Table Of ContentNodar Davitashvili · Valeh Bakhshaliev
Dynamics of
Crank-Piston
Mechanisms
Dynamics of Crank-Piston Mechanisms
Nodar Davitashvili Valeh Bakhshaliev
(cid:129)
Dynamics of Crank-Piston
Mechanisms
123
Nodar Davitashvili Valeh Bakhshaliev
Georgian Technical University Azerbaijan Technical University
Tbilisi Baku
Georgia Azerbaijan
ISBN978-981-10-0322-6 ISBN978-981-10-0323-3 (eBook)
DOI 10.1007/978-981-10-0323-3
LibraryofCongressControlNumber:2015958839
©SpringerScience+BusinessMediaSingapore2016
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Contents
1 General Problem of Dynamics of Crank-Piston Mechanism
with Clearances in Kinematic Pairs . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Analysis of Machines and Mechanisms Used for Oil
and Gas Transportation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Review of Some Scientific Works on Joint Mechanisms
with Clearances and Crank-Piston Mechanisms . . . . . . . . . . . . . 2
1.3 Dynamic Model of Crank-Piston Mechanism with Clearances
in Kinematic Pairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Classification of Slider Motion in Cylinder with Clearances . . . . 5
1.5 Dynamic Model Piston-Cylinder of Sliding Kinematic Pair
with Clearances of Crank-Piston Mechanism. . . . . . . . . . . . . . . 9
1.6 Real Dynamic Model of Crank-Piston Mechanism with
Clearances in Three Kinematic Pairs . . . . . . . . . . . . . . . . . . . . 10
1.7 Movements of Crank-Piston Mechanism with Consideration
of Clearances in Three Kinematic Pairs. . . . . . . . . . . . . . . . . . . 13
2 Dynamic Research of Crank-Piston Mechanism
with Clearances in Two Kinematic Pairs. . . . . . . . . . . . . . . . . . . . . 17
2.1 Dynamic Research of Crank-Piston Mechanism
with Clearances in Two Kinematic Pairs. . . . . . . . . . . . . . . . . . 17
2.2 Calculation of Crank-Piston Mechanism Kinematic
Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 The Forces Acting on the Crank-Piston Mechanism . . . . . . . . . . 21
2.4 The Kinetic Energies of Crank-Piston Mechanism with
Clearances in Two Kinematic Pairs . . . . . . . . . . . . . . . . . . . . . 23
2.5 Differential Equations of Crank-Piston Mechanism Motions. . . . . 29
2.5.1 Definition of Reduced Moment of Mechanism. . . . . . . . 30
2.5.2 Differential Equation of Mechanism,
When Δ = Δ = 0. . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1 2
2.6 Electromechanical Parameters of Motor and Equations
of Motion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
v
vi Contents
2.7 Differential Equations of Basic and Additional Motions
of Crank-Piston Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.8 Calculation of Crank-Piston Mechanism Generalized
Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
2.9 Calculation of Reaction and Friction Forces
of Crank-Piston Mechanism with Clearances
in Kinematic Pairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
2.10 Recommendation and Conclusion. . . . . . . . . . . . . . . . . . . . . . . 74
3 The Operational Characteristics (Friction, Wear) in Kinematic
Pairs of Crank-Piston Mechanism. . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.2 Friction in Kinematic Pairs of Hinged Mechanisms . . . . . . . . . . 78
3.2.1 Friction in the Rotary Kinematic Pair. . . . . . . . . . . . . . 79
3.3 The Wear Investigation Issue in Four-Bar Crank-Piston
Mechanism with Clearances in Rotary Kinematic Pairs. . . . . . . . 87
3.3.1 Calculation of Wear in Kinematic Pair
of Crank-Piston Mechanism. . . . . . . . . . . . . . . . . . . . . 89
4 Research of Operational Characteristics Problem (Cracks
Formation) of Crank-Piston Mechanism . . . . . . . . . . . . . . . . . . . . . 95
4.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.2 Basic Part of Cracks Formation of Crank-Piston Mechanism. . . . 96
4.2.1 Research of Cracks Formation Process in Coupler
of Crank-Piston Mechanism. . . . . . . . . . . . . . . . . . . . . 99
5 Research of Operational Characteristics of Crank-Piston
Mechanism by Computer Engineering . . . . . . . . . . . . . . . . . . . . . . 105
5.1 Describing the Basic and Additional Motions
of Crank-Piston Mechanism Simultaneous Differential
Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.2 Analysis of Crank-Piston Mechanism Operating
Characteristic by Computer Engineering. . . . . . . . . . . . . . . . . . 111
5.3 Automated Transition from One Mode to Another
at Dynamic Study of Crank-Piston Mechanism . . . . . . . . . . . . . 115
5.4 Dynamic Research of Program Complex of Crank-Piston
Mechanism with Clearances . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.5 Dynamic Study Crank-Piston of the Mechanism with
Clearances with Consideration of Characteristics . . . . . . . . . . . . 119
5.6 Research of Operational Characteristics Influence
on Parameters of Crank-Piston Mechanism Elements . . . . . . . . . 120
6 Dynamic Analysis of Crank-Piston Mechanism
with Consideration of Impacts in Kinematic Pairs. . . . . . . . . . . . . . 129
6.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
6.2 On Dynamic Model of Crank-Piston Mechanism. . . . . . . . . . . . 131
Contents vii
6.3 Study of Impacts in Kinematic Pairs of Crank-Piston
Mechanism with Clearances . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.4 Definition of Colliding Links Velocities After the Impact
Due the Absolute Smoothness Hypothesis. . . . . . . . . . . . . . . . . 139
6.5 Definition of Colliding Links Velocity After the Impact
Due Instant (Viscous) Friction Coefficient Hypothesis. . . . . . . . . 140
6.6 Definition of Colliding Link’s Velocities After Impact
by Considering of Dry Friction . . . . . . . . . . . . . . . . . . . . . . . . 141
6.7 Friction at Impact [79] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
6.8 Change of Kinetic Energy at Impact. . . . . . . . . . . . . . . . . . . . . 143
6.9 Dynamic Study of Crank-Piston Mechanism with Clearances
and Impacts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
7 The Study of Cranks-Piston Mechanisms with Taking
into Account the Clearances and Elasticity of Links . . . . . . . . . . . . 151
7.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
7.2 Elastic Deformation of Crank-Piston Mechanisms Coupler . . . . . 153
7.3 Definition of Reduced Stiffness Coefficient of Crank-Piston
Mechanism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
7.4 Differential Equation of Cranks-Piston Mechanism Motion
with Consideration of Clearances and Elasticity of Links . . . . . . 167
7.5 Oscillations of Crank-Piston Mechanism with Elastic Links. . . . . 169
7.6 The Influence of Viscous Friction Force on Crank-Piston
Mechanism Operation Process. . . . . . . . . . . . . . . . . . . . . . . . . 173
7.7 Dynamic Study of the Crank-Piston Mechanisms
with Elastic Links by Computer Engineering. . . . . . . . . . . . . . . 175
8 Dynamic Research of Crank-Piston Mechanism with Clearances
in Kinematic Pairs and Consideration of Elasticity of Links
with Concentrated Masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
8.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
8.2 Conditions for Mechanism’s Links Mass Distribution. . . . . . . . . 184
8.3 Dynamics of Concentrated Masses Crank-Piston Mechanism
with Rigid Links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
8.4 Method for Determining the Stiffness Coefficients
of Concentrated Masses Cranks-Piston Mechanism. . . . . . . . . . . 191
8.5 Determination of Compliance Coefficients of Cranks-Piston
Mechanism with Clearances . . . . . . . . . . . . . . . . . . . . . . . . . . 193
8.6 Dynamics of Cranks-Piston Mechanism with Taking into
Account the Elasticity of Concentrated Masses Links. . . . . . . . . 199
8.7 Experimental Study Crank-Piston Mechanism Operation
Characteristics by Computer Engineering . . . . . . . . . . . . . . . . . 201
viii Contents
9 Research of Kinematic and Dynamic Errors of Crank-Piston
Mechanisms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
9.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
9.2 Errors of Mechanism and Their Determination Methods . . . . . . . 208
9.3 Differential Method for Determination of Mechanism Errors . . . . 209
9.4 Research of Crank-Piston Mechanism Dynamical Precision. . . . . 214
General Conclusions and Recommendations. . . . . . . . . . . . . . . . . . . . . 219
Curriculum Vitae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
Introduction
This monograph comprises authors’ researches published in various scientific
works and research work on European Project BS-ERA.NET “Reliability and
durability of machines and their mechanisms used in gas and oil transportations in
Black Sea Region.” It focuses on the dynamical research work on crank-piston
mechanisms of piston machines considering basic and additional motions.
In order to have full dynamical analyses of piston machines and their mecha-
nisms,thecrank–pistonmechanismswithclearancesinkinematicpairsarestudied.
Thetasksarecarriedoutbyfocusingonfriction,wear,andimpactsonmechanisms,
as well as crack formation in links and elasticity of details, with distributed and
concentrated masses.
The reliability and durability of piston machines and their mechanisms applied
on oil and gas transportation were analyzed in this work.
The general problems of dynamics of crank–piston mechanisms were studied,
and the necessity to carry out dynamical research of these mechanisms was
determined.Here,theresearchwasfirstcarriedoutbylookingatclearancesintwo
kinematic pairs in conjunction with additional and basic motions of mechanism;
thereafter, operational characteristics (friction, wear, crack formation) in kinematic
pairs and mechanisms were considered.
Analysis of kinematic and dynamic errors of crank–piston mechanisms was
done.Thetheoreticalresultsarerealizedwithapplicationsofcomputerengineering.
The reliability and durability of piston machines and their mechanisms are defined
by applying comparative method on theoretical and practical results.
Thismonographismeantforspecialistswhoarerelatedbydesign,research,and
operation of piston machines and their mechanisms. It will also be useful to spe-
cialist manufacturers and designers of piston machines, scientists and lecturers,
doctoral students, and students of universities.
ix
Chapter 1
General Problem of Dynamics
of Crank-Piston Mechanism
with Clearances in Kinematic Pairs
1.1 Analysis of Machines and Mechanisms Used for Oil
and Gas Transportation
Piston machines (PM) are widely applied in all branches of industries, including
aviation, motor and railway transport, refrigeration and construction industry, etc.
PMsarealsousedforproductionandtransportationofnaturalresources,including
oilandgastransportationinBlackSeaRegion.Thesemachinesrepresenttheheavy
dutysystems,onwhichareappliedlargeexternalforces.Undertheactionofthese
forces are deteriorating actuating elements and often failing machines.
Kinematic and dynamic characteristics of PM joint mechanisms mainly depend
on clearances in kinematic pairs. The existence of these clearances is due to the
manufacturing process of covering and enclosing elements of pairs and their
deterioration, caused by friction in pair and machines as well as external techno-
logical forces.
Under the impact of forces in kinematic pairs of crank-piston mechanisms
(CPM), large loadings are developed, leading to increased reactions in them. High
deterioration in kinematic pairs leads to increased clearances.
Additional displacements of links in tolerance zone of clearances under the
impact of various forces lead to collisions of kinematic pair elements. Increased
dynamic stresses in separate links cause the whole mechanism to vibrate. This
results in links additional displacements in clearances used for selecting optimal
values, in which basic dynamic characteristics of CPM as well as reliability and
durability of PM functions are within the permissible ranges and represent the
actual problem. The above is of great importance in design and dynamic calcula-
tions of PM.
In addition, in the PM operation process, the clearances in kinematic pairs
impacteachother.Theseimpactsmakeuplargevalues,andsystematicalrepetition
causes premature deterioration, components breakdown and machines’ failure.
©SpringerScience+BusinessMediaSingapore2016 1
N.DavitashviliandV.Bakhshaliev,DynamicsofCrank-PistonMechanisms,
DOI10.1007/978-981-10-0323-3_1
