CAM DESIGN

Chapter 8CAM DESIGN

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 CEPspecification• dwell• rise• dwell• fall• camat zero displacement for 90 degrees1 in (25 mm) in 90 degreesat 1 in (25 mm) for 90 degrees1 in (25 mm) in 90 degrees2π rad/sec

Double-Dwell Cam

Double-Dwell Cam• Fundamental Law of Cam Design– The cam function must be continuousthrough the first and second derivativesof displacement across the entireinterval (360 degrees)• The jerk function must be finite across theentire 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)sin2cos2sin2cos123322hjhahvhs

Double-Dwell Cam– Cycloidal Displacement• Start with the acceleration function (sinewave)2sin212cos12cos42sin2322hshvhjha

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 includesconstant acceleration, simple harmonic, modifiedtrapezoid, modified sine, and cycloidal curves.• Expression for the functions within each zone aregiven 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 Functionss C Cx Cx 2Cx 3Cx 4Cx 501• 3-4-5 Polynomial2345Cx nns Cv C2345 0 C1 C2 C3 C4 C5 23 1 C2 3C3 4C4 5 2 C5 4a2 2 6C3 12C4 20 2CC5 C 's are found from theBC'sC0,C1,C2are zero3

Double-Dwell Cams C– Polynomial Functions• 4-5 -6-7 Polynomial234567 0 C1 C2 C3 C4 C5 C6 C7 v C2345 1 C2 3C3 4C4 5C5 6C6 7 2 C7 234 2 6C3 12C4 20C5 30C6 42 a 2CC7 56C 's are found from theBC'sC0,C1,C2,C3are zero

Single Dwell Cam Design• Rise-Fall-Dwell (RFD)– Single-dwell cam specifications• rise:• fall:1 in (25.4mm) in 90 degrees1 in (25.4mm) in 90 degrees• dwell: at zero displacement for 180degrees(low dwell)• cam ω:15 rad/sec

Single Dwell Cam Design• Rise-Fall-Dwell (RFD)– Cycloidal Motion2sin212cos12cos42sin2322hshvhjha

Single Dwell Cam Design• Rise-Fall-Dwell (RFD)– Double Harmonicfor therise: 22sinsin22coscos22sin21sin22cos141cos123322hjhahvhs

Single Dwell Cam Design• Rise-Fall-Dwell (RFD)– Double Harmonic:for thefall 22sinsin22coscos22sin21sin22cos141cos123322hjhahvhs

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 in90° 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 in135° 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 smalleracceleration)

Single Dwell Cam Design• Rise-Fall-Dwell (RFD)– Polynomials (Asymmetrical)

Critical Path Motion• Most common application is forconstant velocity motion– intermittent– continuous– Typical problem• Accelerate the follower from zero to 10in/sec• Maintain a constant velocity of 10in/sec for 0.5 sec

Critical Path Motion– Typical problem• decelerate• return• cycle timethe follower to zero velocitythe follower to startpositionexactly 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 tangentto the physical cam surface– Prime circle radius (roller or curved)• The smallest circle that can be drawn tangentto the locus of the centerline of the follower

Sizing

Sizing• Pressure angle– The angle betweenthe direction ofmotion (velocity) ofthe follower and thedirection of the axisof transmission• Between 0° and 30°

Sizing• Pressure angle– Eccentricity• Perpendiculardistance betweenthe follower’s axisof motion and thecenter of the camV I2,4 b b vs• The distance b tothe instant center isequal to the velocityof the follower

Sizing• Pressure angle arctans v 2R P2– Prime CircleRadius

Sizing• Pressure angle– Overturning –Translating Flat-Faced Follower

Sizing• Radius of Curvature (Roller)– No matter how complicated a curve’sshape may be, nor how high thedegree of the describing function, itwill have a instantaneous radius ofcurvature– Concerns• Large radius

Sizing• Radius of Curvature (Roller)– Concerns• Undercutting

Sizing• Radius of Curvature (Roller)– The rule of thumb is to keep theabsolute value of the minimum radiusof curvature of the cam pitch curve 2to 3 times as large as the radius ofthe follower min R fpitch2 23/ 2RP s v2R s 2v aR s2PP

Sizing• Radius ofCurvature (Flat)RAx vx facewidthminR bjRbs v maxv mins a minCam Contour; R ssinvcosq Rb scosvsinrb