Chapter 7, Processes Selection and Cost Video Solutions, Materials Selection in Mechanical Design

Problem 1

Selecting shaping processes. A process is sought to make the rocker arm shown here. It is to be made from and aluminium-silicon alloy. The shape is ' 3 -D solid'. The expected production run (batch size) is 2000 . It weight about $1 \mathrm{~kg}$. Surface roughness and tolerance are not critical because the bores and the boss will be machined to final size.

Sriparna Bhattacharjee

Numerade Educator

05:37

Problem 1

FIGURE E8.1
A tie, of length $L$ loaded in tension, is to support a load $F$, at minimum weight without failing (implying a constraint on strength) or extending elastically by more than $\delta$ (implying a constraint on stiffness, $F / \delta$ ). The table summarizes the requirements.
a. Follow the method of this chapter to establish two performance equations for the mass, one for each constraint, from which two material indices and one coupling equation linking them are derived. Show that the two indices and the coupling equation are (in order):
$$
M_{1}=\frac{\rho}{E} \text { and } M_{2}=\frac{\rho}{\sigma_{y}} \text { and }\left(\frac{\rho}{\sigma_{\gamma}}\right)=\frac{L}{\delta}\left(\frac{\rho}{E}\right)
$$
b. Use these and the material chart of Fig. E8.2, which has the indices as axes, to identify candidate materials for the tie (1) when the permitted elastic strain is $\delta$ $/ L=10^{-3}$ and (2) when $\delta / L=10^{-2}$.

Eric Mockensturm

Numerade Educator

05:34

Problem 2

A camera body is shown on the right. The design requires that it be made of a magnesium alloy and that the initial production run will be 10,000 units. You are asked to suggest processes by which the shape could be made. Surface finish and tolerance must be high. Use the matrices of Figs. $7.3,7.4$ and $7.6$ to identify potential candidates. Lay out the results in a table like that in the in-text example.
a. Proceed as follows
1. Write an expression for the material cost of the column - its mass times its cost per unit mass, $C_{m}$.
2. Express the two constraints as equations and use them to substitute for the free variable, $D$, to find the cost of the column that will just support the load without failing by either mechanism
3. Identify the material indices $M_{1}$ and $M_{2}$ that enter the two equations for the mass, showing that they are
$$
M_{1}=\left(\frac{C_{m} \rho}{\sigma_{c}}\right) \text { and } M_{2}=\left[\frac{C_{m} \rho}{E^{1 / 2}}\right]
$$
where $C_{m}$ is the material cost per kg, $\rho_{\text {the material density, }} \sigma_{c}$ its crushing strength and $E$ its modulus.
b. Data for six possible candidates for the column are listed in the table with this problem. Use these to identify candidate materials when $F=10^{5} \mathrm{~N}$ and $H=3 \mathrm{~m}$. Ceramics are admissible here, because they have high strength in compression.

Sarah Mccrumb

Numerade Educator

03:57

Problem 2

Multiple constraints: a cheap column that must not buckle or crush (Fig. E8.3). The best choice of material for a light strong column depends on its aspect ratio: the ratio of its height $H$ to its diameter $D$. This is because short, fat columns fail by crushing; tall slender columns buckle instead. Derive two performance equations for the material cost of a column of solid circular
section and specified height $H$, designed to support a load $F$ large compared to its self-load, the first using the constraints that the column must not crush, the second that it must not buckle. The table summarizes the needs.

William Affel

Numerade Educator

02:56

Problem 3

The car roof box shown in the image is to be made of glass-fibre reinforced polyester in a batch of 10,000 . It is made up of two separate shell-like components - an upper and a lower half. What processes are available to shape them? Use the matrices of Figs. $7.3,7.4$ and $7.6$ to identify potential candidates.

Ian Kaigh

Numerade Educator

02:17

Problem 3

Fig. E8.4 shows a material chart with the two indices of Exercise E8.2 as axes. Identify and plot coupling lines for selecting materials for a column with
$F=10^{6} \mathrm{~N}$ and $H=3 \mathrm{~m}$ (the same conditions as above), and for a second column with $F=10^{3} \mathrm{~N}$ and $H=20 \mathrm{~m}$.

James Kiss

Numerade Educator

01:33

Problem 4

Metal foams can be made by first making an open-cell polymer foam, then embedding this in plaster, burning out the polymer and finally forcing metal under pressure into the resulting mould to replicate the foam. If the cell walls of the polymer foam are cylindrical with a diameter of is $0.5 \mathrm{~mm}$, what pressure will be needed to replicated it using a zinc die-casting alloy? The surface tension of the zinc alloy is $0.76 \mathrm{~J} / \mathrm{m}^{2}$.

Narayan Hari

Numerade Educator

00:48

Problem 4

Approximate values for exchange constants (1). In the US a typical family car covers 120,000 miles over its life and delivers, on average 25 miles per US gallon ( $6.6$ miles per litre). Petrol in the US costs $\$ 0.63$ per litre, so the life cost for fuel is $\$ 11,455$. The typical family car, when loaded, weighs $2315 \mathrm{~kg}$. If the petrol consumption is directly proportional to the weight, what is the value of reducing the weight of the car by $1 \mathrm{~kg}$ (Fig. E8.5)?

Aadit Sharma

Numerade Educator

06:14

Problem 5

Approximate values for exchange constants (2). The makers of the car shown in Fig. $8.5$ plan to market it in Europe. If the car covers 120,000 miles $(193,000 \mathrm{~km})$ over its life and consumes on average $9.5$ litres per $100 \mathrm{~km}$. Petrol in the Europe costs $€ 1.3$ per litre ( $\$ 1.5$ per litre), so the life cost for fuel is $\$ 27,500$. The car, when loaded, weighs $2315 \mathrm{~kg}$. If the petrol consumption is directly proportional to the weight, what is the value of reducing the weight of the car by $1 \mathrm{~kg}$ ?

Trinity Steen

Numerade Educator

01:03

Problem 5

A copper ingot is compressed between two anvils. If the yield strength $\sigma_{y}$ of copper is $80 \mathrm{MPa}$ and the coefficient of friction $\mu$ at the interface between the copper and the anvil is $0.1$, what is the maximum forming pressure at the centre of the ingot when the aspect ratio $2 w / h$ is $20: 1$ ?

Narayan Hari

Numerade Educator

01:37

Problem 6

A cylindrical magnet is to be made from Alnico (an iron-aluminium-nickelcobalt alloy) by powder compaction and sintering. The aspect ratio of the cylinder, $h / 2 r$, is 2 . The coefficient of friction $\mu$ of the powder with the die wall, if unlubricated, is $0.5$. By what factor will the compaction pressure have fallen at the mid plane of the cylinder because of die wall friction? If, instead, a lubricant is mixed with the powder (it will burn out during sintering), which reduces the coefficient of friction to $0.05$, by how much will the compaction pressure have fallen at the mid plane?

Kratika Bhadauria

Numerade Educator

04:07

Problem 7

Elevator control quadrant. The quadrant sketched here is part of the control system for the wing-elevator of a commercial aircraft. It is to be made of a light alloy (aluminium or magnesium) with the shape shown in the figure. It weighs about $5 \mathrm{~kg}$. The minimum section thickness is $5 \mathrm{~mm}$, and -apart from the bearing surfaces - the requirements on surface finish and precision are not strict: surface
finish $\leq 10 \mu \mathrm{m}$ and precision $\leq 0.5 \mathrm{~mm}$. The bearing surfaces require a surface finish $\leq 1 \mu \mathrm{m}$ and a precision $\leq 0.05 \mathrm{~mm}$. A production run of 100 is planned.

Averell Hause

Carnegie Mellon University

04:42

Problem 8

Casing for an electric plug. The electric plug is perhaps the commonest of electrical products. It has a number of components: the casing, the pins, connectors, a cable clamp, fasteners, and, in some plugs, a fuse. The task is to investigate processes for shaping the two-part insulating casing, which, for safety reasons, is to be made of a thermosetting plastic. Each part weighs about 30 grams and is to be made in one step from with a planned batch size of $2 \times 10^{6}$. The required tolerance of $0.3 \mathrm{~mm}$ and surface roughness of $1 \mu \mathrm{m}$ must be achieved without using secondary operations.

Khoobchandra Agrawal

Numerade Educator

00:31

Problem 9

Ceramic valves for taps. Few things are more irritating than a dripping tap. Taps drip because the rubber washer is worn or the brass seat is pitted by corrosion, or both. Ceramics have good wear resistance, and they have excellent corrosion resistance in both pure and salt water. Many household taps now use ceramic valves.
The sketch shows how they work. A ceramic valve consists of two disks mounted one above the other, spring-loaded so that their faces are in contact. Each disk has a diameter of $20 \mathrm{~mm}$, a thickness of $3 \mathrm{~mm}$ and weighs about 10 grams. In order to seal well, the mating surfaces of the two disks must be flat and smooth, requiring high levels of precision and surface finish; typically tolerance $<0.02 \mathrm{~mm}$ and surface roughness $<0.1 \mu \mathrm{m}$. The outer face of each has a slot that registers it and allows the upper disc to be rotated through $90^{\circ}(1 / 4$ turn). In the 'off' position the holes in the upper disc are blanked off by the solid part of the lower one; in the 'on' position the holes are aligned. A production run of $10^{5}-10^{6}$ is envisaged. The task is to select a process to make the ceramic disks.
a. List the function and constraints, leave the objective blank and enter 'Choice of process' for the free variable.
b. Use the charts of Figs. $7.3,7.4$ and $7.6$ to identify processes to shape the casing.

Mayukh Banik

Numerade Educator

02:12

Problem 10

Shaping plastic bottles. Polyethylene bottles are used to contain fluids as various as milk and engine oil. A typical polyethylene bottle weighs about 30 grams and has a wall thickness of about $0.8 \mathrm{~mm}$. The shape is 3 -D hollow. The batch size is large $(1,000,000$ bottles). What process could be used to make them?
a. List the function and constraints, leave the objective blank and enter 'Choice of process' for the free variable.
b. Use the charts of Figs. $7.3,7.4$ and $7.6$ to identify processes to shape the casing.

Rabia Bibi

Numerade Educator

00:34

Problem 11

Car hood (bonnet). As weight-saving assumes greater importance in automobile design, the replacement of steel parts with polymer-composite substitutes becomes increasingly attractive. Weight can be saved by replacing a steel hood with one made from a thermosetting composites. The weight of the hood depends on the car model: a typical composite hood weighs is $8-10 \mathrm{~kg}$. The shape is a dished-sheet and the requirements on tolerance and roughness are $1 \mathrm{~mm}$ and $2 \mu \mathrm{m}$, respectively. A production run of 100,000 is envisaged.
FIGURE E7.11
a. List the function and constraints, leave the objective blank and enter 'Choice of process' for the free variable.
b. Use the charts of Figs. $7.3,7.4$ and $7.6$ to identify processes to shape the casing.

Ly Tran

Numerade Educator

01:00

Problem 12

Selecting joining processes. This exercise and the next require the use of the CES EduPack Materials Selection software.
a. Use CES to select a joining process to meet the following requirements.
b. Use CES to select a joining process to meet the following requirements.

James Kiss

Numerade Educator

06:40

Problem 13

Selecting surface-treatment processes. This exercise, like the last, requires the use of the CES EduPack Materials Selection software.
a. Use CES to select a surface-treatment process to meet the following requirements.

Khaled Yasein

Numerade Educator

01:05

Problem 14

Cost. A method is sought to mould the wide-necked containers show in the image. It suggested that they might be blow-moulded, injection moulded or rotation moulded. The table lists approximate values for the parameters that enter the cost model. Use these to assess the cheapest process choice.

Carson Merrill

Numerade Educator