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Notes on Lesson

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Notes on Lesson Faculty Name: V. KIRAN KUMAR Code: AU28 Subject Name: DESIGN OF MACHINE ELEMENTS Code: ME2303 Year: III Semester: V Degree & Branch: B.E. AUTOMOBILE – PowerPoint PPT presentation

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Title: Notes on Lesson


1
Notes on Lesson
Faculty Name V. KIRAN KUMAR Code AU28
Subject Name DESIGN OF MACHINE ELEMENTS Code ME2303
Year III Semester V
Degree Branch B.E. AUTOMOBILE Section -
2
Failure Theories
  • Stress in machine components should be accurately
    computed.
  • Designer must understand material limits to
    ensure a safe design.

3
Design Factor
  • Factor of Safety (N)
  • Suitable values depend on inherent danger,
    certainty of calculations, certainty of material
    properties, etc.

4
Static Stresses - Brittle Materials
  • Percent elongation lt 5
  • for parts in tension
  • for parts in compression
  • for parts with general stress

5
Example
  • The Gray Cast Iron (Grade 40) cylinder carries an
    axial compressive load of 75,000 lbs and a torque
    of 20,000 in lbs. Compute the resulting design
    factor.

6
Static Stresses - Ductile Materials
  • Percent elongation gt 5
  • Distortion Energy Theory
  • Define von Mises Stress
  • For nominal stress
  • For localized stress

7
Static Stresses - Ductile Materials
  • Percent elongation gt 5
  • Maximum Shear Stress Theory
  • For nominal stress
  • For localized stress

8
Example
  • Specify a diameter for the middle portion of the
    rod, if it is to be made from AISI 1040-hot
    rolled steel.

9
Example
  • For the seat support shown, specify a standard
    structural tube to resist static loads shown. The
    tube has properties similar to AISI 1020
    hot-rolled steel. Use a design factor of 3.

10
Repeated Loads
11
Example
  • The notched bar is machined from AISI 1020 steel.
    This bar is subjected to a load that varies from
    2000 lb to 3000 lb. Determine the mean and
    alternating nominal stresses.

12
Fatigue Strength
  • R.R. Moore Test

13
Endurance Strength
  • sn Endurance strength
  • Listed in tables
  • If no information is available, use
  • sn ? 0.5 su (Steel)
  • sn ? 0.4 su (Aluminum)

14
Adjusted Endurance Strength
  • The data from the standard R.R. Moore test is
    adjusted for a particular application.
  • sn Adjusted endurance strength
  • (Cs) (Cm) (Cst) (CR) (sn)

15
Size and Stress Type Factors
  • Cs Size Factor
  • Dlt 0.4 in Cs 1.0
  • 0.4 lt D 2.0 in Cs (D/0.3)-0.068
  • 2.0 lt D 10.0 in Cs D-0.19
  • For rectangular sections, D.808(h b)1/2
  • Cst Stress Type Factor
  • 1.0 for bending
  • 0.80 for axial tension
  • 0.50 for torsion

16
Material and Reliability Factor
  • Cm Material Factor
  • 1.0 for wrought steel
  • 0.80 for cast steel
  • 0.70 for cast iron
  • CR Reliability Factor
  • 50 CR 1.0
  • 90 CR 0.90
  • 99 CR 0.81
  • 99.9 CR 0.75

17
Example
  • The notched bar is machined from AISI 1020 steel.
    This bar is subjected to a load that varies from
    2000 lb to 3000 lb. Determine the endurance limit
    of the material.

18
Repeated Stresses - Ductile Materials
  • Distortion Energy Theory
  • Define repeated von Mises Stress
  • Solderberg criterion

19
Repeated Stresses - Ductile Materials
  • Maximum Shear Stress Theory
  • ssy 0.5 sy
  • ssn 0.5 sn

20
Example
  • The notched bar is machined from AISI 1020 steel.
    This bar is subjected to a load that varies from
    2000 lb to 3000 lb. Comment on the robustness of
    the design.

21
Example
  • Comment on the robustness of a 1-1/4 round bar
    made from AISI 1213 C-D steel. It carries a
    constant tensile load of 1500 lbs, a bending load
    that varies from 0 to 800 lbs at the senter of
    the 48 length and a constant torque of 1200 in
    lbs.

22
Shafts
  • Connect power transmission components.
  • Inherently subjected to transverse loads and
    torsion.

23
Shaft Forces
  • Gears
  • As before

24
Shaft Forces
  • Chains

25
Shaft Forces
  • V-belts

Ftight
D
T
Fslack
26
Shaft Forces
  • Flat belts

Ftight
D
T
Fslack
27
Material Properties
  • For steady load (torsion)
  • sys.5sy
  • For fatique load ( bending)
  • sncs cR sn
  • cT 1 (bending)
  • cm 1 (wrought steel)

28
Stress Concentrations
  • Keyseats
  • Sled Runner Kt 1.6
  • Profile Kt 2.0
  • Woodruff Kt 1.5

29
Stress Concentrations
  • Shoulders
  • Sharp, Bearing (r/d ?.03) Kt 2.5
  • Round, Gear Bore (r/d ?.17) Kt 1.5
  • Grooves
  • Retaining Rings Kt 1.5

Try not to let Kts overlap. Leave .10 - .15
between
30
Strength Analysis
  • Bending stress
  • Torsion stress

For round sections
For round sections
31
Strength Analysis
  • Mohrs circle and Solderberg
  • Suggested Design Factors
  • N2 smooth operation
  • N3 typical industrial operation
  • N4 shock or impact loading

32
Minimum Acceptable Diameter
  • The designer must size the shaft.
  • Solve for appropriate diameters

33
Example
  • Determine a suitable diameter for a shaft made
    from AISI 1144 OQT 1000. It is subjected to a
    reversing bending moment of 3000 ft lbs and a
    steady torque of 1800 ft lbs. The shaft has a
    profile keyway.

34
Example
  • The shaft shown is part of a grain drying system
  • At A, a 34 lb. propeller-type fan requires 12 hp
    when rotating at 475 rpm.
  • A flat belt pulley at D delivers 3.5 hp to a
    screw conveyor handling the grain.
  • All power comes to the shaft through the v-belt
    at C.

Using AISI 1144 cold drawn steel, determine the
minimum acceptable diameter at C.
35
Example
36
Shafts Accessories
  • Components used to securely mount power
    transmitting elements on a shaft.
  • Axial
  • Rotational

37
Keys
  • Allow torque to be transferred from a shaft to a
    power transmitting element (gear, sprocket,
    sheave, etc.)

38
Key Design
  • Use a soft, low strength material
  • (ie, low carbon steel)
  • Standard size HW1/4 D
  • Design length
  • based on strength

39
Standard Key Sizes
40
Key Design
  • Key Shear
  • Failure Theory
  • Length

41
Example
  • Specify a key for a gear (grade 40, gray cast
    iron) to be mounted on a shaft (AISI 1144, hot
    rolled) with a 2.00 in. diameter. The gear
    transmits 21000 lb-in of torque and has a hub
    length of 4 in.

42
Retaining Rings
  • Also known as snap rings
  • Provides a removable shoulder to lock components
    on shafts or in bores.
  • Made of spring steel, with a high shear strength.
  • Stamped, bent-wire, and spiral-wound.

43
Retaining Ring Selection
  • Based on shaft diameter thrust force

44
Set Screws
  • Setscrews are fasteners that hold collars,
    pulleys, or gears on shafts.
  • They are categorized by drive type and point
    style.

45
Standard Set Screw Sizes
46
Set Screw Holding
47
Pins
  • A pin is placed in double shear
  • Holds torsion and axial loads
  • Hole is made slightly smaller than the pin (FN1
    fit)

48
Example
  • Specify a pin for a gear (grade 40, gray cast
    iron) to be mounted on a shaft (AISI 1144, hot
    rolled) with a 2.00 in. diameter. The gear
    transmits 21000 lb-in of torque and has a hub
    length of 4 in.

49
Roll Pins
  • Easier disassembly

50
Collars
  • Creates a shoulder on shaft without increasing
    stock size.
  • Held with either set screw or friction (clamped)

51
Mechanical Couplings
  • Couplings are used to join two shafts
  • Rigid couplings are simple and low cost. But they
    demand almost perfect alignment of the mating
    shafts.
  • Misalignment causes undue forces and accelerated
    wear on the shafts, coupling, shaft bearings, or
    machine housing.

52
Mechanical Couplings
  • In connecting two shafts, misalignment is the
    rule rather than the exception. It comes from
    such sources as bearing wear, structural
    deflection, thermal expansion, or settling
    machine foundations.
  • When misalignment is expected, a flexible
    coupling must be used.

53
Mechanical Couplings
  • Selection factors include
  • Amount of torque (or power speed)
  • Shaft Size
  • Misalignment tolerance

54
Fasteners, Powers Screws, Connections
  • Helical thread screw was an important invention.
  • Power Screw, transmit angular motion to liner
    motion
  • Transmit large or produce large axial force
  • It is always desired to reduce number of screws

55
Definition of important Terminologies
Major diameter d, Minor diameter dr Mean dia or
pitch diameter dp Lead l, distance the nut moves
for one turn rotation
56
Single and Double threaded screws
Double threaded screws are stronger and moves
faster
57
Screw Designations
  • United National Standard UNS
  • International Standard Organization

Roots and crest can be either flat or round
Pitch diameter produce same width in the thread
and space,
58
Coarse thread Designated by UNC
  • Fine Thread UNF, is more resistance to
    loosening, because of its small helix angle.
  • They are used when Vibration is present
  • Class of screw, defines its fit, Class 1 fits
    have widest tolerances, Class 2 is the most
    commonly used
  • Class three for very precision application
  • Example1in-12 UNRF-2A-LH, A for Ext. Thread and
    B for Internal, R root radius
  • Metric M10x1.5 10 diameter mm major diameter,1.5
    pitch

59
Some important Data for UNC, UNF and M threads
  • Lets Look at the Table 8-1 on Page 398

60
Square and Acme Threads are used for the power
screw
Preferred pitch for Acme Thread
d, in 1/4 5/16 3/8 1/2 5/8 3/4 7/8 1 1 1/4
p,in 1/16 1/14 1/12 1/10 1/8 1/6 1/6 1/5 1/5
61
Mechanics of Power Screws
62
Used in design to change the angular motion to
linear motion, Could you recall recent failure of
power screw leading to significant causalities
63
What is the relationship between the applied
torque on power screw and lifting force F
64
Torque for single flat thread
If the thread as an angle a, the torque will be
Wedging action, it increases friction
65
Stresses in the power Screw
Shear stress in the base of the screw Bearing
stress Bending stress at the root of the
screw Shear stress in the thread nt number of
engaged thread
66
Loading to the fasteners and their Failure
considerations
67
Bolts are used to clamp two or more partsIt
causes pre tension in the bolt Grip length is
the total thickness of parts and washers
d
t
68
ld
h
t2
ltL- ld
L effective grip ht2 if t2ltd
hd/2 for t2 d
69
Failure of bolted or riveted joints
70
Type of Joints
  • Lap Joint (single Joint) But Joint

71
Example 1
72
Example 2
73
Example 2
74
Example 3
75
Weld
76
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77
Weld under Bending
78
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79
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80
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81
Springs
Flexible machine elements
  • Used to
  • Exert force
  • Store energy

82
Spring Rate
  • Effective springs have a linear deflection curve.
  • Slope of the spring deflection curve is the rate

83
Example
  • A compression spring with a rate of 20 lb/in is
    loaded with 6 lbs and has a length of 1.5 in.
    Determine the unloaded spring length (free length)

84
Geometry
  • Wire diameter, Dw (Standard gages)
  • Mean Diameter, Dm
  • Dm Do - Dw

85
Spring Parameters
  • Spring index
  • C gt 5 (manufacturing limits)
  • Active coils, Na
  • N for plain ends
  • N-1 for ground ends
  • N-2 for closed ends

86
Deflection
  • Deflection for helical springs

G Shear modulus
  • Spring rate for helical springs

87
Example
  • A helical compression spring is formed from 35
    gage music wire with 10-1/4 turns and an O.D. if
    0.850 in. Its ends are squared. The free length
    is 2 inches. Determine the force to press the
    spring solid.

88
Stress Analysis
  • Spring wire is in torsion
  • Wahl factor, K
  • Accounts for the curvature of the wire

89
Example
  • A helical compression spring is formed from 35
    gage music wire with 10-1/4 turns and an O.D. if
    0.850 in. Its made from A228 and the ends are
    squared. The free length is 2 inches.
  • If the spring is repeatedly compressed to 1.3 in,
    do you expect problems?

90
Design Procedure
  • Select a material
  • Compute required spring rate
  • Estimate Dm based on size constraints
  • Determine required Dw (use K1.2)
  • Select standard wire
  • Verify actual stress is satisfactory.
  • Compute number of coils required.

91
Example
  • Design a helical compression spring to exert a
    force of 22 lbs when compressed to a length of
    1.75 in. When its length is 3.0 in, it must exert
    5 lb. The spring will be cycled rapidly. Use ASTM
    A401 steel wire.

92
Rolling Element Bearings
  • Provides support for machine elements, while
    allowing smooth motion.
  • m0.001 - 0.005

93
Types
Radial Roller
Single-row Radial Ball
Angular Contact Ball
Angular Roller
94
Types
Tapered Roller
Spherical Roller
Needle
Thrust
95
Ball Bearings
96
Stress Analysis
  • Contact Stress
  • sc300,000 is not unusual
  • Balls, rollers and races are made from extremely
    high strength steel
  • ex. AISI 52100
  • sy 260,000 psi
  • su322,000 psi

97
Bearing Load/Life
  • Test (fatigue) data

Empirical relationship
  • k3.0 (ball)
  • k3.33 (roller)

98
Example
  • A bearing is mounted on a shaft rotating at 1200
    rpm. The bearing has been tested to have a L10
    life of 300 hrs, when loaded with 500 lbs.
    Determine the expected L10 life, if the load is
    increased to 700 lbs.

99
Manufacturers Data
  • Vendors publish the Basic Dynamic Load rating (C)
    of a bearing at an L10 life of 1 million cycles.

100
Bearing Selection
  • Determine the design life (in cycles)
  • Determine the design load
  • Pd V R
  • Calculate the required basic dynamic load
  • Select a bearing with (C gt Creqd) and a bore
    that closely matches the shaft diameter.
  • V1 for inner race rotation
  • V1.2 for outer race rotation

101
Example
  • Specify suitable bearings for a shaft used in an
    grain dryer. The shaft rotates at 1700 rpm. The
    required supporting loads at the bearing are
  • and the minimum acceptable diameter is 2.16.

RBx589 lb RBy164 lb
102
Mounting of Bearings
  • Shaft/bearing bore has a light interference fit.
  • Housing/outer race has a slight clearance fit.
  • Check manufacturers catalog
  • Match maximum permissible fillet radius.
  • Shaft or housing shoulders not to exceed 20 of
    diameter.

103
Mounted Bearings
  • Pillow block
  • Bearing is inserted into a cast housing, with
    base or flange slots, which can be readily
    attached to a machine base.

104
Bearings with Varying Loads
  • Compute a weighted average load based on duty
    cycle.

Fmequivalent load Fi load level for condition
i Ni cycles for condition i p exponent for
load/life
105
Example
  • Bearing 6211 is carrying the following load
    cycle, while rotating at 1700 rpm.
  • Stage Load (lbs) Time (min)
  • 1 600 480
  • 2 200 115
  • 3 100 45
  • Compute the bearing L10 life in minutes.

106
Radial Thrust Loads
  • Calculate an equivalent load
  • PVXR YT

107
Thrust factors, Y
  • Deep -groove, ball bearings

X 0.56 for all values of Y
108
Example
  • A bearing is to carry a radial load of 650 lb and
    a thrust load of 270 lb. Specify a suitable
    single-row, deep-groove ball bearing if the shaft
    rotates at 1150 rpm and the design life is 20,000
    hrs.
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