Transformation of tracking error in parallel kinematic machining [Elektronische Ressource] / von Ghasem Amirian

Ghasem

Informations

• Publié par: universitat_bremen
• Publié le: 01 janvier 2008
• Nombre de lectures: 78
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

Transformation of Tracking Error in Parallel Kinematic Machining
Vom Fachbereich Produktionstechnik
der
Universität Bremen
Zur Erlangung des Grades
Doktor- Ingenieur
genehmigte
Dissertation
von
M.Sc. Ghasem Amirian
Gutachter: Prof. Dr.-Ing. Bernd Kuhfuss
Prof. Dr.-Ing. Gert Goch
Tag der mündlichen Prüfung: 28. November 2008 Acknowledgements
I would like to express my deepest sense of gratitude to my advisor Prof. Dr.-Ing. Bernd
Kuhfuss, for the patient guidance, valuable advices and moral support. In addition, I would
like to thank him for his support during my Ph.D. studies.
I also wish to express my deep appreciation to Prof. Dr.-Ing. Gert Goch for serving on my
dissertation and Prof. Dr.-Ing. habil. Reinhold Kienzler for serving on my candidacy exam
and dissertation committee.
Especially, I would like to thank Dr.-Ing. Christian Schenck for introducing me to the new
area of PKM. His ideas and inspirations have greatly helped the development of my
dissertation.
I would also like to acknowledge my colleagues at the Machine Tools Institute in University
of Bremen, especially, Mrs. Birgit Taeger, Dipl.-Ing. Sebastian Allers, Dipl.-Ing. Frank
Lichthorn, Dipl.-Ing. Stephan Schädlich and Dipl.-Ing. Linghan Li.
I am indebted to my friend, Dr.-Ing. Mostafa Mehrafza, for the valuable discussions and help.
Special thanks are due to Mrs. Tatjana Evas for their warm friendship and help.
Thanks to Miss. Özlem Yilmaz for the support. I also wish to express my appreciation to
Dipl.-Ing. Seyed Jafar Tavakkoli and M.Sc. Reza Malek Mohammadi Nourifar.
Finally, I can never thank enough for my parents for their love and encouragement. I always
owe my wife, a lot for her support and understanding. She has always been a smart consultant
of mine in my life and work. The words are too little to describe my thanks to my wife and
dearest daughter, Alae, for their patience and endless support.
IIIContents
- Zusammenfassung 1
- Abstract 2

1 Introduction 3
2 State of the art 5
2.1 Parallel Kinematics Machines 5
2.1.1 Introduction 5
2.1.2 High Speed Machining 5
2.1.3 Parallel mechanisms 6
2.1.4 Hybrid ms 9
2.2 Servo Motion Control 9

2.2.1 Introduction 9
2.2.2 Step and impulse response of a system 9
2.2.3 PID control algorithm 11
2.2.4 Cascade tracking controller structure 13
2.2.5 Contour error model originated from servo tracking errors in SKM 16
2.2.6 Tracking and contour error control 20
3 Description of problem 26
4 Principle of Tracking Error Transformation in a Simplified Test Bench 28
4.1 Introduction 28
4.2 Structure of Monopod
4.2.1 Mechanical and measuring system 29
4.2.2 Geometric calibration of Monopod by NN method 31
4.2.3 Kinematics transformation 33
4.2.4 Controller gain setting 36
4.3 Simulation model 39
4.4 Results
4.4.1 Effect of position 40
4.4.2 Effect of velocity 40
4.4.3 Effect of direction 41
4.4.4 Effect of velocity feed forward control 42
5 Effect of Transformed Controller Gain in 2-DOF PKM 44
5.1 Introduction 44
5.2 Design of 2-DOF PKM 44
5.2.1 Inverse and forward kinematics of Bipod 44

5.2.2 Position and tracking error transformation 46
5.3 Simulation model 48
5.3.1 Star test 48
5.3.2 The proposed contour error model for a circular trajectory 50
III6 Effect of Transformed Controller Gain in a 3-DOF PKM 54
6.1 Introduction 54
6.2 Tripod configuratin 54
6.2.1 Structural design 55
6.2.2 Measurement system 57
6.2.3 Controller 58
6.3 Kinematic model 59
6.3.1 Inverse transformation 59
6.3.2 Forward transformation 60
6.4 Experimental tests 62
6.4.1 Star test 62
6.4.1.1 Measurement device 62
6.4.1.2 Measuring strategy 65
6.4.2 Circular test 70
6.5 Simulation model 71
6.5.1 Star test 71
6.5.2 Circular test 73
6.6 The effect of mismatches the K factors 78 V
7 Compensation algorithm in Tripod 80
7.1 Introduction 80
7.2 Compensation algorithm
7.3 Tool path compensation strategy 82
7.4 Modelling of Tripod motion 83
7.5 Results of usage compensated trajectory 87
7.6 Machine parameter identification principle 88
8 Conclusions and suggestions for future work 93
9 References 96
IVList of abbreviations
AFLC Adaptive Fuzzy Logic Controller
CAD Computrized Aided Design
CCC Cross Coupling Controller
CNC puter Numerical Control
D Dimension
DBB Double Ball Bar
DOF Degree Of Freedom
FK Forward Kinematic
G.R Gear Ratio
HSM High Speed Machining
IK Inverse Kinematic
IKF Compensation Filter
LVDT Linear Variable Displacement Transformer
MITF Modified Inverse Transfer Function
NN Neural Network
P Proportional
PC Personal Computer
PI and Integration
PID Proportional, and Deviation
PKM Parallel Kinematics Machining
PTP Point To Point
SKM Serial Kinematics
TCP Tool Center Point
ZPETC Zero Phase Error Tracking Controller
List of symbols
A mm platforms displacement i
B mm base plates displacemi
C - cross coupling gain x
C - y
c mm compensated contour error
D - coefficients of the denominator
V
BE - geometric error matrix
e steady state error ss -
f Hz frequency
G - actual transfer function a
-1G - inverse actual transfer function a
G - servo controller transfer function c
G mechanical transfer function m -
i - index number
J - Jacobian matrix
2
J kgm motor shaft inertia e
j - imaginary unit
radK / transmission ratio 1 mm
mm
K / transmission ratio 2 rev
K - cross coupled controller c
NmK / motor constant m A
K - feed forward control factor nV
As
K / velocity loop proportional gain p rad
VK / current regulator proportional gain pi A
-1 m/min
K s , / velocity gain in closed loop control in Cartesian coordinateV mm
-1 m/min
K s , / velocity gain of x axis in Cartesian coordinates Vx mm
-1 m/minK s , / velocity gain of y axis in Cartesian coordinates Vy mm
-1 m/min
K s , / velocity gain in Cartesian coordinates V_X mm
-1 m/min
K s , / velocity gain in machine axesV_U mm
K - relative velocity gain V - rel
L mm length of strut
L H armature inductance a
N - coefficients of the numerator
n - number of samples
mm
p / pitch of ball screw rev
p mm actual position a
p mm x-component of pax a
p mm y-comay a
p mm setpoint position s
'p mm position on the setpoint contour, close to actual position s
VIR mm actual radius a
R mm radius of base plate b
R armature resistance e
R mm radius of platform p
R mm setpoint radius s
R m x-component of Rs