior."

"What is vulcanization?"

"Cross-linking of rubber. A vulcanized tire can be thought of as one giant molecule."

"What is the glass transition temperature (Tg)?"

"Below Tg

"What is the melting temperature (Tm)?"

"The melting point of a crystalline polymer."

"What happens to crystallinity when a polymer cools slowly vs. rapidly?"

"Slow cooling allows crystallization (lower specific volume). Rapid cooling retains an amorphous

"How does crystallinity affect properties?"

"It increases density and mechanical strength. Amorphous polymers are easier to process but generally weaker."

"How do polymers compare to metals?"

"Polymers have low density

"Polyethylene and PTFE are used above Tg. What does that mean at room temperature?"

"They feel soft and flexible at room temperature."

"Nylon is used below Tg. What does that mean at room temperature?"

"It feels stiff at room temperature."

"What is the Maxwell model?"

"A spring and dashpot in series. It describes time-dependent (viscoelastic) deformation."

"What is the Voigt model?"

"A spring and dashpot in parallel. It describes time-dependent (viscoelastic) deformation."

"How does polymer melt viscosity change with temperature and shear rate?"

"Viscosity decreases as temperature and shear rate increase. Most polymers are pseudo-plastic (power-law) fluids. Caramel and toffee show the same behavior."

"What is a composite material?"

"A polymer matrix combined with a reinforcing phase to achieve properties that neither constituent has alone."

"What makes up about 80% of composite matrices?"

"Epoxy."

"What are the common reinforcing fibers?"

"E-glass (low cost

"What are specific strength and specific stiffness?"

"Specific strength = strength / density. Specific stiffness = modulus / density. They are the key metrics for comparing materials."

"How do continuous and short fibers compare?"

"Continuous fibers perform better because short fibers lose load transfer at their ends. Short fibers are cheaper to produce and process."

"What does a strong fiber-matrix bond cause?"

"It transfers fracture across the interface

"Why does a weak fiber-matrix bond improve toughness?"

"It allows crack deflection along the interface and fiber pullout

"Where is the strength of a unidirectional composite highest?"

"Along the fiber axis."

"What are the properties of random short-fiber composites?"

"Near-isotropic

"What is a honeycomb sandwich composite?"

"A core (aluminum or polymer) between face sheets. It has high stiffness-to-weight ratio and is used in aircraft and sporting equipment."

"What is extrusion?"

"A rotating screw in a heated barrel melts polymer and pushes it through a die to make continuous profiles such as sheets

"What is a coat hanger die used for?"

"Flat sheets."

"What is a spider die used for?"

"Tubes and pipes."

"What is blown film extrusion?"

"A molten polymer tube is inflated vertically to make thin film

"What is injection molding?"

"Molten polymer is forced into a closed mold under high clamping force. It suits high-volume

"What is a hot runner system?"

"It keeps the material molten between shots

"What is insert injection molding?"

"Polymer is molded around pre-placed inserts

"What is blow molding?"

"A molten parison is inflated inside a mold to form hollow parts such as bottles."

"How do extrusion blow molding and injection blow molding differ?"

"Extrusion blow molding leaves a pinch-off line at the base. Injection blow molding gives cleaner parisons and is used for high-precision bottles."

"What is thermoforming?"

"Thermoplastic sheet is heated near Tg and formed over a mold using vacuum

"What is rotational molding (roto molding)?"

"Polymer powder is heated in a mold that rotates biaxially to coat the interior. It makes large hollow parts. It is slower but less capital-intensive than injection molding."

"Which processes are used for thermoset parts?"

"Compression molding and reaction injection molding (RIM)

"What is pultrusion?"

"Continuous fibers are pulled through resin to make constant cross-section profiles such as ladder rails and golf shafts."

"What is filament winding used for?"

"Making pressure vessels."

"What are the main additive manufacturing processes?"

"SLA

"How is material removal rate (MRR) calculated in surface grinding?"

"MRR = depth of cut x width of cut x workpiece speed (speed in mm/s). Example: 0.05 x 25 x 1500 = 1

"How is grinding power calculated?"

"P = specific energy x MRR. Example: 41 J/mm^3 x 1

"How does grinding normal force compare to cutting force?"

"FN is about 1.3 x Fc. Blunt abrasive grains make the normal force about 30% greater."

"What units must angular speed use in torque calculations?"

"Radians per second. T = P / omega."

"What is the rule of mixtures for composite modulus?"

"Ec = Vf x Ef + Vm x Em. Example: 0.3 x 73 + 0.7 x 3.5 = 24.35 GPa."

"Polycarbonate example: how sensitive is melt viscosity to temperature?"

"In the worked example

"Polystyrene example: what is the degree of polymerization?"

"Average molecular weight 2