cam design
TRANSCRIPT
CAM DESIGN
Chapter 8
Introduction
Terminology
• Type of Follower Motion
– Rotating follower
Terminology
• Type of Follower Motion
– Translating follower
Terminology
• Type of Joint Closure
– Force
Terminology
• Type of Joint Closure
– Form
Terminology
• Type of Follower
– Flat-faced – Roller
Terminology
• Type of Follower
– Mushroom
Terminology
• Type of Cam
– Radial
• Previous Figures
– Axial
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
SVAJ Diagrams
Double-Dwell Cam
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
Double-Dwell Cam
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
Double-Dwell Cam
– Combine
» Constant Acceleration
» Trapezoidal Acceleration
» Modified Trapezoidal Acceleration
» Modified Sinusoidal Acceleration
– Sine-Constant-Cosine-Acceleration (SCCA)
– Polynomials
Double-Dwell Cam
– Simple Harmonic Motion (SHM)
sin2
cos2
sin2
cos12
3
3
2
2
hj
ha
hv
hs
Double-Dwell Cam
– Cycloidal Displacement
• Start with the acceleration function (sine
wave)
2sin2
1
2cos1
2cos4
2sin2
3
2
2
hs
hv
hj
ha
Double-Dwell Cam
– Combined Functions
• Constant Acceleration
Double-Dwell Cam
– Combined Functions
• Trapezoidal Acceleration
Double-Dwell Cam
– Combined Functions
• Modified Trapezoidal Acceleration
Double-Dwell Cam
– Combined Functions
• Modified Trapezoidal Acceleration
Double-Dwell Cam
– Combined Functions
• Modified Sinunusoidal Acceleration
Double-Dwell Cam
– Combined Functions
• Modified Sinunusoidal Acceleration
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
Double-Dwell Cam
– Sine-Constant-Cosine-Constant (SCCA)
Double-Dwell Cam
– Comparison of five cam acceleration program
• Acceleration
Double-Dwell Cam
– Comparison of five cam acceleration program
• jerk
Double-Dwell Cam
– Comparison of five cam acceleration program
• velocity
Double-Dwell Cam
– Comparison of three cam acceleration program
• displacement
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
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
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
Single Dwell Cam Design
• Rise-Fall-Dwell (RFD)
– Cycloidal Motion
2sin2
1
2cos1
2cos4
2sin2
3
2
2
hs
hv
hj
ha
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
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
Single Dwell Cam Design
• Rise-Fall-Dwell (RFD)
– Double Harmonic
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
Single Dwell Cam Design
• Rise-Fall-Dwell (RFD)
– Polynomials
• Boundary Conditions
Single Dwell Cam Design
• Rise-Fall-Dwell (RFD)
– Polynomials
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)
Single Dwell Cam Design
• Rise-Fall-Dwell (RFD)
– Polynomials (Asymmetrical)
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
Critical Path Motion
– Typical problem
• decelerate the follower to zero velocity
• return the follower to start
position
• cycle time exactly 1 sec
Critical Path Motion
Critical Path Motion
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
Sizing
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°
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
Sizing
• Pressure angle
– Prime Circle
Radius
22arctan
PRs
v
Sizing
• Pressure angle
– Overturning –
Translating Flat-
Faced Follower
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
Sizing
• Radius of Curvature (Roller)
– Concerns
• Undercutting
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
Sizing
• Radius of
Curvature (Flat)
sRjx bA R
vx
minmax vvfacewidth
minmin asRb
Contour; Cam
cossin vsRr b sincos vsRq b