Technique for Measurement of Weld Resistance for AC Resistance Spot Welding via

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Mian Mohsin Irshad, The University of Western Ontario
Supervisor: Dr Lyndon J. Brown, The University of Western Ontario
A thesis submitted in partial fulfillment of the requirements for the Master of Engineering
Science degree in Electrical and Computer Engineering
© Mian Mohsin Irshad 2012
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Irshad, Mian Mohsin, "Technique for Measurement of Weld Resistance for AC Resistance Spot Welding
via Instantaneous Phasor Measurement" (2012). Electronic Thesis and Dissertation Repository. 796.
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TECHNIQUE FOR MEASUREMENT OF WELD RESISTANCE FOR AC
RESISTANCE SPOT WELDING VIA INSTANTANEOUS PHASOR
MEASUREMENT
(Thesis format: Monograph)
by
Mian Mohsin Irshad
Graduate Program in Department of Electrical and Computer Engineering
A thesis submitted in partial fulfillment
of the requirements for the degree of
Master of Engineering Science
The School of Graduate and Postdoctoral Studies
The University of Western Ontario
London, Ontario, Canada
(cid:2)c Mian Mohsin Irshad 2012
THE UNIVERSITY OF WESTERN ONTARIO
School of Graduate and Postdoctoral Studies
CERTIFICATE OF EXAMINATION
Examiners:
Supervisor:
..................... .....................
Dr. LyndonJ.Brown Dr. RajivK.Varma
SupervisoryCommittee:
.....................
Dr. KenMcIsaac
.....................
Dr.
.....................
Dr. BjarniTryggvason
.....................
Dr.
Thethesisby
MianMohsin Irshad
entitled:
Technique forMeasurement ofWeldResistanceforACResistanceSpotWeldingvia
Instantaneous PhasorMeasurement
isaccepted inpartialfulfillmentofthe
requirementsforthedegreeof
MasterofEngineeringScience
............... ..............................
Date ChairoftheThesisExaminationBoard
ii
Abstract
The resistance measurement in the resistance spot welding (RSW), is an ongoing research
topic. Thehighcurrentflowduringtheweldingprocessinducesanelectromagneticfieldinthe
wires which are attached to the electrodes to measure tip voltage. This results an additional
voltage drop which is proportional to the derivative of current. Also the presence of silicon
controlled rectifier (SCR) in the welding power supply generates harmonics in both supply
voltageandcurrent. Theseissuestogethercomplicatethemethodsforresistanceestimation.
A set of simultaneous linear equations is derived for the on-line measurement of dynamic re-
sistance and induced voltage constant by using the dynamic circuit analysis of weld setup.
Thiscanbesolvedtodeterminetheweldresistanceusinginstantaneousphasorsmeasurements
for the 1st, 3rd and 5th harmonics of current and measured voltage signals. The instantaneous
phasor measurements for these desired harmonics are obtained by employing the following
proposedmethod.
In this thesis, a new method for the measurement of instantaneous phasor is proposed for the
narrow band signals. The proposed algorithm is based on the internal model principle (IMP)
definedforthecancellationofasinusoidaldisturbancesignal. TheIMPhastwostates,exhibit-
ing the properties of being sinusoidal and orthogonal. The instantaneousvalues of IMP states
are defined as real and imaginary components of a complex signal at each time instant. The
instantaneousmeasurementsofenvelopeandphaseofasinusoidalsignalaredeterminedfrom
instantaneousvaluesofcomplexsignalbyusingarithmeticpropertiesofcomplexnumbers. In
caseofsignalcomprisingofsumofsinusoidsofdifferentfrequencies,theapproachforobtain-
ing instantaneous phasor for each sinusoidal component is presented by connecting multiple
internalmodelsintheparallelandopen-loopconfiguration.
The instantaneous phasor measurement of fundamental frequency signal is not only advanta-
geousindetectingfaultslikeshortcircuiting,harmonicdistortionandfrequencyvariationsbut
it can also be applied to protect power system from these faults. In this work, the applicabil-
ity of the proposed instantaneous phasor measurement algorithm is analyzed for scenarios of
iii
powerdisturbancesduetothetheharmonicdistortionanddecayingDCoffset. Theresultsare
discussedandcomparedwithfewexistingmethods.
Keywords: Instantaneous phasor, Internal model principle, Narrow band signals, Resis-
tancespotwelding,Harmonicdistortion,DecayingDCoffset
iv
Acknowledgments
I would like to express my sincere gratitude to my supervisor, Dr. Lyndon J. Brown, for his
consistentsupport,guidanceandpatienceduringthepasttwoyearsofmystudyatWestern. It
hasbeenanhonorformetoworkwithsuchanintelligentandgraciousprofessor.
Iwouldliketothanksmyparentsandfriendsfortheirloveandencouragementthroughoutmy
studies.
v
Contents
Certificate ofExamination ii
Abstract iii
Acknowledgments v
ListofFigures ix
ListofTables xiv
1 Introduction 1
1.1 ProblemFormulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 LiteratureReview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.1 SignalDecomposition . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.1.1 FourierAnalysis . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.1.2 WaveletTransform . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.1.3 Hilbert-HaungTransform . . . . . . . . . . . . . . . . . . . 11
1.3.1.4 NotchFilters . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.3.2 PhasorEstimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.4 ResistanceSpotWeldingBackground . . . . . . . . . . . . . . . . . . . . . . 20
1.4.1 TheProcessVariables . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.4.2 TheRSWProcess . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
vi
1.4.3 ResistanceEstimationTechniques . . . . . . . . . . . . . . . . . . . . 28
1.5 InternalModelPrincipleAlgorithm . . . . . . . . . . . . . . . . . . . . . . . . 31
1.6 DynamicCircuitAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.7 ContributionoftheThesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
1.8 StructureoftheThesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2 Instantaneous PhasorMeasurement Algorithm 37
2.1 AlgorithmDesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.1.1 NotchFilterBank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.1.2 ModifiedInternalModel . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.1.3 InstantaneousPhasorMeasurement . . . . . . . . . . . . . . . . . . . 44
2.1.4 MagnitudeandPhase Compensation . . . . . . . . . . . . . . . . . . . 44
2.2 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.2.1 ASinusoidwithConstantAmplitudeandPhase . . . . . . . . . . . . . 46
2.2.2 ASinusoidwithTime-VaryingAmplitudeandPhase . . . . . . . . . . 46
2.2.3 AnAmplitudeModulatedSignal . . . . . . . . . . . . . . . . . . . . . 47
2.2.4 AnAlternativeApproachforAmplitudeModulatedSignal . . . . . . . 49
2.2.5 ASumofThreeSinusoids . . . . . . . . . . . . . . . . . . . . . . . . 51
3 ResistanceEstimationand TipVoltageMeasurement 56
3.1 DynamicAnalysisofWeldingCircuit . . . . . . . . . . . . . . . . . . . . . . 57
3.2 InstantaneousPhasorMeasurementsforHarmonicsofCurrentandVoltageSig-
nals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.2.1 ChebyshevFilter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.2.2 NotchFilterBankandModifiedInternalModel . . . . . . . . . . . . . 64
3.2.3 MagnitudeandPhase Compensation . . . . . . . . . . . . . . . . . . . 65
3.2.4 InstantaneousPhasorMeasurement . . . . . . . . . . . . . . . . . . . 66
3.3 SolvingtheLinearSystem Y = ΦΘ . . . . . . . . . . . . . . . . . . . . . . . . 70
vii
3.3.1 MatrixInversionApproach . . . . . . . . . . . . . . . . . . . . . . . . 71
3.3.2 RecursiveLeastSquares(RLS) Approach . . . . . . . . . . . . . . . . 72
3.4 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.4.1 ProcessVariablesEstimationwithConstant R . . . . . . . . . . . . . 75
d
3.4.2 ProcessVariablesEstimationwithTimeVarying R . . . . . . . . . . . 76
d
3.4.3 Process Variables EstimationwithtimevaryingR and inthepresence
d
of2nd harmonicofsinusoidalresistance . . . . . . . . . . . . . . . . . 84
3.4.4 ProcessVariablesEstimationwithtimevaryingR duringtheExpulsion 85
d
4 ApplicationsofInstantaneousPhasorMeasurement Algorithm 91
4.1 PowerSystem’sHarmonics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.2 ExponentiallyDecayingDC Offset . . . . . . . . . . . . . . . . . . . . . . . . 97
5 Conclusions 105
5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.2 FutureWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Bibliography 109
Curriculum Vitae 114
viii
List of Figures
1.1 ShapesofcommonlyusedwindowfunctionsinSTFT . . . . . . . . . . . . . . 9
1.2 Shapesofcommonlyusedwaveletfunctions . . . . . . . . . . . . . . . . . . . 10
1.3 Illustrationofendeffectsininstantaneousfrequency . . . . . . . . . . . . . . . 14
1.4 TheIMFsfromdifferentsiftingiterationnumbersintheEMDimplementation.
(a)5iterations(b)10iterations(c)100iterations . . . . . . . . . . . . . . . . 15
1.5 MagnituderesponseofnotchfilterforvariousvaluesofQfactor . . . . . . . . 18
1.6 PhasorrepresentationofasinusoidofamplitudeA = 1 . . . . . . . . . . . . . 19
1.7 VariablesassociatedwiththeRSW process . . . . . . . . . . . . . . . . . . . . 23
1.8 NuggetformationandresistancesinvolvedinRSWprocess . . . . . . . . . . . 24
1.9 EvolutionofBulkandContactResistanceswithWeldtime . . . . . . . . . . . 25
1.10 Fourphasesofweldingprocesscycle . . . . . . . . . . . . . . . . . . . . . . . 25
1.11 Timevariationofdynamicresistanceduringtheweldprocess . . . . . . . . . . 26
1.12 WireloopcausinginducednoiseduetoEMI . . . . . . . . . . . . . . . . . . . 27
1.13 BlockdiagramofalgorithmproposedbyMalhotra . . . . . . . . . . . . . . . . 30
1.14 Spectrumofmeasuredtipvoltagebetween1st and17th harmonics . . . . . . . . 31
1.15 Electricalschematicofsecondaryweldingcircuit . . . . . . . . . . . . . . . . 33
2.1 BlockdiagramofalgorithmproposedbyNitinandSun . . . . . . . . . . . . . 39
2.2 Blockdiagramofourproposedalgorithm . . . . . . . . . . . . . . . . . . . . 40
2.3 Descriptionofanotchfilterbank . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.4 BlockdiagramofthestructureofMIM . . . . . . . . . . . . . . . . . . . . . . 43
ix