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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 Section -

Failure Theories

- Stress in machine components should be accurately

computed. - Designer must understand material limits to

ensure a safe design.

Design Factor

- Factor of Safety (N)
- Suitable values depend on inherent danger,

certainty of calculations, certainty of material

properties, etc.

Static Stresses - Brittle Materials

- Percent elongation lt 5
- for parts in tension
- for parts in compression
- for parts with general stress

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.

Static Stresses - Ductile Materials

- Percent elongation gt 5
- Distortion Energy Theory
- Define von Mises Stress
- For nominal stress
- For localized stress

Static Stresses - Ductile Materials

- Percent elongation gt 5
- Maximum Shear Stress Theory
- For nominal stress
- For localized stress

Example

- Specify a diameter for the middle portion of the

rod, if it is to be made from AISI 1040-hot

rolled steel.

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.

Repeated Loads

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.

Fatigue Strength

- R.R. Moore Test

Endurance Strength

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

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)

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

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

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.

Repeated Stresses - Ductile Materials

- Distortion Energy Theory
- Define repeated von Mises Stress
- Solderberg criterion

Repeated Stresses - Ductile Materials

- Maximum Shear Stress Theory

- ssy 0.5 sy
- ssn 0.5 sn

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.

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.

Shafts

- Connect power transmission components.
- Inherently subjected to transverse loads and

torsion.

Shaft Forces

- Gears
- As before

Shaft Forces

- Chains

Shaft Forces

- V-belts

Ftight

D

T

Fslack

Shaft Forces

- Flat belts

Ftight

D

T

Fslack

Material Properties

- For steady load (torsion)
- sys.5sy
- For fatique load ( bending)
- sncs cR sn
- cT 1 (bending)
- cm 1 (wrought steel)

Stress Concentrations

- Keyseats
- Sled Runner Kt 1.6
- Profile Kt 2.0
- Woodruff Kt 1.5

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

Strength Analysis

- Bending stress
- Torsion stress

For round sections

For round sections

Strength Analysis

- Mohrs circle and Solderberg

- Suggested Design Factors
- N2 smooth operation
- N3 typical industrial operation
- N4 shock or impact loading

Minimum Acceptable Diameter

- The designer must size the shaft.
- Solve for appropriate diameters

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.

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.

Example

Shafts Accessories

- Components used to securely mount power

transmitting elements on a shaft.

- Axial
- Rotational

Keys

- Allow torque to be transferred from a shaft to a

power transmitting element (gear, sprocket,

sheave, etc.)

Key Design

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

Standard Key Sizes

Key Design

- Key Shear
- Failure Theory
- Length

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.

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.

Retaining Ring Selection

- Based on shaft diameter thrust force

Set Screws

- Setscrews are fasteners that hold collars,

pulleys, or gears on shafts. - They are categorized by drive type and point

style.

Standard Set Screw Sizes

Set Screw Holding

Pins

- A pin is placed in double shear
- Holds torsion and axial loads

- Hole is made slightly smaller than the pin (FN1

fit)

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.

Roll Pins

- Easier disassembly

Collars

- Creates a shoulder on shaft without increasing

stock size. - Held with either set screw or friction (clamped)

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.

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.

Mechanical Couplings

- Selection factors include
- Amount of torque (or power speed)
- Shaft Size
- Misalignment tolerance

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

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

Single and Double threaded screws

Double threaded screws are stronger and moves

faster

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,

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

Some important Data for UNC, UNF and M threads

- Lets Look at the Table 8-1 on Page 398

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

Mechanics of Power Screws

Used in design to change the angular motion to

linear motion, Could you recall recent failure of

power screw leading to significant causalities

What is the relationship between the applied

torque on power screw and lifting force F

Torque for single flat thread

If the thread as an angle a, the torque will be

Wedging action, it increases friction

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

Loading to the fasteners and their Failure

considerations

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

ld

h

t2

ltL- ld

L effective grip ht2 if t2ltd

hd/2 for t2 d

Failure of bolted or riveted joints

Type of Joints

- Lap Joint (single Joint) But Joint

Example 1

Example 2

Example 2

Example 3

Weld

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Weld under Bending

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Springs

Flexible machine elements

- Used to
- Exert force
- Store energy

Spring Rate

- Effective springs have a linear deflection curve.
- Slope of the spring deflection curve is the rate

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)

Geometry

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

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

Deflection

- Deflection for helical springs

G Shear modulus

- Spring rate for helical springs

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.

Stress Analysis

- Spring wire is in torsion

- Wahl factor, K
- Accounts for the curvature of the wire

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?

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.

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.

Rolling Element Bearings

- Provides support for machine elements, while

allowing smooth motion. - m0.001 - 0.005

Types

Radial Roller

Single-row Radial Ball

Angular Contact Ball

Angular Roller

Types

Tapered Roller

Spherical Roller

Needle

Thrust

Ball Bearings

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

Bearing Load/Life

- Test (fatigue) data

Empirical relationship

- k3.0 (ball)
- k3.33 (roller)

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.

Manufacturers Data

- Vendors publish the Basic Dynamic Load rating (C)

of a bearing at an L10 life of 1 million cycles.

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

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

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.

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.

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

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.

Radial Thrust Loads

- Calculate an equivalent load
- PVXR YT

Thrust factors, Y

- Deep -groove, ball bearings

X 0.56 for all values of Y

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.