Table Of ContentK10471_cover 8/29/11 12:00 PM Page 1
C M Y CM MY CY CMY K
MECHANICAL ENGINEERING Borboni Parasitic
•
Parasitic Phenomena in the
Faglia
Phenomena in the
Dynamics of Industrial Devices
In the real world the dynamic behavior of a real machine presents either unforeseen Dynamics of
or limiting phenomena: both are undesired, and can be therefore be classified as
parasitic phenomena — unwanted, unforeseen, or limiting behaviors. Parasitic
Phenomena in the Dynamics of Industrial Devices describes the potential causes
i
and effects of these behaviors and provides indications that could minimize their n Industrial Devices
influence on the mechanical system in question. t
h
e
The authors introduce the phenomena and explore them through real cases, avoiding
D
academic introductions, but inserting the entire academic and experimental knowledge
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that is useful to understand and solve real-world problems. They then examine these
n
a
parasitic phenomena in the machine dynamics, using two cases that cover the a
r
classical cultural division between cam devices and mechanisms. They also present ma
concrete cases with an amount of experimental data higher than the proposed ones s
i
and with a modern approach that can be applied to various mechanical devices, cit
si
acquiring real knowledge superior to one of the mere finite element systems or c
collections of mechanical devices. o
P
f
h
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• Organizes machine dynamics through systems theory to give a comprehensive ne
vision of the design problem dn
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• Details machine dynamics at an advanced mathematics level and avoids redundancy sm
of fundamental knowledge t
r
e
• Introduces real machine cases for solutions to practical problems i
an
• Covers two broad classes of mechanical devices that are widely used in the la
construction of instrumental goods D
e
• Employs a mechatronic approach that can be applied to electro-mechanical,
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hydro-mechanical, or pneumo-mechanical machines
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c
e
Highlighting industrial devices in the manufacturing industry, including industrial
s
indexing devices and industrial robots, the book offers case studies, advanced
models, design methods, and short examples of applications. It is of critical importance
for any manufacturing enterprise that produces significant amounts of objects through
a process with one or more automated phases.
K10471
Alberto Borboni
6000 Broken Sound Parkway, NW
Suite 300, Boca Raton, FL 33487
711 Third Avenue
an informa business New York, NY 10017 Rodolfo Faglia
www.crcpress.com 2 Park Square, Milton Park www.crcpress.com
Abingdon, Oxon OX14 4RN, UK
Composite
Parasitic
Phenomena in the
Dynamics of
Industrial Devices
Parasitic
Phenomena in the
Dynamics of
Industrial Devices
Alberto Borboni
Rodolfo Faglia
Boca Raton London New York
CRC Press is an imprint of the
Taylor & Francis Group, an informa business
CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2012 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
Version Date: 20110824
International Standard Book Number-13: 978-1-4398-0947-1 (eBook - PDF)
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Contents
Preface....................................................................................................................xiii
Acknowledgments.....................................................................................................xv
The.Authors............................................................................................................xvii
Chapter 1 Dynamics.of.a.Machine.System............................................................1
1.1. Composition.of.a.Machine.(as.a.Dynamic.System)...................1
1.2. Operation.Point.versus.Transmission.Ratio...............................2
1.3. Power.Theorem.in.a.Machine.....................................................6
1.4. Reduction.of.Torques.(and.Forces).............................................7
1.5. The.Transitory..........................................................................10
1.6. Reduction.of.Inertias.(and.Masses)..........................................10
1.7. Backward.Motion.....................................................................12
1.8. Periodic.Rate............................................................................13
1.9. Transmission.at.Constant.τ.......................................................14
1.9.1. Selection.of.a.Transmission.with.Constant.τ..............14
1.10. Transmission.at.Nonconstant.τ.................................................15
1.10.1. Planar.Linkages...........................................................17
1.10.2. Analytical.Methods.for.Planar.Linkages....................26
1.10.3. Cam.Systems...............................................................29
1.11. Constraints.between.Motor.and.Transmission:.Clutches.........37
1.12. Crank.Slider.Mechanism:.Dynamics.and.Balancing...............46
1.12.1. Mass.Distribution.in.the.Crank.Slider.
Mechanism..................................................................46
1.12.2. Dynamics.of.the.Crank-Slider.Mechanism.................47
1.12.3. Vibration.and.Balancing.of.Engine.Unit.....................54
1.12.4. Discussion.of.Ratio.λ.Characteristics.........................58
1.13. Notes.on.Friction.Phenomena.in.Machines..............................58
1.14. Tribology.Elements.and.Lubrication.of.Machines...................62
1.14.1. General........................................................................62
1.14.2. A.Thorough.Analysis.of.Lubrication.Typologies........63
1.14.3. Lubrication.Systems....................................................76
1.14.4. Particular.Applications................................................76
1.15. Critical.Speeds..........................................................................79
1.15.1. Bending.Critical.Speeds.(Bending.Vibrations)...........79
1.15.2. Torsional.Critical.Speeds.(Torsional.Vibrations)........83
Chapter 2 Lubrication.and.Friction.in.Machines.................................................87
2.1. Elastohydrodynamic.Lubrication.............................................87
2.2. Friction.Coefficient.Computation.............................................89
v
vi Contents
2.3. Lubricated.Contacts.in.Mechanisms.with.Planar.Cam............99
2.3.1. Kinematics,.Geometry,.and.Dynamics.
Inferences.on.Friction...............................................101
2.3.2. Transient.and.Localization........................................110
2.3.3. Properties.of.Fluid.and.Surface................................112
Chapter 3 Compliance-Manipulators.with.Flexible.Links.................................121
3.1. Model.for.the.Bending.Vibrations.of.a.Link..........................121
3.2. Approximation.to.Continuous.Model.....................................124
3.2.1. Rotating.Flexible.Link..............................................124
3.2.2. Translating.Flexible.Link..........................................126
3.3. Modeling.of.Flexible.Multilink.Manipulator.........................129
3.3.1. Kinematics.of.Flexible.Link......................................129
3.3.2. Discretization.Methods.............................................132
3.3.2.1. Assumed-Modes.Method...........................132
3.3.2.2. Finite.Element.Model................................137
3.3.3. Dynamic.Equations.of.Motion..................................141
3.4. Control.of.Mono-Link.Rotating.Flexible.Manipulator..........144
3.4.1. Transfer.Function.of.Single.Flexible.Link................144
3.4.2. Determination.of.Motion.through.Dynamic.
Inversion....................................................................146
3.4.3. Experimental.Verification.of.Results........................147
Chapter 4 Backlash—Cam.Mechanisms.and.Coupling.with.Backlash............151
4.1. Dynamic.Response.................................................................151
4.2. Multibody.System.Impact.in.the.Presence.of.
Hysteretic.Dissipation.............................................................153
4.3. Multibody.System.Impact.in.the.Case.
of.Lubricated.Joints................................................................159
4.4. Simplified.Model.for.Systems.Impacts..................................163
4.5. Model.of.a.Cam.Mechanism..................................................164
4.6. Reduction.of.Backlash.Dynamic.Effects...............................166
4.7. Dynamic.Optimization.through.Controlled.Servomotors......173
4.8. Dynamic.Optimization.Limits...............................................175
Chapter 5 Calibration.of.Industrial.Manipulators.............................................177
5.1. Parameters.Characterizing.Geometrical.Performance..........177
5.1.1. Introduction...............................................................177
5.1.2. Resolution,.Repeatability,.and.Accuracy..................178
5.1.3. Performance.Characteristics.Evaluation...................180
5.1.4. Testing.Conditions.....................................................181
5.1.5. Pose.Accuracy.and.Repeatability..............................182
5.1.6. Multidirectional.Pose.Accuracy.Variation................184
Contents vii
5.1.7. Distance.Accuracy.and.Repeatability.......................184
5.1.8. Path.Accuracy.and.Path.Repeatability......................185
5.1.9. Path.Velocity.Performance.Criteria..........................185
5.1.10. Considerations...........................................................186
5.2. Sources.of.Geometrical.Errors...............................................187
5.2.1. Introduction...............................................................187
5.2.2. Nongeometric.Errors.................................................187
5.2.3. Geometric.Errors.......................................................188
5.2.4. Significance.of.Errors................................................192
5.3. Restraint.of.the.Consequences.Triggered.by.the.
Presence.of.Geometrical.Errors.............................................192
5.3.1. Introduction...............................................................192
5.3.2. Robot.Design.............................................................193
5.3.3. Robot.Calibration......................................................194
5.4. Robot.Calibration...................................................................195
5.4.1. Classification.............................................................195
5.4.2. Calibration.Process...................................................196
5.4.2.1. Modeling....................................................197
5.4.2.2. Measurement..............................................202
5.4.2.3. Identification..............................................209
5.4.2.4. Implementation..........................................212
5.4.3. Case.of.Study............................................................213
Chapter 6 Dynamic.Modeling.of.Industrial.Robots..........................................219
6.1. Robotic.System.......................................................................219
6.2. Experimental.Tests.on.a.Mono-Axis.Prototype.....................220
6.2.1. Description.of.the.Mono-Axis.System......................220
6.2.2. Requirements.Satisfied.by.the.System......................223
6.2.3. Possible.Applications.of.the.Mono-Axis.System......223
6.2.4. Experimental.Evaluation.of.Some.Mechanical.
Parameters.of.the.Mono-Axis.System.......................225
6.2.4.1. Experimental.Evaluation.of.the.
Stiffness.in.the.Spring.for.Connecting.
the.Two.Bogies..........................................225
6.2.4.2. Experimental.Evaluation.of.Viscous.
Damping.and.Sliding.Friction...................226
6.2.5. The.Backlash.Effect.on.an.Elastic.Mechanical.
Transmission.............................................................231
6.2.6. Analysis.of.the.Dynamic.Behavior.of.the.
Single-Axis.System...................................................237
6.2.7. Bibliographic.Notes...................................................240
6.3. Model.of.a.SCARA.Industrial.Robot.....................................242
6.3.1. Introduction...............................................................242
6.3.2. The.SCARA.Robot.ICOMATIC.03..........................243
viii Contents
6.3.3. The.Mathematical.Model.of.the.Robot.SCARA.
ICOMATIC.03..........................................................243
6.3.4. Estimation.of.the.Model.Parameters.........................247
6.3.4.1. Measurements.of.Mass.and.Length...........248
6.3.4.2. Dynamic.Tests.for.Estimating.the.
Joints’.Pliability.........................................248
6.3.4.3. Static.Tests.for.Estimating.the.Joints’.
Pliability.....................................................251
6.3.4.4. Summary.and.Comment.of.the.Model.
Parameters.Estimate..................................252
6.3.5. Disturbance.Induced.by.the.Robot.Controller..........255
6.3.6. Analysis.of.Real.and.Simulated.Data........................258
6.3.7. Advantages.and.Defects.of.the.Model......................264
6.3.8. Comparison.of.Reality.Model:.Conclusions.............265
6.3.9. Bibliographic.Notes...................................................266
Chapter 7 Intermittors........................................................................................267
7.1. Cam.Intermittors....................................................................267
7.2. Mathematical.Models.............................................................268
7.2.1. Rigid.Model...............................................................270
7.2.2. Rigid.Model.with.Assigned.Velocity.
of.the.Motor...............................................................273
7.2.3. Rigid.Model.with.Characteristic.Curve.
of.the.Motor...............................................................273
7.2.4. Elastic.Model.with.One.Degree.of.Freedom.............273
7.2.4.1. Motor.Transmission.Intermittor.
and.Joint-Table...........................................273
7.2.5. Elastic.Model.with.One.Degree.of.Freedom.
with.Constant.Motor.Velocity...................................276
7.2.6. Elastic.Model.with.One.Degree.of.Freedom.
with.Characteristic.Curve.of.the.Motor....................276
7.2.7. Elastic.Model.with.Two.Degrees.of.Freedom...........277
7.2.7.1. Subsystem.Motor-Reducer.........................277
7.2.7.2. Subsystem-Compliant.Elastoviscous.
Joint.on.the.Drive.Shaft.............................278
7.2.7.3. Subsystem.Intermittor................................278
7.2.7.4. Subsystem.Downstream.of.the.
Intermittor..................................................279
7.2.8. Elastic.Model.with.Two.Degrees.of.Freedom.
and.Constant.Motor.Velocity....................................281
7.2.9. Elastic.Model.with.Two.Degrees.of.Freedom.
and.Characteristic.Curve.of.the.Motor.....................282
7.3. Model.Utilization.in.the.Simulations.....................................282
Contents ix
7.3.1. Integration.of.the.Differential.Equations.
of.the.Models.............................................................283
7.3.2. Models.Validation.and.Analysis.of.Parametric.
Sensibility..................................................................283
7.3.3. Automatic.Estimation.of.the.Compliance.
Parameters.at.the.Joints.............................................284
7.3.4. The.Implemented.Genetic.Algorithm.......................285
7.3.4.1. Selection.Operator.....................................285
7.3.4.2. Crossover.Operator....................................286
7.3.4.3. Mutation.Operator.....................................286
7.4. Validation.of.the.Parametric.Identification............................286
7.4.1. Comparison.between.Simulated.and.Experimental.
Data.after.Parametric.Identification...........................286
7.4.2. Approximate.Estimation.of.the.Compliance.
Parameters.of.the.Joint.Downstream.
of.the.Intermittor.......................................................288
7.5. Comparison.between.the.Developed.Models.........................289
7.6. Analysis.of.Parametric.Sensibility.........................................294
7.7. Optimization.of.the.Dynamic.Behavior.and.Other.
Application.Examples.of.the.Developed.Models...................297
7.7.1. Optimization.of.the.Cam.Profile...............................297
7.7.2. Optimization.of.the.Cam.Profile.with.
Minimization.of.Negative.Peak.as.Objective.
Function.....................................................................297
7.7.3. Optimization.of.the.Cam.Profile.with.
Minimization.of.the.Overshooting.
as.Objective.Function................................................298
7.7.4. Optimization.of.the.Cam.Profile.with.
Minimization.of.the.Average.Torque.Provided.
by.the.Motor.as.Objective.Function..........................299
7.8. Utilization.of.the.Model.for.the.Foreknowledge.of.the.
System.Dynamic.Behavior.....................................................300
7.8.1. Approximate.Estimation.of.Overshooting................301
7.8.1.1. Calculation.of.the.Elasticity.and.
Dampening.of.the.Joint.Downstream.
of.the.Intermittor.......................................301
7.8.1.2. Estimated.Backlash.in.the.Reducer...........301
7.8.1.3. Estimated.Overshooting.for.J.Equal.to.
c
190000.kg⋅m2.............................................302
7.8.1.4. Approximate.Estimation.of.Overshooting.
by.Means.of.the.Model.with.Two.
Degrees.of.Freedom....................................303
7.8.1.5. Simulation.and.Calculation.of.
the.Overshooting.for.J.Equal.
c
to.190000.kg⋅m2.........................................305
