Machine Design Databook Episode 1 part 6 ppt

Machine Design Data Handbook, McGraw-Hill Publishing Company, New York, 1994.. 6 CAMS a radius of circular area of contact, m in A acceleration of the follower, m/s2in/s2 follower overha

The area under normal distribution curve to the right

of t (Fig 5-11)

Error function or probability integral

The resultant mean of adding the means of two

The resultant standard deviation for both subtraction

and addition of two standard deviations ^sand^

Refer to Table 5-8 for area under the standard normaldistribution curve

where AðtÞ is the area to the left of t

The area under the entire normal distribution curve isAðtÞ þ BðtÞ and is equal to unity The term BðtÞ can befound from Table 5-8 or by integrating the area underthe curve

FIGURE 5-10 The shapes of normal distribution curves

for various  and constant . FIGURE 5-11 The Gaussian (normal) distribution curve.

The standard variable tR (deviation multiplication

factor) in order to determine the probability of failure

The fatigue strength reduction factor based on

reliability

If a factor of safety n0is to be specified together with

reliability, then Eq (5-112) is rewritten to give a new

expression for tR

The expression for safety factor n0from Eq (5-115)

The best-fitting straight line which fits a set of

scattered data points as per linear regression

The equations for regression

The correlation coefficient

A safety factor of 1 is taken into account in ing the reliability from Eq (5-113)

x2

 P

x2n

where r lies between 1 and þ1

If r is negative, it indicates that the regression line has

The cumulative distribution function

Equation (5-121) after simplification

3 Faires, V M., Design of Machine Elements, The Macmillan Company, New York, 1965

4 Lingaiah, K., and B R Narayana Iyengar, Machine Design Data Handbook, Engineering Co-operativeSociety, Bangalore, India, Bangalore, India, 1962

5 Lingaiah, K., and B R Narayana Iyengar, Machine Design Data Handbook, Vol I (SI and Customary Units),Suma Publishers, Bangalore, India, 1986

6 Lingaiah, K., Machine Design Data Handbook, Vol II (SI and Customary Metric Units), Suma Publishers,Bangalore, India, 1986

7 Juvinall, R C., Fundamentals of Machine Component Design, John Wiley and Sons, New York, 1983

8 Deutschman, A D., W J Michels, and C E Wilson, Machine Design—Theory and Practice, MacmillanPublishing Company, New York, 1975

9 Edwards, Jr., K S., and R B McKee, Fundamentals of Mechanical Component Design, McGraw-HillPublishing Company, New York, 1991

10 Norton, R L., Machine Design—An Integrated Approach, Prentice Hall International, Inc., Upper SaddleRiver, New Jersey, 1996

11 Lingaiah, K Machine Design Data Handbook, McGraw-Hill Publishing Company, New York, 1994

12 Metals Handbook, American Society for Metals, Vol 10, 8th edition, p 102, Metals Park, Ohio, 1975



b

ð5-122Þ

6

CAMS

a radius of circular area of contact, m (in)

A acceleration of the follower, m/s2(in/s2)

follower overhang, m (in)

Ac arc of pitch circle, m (in)

b half the band of width of contact, m (in)

B follower bearing length, m (in)

ao¼
oþ
i distance between centers of rotation, m (in)

d diameter of shaft, m (in)

dh hub diameter, m (in)

Do minimum diameter of the pitch surface of cam, m (in)

E1, E2 moduli of elasticity of the materials which are in contact, GPa

(Mpsi)

f cam factor, dimensionless

f ðÞ the desired motion of follower, as a function of cam angle

F applied load, kN (lbf )

F total external load on follower (includes weight, spring force,

inertia, friction, etc.), kN (lbf )

Fn force normal to cam profile (Fig 6-6), kN (lbf )

Ft side thrust, kN (lbf )

h depth to the point of maximum shear, m (in)

Ki, Ko constants for input and output cams, respectively

L length of cylinder in contact, m (in)

total distance through which the follower is to rise, m (in)

N1, N2 forces normal to follower stem, kN (lbf )

r radius of follower, m (in)

Rc radius of the circular arc, m (in)

Ro minimum radius of the pitch surface of the cam, m (in)

Rp pitch circle radius, m (in)

Rr radius of the roller, m (in)

R, S functions ofiando, in basic spiral contour cams

S displacement of the follower corresponding to any cam angle,

m (in)

S1 initial compression spring force with weight w, at zero position,

kN (lbf )

v velocity of the follower, m/s (in/s)

w equivalent weight at follower ends, kN (lbf )

yc rise of cam, m (in)

radius of curvature of the pitch curve, m (in)

1,
2 radii of curvature of the contact surfaces, m (in)

m maximum pressure angle, deg

 angle through which cam is to rotate to effect the rise L, rad

 cam angle corresponding to the follower displacement S, rad

o angle rotated by the output-driven member, deg

i angle rotated by the input driver, deg

! angular velocity of cam, rad/s

 coefficient of friction between follower stem and its guide

bearing

1,2 Poisson’s ratios for the materials of contact surfaces

c;max maximum compressive stress, MPa (kpsi)

 shear stress, MPa (kpsi)

Cam factor

The length of arc of the pitch circle

The pitch circle radius

RADIUS OF CURVATURE OF DISK CAM

WITH ROLLER FOLLOWER

The displacement of the center of the follower from

the center of cam (Fig 6-1)

For pointed cam, the radius of curvature of the pitch

curve to roller follower

For roller follower, the radius of curvature of the

pitch curve must always be greater than the roller

radius to prevent points or undercuts

The radius of curvature for concave pitch curve

The minimum radius of curvature

R ¼ Roþ f ðÞ; dR

d¼ f0ðÞ; d

2Rd2 ¼ f00ðÞ ð6-7aÞ

min¼ R2o

where f00ðÞois the acceleration at ¼ 0

The minimum radius of curvature of the cam curve
c

The minimum radius of a mushroom cam for

uniformly accelerated and retarded motion

For cast-iron cam, the hub diameter

For cycloidal motion

For harmonic motion

For eight-power polynomial motion

RADIUS OF CURVATURE OF DISK CAM

WITH FLAT-FACED FOLLOWER

The displacement of the follower from the origin

2
12

x ¼ ½a þ f ðÞ cos 
f0ðÞ sin  ð6-15aÞ

y ¼ ½a þ f ðÞ sin  þ f0ðÞ cos  ð6-15bÞ

The cam contour given by equations will be free of

cusps if

Half of the minimum length of the flat-faced follower

or the minimum length of contact of the follower

FIGURE 6-2 (Courtesy of H H Mabie and F W Ocvivk,

Dynamics of Machinery, John Wiley and Sons, 1957.)

PRESSURE ANGLE (Figs 6-3 and 6-4)

The pressure angle for roller follower

The pressure angle for a plate cam or any cylindrical

cam giving uniform velocity to the follower

The pressure angle for a plate cam giving uniformly

accelerated and retarded motion to the follower

A precise pressure angle equation for a plate cam

giving harmonic motion to the follower or a

tangen-tial cam

For measuring maximum pressure angle of a

para-bolic cam with radially moving roller follower

Do

swhen L > Do ð6-20bÞ

FIGURE 6-3 Nomogram for parabolic cam with radially moving follower.

Source: Rudolph Gruenberg, ‘‘Nomogram for Parabolic Cam with Radially Moving Follower,’’ in Douglas C Greenwood, Editor, Engineering Data for Product Design, McGraw-Hill Book Company, New York, 1961.

FIGURE 6-4 Nomogram to determine maximum pressure

angle (Courtesy of E C Varnum, Barber-Coleman Co.)

Reproduced with permission from Machine Design,

Cleve-land, Ohio.

RADIAL CAM-TRANSLATING

ROLLER-FOLLOWER-FORCE ANALYSIS (Fig 6-5)

The forces normal to follower stem (Fig 6-5)

The total external load

The force normal to the cam profile

The maximum pressure angle for locking the follower

lg

sin

lg

sin

ð6-25Þ

m¼ tan
1 lg

FIGURE 6-5 Radial cam-translating roller-follower force analysis.

SIDE THRUST (Fig 6-5)

The side thrust produced on the follower bearing

BASIC SPIRAL CONTOUR CAM

The radius to point of contact at angleo(Fig 6-6)

The radius to point of contact at anglei(Fig 6-6)

FIGURE 6-6 Basic spiral contour cam.

o¼ ao

1þdodi

ð6-28Þ

i¼ ao

dodi

1þdodi

ð6-29Þ

BASIC SPIRAL CONTOUR CAM

CONSTANTS

The radius to point of contact at angleo

The radius to point of contact at anglei

For characteristic curves of cycloidal, harmonic, and

eight-power polynomial motions

HERTZ CONTACT STRESSES

Contact of sphere on sphere

The radius of circular area of contact

The maximum compressive stress

Contact of cylindrical surface on cylindrical

surface

Width of band of contact

The maximum compressive stress

The maximum compressive stress for1¼ 2¼ 0:3

o¼ ao

1þKo

Ki

dSdR



1þKo

Ki

dSdR

a ¼ 3

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3F

1
v2

E1

þ

1
v2

E1

þ

1

þ
12



vuu

1

þ
12



L

1

FIGURE 6-7 Cycloidal motion characteristics S ¼ displacement, inches; V ¼ velocity, inches per degree; A ¼ acceleration, inches per degree2 (From ‘‘Plate Cam Design—with Emphasis on Dynamic Effects,’’ by M Kloomok and R V Muffley, Product Eng., February 1955.) Reproduced with permission from Machine Design, Cleveland, Ohio.

FIGURE 6-8 Harmonic motion characteristics S ¼ displacement, inches; V ¼ velocity, inches per degree; A ¼ acceleration, inches per degree2 (From ‘‘Plate Cam Design—with Emphasis on Dynamic Effects,’’ by M Kloomok and R V Muffley, Product Eng., February 1955.) Reproduced with permission from Machine Design, Cleveland, Ohio.

FIGURE 6-9 Eighth-power polynomial motion characteristics S ¼ displacement, inches; V ¼ velocity, inches per degree;

A ¼ acceleration, inches per degree2 (From ‘‘Plate Cam Design—with Emphasis on Dynamic Effects,’’ by M Kloomok and

R V Muffley, Product Eng., February 1955.) Reproduced with permission from Machine Design, Cleveland, Ohio.

FIGURE 6-10 Cycloidal motion (From ‘‘Plate Cam Design—Radius of Curvature,’’ by M Kloomok and R V Muffley, Product Eng., September 1955.) Reproduced with permission from Machine Design, Cleveland, Ohio.

FIGURE 6-11 Harmonic motion (From ‘‘Plate Cam Design—Radius of Curvature,’’ by M Kloomok and R V Muffley, Product Eng., September 1955.) Reproduced with permission from Machine Design, Cleveland, Ohio.

FIGURE 6-12 Eighth-power polynomial motion (From ‘‘Plate Cam Design—Radius of Curvature,’’ by M Kloomok and

R V Muffley, Product Eng., September 1955.) Reproduced with permission from Machine Design, Cleveland, Ohio.

The maximum shear stress

The depth to the point of maximum shear

For further data on characteristic equations of basic

curves, different motion characteristics, cam factors,

materials for cams and followers, and displacement

ratios

REFERENCES

1 Rothbart, H A., Cams, John Wiley and Sons, New York, 1956

2 Marks, L S., Mechanical Engineers’ Handbook, McGraw-Hill Book Company, New York, 1951

3 Lingaiah, K., and B R Narayana Iyengar, Machine Design Data Handbook, Engineering College tive Society, Bangalore, India, 1962

Co-opera-4 Lingaiah, K., Machine Design Data Handbook, Vol II (SI and Customary Metric Units), Suma Publishers,Bangalore, India, 1986

5 Rothbart, H A., Mechanical Design and Systems Handbook, McGraw-Hill Book Company, New York, 1964

6 Shigley, J E., Theory of Machines, McGraw-Hill Book Company, New York, 1961

7 Mabie, H H., and F W Ocvirk, Mechanisms and Dynamics of Machinery, John Wiley and Sons, New York,1957

8 Kent, R T., Mechanical Engineers’ Handbook—Design and Production, Vol II John Wiley and Sons, NewYork, 1961

9 Klcomok, M., and R V Muffley, ‘‘Plate Cam Design—with Emphasis on Dynamic Effects,’’ Product Eng.,February 1955

10 Klcomok, M., and R V Muffley, ‘‘Plate Cam Design—Radius of Curvature,’’ Product Eng., February 1955

11 Varnum, E C., ‘‘Circular Nomogram—Theory and Practice Construction Technique,’’ Barber-Coleman Co.,Product Eng

12 Gruenberg, R., ‘‘Nomogram for Parabolic Cam with Radially Moving Follower,’’, in Douglas C Greenwood,Editor, Engineering Data for Product Design, McGraw-Hill Book Company, New York, 1996

Refer to Tables 6-1 and Figures 6-7, 6-8 and 6-9.For materials of cams refer to Chapter 1 on ‘‘Proper-ties of Engineering Materials.’’

TABLE 6-1

Cam factors for basic curves

Types of motion Pressure angle ,

7

PIPES, TUBES, AND CYLINDERS

d diameter of cylinder, m (in)

dc diameter of contact surface in compound cylinder, m (in)

di inside diameter of cylinder or pipe or tube, m (in)

do outside diameter of cylinder or pipe or tube, m (in)

e factor for expanded tube ends

E modulus of elasticity, GPa (Mpsi)

hor t thickness of cylinder or pipe or tube, m (in)

I moment of inertia, area, m4or cm4(in4)

L maximum distance between supports or stiffening rings, m

(in)

p maximum allowable working pressure, MPa (psi)

pc unit pressure between the compound cylinders, MPa (psi)

pcr collapsing pressure, MPa (psi)

pi internal pressure, MPa (psi)

po external pressure, MPa (psi)

ri inside radius of tube or pipe, m (in)

permissible working stress, from Table 7-1, MPa (psi)

c crushing stress, MPa (psi)

r radial stress (also with primes), MPa (psi)

rðmaxÞ maximum radial stress, MPa (psi)

sa maximum allowable stress value at design condition, MPa

(psi)

su ultimate strength, MPa (psi)

 tangential stress (also with primes), MPa (psi)

ðmaxÞ maximum tangential stress, MPa (psi)

max maximum shear stress, MPa (psi)

 efficiency, from Table 7-4

Note:The initial subscript s, along with
, which stands for strength, is used throughout this book

LONG THIN TUBES WITH INTERNAL

PRESSURE

The permissible steam pressure in steel and iron pipes

(Table 7-1) according to ASME Power Boiler Code

The minimum required thickness of ferrous tube up

to and including 125 mm (5 in) outside diameter

subjected to internal pressure as per ASME Power

Boiler Code

The maximum allowable working pressure (MAWP)

from Eq (7-3) as per ASME Power Boiler Code

For maximum allowable working pressure

The minimum required thickness of ferrous pipe

under internal pressure as per ASME Power Boiler

Code

p ¼2
sa

do ðh
1:625  10
3Þ
0:9 SI ð7-1aÞwhere h, doin m, and p and
in MPa

p ¼2
sa

do ðh
0:065Þ
125 USCS ð7-1bÞwhere h, doin in, and p and
in psi

For tubes from 6.35 mm (0.25 in) to 127 mm (5 in)nominal diameter

p ¼2
sa

do

ðh
2:54  10
3Þ SI ð7-2aÞwhere h, doin m, and p and
in MPa

p ¼2
sa

do

where h, doin in, and p and
in psi

For over 127 mm (5 in) diameter

h ¼2
pdsaþ po þ 0:005doþ e ð7-3Þwhere
sais the maximum allowable stress value atdesign condition and e is the thickness factorfor expanded tube ends

Refer to Table 7-1 for
sa.Refer to table 7-2 for e

p ¼
sa

2h
0:01do
2e

 ¼ efficiency (refer to Table 7-4 for )

y ¼ temperature coefficient (refer to Table 7-3 for y)

C ¼ minimum allowance for the threading and tural stability, mm (in) (refer to Table 7-5 for hvalues and Table 7-6 for C values)

Particular Value of e Over a length at least equal to the length of the seat plus 25 mm (1 in) for tubes expanded into tube seats, 0.04 except

For tubes expanded into tube seats provided the thickness of the tube ends over a length of the seat plus 0

25 mm (1 in) is not less than the following:

2.375 mm (0.095 in) for tubes 31.25 mm (1.25 in) OD

2.625 mm (0.105 in) for tubes >31.25 mm (1.25 in) OD and 50 mm (2 in) OD, including

3.000 mm (0.120 in) for tubes >50 mm (2 in) and 75 mm (3 in) OD, including

3.375 mm (0.135 in) for tubes >75 mm (3 in) OD and 100 mm (4 in) OD, including

3.75 mm (0.150 in) for tubes >100 mm (4 in) and 125 mm (5 in) OD, including

Source: ASME Boiler and Pressure Vessel Code, Section 1, 1983.

Source: ASME Boiler and Pressure Vessel Code, Section 1, 1983.

For welded joints provided all weld reinforcement on the longitudinal joints is removed

substantially flush with the surface of the plate

1.00

For welded joints with the reinforcement on the longitudinal joints left in place 0.90