Dynamic Behaviour of a Two-Stage Cycloidal Speed Reducer ...
Source: Norton, Design of Machinery Introduction to … Rise Cycloidal Fall Ú Title Microsoft...
Transcript of Source: Norton, Design of Machinery Introduction to … Rise Cycloidal Fall Ú Title Microsoft...
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At the end of this video, you should be able to:• Explain what a cam is, how it is used, and the typical types of cams• Identify force closed and form closed followers and explain the
benefits and limitations of each• Describe the primary types of cam motion programs
Introduction to Cam DesignSource: Norton, Design of Machinery
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What is a Cam and Follower?Cam: specially shaped part designed to move a follower in a controlled fashionFollower: a link constrained to rotate or translate
• A cam‐follower is a degenerate 4‐bar linkage
Source: Norton, Design of Machinery
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What are Cams Used For?
• Valve actuation in IC engines• Motion control in machinery• Force generation• Precise positioning• Event timing
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Overhead Valve Overhead Camshaft
Valve Trains
Source: Norton, Cam Design and Manufacturing Handbook
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Industrial Cam Trains
Source: Norton, Cam Design and Manufacturing Handbook
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Hydraulic Pump Application
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Stationary segment
Stationary-axial-track
Radial or plate
Barrel or axial - track
Radial or plate
Radial track
Types of Cams
Source: Norton, Cam Design and Manufacturing Handbook
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Types of Followers
Source: Norton, Design of Machinery
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Force Closed:
Two Ways to Close Follower Joint
Form Closed: Source: Norton, Design of Machinery
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Conjugate Cams
Source: Norton, Design of Machinery
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Barrel Cams
Tracked:z
FIGURE 13-13
Ribbed barrel cam with oscillating roller follower
Ribbed:
Source: Norton, Design of Machinery
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Rotary Indexers Use Ribbed Barrel Cams
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Types of Cam Motion Programs
• No‐Dwell or Rise‐Fall (RF)• Single‐Dwell or Rise‐Fall‐Dwell (RFD)• Double‐Dwell (RDFD)• Multi‐Rise‐Multi‐Dwell‐Multi‐Fall
• Different Motion Programs Needed for Each
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A Cam Timing Diagram
FIGURE 2-2
A cam timing diagram
1
0
Motionmm or in
Lowdwell
Highdwell
Rise Fall
1.00.25 0.50 0.750 Time t sec
90 180 270 3600 Cam angle θ deg
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SVAJ Diagrams
S
V
A
J
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At the end of this video, you should be able to:• Describe the difference between critical extreme position and
critical path motion• Explain how the fundamental law of cam design applies to selecting
an appropriate cam profile• Design double dwell cam profiles using a variety of motion types
Cam Motion Design: Critical Extreme Position
Source: Norton, Design of Machinery
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Unwrapping Cam Profile
θ
S - Position
Source: Norton, Design of Machinery
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Type of Motion Constraints
• Critical Extreme Position (CEP)– End points of motion are critical– Path between endpoints is not critical
• Critical Path Motion (CPM)– The path between endpoints is critical– Displacements, velocities, etc. may be specified– Endpoints usually also critical
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Double Dwell Cam Timing Diagram
FIGURE 2-2
A cam timing diagram
1
0
Motionmm or in
Lowdwell
Highdwell
Rise Fall
1.00.25 0.50 0.750 Time t sec
90 180 270 3600 Cam angle θ deg
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Naïve and Poor Cam Design: Constant Velocity
FIGURE 2-3
The s v a j diagrams of a "bad" cam design—pure constant velocity
h
0
s
v
0
90 180 270 3600
a
0
j
0
∞ ∞
∞∞
Lowdwell
HighdwellRise Fall
degθ
degθ
degθ
degθ
∞ 2
(a)
(b)
(c)
(d )
∞ 2
∞ 2 ∞ 2
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Constant Acceleration (Parabolic Displacement)?
FIGURE 2-6
Constant acceleration gives infinite jerk
(a) Acceleration
(b) Jerk
Lowdwell
HighdwellRisea
0
j
∞
∞
∞
θ
θ
maxa
mina
0
0 β
0 β
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Simple Harmonic Motion (SHM)?
sh
vh
ah
jh
= (2.6a)
= (2.6b)
= (2.6c)
= – (2.6d)
2
3
21
2
2
2
2
3
−⎛⎝⎜
⎞⎠⎟
⎡
⎣⎢⎢
⎤
⎦⎥⎥
⎛⎝⎜
⎞⎠⎟
⎛⎝⎜
⎞⎠⎟
⎛⎝⎜
⎞⎠⎟
cos
sin
cos
sin
π θβ
πβ
π θβ
πβ
π θβ
πβ
π θβ
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Norton’s Fundamental Law of Cam Design:The cam-follower function must have continuous
velocity and acceleration across the entire interval, thus making the jerk finite.
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Choosing Cam Functions
• They must obey the fundamental law• Lower peak acceleration is better: F = ma• Lower peak velocity lowers KE = 0.5mv2
• Smoother jerk means lower vibrations• Magnitude of jerk is poorly controlled in manufacturing
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Acceptable Double Dwell Function:Cycloidal Motion
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Acceptable Double Dwell Function:Modified Trapezoidal Acceleration
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Acceptable Double Dwell Function:Modified Sine Acceleration
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FIGURE 3-13
Minimum boundary conditions for the double-dwell case
(a)
(b)
(c)
(d )
h
0
s
v
0
a
0
j
0
Lowdwell
HighdwellRise Fall
degθ
degθ
degθ
degθβ20 0β1
β20 0β1
β20 0β1
β20 0β1
Polynomial Functionss C C x C x C x C x C x C x C xn
n= + + + + + + + +0 1 22
33
44
55
66 3 19 ( . )
when then(a)
when then
θ
θ β
= = = =
= = = =
0 0 0 0
0 01
; , ,
; , ,
s v a
s h v a
v C C C C C= +⎛⎝⎜
⎞⎠⎟
+⎛⎝⎜
⎞⎠⎟
+⎛⎝⎜
⎞⎠⎟
+⎛⎝⎜
⎞⎠⎟
⎡
⎣⎢⎢
⎤
⎦⎥⎥
12 3 4 51 2 3
2
4
3
5
4
βθβ
θβ
θβ
θβ
(d)
a C C C C= +⎛⎝⎜
⎞⎠⎟
+⎛⎝⎜
⎞⎠⎟
+⎛⎝⎜
⎞⎠⎟
⎡
⎣⎢⎢
⎤
⎦⎥⎥
12 6 12 202 2 3 4
2
5
3
βθβ
θβ
θβ
(e)
s C C C C C C= +⎛⎝⎜
⎞⎠⎟
+⎛⎝⎜
⎞⎠⎟
+⎛⎝⎜
⎞⎠⎟
+⎛⎝⎜
⎞⎠⎟
+⎛⎝⎜
⎞⎠⎟0 1 2
2
3
3
4
4
5
5θβ
θβ
θβ
θβ
θβ
(c)
0 0 0
00
0
= + + +=
C
C
(f)
01
0 0
0
1
1
= + + +[ ]=
βC
C
(g)
01
0 0
0
2 2
2
= + + +[ ]=
βC
C
(h)
h C C C= + +3 4 5 (i)
01
3 4 53 4 5= + +[ ]βC C C (j)
01
6 12 202 3 4 5= + +[ ]β
C C C ( )k
C h C h C h3 4 510 15 6= = − =; ; (l)
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The 3‐4‐5 and 4‐5‐6‐7 Polynomials3-4-5 Polynomial 4-5-6-7 Polynomial
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Comparison of Five Double-Dwell Fcns
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At the end of this video, you should be able to:• Describe why a double‐dwell profile is not ideal for a single‐dwell
cam• Construct the boundary conditions for a polynomial cam segment• Solve for the coefficients of a polynomial cam segment
Cam Motion Design: Polynomial Deep Dive
Source: http://nptel.ac.in
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Single Dwell Cam Design• Rise: 1 inch in 90°• Fall: 1 inch in 90°• Dwell: 180°360°
2 Double‐Dwell Profiles?
Task: Rise‐Fall‐Dwell
Source: http://nptel.ac.in
0 Cycloidal Rise Cycloidal Fall