ME F241/MF F 241

Machine Design and Drawing

BITS Pilani Gaurav Watts

gaurav.watts@pilani.bits-pilani.ac.in
Pilani|Dubai|Goa|Hyderabad
 BITS Pilani
Pilani|Dubai|Goa|Hyderabad

Lecture 2
Introduction
 Example 1–2

Solution

Answer

Answer

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 Dimensions and Tolerances

 Nominal size – The size we use in speaking of an element.

◦ Is not required to match the actual dimension
 Limits – The stated maximum and minimum dimensions
 Tolerance – The difference between the two limits
 Bilateral tolerance – The variation in both directions from the
basic dimension, e.g. 1.005 ± 0.002 in.
 Unilateral tolerance – The basic dimension is taken as one of
the limits, and variation is permitted in only one direction, e.g.

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 Dimensions and Tolerances
 Clearance – Refers to the difference in sizes of two mating cylindrical
parts such as a bolt and a hole.
◦ Assumes the internal member is smaller than the external member
◦ Diametral clearance – difference in the two diameters
◦ Radial clearance – difference in the two radii
 Interference – The opposite of clearance, when the internal member is
larger than the external member
 Allowance – The minimum stated clearance or the maximum stated
interference or mating parts
 Fit – The amount of clearance or interference between mating parts
 GD&T – Geometric Dimensioning and Tolerancing, a comprehensive
system of symbols, rules, and definitions for defining the theoretically
perfect geometry, along with the allowable variation.

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 Choice of Tolerances

 The designer is responsible for specifying tolerances for every

dimension.
 Consideration is given to functionality, fit, assembly,
manufacturing process ability, quality control, and cost.
 Excessive precision is a poor design choice, in that it limits
manufacturing options and drives up the cost.
 Less expensive manufacturing options should be selected, even
though the part may be less than perfect, so long as the needs are
satisfactorily met.

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 Choice of Dimensions

 Dimensioning a part is the designer’s responsibility.

 Include just enough dimensions
 Avoid extraneous information that can lead to confusion or
multiple interpretations.
 Example of over-specified dimensions. With +/– 1 tolerances,
two dimensions are incompatible.

Fig. 1–8 Shigley’s Mechanical Engineering Design

 Choice of Dimensions

 Four examples of which dimensions to specify

Fig. 1–9
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 Tolerance Stack-up

 The cumulative effect of individual tolerances must be allowed to

accumulate somewhere. This is known as tolerance stack-up.
 Chain dimensioning allows large stack-up of many small
tolerances in series.

 Baseline dimensioning minimizes large tolerance stack-up.

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 BITS Pilani
Pilani|Dubai|Goa|Hyderabad

Material Selection in Design

Factors/Criteria in Material Selection

– Function
– Mechanical Properties
– Failure Modes
– Manufacturability
– Cost
– Environmental Considerations

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Material ↔ Design

Properties of a newly discovered material can

suggest new product
eg: Transistor: High-purity silicon

Need for a new product can demand the

development of a new material
eg: Space Technology: Lightweight Composites
Important classes of materials (6)

– Metals  Ceramics
– Polymers  Glasses
– Elastomers  Composites

A good design exploits and brings out the

true potential of materials selected.
Key MaterialProperties for Design

• General: • Thermal
– Cost – Thermal Conductivity
– Density – Thermal Diffusivity
• Mechanical – Specific Heat
– Melting Point
– Elastic Modulus
– Glass Temperature
– Strength
– Thermal Expansion Coefficient
– Toughness
– Thermal Shock Resistance
– Fracture Toughness
– Creep Resistance
– Damping Capacity
– Fatigue Endurance Limit • Corrosion/Oxidation
• Wear – Corrosion Rate
– Archard Wear Constant – Parabolic Rate Constant
 Material Types

• Metals • Ceramics/Glasses
– High Moduli – High Moduli, Hard,
– Can undergo Abrasion/Corrosion
• Alloying, Heat Treatment
resistant
– Cutting Tools
– Formed by Deformation – Retain Strength at
– Ductile High Temperature
• Yields before fracture
– Brittle
– Prey to Fatigue, – Prey to high contact
Corrosion stresses, low
tolerance for cracks
M S Dasgupta, BITS Pilani 6
 Material Types

 Polymers and Elastomers  Composites

 Low Moduli, High Strength  High Moduli, Strength,

» High Elastic Deflection Lightweight
• Snap fits  Can be Tough
 Corrosion Resistant  Optimal performance
 Easy to Shape at room temperature
 Minimize Finishing  Expensive
Operations  Difficult to Form/Join
 Temperature Dependent
Properties
Material Families and Classes (Table 2-4)

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Material Families and Classes (Table 2-4)

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Material Families and Classes (Table 2-4)

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Material Families and Classes (Table 2-4)

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 Standard Tensile Test

Fig. 2–1

 Used to obtain material characteristics and strengths

 Loaded in tension with slowly increasing P
 Load and deflection are recorded

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 Stress and Strain
The stress is calculated from

where is the original cross-sectional area.

The normalstrain is calculated from

where l0 is the original gauge length and l is the current length

corresponding to the current P.

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 Stress-Strain Diagram

 Plot stress vs. normal strain

 Typically linear relation until
the proportional limit, pl
 No permanent deformation Ductile material
until the elastic limit, el
 Yield strength, Sy , defined at
point where significant
plastic deformation begins, or
where permanent set reaches
a fixed amount, usually 0.2%
of the original gauge length
 Ultimate strength, Su , Brittle material
defined as the maximum
stress on the diagram
Fig. 2–2 Shigley’s Mechanical Engineering Design
 Elastic Relationship of Stress and Strain

 Slope of linear section is

Young’s Modulus, or
modulus of elasticity, E
 Hooke’s law

 E is relatively constant for a

given type of material (e.g.
steel, copper, aluminum)
 See Table A-5 for typical Fig. 2–2 (a)
values
 Usually independent of heat
treatment, carbon content, or
alloying

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 True Stress-Strain Diagram
 Engineering stress-strain diagrams
(commonly used) are based on
original area.
 Area typically reduces under load, Engineering
particularly during “necking” after stress-strain
point u.

 True stress is based on actual area

corresponding to current P.
 True strain is the sum of the
incremental elongations divided by
the current gauge length at load P.
True Stress-strain
(2-4)
 Note that true stress continually
increases all the way to fracture.
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 Compression Strength

 Compression tests are used to obtain compressive strengths.

 Buckling and bulging can be problematic.
 For ductile materials, compressive strengths are usually about
the same as tensile strengths, Suc = Sut .
 For brittle materials, compressive strengths, Suc , are often
greater than tensile strengths, Sut .

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 Torsional Strengths
 Torsional strengths are found by twisting solid circular bars.
 Results are plotted as a torque-twist diagram.
 Shear stresses in the specimen are linear with respect to the radial
location – zero at the center and maximum at the outer radius.
 Maximum shear stress is related to the angle of twist by

◦ q is the angle of twist (in radians)

◦ r is the radius of the bar
◦ l0 is the gauge length
◦ G is the material stiffness property called the shear modulus or
modulus of rigidity.

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 Torsional Strengths

 Maximum shear stress is related to the applied torque by

◦ J is the polar second moment of area of the cross section

◦ For round cross section,
 Torsional yield strength, Ssy corresponds to the maximum shear
stress at the point where the torque-twist diagram becomes
significantly non-linear
 Modulus of rupture, Ssu corresponds to the torque Tu at the
maximum point on the torque-twist diagram

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 Resilience
 Resilience – Capacity of a
material to absorb energy within
its elastic range
 Modulus of resilience, uR
◦ Energy absorbed per unit
volume without permanent
deformation
◦ Equals the area under the stress-
strain curve up to the elastic
limit
◦ Elastic limit often approximated
by yield point

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 Resilience
 Area under curve to yield point gives approximation

 If elastic region is linear,

 For two materials with the same yield strength, the less stiff
material (lower E) has greater resilience
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 Toughness

 Toughness – capacity of a material to

absorb energy without fracture
 Modulus of toughness, uT
◦ Energy absorbed per unit volume
without fracture
◦ Equals area under the stress-strain
curve up to the fracture point

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 Toughness

 Area under curve up to fracture point

 Often estimated graphically from stress-strain data

 Approximated by using the average of yield and ultimate
strengths and the strain at fracture

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 Resilience and Toughness

 Measures of energy absorbing characteristics of a material

 Units are energy per unit volume
◦ lbf·in/in3 or J/m3
 Assumes low strain rates
 For higher strain rates, use impact methods

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 Statistical Significance of Material Properties

 Strength values are obtained from testing many nominally

identical specimens
 Strength, a material property, is distributional and thus statistical
in nature
 Example – Histographic report for maximum stress of 1000
tensile tests on 1020 steel

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 Example for Statistical Material Property
 Histographic report for maximum stress of 1000 tensile tests on
1020 steel

 Probability density – number of occurrences divided by the total

sample number
 Histogram of probability density for 1020 steel

Fig. 2–5
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 Strengths from Tables

 Property tables often only report a single value for a strength

term
 Important to check if it is mean, minimum, or some percentile
 Common to use 99% minimum strength, indicating 99% of the
samples exceed the reported value

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 Hot-working Processes

 Process in which metal is formed while heated above

recrystallization temperature
 Refined grain size
 Rough surface finish
 Rolling, forging, extrusion, pressing
 Common bar cross-sections from hot-rolling

Fig. 2–11

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 Cold Work
 Cold work – Process of plastic
straining below recrystallization
temperature in the plastic region of
the stress-strain diagram
 Loading to point i beyond the yield
point, then unloading, causes
permanent plastic deformation, ϵp

Reloading to point i behaves
elastically all the way to i, with
additional elastic strain ϵe
Fig. 2–6 (a)

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 Cold Work
 The yield point is effectively
increased to point i
 Material is said to have been cold
worked, or strain hardened
 Material is less ductile (more brittle)
since the plastic zone between yield
strength and ultimate strength is
reduced
 Repeated strain hardening can lead to
brittle failure Fig. 2–6 (a)

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 Reduction in Area

 Plot load P vs. Area Reduction

 Reduction in area corresponding to
load Pf at fracture is

(2-12)

 R is a measure of ductility
 Ductility represents the ability of a
material to absorb overloads and to
be cold-worked
Fig. 2–6 (b)

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 Cold-work Factor

 Cold-work factor W – A measure of

the quantity of cold work

Fig. 2–6 (b) Shigley’s Mechanical Engineering Design

Equations for Cold-worked Strengths

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 Example 2–2

Solution

15% cold workingfactor

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Example 2–2 (Continued)

Answer

Answer

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 Cold-working Processes

 Forming of metal without elevating

temperature
 Strain hardens, resulting in increase
in yield strength
 Increases hardness and ultimate
strength, decreases ductility
 Produces bright, smooth, reasonably
accurate finish
 Cold-rolling used to produce wide
flats and sheets Fig. 2–12
 Cold-drawing draws a hot-rolled bar
through a smaller die

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 Hardness

 Hardness – The resistance of a material to penetration by a

pointed tool
 Two most common hardness-measuring systems
◦ Rockwell
 A, B, and C scales
 Specified indenters and loads for each scale
 Hardness numbers are relative
◦ Brinell
 Hardness number HB is the applied load divided by the
spherical surface area of the indentation

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 Strength and Hardness

 For many materials, relationship between ultimate strength and

Brinell hardness number is roughly linear
 For steels

 For cast iron

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 Example 2–3

Solution

Answer

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 Impact Properties

 Charpy notched-bar test used to determine brittleness and

impact strength
 Specimen struck by pendulum
 Energy absorbed, called impact value, is computed from height
of swing after fracture

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 Effect of Temperature on Impact

 Some materials experience a sharp transition from ductile to

brittle at a certain temperature

Fig. 2–7

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 Effect of Strain Rate on Impact

 Average strain rate for

stress-strain diagram is
0.001 in/(in·s)
 Increasing strain rate
increases strengths
 Due to yield strength
approaching ultimate
strength, a mild steel
could be expected to
behave elastically
through practically its
entire strength range Fig. 2–8
under impact conditions

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 Composite Materials

 Formed from two or more dissimilar materials, each of which

contributes to the final properties
 Materials remain distinct from each other at the macroscopic
level
 Usually amorphous and non-isotropic
 Often consists of laminates of filler to provide stiffness and
strength and a matrix to hold the material together
 Common filler types:

Fig. 2–14 Shigley’s Mechanical Engineering Design

Young’s Modulus for Various Materials

Fig. 2–15
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Young’s Modulus vs. Density

Fig. 2–16 Shigley’s Mechanical Engineering Design

 Specific Modulus

 Specific Modulus – ratio of

Young’s modulus to density,
E/
 Also called specific stiffness
 Useful to minimize weight
with primary design
limitation of deflection,
stiffness, or natural
frequency
Fig. 2–16
 Parallel lines representing
different values of E / 
allow comparison of
specific modulus between
materials
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 Minimum Mass Guidelines for
Young’s Modulus -Density Plot
 Guidelines plot
constant values of
E  /
  depends on type
of loading
  = 1 for axial
  = 1/2 for
bending

Example, for axial loading, Fig. 2–16

k = AE/l  A = kl/E
m = Al = (kl/E) l =kl2  /E
Thus, to minimize mass, maximize E/ ( = 1)
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 The Performance Metric

The performance metric depends on (1) the

functional requirements, (2) the geometry, and (3)
the material properties.

The function is often separable,

f3 (M) is called the material efficiency coefficient.

Maximizing or minimizing f3 (M) allows the material

choice to be used to optimize P.
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 Performance Metric Example

 Requirements: light, stiff, end-loaded cantilever beam with

circular cross section
 Mass m of the beam is chosen as the performance metric to
minimize
 Stiffness is functional requirement
 Stiffness is related to material and geometry

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 Performance Metric Example
Fl 3
From beam deflection table,  
3EI

Sub Eq. (2-26) into Eq. (2-25) and solve for A

The performance metric is

Sub Eq. (2-27) into Eq. (2-28),

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 Performance Metric Example

Separating into the form of Eq. (2-24),

To minimize m, need to minimize f3 (M), or maximize

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 Performance Metric Example

 M is called material
index
 For this example,  = ½
 Use guidelines parallel
to E1/2/
 Increasing M, move up
and to the left
 Good candidates for this
example are
woods, composites, and
ceramics
Fig. 2–17

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 Performance Metric Example

 Additional constraints
can be added as needed
 For example, if it is
desired that E > 50 GPa,
add horizontal line to
limit the solution space
 Wood is eliminated as a
viable option

Fig. 2–18

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 Strength vs. Density

Fig. 2–19 Shigley’s Mechanical Engineering Design

 Specific Modulus

 Specific Strength – ratio of

strength to density, S / 
 Useful to minimize weight
with primary design
limitation of strength
 Parallel lines representing
different values of S / 
allow comparison of
specific strength between
materials
Fig. 2–19

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 Minimum Mass Guidelines for
Strength-Density Plot
 Guidelines plot
constant values of
S / 
  depends on type of
loading
  = 1 for axial
  = 2/3 for bending

Example, for axial loading, Fig. 2–19

 = F/A = S  A = F/S
m = Al = (F/S) l
Thus, to minimize m, maximize S/ ( = 1)

Shigley’s Mechanical Engineering Design