cam design
TRANSCRIPT
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CAM DESIGN
Chapter 8
![Page 2: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/2.jpg)
Introduction
![Page 3: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/3.jpg)
Terminology
• Type of Follower Motion
– Rotating follower
![Page 4: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/4.jpg)
Terminology
• Type of Follower Motion
– Translating follower
![Page 5: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/5.jpg)
Terminology
• Type of Joint Closure
– Force
![Page 6: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/6.jpg)
Terminology
• Type of Joint Closure
– Form
![Page 7: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/7.jpg)
Terminology
• Type of Follower
– Flat-faced – Roller
![Page 8: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/8.jpg)
Terminology
• Type of Follower
– Mushroom
![Page 9: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/9.jpg)
Terminology
• Type of Cam
– Radial
• Previous Figures
– Axial
![Page 10: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/10.jpg)
Terminology
• Type of Motion Constrains
– Critical Extreme Position (CEP)
– Critical Path Motion (CPM)
• Type of Motion Program
– RF: rise-fall
– RFD: rise-fall-dwell
– RDFD: rise-dwell-fall-dwell
![Page 11: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/11.jpg)
SVAJ Diagrams
![Page 12: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/12.jpg)
Double-Dwell Cam
![Page 13: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/13.jpg)
Double-Dwell Cam
• Example 8.1 A Bad Cam!
– Consider the following cam design CEP
specification• dwell at zero displacement for 90 degrees
• rise 1 in (25 mm) in 90 degrees
• dwell at 1 in (25 mm) for 90 degrees
• fall 1 in (25 mm) in 90 degrees
• cam 2π rad/sec
![Page 14: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/14.jpg)
Double-Dwell Cam
![Page 15: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/15.jpg)
Double-Dwell Cam
• Fundamental Law of Cam Design
– The cam function must be continuous
through the first and second derivatives
of displacement across the entire
interval (360 degrees)
• The jerk function must be finite across the
entire interval
• Functions
– Simple Harmonic Motion (SHM)
– Cycloidal Displacement
![Page 16: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/16.jpg)
Double-Dwell Cam
– Combine
» Constant Acceleration
» Trapezoidal Acceleration
» Modified Trapezoidal Acceleration
» Modified Sinusoidal Acceleration
– Sine-Constant-Cosine-Acceleration (SCCA)
– Polynomials
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Double-Dwell Cam
– Simple Harmonic Motion (SHM)
sin2
cos2
sin2
cos12
3
3
2
2
hj
ha
hv
hs
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Double-Dwell Cam
– Cycloidal Displacement
• Start with the acceleration function (sine
wave)
2sin2
1
2cos1
2cos4
2sin2
3
2
2
hs
hv
hj
ha
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Double-Dwell Cam
– Combined Functions
• Constant Acceleration
![Page 20: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/20.jpg)
Double-Dwell Cam
– Combined Functions
• Trapezoidal Acceleration
![Page 21: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/21.jpg)
Double-Dwell Cam
– Combined Functions
• Modified Trapezoidal Acceleration
![Page 22: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/22.jpg)
Double-Dwell Cam
– Combined Functions
• Modified Trapezoidal Acceleration
![Page 23: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/23.jpg)
Double-Dwell Cam
– Combined Functions
• Modified Sinunusoidal Acceleration
![Page 24: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/24.jpg)
Double-Dwell Cam
– Combined Functions
• Modified Sinunusoidal Acceleration
![Page 25: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/25.jpg)
Double-Dwell Cam
– Sine-Constant-Cosine-Constant (SCCA)
• A family of acceleration functions that includes
constant acceleration, simple harmonic, modified
trapezoid, modified sine, and cycloidal curves.
• Expression for the functions within each zone are
given in pages 413-415
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Double-Dwell Cam
– Sine-Constant-Cosine-Constant (SCCA)
![Page 27: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/27.jpg)
Double-Dwell Cam
– Comparison of five cam acceleration program
• Acceleration
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Double-Dwell Cam
– Comparison of five cam acceleration program
• jerk
![Page 29: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/29.jpg)
Double-Dwell Cam
– Comparison of five cam acceleration program
• velocity
![Page 30: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/30.jpg)
Double-Dwell Cam
– Comparison of three cam acceleration program
• displacement
![Page 31: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/31.jpg)
Double-Dwell Cam
– Polynomial Functions
• 3-4-5 Polynomial
n
nxCxCxCxCxCxCCs 5
5
4
4
3
3
2
210
5
5
4
4
3
3
2
210
CCCCCCs
4
5
3
4
2
321 5432
CCCCCv
3
5
2
432 201262
CCCCa
sBC' thefrom found are s' C
zero are ,, 210 CCC
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Double-Dwell Cam
– Polynomial Functions
• 4-5 -6-7 Polynomial7
7
6
6
5
5
4
4
3
3
2
210
CCCCCCCCs
6
7
5
6
4
5
3
4
2
321 765432
CCCCCCCv
5
7
4
6
3
5
2
432 4230201262
CCCCCCa
sBC' thefrom found are s' C
zero are ,,, 3210 CCCC
![Page 33: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/33.jpg)
Single Dwell Cam Design
• Rise-Fall-Dwell (RFD)
– Single-dwell cam specifications
• rise: 1 in (25.4mm) in 90 degrees
• fall: 1 in (25.4mm) in 90 degrees
• dwell: at zero displacement for 180
degrees(low dwell)
• cam ω: 15 rad/sec
![Page 34: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/34.jpg)
Single Dwell Cam Design
• Rise-Fall-Dwell (RFD)
– Cycloidal Motion
2sin2
1
2cos1
2cos4
2sin2
3
2
2
hs
hv
hj
ha
![Page 35: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/35.jpg)
Single Dwell Cam Design
• Rise-Fall-Dwell (RFD)
– Double Harmonic
:rise for the
2sin2sin2
2coscos2
2sin2
1sin
2
2cos14
1cos1
2
3
3
2
2
hj
ha
hv
hs
![Page 36: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/36.jpg)
Single Dwell Cam Design
• Rise-Fall-Dwell (RFD)
– Double Harmonic
:fall for the
2sin2sin2
2coscos2
2sin2
1sin
2
2cos14
1cos1
2
3
3
2
2
hj
ha
hv
hs
![Page 37: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/37.jpg)
Single Dwell Cam Design
• Rise-Fall-Dwell (RFD)
– Double Harmonic
![Page 38: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/38.jpg)
Single Dwell Cam Design
• Rise-Fall-Dwell (RFD)
– Polynomials
• Minimize the number of segments (2)
• Minimize the number of boundary conditions
• Redefine the CEP specifications
• rise-fall: 1 in (25.4 mm) in 90° and fall 1 in
90° for a total of 180° (low dwell)
• dwell: at zero displacement for 180°
• Cam ω: 15 rad/sec
![Page 39: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/39.jpg)
Single Dwell Cam Design
• Rise-Fall-Dwell (RFD)
– Polynomials
• Boundary Conditions
![Page 40: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/40.jpg)
Single Dwell Cam Design
• Rise-Fall-Dwell (RFD)
– Polynomials
![Page 41: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/41.jpg)
Single Dwell Cam Design
• Rise-Fall-Dwell (RFD)
– Polynomials (Asymmetrical)
• Redefine the CEP specifications
• rise-fall: 1 in (25.4 mm) in 45° and fall 1 in
135° for a total of 180° (low dwell)
• dwell: at zero displacement for 180°
• Cam ω: 15 rad/sec
• Two segments( Different order, 6 &7)
• Three segments (segment with the smaller
acceleration)
![Page 42: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/42.jpg)
Single Dwell Cam Design
• Rise-Fall-Dwell (RFD)
– Polynomials (Asymmetrical)
![Page 43: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/43.jpg)
Critical Path Motion
• Most common application is for
constant velocity motion
– intermittent
– continuous
– Typical problem
• Accelerate the follower from zero to 10
in/sec
• Maintain a constant velocity of 10
in/sec for 0.5 sec
![Page 44: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/44.jpg)
Critical Path Motion
– Typical problem
• decelerate the follower to zero velocity
• return the follower to start
position
• cycle time exactly 1 sec
![Page 45: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/45.jpg)
Critical Path Motion
![Page 46: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/46.jpg)
Critical Path Motion
![Page 47: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/47.jpg)
Sizing
• Major factor that affect cam size
– Pressure angle
– Radius of curvature
– Base circle radius (flat)
• The smallest circle that can be drawn tangent
to the physical cam surface
– Prime circle radius (roller or curved)
• The smallest circle that can be drawn tangent
to the locus of the centerline of the follower
![Page 48: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/48.jpg)
Sizing
![Page 49: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/49.jpg)
Sizing
• Pressure angle
– The angle between
the direction of
motion (velocity) of
the follower and the
direction of the axis
of transmission
• Between 0° and 30°
![Page 50: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/50.jpg)
Sizing
• Pressure angle
– Eccentricity
• Perpendicular
distance between
the follower’s axis
of motion and the
center of the cam
• The distance b to
the instant center is
equal to the velocity
of the follower
sbVI
4,2
vb
![Page 51: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/51.jpg)
Sizing
• Pressure angle
– Prime Circle
Radius
22arctan
PRs
v
![Page 52: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/52.jpg)
Sizing
• Pressure angle
– Overturning –
Translating Flat-
Faced Follower
![Page 53: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/53.jpg)
Sizing
• Radius of Curvature (Roller)
– No matter how complicated a curve’s
shape may be, nor how high the
degree of the describing function, it
will have a instantaneous radius of
curvature
– Concerns
• Large radius
![Page 54: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/54.jpg)
Sizing
• Radius of Curvature (Roller)
– Concerns
• Undercutting
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Sizing
• Radius of Curvature (Roller)
– The rule of thumb is to keep the
absolute value of the minimum radius
of curvature of the cam pitch curve 2
to 3 times as large as the radius of
the follower
fRmin
sRavsR
vsR
PP
Ppitch
22
2/322
2
![Page 56: Cam Design](https://reader031.vdocument.in/reader031/viewer/2022013102/544008cbafaf9fff098b4c49/html5/thumbnails/56.jpg)
Sizing
• Radius of
Curvature (Flat)
sRjx bA R
vx
minmax vvfacewidth
minmin asRb
Contour; Cam
cossin vsRr b sincos vsRq b