chapter8-131224105351-phpapp02.ppt

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11

All figures taken fromDesign of Machinery, 3rd ed. Robert Norton2003

MENG 372

Chapter 8Cam Design



22

Cams

• Function generator • Can generate a true dwell



33

Cam Terminology

• Type of follower motion (rotation, translation)• Type of joint closure (force, form)

• Type of follower (roller, mushroom, flat)

• Direction of follower motion (radial, aial)

• Type of motion constraints (critical etreme

position(C!") and critical path motion (C"#))

• Type of motion program (rise$fall (%&), rise$fall$

dwell (%&D), rise$dwell$fall$dwell (%D&D)



'4

Type of &ollower #otion

scillating follower

Translating follower



5

Type of *oint Closure

Force and form clo

sed cams• Force closed cams

re+uire an eternal

force to eep thecam in contact with

the follower

• - spring usuallypro.ides this force



/6

Type of *oint Closure

• Form closed cams areclosed 0y joint geometry

• lot milled out of the

cam



• Roller Follower • Mushroom Follower

• Flat-Faced Follower

Types of &ollowers

&lat$&aced

&ollower #ushroom&ollower

%oller&ollower



Direction of &ollower #otion

• Radial or !ialRadial Cam

!ial Cam


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Cam Terminology (re.iew)• Type of follower motion (rotation, translation)

• Type of joint closure (force, form)• Type of follower (roller, mushroom, flat)

• Direction of follower motion (radial, aial)


http://slidepdf.com/reader/full/chapter8-131224105351-phpapp02ppt 10/55151#

Type of #otion Constraints

• Critical !treme "osition (C!") 6 start and endpositions are specified 0ut not the path

0etween

• Critical "ath #otion (C"#) 6 path or deri.ati.eis defined o.er all or part of the cam



1111

Type of #otion "rogram

• &rom the C!" cam profile• Dwell 6 period with no output motion with input

motion7

• %ise$&all (%&) 6 no dwell (thin a0out using acran$rocer)

• %ise$&all$Dwell (%&D) 6 one dwell

• %ise$Dwell$&all$Dwell (%D&D) 6 two dwells



1212

Unwrap the cam"lot position (s),

.elocity (.),

acceleration (a) and jer (j) .ersus cam

angle

8asis for cam design

9-* Diagrams



1313

%D&D Cam Design

• #otion is 0etween two dwells



1'14

%D&D Cam, :a;.e Cam Design

• Connect points usingstraight lines

• Constant .elocity

<nfinite accelerationand jer

:ot an accepta0le

cam program



115

&undamental =aw of Cam Design

-ny cam designed for operation at other than.ery low speeds must 0e designed with the

following constraints>

• The cam function must 0e continuous throughthe first and second deri.ati.es of displacement

across the entire inter.al (3/5?)7

Corollary>• The jer must 0e finite across the entire inter.al

(3/5?)7

%D&D C h D i



1/16

%D&D Cam ophomore Design

imple @armonic #otion•

$ine %unction hascontinuous deri&ati&es

∞ ∞

2

2

3

3

1 cos2

sin2

cos2

sin2

h s -

ds hv dθ

dv ha

d

da h j d

πθ

β

π πθ

β β

π πθ

θ β β

π πθ

θ β β

= ÷

= = ÷

= = ÷ −

= = ÷

-cceleration is discontinuous

*er is infinite (0ad cam design)

h



117

%D&D Cam, Cycloidal

1

2

sin

2cos

2

a C

C v k

πθ

β

β πθ

π β

= ÷

= − + ÷

1

2

2

2

2

1 cos2

2sin

2 2

C k

C

v

C s C k

β

π

β πθ

π β

β β πθ θ

π π β

=

= − ÷

= − + ÷ ÷

tart with acceleration A integrate>

#v = #θ =ince at then>

h



118

%D&D Cam, Cycloidal

• $ince s=0 at θ =0' k 2=0

• $ince s=h at θ=β '

2

2

2

C h

h C

β π β π β = ⇒ = ÷

( )

=

=

−=

−=

β πθ

β

π

β πθ

β π

β

πθ

β

β πθ

π θ

β

2cos2

2sin2

2cos1

2sin2

3

2

2

h j

ha

hv

hh s

2

2

2sin

2 2

C s C k

β β πθ θ

π π β

= − + ÷ ÷

h



141"

%D&D Cam, Cycloidal

9alid cam design (followsfundamental law of cam design)

-cceleration and .elocity are

higher than other functionsBeneral procedure for design is to

start with a continuous cur.e for

acceleration and integrate7

( )2sin2

h h s πθ θ β π β

= −

!+uation for a cycloid7

Cam has a cycloidal displacement

or sinusoidal acceleration

h



252#

%D&D Cam, Trapeoidal

• Constant acceleration gi.es infinite jer• Trapeoidal acceleration gi.es finite jer, 0ut

the acceleration is higher



2121

%D&D Cam, #odified Trapeoidal

• Com(ination o% sinusoidal and constant acceleration• )eed to integrate to get the magnitude



2222

%D&D Cam, #odified Trapeoidal

• %ter integrating' we get the %ollowing cur&es• *as lowest magnitude o% +ea, acceleration o%

standard cam %unctions

lowest %orces.



2323

• Com0ination ofa low and high

fre+uency sine

function• @as lowest

pea .elocity

(lowest ineticenergy)

%D&D Cam,

#odified ine



2'24

%D&D Cam, CC- &amily

The cam functions discussed so far 0elong to the CC-family (ine$Constant$Cosine$-cceleration)



225

%D&D Cam, CC- &amily• Com+arison o% accelerations in $CC %amil/

• ll are com(ination o% sine' constant' cosine %amil/



2/26

"olynomial &unctions

• 0e can also choose +ol/nomials %or cam %unctions• eneral %orm

where x=θ/β or t

• Choose the num(er o% (oundar/ conditions Cs.

to satis%/ the %undamental law o% cam design

nn xC xC xC xC xC C s ++++++=

44

33

221#



227

3$'$ "olynomial

• oundar/ conditions @θ =0, s=0,v=0,a=0

@θ=β , s=h,v=0,a=0

• $i! (oundar/ conditions' soorder 5 since C# term

5

5

4

4

3

3

2

21#

+

+

+

+

+=

β

θ

β

θ

β

θ

β

θ

β

θ

C C C

C C C s



228

3$'$ "olynomial

@θ =0, s=0=C 0 v=0=C 1 / β a=0=2C 2 / β 2

C 0=0 C 1=0 C 2=0

@θ =β , s=h= C 3+C 4+C 5 , v=0=2C 3+3C 4+5C 5 a=0=6C 3+12C 4+20C 5

Solve the 3 eqat!ons to "et

+

+

+=

+

+

+

+=

+

+

+

+

+=

3

5

2

4322

4

5

3

4

2

321

5

5

4

4

3

3

2

21#

2#12621

54321

β

θ

β

θ

β

θ

β

β

θ

β

θ

β

θ

β

θ

β

β

θ

β

θ

β

θ

β

θ

β

θ

C C C C a

C C C C C v

C C C C C C s

+

−

=

543

6151#β

θ

β

θ

β

θ h s



242"

3$'$ and '$$/$ "olynomial• 3-4-5 +ol/nomial

$imilar in sha+e to c/cloidal

iscontinuous er,

• 4-5-6-7 +ol/nomial set the er, to (e

ero at # and β

• *as continuous er,' (ut e&er/thing

else is larger

+

−

=

543

6151#β

θ

β

θ

β

θ h s

−

+

−

=

7654

2#7#8435 β

θ

β

θ

β

θ

β

θ

hs

4-5-6-7 9ol/nomial



353#

-cceleration Comparisons• Modi%ied tra+eoid is the (est' %ollowed (/ modi%ied

sine and 3-4-5• :ow accelerations im+l/ low %orces



3131

*er Comparison

• C/cloidal is lowest' %ollowed (/ 4-5-6-7 +ol/nomialand 3-4-5 +ol/nomial

• :ow er, im+lies lower &i(rations



3232

9elocity Comparison

• Modi%ied sine is (est' %ollowed (/ 3-4-5 +ol/nomial• :ow &elocit/ means low ,inetic energ/



3333

"osition Comparison• ;here is not much di%%erence in the +osition cur&es

• $mall +osition changes can lead to large

acceleration changes



3'34

Ta0le for "ea 9-* for Cam &unctions

• <elocit/ is in m=rad' cceleration is in m=rad2' >er,is in m=rad3?

ingle Dwell Cam Design sing



335

ingle Dwell Cam Design, sing

Dou0le Dwell &unctions

• ;he dou(le dwell cam %unctions ha&e anunnecessar/ return to ero in the acceleration'

causing the acceleration to (e higher elsewhere?

$ingle well Cam esign ou(le



3/36

$ingle well Cam esign' ou(le

*armonic %unction• :arge negati&e acceleration

%all%or2cos14

1cos1

2

rise%or2cos14

1cos1

2

−−

+=

−−

−=

β

θ π

β

θ π

β

θ π

β

θ π

hs

hs

$ingle well Cam esign 3 4 5 6



337

$ingle well Cam esign' 3-4-5-6

9ol/nomial

• oundar/ conditions @θ A# sA&AaA#@θ Aβ sA&AaA# @θ Aβ/2 s=h

−

+

−

=

6543

641"21"264β

θ

β

θ

β

θ

β

θ hs

• #as lo$e% &eak

a''ele%at!on (54)*

than ''lo!dal (5)3*

o% dole ha%on!'

(.00*



338

Bns/mmetrical RF Cams

• % the rise has di%%erent time than the %all' need more (oundar/ conditions?

• 0ith 7Cs



343"


• % /ou set the &elocit/ to ero at the +ea,



'54#


• 0ith 3 segments' segment 1 with 5Cs' segment 2with 6Cs get a large +ea, acceleration



'141


• est to start with segment with lowest accelerationwith 5Cs then do the other segment with 6Cs



'242

Critical 9ath Motion C9M.

• 9osition or one o% its deri&ati&es is s+eci%ied• D! Constant &elocit/ %or hal% the rotation

• rea, the motion into the %ollowing +arts



'343

Critical 9ath Motion C9M.

• $egment 1 has4Cs

• $egment 2 has

2Cs constant <.• $egment 3 has

4Cs

• :ast segment has6Cs almost

alwa/s.



''44

Resulting Cur&es



'45

Constant <elocit/' 2 $egments• ;he di&isions on the +re&ious a++roach are not

gi&en' onl/ one segment o% constant &elocit/



'/46

Resulting $<> diagram• 2 segment design has (etter +ro+erties

• 4 segment design had ∆sA6?112' &A-2"?4' aA257



'47

$iing the Cam' ;erminolog/• ase circle R (. smallest circle that can (e drawn

tangent to the +h/sical cam sur%ace

• 9rime circle R +. smallest circle that can (e drawn

tangent to the locus o% the centerline o% the %ollower

• 9itch cur&e locuso% the centerline o%

the %ollower



'48

Cam 9ressure ngle

• 9ressure ngle φ. the angle (etween

the direction o%motion &elocit/. o%the %ollower and thedirection o% the a!iso% transmission

• 0ant φ E3# %ortranslating and φ E35%or oscillating%ollowers

φ



'44"

Cam Dccentricit/

• Dccentrict/ ε. the +er+endicular distance

(etween the %ollowers

a!is o% motion and thecenter o% the cam

• ligned %ollower εA#

(ε

i



55#

&erturning Moment

For %lat %aced %ollower'

the +ressure angle is

ero

;here is a moment on

the %ollower since the

%orce is not aligned

with the direction o%

%ollower motion? ;hisis called the

overturning moment

di % C



151

Radius o% Cur&ature• D&er/ +oint on the cam has an associated radius o%

cur&ature• % the radius o% cur&ature is smaller than the radius o% the

%ollower the %ollower doesnt mo&e +ro+erl/

• Rule o% thum(

ρmin A2

→3.

R %

Radius o% Cur&ature Flat Faced



252

Radius o% Cur&ature Flat Faced

Follower

• 0e cant ha&e a negati&eradius o% cur&ature

C M % i C id i



353

Cam Manu%acturing Considerations

• Medium to high car(on steels' or cast ductile iron• Milled or ground

• *eat treated %or hardness Roc,well *RC 5#-55.

• C)C machines o%ten use linear inter+olation largeraccelerations.

ctual &s



'54

ctual &s?

;heoretical Cam

9er%ormance• :arger acceleration

due to

manu%acturingerrors' and

&i(rations %rom er,

9 i l i C id i



9ractical esign Considerations

• ;ranslating or oscillating %ollowerG• Force or Form-ClosedG

Follower >um+ &s? Crosso&er $hoc,

• Radial or !ial CamG• Roller or Flat-Faced FollowerG

• ;o well or )ot to wellG

• ;o rind or not to rindG

• ;o :u(ricate or )ot to :u(ricateG

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