Mechanical design and manufacturing of a
high speed induction machine rotor
A dissertation presented to
The School of Electrical, Electronic and Computer Engineering North-West University (Potchefstroom campus)
In partial fulfilment of the requirements for the degree Magister Ingeneriae
in Mechanical Engineering
by
Cornelius Ranft 20086989
Supervisor: Prof. G. Van Schoor Co-supervisor: Mr. N. Bessinger
Declaration i
D
ECLARATION
I, the undersigned, hereby declare that the work done in this project is my own original work.
... Cornelius Jacobus Gerhardus Ranft November 2010
Abstract iii
A
BSTRACT
The McTronX research group at the North-West University designs and develops Active Magnetic Bearings (AMBs). The group’s focus shifted to the design and development of AMB supported drive systems. This includes the electromagnetic and mechanical design of the electric machine, AMBs, auxiliary bearings as well as the development of the control system.
The research group is currently developing an AMB supported high speed Induction Machine (IM) drive system that will facilitate tests in order to verify the design capability of the group. The research presented in this thesis describes the mechanical design and manufacturing of a high speed IM rotor section. The design includes; selecting the IM rotor topology, material selection, detail stress analysis and selecting appropriate manufacturing and assembly procedures.
A comprehensive literature study identifies six main design considerations during the mechanical design of a high speed IM rotor section. These considerations include; magnetic core selection, rotor cage design, shaft design, shaft/magnetic core connection, stress due to operation at elevated temperatures and design for manufacture and assemble (DFMA). A critical overview of the literature leads to some design decisions being made and is used as a starting point for the detail design. The design choices include using a laminated cage rotor with a shrink fit for the shaft/magnetic core connection.
Throughout the detail design an iterative process was followed incorporating both electromagnetic and mechanical considerations to deliver a good design solution. The first step of the iterative design process was, roughly calculating the material strengths required for first iteration material selection followed by more detailed interference fit calculations. From the detail stress analysis it became apparent that the stress in the IM rotor section cannot be calculated accurately using analytical methods. Consequently, a systematically verified and validated Finite Element Analysis (FEA) model was used to calculate the interferences required for each component. The detail stress analysis of the assembly also determined the allowable manufacturing dimensional tolerances. From the detail stress analysis it was found that the available lamination and squirrel cage material strengths were inadequate for the design speed specification of 27,000 r/min. The analysis showed that a maximum operating speed of 19,000 r/min can be achieved while complying with the minimum factor of safety (FOS) of 2.
Each component was manufactured to the prescribed dimensional tolerances and the IM rotor section was assembled. With the failure of the first assembly process, machine experts were consulted and a revised process was implemented. The revised process entailed manufacturing five small lamination stacks and assembling the stack and squirrel cage afterwards. The end ring/conductive bar connection utilises interference fits due to the fact that the materials could not be welded. The process was successful and the IM rotor section was shrink fitted onto the shaft.
However, after final machining of the rotor’s outer diameter (OD), inspections revealed axial displacement of the end rings and a revised FEA was implemented to simulate the effect. The results indicated a minimum FOS ≈ 0.6 at very small sections and with further analytical investigation it was shown that the minimum FOS was reduced to only 1.34.
iv Abstract
Although the calculations indicated the FOS was below the minimum prescribed FOS ≥ 2, the rotor spin tests were scheduled to continue as planned. The main reasons being that the lowest FOS is at very small areas and is located at non critical structural positions. The fact that the rotor speed was incrementally increased and multiple parameters were monitored, which could detect early signs of failure, further supported the decision.
In testing the rotor was successfully spun up to 19,000 r/min and 27 rotor delevitation test were conducted at speeds of up to 10,000 r/min. After continuous testing a secondary rotor inspection was conducted and no visible changes could be detected.
The lessons learnt leads to mechanical design and manufacturing recommendations and the research required to realise a 27,000 r/min rotor design.
Keywords: Induction machine, rotor section, laminations, magnetic core, squirrel cage, shrink fit,
material, finite element analysis, factor of safety, contact pressure, tangential stress, Von Mises, high speed.
Acknowledgments v
A
CKNOWLEDGMENTS
I want to thank THRIP and M-Tech Industrial for funding the research, enabling me to further my studies.
I also want to thank the following people for their contribution towards this success of the project: • Marize Ranft for her support, patience and love
• Prof. George van Schoor for his guidance, text editing this thesis and support • Janik Bessinger for his advice and guidance
• My family for their support and guidance • Denel Dynamics Pty Ltd. for the manufacturing • The McTronX research group
Table of contents vii
T
ABLE OF CONTENTS
1 Introduction ... 1
1.1 Background ... 1
1.1.1 High speed machine classification ... 1
1.1.2 High speed machine applications ... 2
1.1.3 High speed machine selection... 2
1.1.4 High speed machine mechanical design challenges... 3
1.2 Problem statement... 4
1.3 Issues to be addressed ... 4
1.3.1 Magnetic core selection ... 6
1.3.2 Squirrel cage design ... 6
1.3.3 Selection of the magnetic core/shaft connection ... 7
1.3.4 Shaft design ... 7
1.3.5 Implications due to elevated operating temperature ... 7
1.3.6 Manufacturing and assembly procedures ... 7
1.4 Research methodology ... 8
1.4.1 Magnetic core selection, shaft design and core/shaft connection ... 8
1.4.2 Squirrel cage design ... 8
1.4.3 Implications due to elevated operating temperature ... 8
1.4.4 Manufacturing and assembly procedures ... 8
1.5 Dissertation layout ... 8
1.6 Conclusion ... 9
2 Mechanical design considerations ... 11
2.1 Literature overview ... 11
2.2 Induction machine rotor construction ... 13
2.2.1 Current rotor design solutions ... 14
2.2.2 Solid coated rotor ... 16
2.2.3 Solid cage rotor ... 16
2.2.4 Laminated cage rotor ... 17
viii Table of contents
2.3 Rotor cage design ... 19
2.3.1 Current rotor cage design solutions ... 19
2.3.2 Aluminium and copper die cast squirrel cages ... 22
2.3.3 Manufactured aluminium and copper squirrel cages ... 23
2.4 Magnetic core/shaft connection ... 25
2.4.1 Current design solutions for the magnetic core/shaft connection ... 26
2.4.2 Keys or splines ... 26
2.4.3 Diffusion bonding ... 27
2.4.4 Elastic shrink fits ... 28
2.4.5 Elastic-plastic shrink fits ... 28
2.5 Thermal effects on machine assembly ... 29
2.5.1 Current thermal effect solutions ... 30
2.6 Manufacturing and assembly procedures ... 31
2.6.1 Manufacturing processes ... 32
2.7 Critical overview ... 37
2.8 Initial induction machine rotor design decisions ... 38
3 Mechanical design of induction machine rotor ... 39
3.1 Iterative design process ... 39
3.2 Drive specifications ... 40
3.3 Conceptual design ... 41
3.4 Preliminary mechanical design ... 41
3.4.1 Preliminary interference calculations ... 44
3.4.2 Analytical stress concentration factor ... 47
3.5 Verification of the analytical stress concentration ... 48
3.5.1 Verification of stress in a solid outer ring ... 49
3.5.2 Verification of the FEM symmetry function ... 50
3.5.3 Verification of analytical stress concentration factor ... 52
3.6 Validating the stress concentration factors ... 53
3.6.1 Dynamic stress measurements on a multi-ring test rotor ... 53
Table of contents ix
3.6.3 Conclusion of static stress measured results ... 62
3.7 Detail IM mechanical design ... 63
3.7.1 Investigating the optimum bar slot design ... 63
3.7.2 Material selection and final dimension specifications ... 67
3.7.3 Detail magnetic core stress analysis ... 70
3.7.4 Detail spacer stress analysis ... 71
3.7.5 Detail conductive bar stress analysis ... 73
3.7.6 Validating end ring/bar connection electrical contact resistance ... 78
3.7.7 Detail end ring stress analysis ... 79
3.7.8 Detail stress analysis of the complete IM rotor section ... 81
3.8 Conclusion ... 84
4 Manufacturing and assembly ... 85
4.1 Methodology behind designing for manufacture and assembly ... 85
4.2 Rotor manufacturing and assembly, first iteration ... 85
4.2.1 Manufacturing lamination discs ... 85
4.2.2 Manufacturing the spacer (clamping plates) ... 87
4.2.3 Manufacturing of the end ring ... 87
4.2.4 Manufacturing of the conductive bars ... 88
4.2.5 Manufacturing of the stacking mandrel with a keyway ... 89
4.2.6 Assembly of lamination stack ... 90
4.2.7 Lessons learnt ... 90
4.3 Rotor manufacturing and assembly revised iteration ... 91
4.3.1 Laser cut laminations ... 91
4.3.2 Manufacturing of the five lamination stacks ... 92
4.3.3 Assembling the smaller lamination stacks onto a mandrel... 92
4.3.4 Squirrel cage assembly ... 94
4.3.5 Shrink fitting the IM rotor section ... 95
4.3.6 Insert dowels into rod ends ... 98
4.3.7 Machine final OD of entire rotor ... 99
4.4 Conclusion of assembly and manufacturing ... 100
x Table of contents
5.1 Context ... 103
5.2 Nondestructive inspection methods ... 104
5.2.1 Liquid penetration inspection ... 104
5.2.2 Magnetic-particle inspection ... 104
5.2.3 Ultrasonic inspection... 104
5.2.4 Acoustic inspection methods ... 104
5.2.5 Radiography ... 105
5.2.6 Eddy-current inspection ... 105
5.3 Stress analysis of IM rotor section with final measured dimensions ... 105
5.4 Visual inspection findings ... 108
5.4.1 Buckling of a shrink fitted lamination disc ... 109
5.4.2 Cutting forces ... 110
5.5 Stress due to IM rotor section axial deflection ... 114
5.6 Assembly of induction machine ... 119
5.6.1 Disassemble and secondary inspection of rotor ... 120
5.7 Conclusion ... 120
6 Conclusions and recommendations ... 121
6.1 Shortfalls of current IM rotor section design ... 121
6.1.1 Magnetic core-type and material selection ... 121
6.1.2 Material selection and detail stress analysis ... 121
6.1.3 Squirrel cage material selection and construction ... 122
6.1.4 Manufacturing dimensional tolerances ... 122
6.1.5 IM rotor section assembly process ... 123
6.1.6 Summary ... 123
6.2 Proposed solutions ... 124
6.2.1 Material selection considerations ... 124
6.2.2 Reduction in factor of safety ... 124
6.2.3 Proposed magnetic core/shaft connections ... 124
6.2.4 Assembly process ... 125
6.2.5 Alternative machine rotor design layouts ... 125
Table of contents xi
6.4 Closure ... 127
Bibliography ... 129
Appendix A : Matlab® program ... 133
List of tables xiii
L
IST OF TABLES
Table 1-1: Design specifications ... 4
Table 2-1: Different rotor configurations and the speed achieved ... 18
Table 2-2: Summary of current high speed IM design solutions ... 38
Table 3-1: Drive specifications... 41
Table 3-2: Geometry specifications ... 43
Table 3-3: Preliminary material selection and interference calculations ... 47
Table 3-4: Dynamic stress measurements of the additional tangential strain gages ... 57
Table 3-5: Tangential stress calculated and measured at strain gage 1 and 2... 60
Table 3-6: Tangential stress measurement at root of bar slots with no stress relieving cut ... 61
Table 3-7: Tangential stress measurement at tip of bar slots with no stress relieving cut ... 61
Table 3-8: Summary of strain gage measurements ... 62
Table 3-9: Summary of geometry affects on maximum stress and contact pressure ... 67
Table 3-10: Material data as used in calculations ... 68
Table 3-11: Revised drive specifications ... 68
Table 3-12: Component dimensions as used in calculations ... 69
Table 3-13: Summary of the CP at the shaft/laminations interface ... 71
Table 3-14: Summary of the CP at the shaft/spacer interface ... 73
Table 3-15: Conductive bar diameter growth calculations and test measurements ... 78
Table 3-16: Contact resistance measurements ... 79
Table 3-17: Conductive bar and slot dimensions ... 80
Table 3-18: Comparison of Von Mises stress for maximum interference of the sub- and complete assembly ... 82
Table 3-19: Comparison of CP stress for minimum interference for the sub- and complete assembly... 83
Table 5-1: Tabulated final measured dimensions ... 106
Table 5-2: Summary of CP at the individual component interfaces ... 107
List of figures xv
L
IST OF FIGURES
Figure 1-1: Simple illustration of complete induction machine ... 3
Figure 1-2: Induction machine cage rotor illustration ... 3
Figure 1-3: AMB supported high speed induction machine assembly ... 5
Figure 1-4: Induction machine rotor’s main design considerations ... 6
Figure 2-1: Mechanical design considerations detail breakdown ... 12
Figure 2-2: M.T. Caprio, V.L. John and J.D. Herbst, rotor configuration [9] ... 14
Figure 2-3: Rotor lamination material’s tradeoff between strength and ductility [7]... 15
Figure 2-4: Solid coated rotor illustration ... 16
Figure 2-5: Solid cage rotor illustration ... 17
Figure 2-6: Laminated cage rotor illustration ... 17
Figure 2-7: M.T. Caprio, V.L. John and J.D. Herbst, novel end ring design [9] ... 19
Figure 2-8: Exaggerated deformation due to temperature [9] ... 20
Figure 2-9: End ring boss feature [9] ... 20
Figure 2-10: Rotor cage material trade off between conductivity and strength [7] ... 21
Figure 2-11Traditional IM rotor construction [15] ... 23
Figure 2-12: Section view of taper interference fit bar/end ring connection ... 25
Figure 2-13: Section view of parallel interference fit bar/end ring connection ... 25
Figure 2-14: (a) Illustrates a dove-tail and (b) a square spline shaft ... 26
Figure 2-15: Schematic illustration of the solid-state diffusion bonding mechanism [13] ... 27
Figure 2-16: Shear and bending in the rotor bars due to elevated operating temperatures ... 29
Figure 2-17: Exaggerated deformation due to temperature [9] ... 30
Figure 2-18: L.M. Mhango's end stop design feature [4] ... 30
Figure 2-19: DFMA shortens the design process [23] ... 31
Figure 2-20: Typical DFMA procedure used by DFMA software [23] ... 32
Figure 2-21: Comparing time required to obtain a specific surface roughness using different manufacturing processes [46] ... 35
Figure 2-22: Typical surface roughness for specific manufacturing processes [47] ... 36
Figure 3-1: Schematic illustration of the iterative design process ... 40
Figure 3-2: Drive conceptual layout ... 41
Figure 3-3: Induction machine illustration ... 42
Figure 3-4: Illustration of the stress distribution for a shrink fitted solid ring onto a solid shaft [3] ... 44
Figure 3-5: Radial stress in a rotating two ring shrink fitted assembly ... 45
Figure 3-6: Radial stress at the interface at different rotating speeds ... 45
Figure 3-7: Tangential stress in a rotating two ring shrink fitted assembly ... 46
Figure 3-8: Equivalent Von Mises stress in a rotating two ring shrink fitted assembly ... 46
Figure 3-9: Paterson’s stress concentration factor graph [48] ... 48
Figure 3-10: Full FEM model for a solid shaft and shrink fitted solid outer ring ... 49
Figure 3-11: Comparison of analytical and FEM calculated Von Mises stress ... 49
xvi List of figures
Figure 3-13: 1/24 section FEM of a solid shaft and shrink fitted solid outer ring ... 50
Figure 3-14: Comparison of the FEM calculated radial stress of the full and 1/24 section models ... 51
Figure 3-15: Comparison of the FEM calculated Von Mises stress of the full and 1/24 section models ... 51
Figure 3-16: 1/24 section FEM of a solid shaft and shrink fitted outer ring with bar slots showing the stress concentrations positions ... 52
Figure 3-17: Verification of analytic stress concentration factor ... 53
Figure 3-18: Strain gage positions on multi-ring dynamic test rotor [43] ... 54
Figure 3-19: Slip ring integration onto dynamic test rotor [43] ... 54
Figure 3-20: Illustration of strain gage amplifier integration [43] ... 55
Figure 3-21: Dynamic test rotor radial stress measurements [43] ... 55
Figure 3-22: Dynamic test rotor tangential stress measurements [43] ... 56
Figure 3-23: Illustration of the additional tangential strain gage position at the outer surface of the dynamic test rotor ... 56
Figure 3-24: Illustration of the FEM model used to calculate the stress at the strain gage locations ... 58
Figure 3-25: (a) illustrates the static test rotor after shrink fit and (b) is a detail view of two of the strain gages ... 58
Figure 3-26: Static test rotor FEM tangential stress results ... 59
Figure 3-27: Cantilever beam test setup used for calibration ... 59
Figure 3-28: Tangential stress distribution at gage 4's position ... 62
Figure 3-29: Von Mises stress and contact pressure at interface for a solid rotor ... 64
Figure 3-30: Von Mises stress and contact pressure at interface for a circular slot ... 64
Figure 3-31: Von Mises stress and contact pressure at interface for a square slot ... 65
Figure 3-32: Von Mises stress and contact pressure at interface for an oval slot ... 65
Figure 3-33: Von Mises stress and contact pressure at interface for a circular slot with stress relieving cuts ... 66
Figure 3-34: Von Mises stress and contact pressure at interface for a circular slot with stress relieving slit ... 66
Figure 3-35: Illustration of IM rotor section layout ... 69
Figure 3-36: Shaft, lamination and conductive bar assembly, Von Mises stress ... 70
Figure 3-37: Shaft, lamination and conductive bar assembly, contact pressure ... 71
Figure 3-38: Shaft and spacer assembly, Von Mises stress ... 72
Figure 3-39: Shaft and spacer assembly, contact pressure ... 73
Figure 3-40: FOS plot of maximum shaft/end ring interference and 30 µm bar interference ... 75
Figure 3-41: Schematic illustration of the interference fit produced by the dowel insert ... 75
Figure 3-42: Analytically calculated bar radial growth ... 76
Figure 3-43: Von Mises stress distribution in the dowel and bar assembly ... 76
Figure 3-44: Section view of the Non-linear material FEM model for the dowel/bar interference fit ... 77
Figure 3-45: Illustration of the bar test samples ... 77
Figure 3-46: End ring/bar interface contact resistance measurement setup ... 79
Figure 3-47: Von Mises stress distribution of the shaft, end ring and bar assembly ... 80
Figure 3-48: Exaggerated displacement of the complete IM rotor section under load ... 81
List of figures xvii
Figure 3-50: Calculated CP for complete IM rotor section with minimum interferences ... 83
Figure 4-1: Illustration of the laser cut laminations ... 86
Figure 4-2: Illustration of the spacer (clamping plate) ... 87
Figure 4-3; Illustration of oversized end ring with dowel slots ... 88
Figure 4-4: Illustration of the conductive bar with a dowel hole ... 89
Figure 4-5: Lamination stacking mandrel with keyway ... 89
Figure 4-6: An illustration of stacking the mandrel and clamping the lamination stack ... 90
Figure 4-7: Illustration of solid lamination disc ... 91
Figure 4-8: Illustration of 30 mm lamination stack after machining ... 92
Figure 4-9: Illustration of the assembled and clamped second lamination stack ... 93
Figure 4-10: Illustration of the jagged mandrel surface due to the bottom spacer removing material .... 93
Figure 4-11: Illustration of clamped IM rotor section ... 94
Figure 4-12: IM rotor section stress due to heating up to 250 °C ... 97
Figure 4-13: Picture of the assembled IM rotor section onto the shaft ... 98
Figure 4-14: Inserting the 3mm dowel pins into the bars ... 98
Figure 4-15: Illustration of the inserted 3mm dowel pins ... 99
Figure 4-16: Illustration of the completed IM rotor ... 100
Figure 5-1: FOS plot of the IM rotor section with actual interferences at maximum operating conditions ... 106
Figure 5-2: IM rotor section’s CP at maximum operating conditions with actual measured interference ... 107
Figure 5-3: Illustration of the axial displacement of the end ring ... 108
Figure 5-4: IM rotor section after final machining ... 109
Figure 5-5: Illustration of a single lamination disc’s first and second conical buckling modes: (a) isometric view of first model (CP =1650 MPa), (b) isometric view of second model (CP =3855 MPa)... 110
Figure 5-6: Illustration of parameters and equations for calculating cutting forces [53] ... 110
Figure 5-7: Calculated required power for a depth of cut ... 111
Figure 5-8: Calculated ratio between ECT and Kc for different cutting speeds [53] ... 112
Figure 5-9: Illustration of ratio between cutting forces at different cutting speeds [53] ... 113
Figure 5-10: Calculated required power for a specific axial force ... 113
Figure 5-11: A side view of an exaggerated illustration of the axial deflection of the lamination stack .. 114
Figure 5-12: FOS fringe plot of the axially deflected lamination stack assembly ... 115
Figure 5-13: Detailed view on the FOS plot of the end ring ... 115
Figure 5-14: Side view of CP distribution ... 116
Figure 5-15: Illustration of (a) actual distribution, (b) assumed distribution of force due to reaction force FR ... 116
Figure 5-16: Bearing stress distribution ... 117
Figure 5-17: Illustration of reaction forces present due to the deflection ... 117
Figure 5-18: Assembling the IM rotor into the stator ... 119
Figure 6-1: Mhango’s alternative IM rotor section layout [4] ... 126
List of abbreviations xix
L
IST OF ABBREVIATIONS
AMB Active Magnetic Bearing AC Alternating current
IACS International annealed copper standard EDM Electrical-discharge machining
IM Induction Machine
SRM Switched-reluctance motor
PM Permanent magnet
r/min Revolutions per minute HTR High temperature reactor OD Outer diameter
ID Inner diameter
FOS Mechanical factor of safety CP Contact pressure
RMS Root mean squared
EES Engineering equation solver PCD Pitch circle diameter FEA Finite element analysis FEM Finite element model CNC Computer numerical control
List of symbols xxi
L
IST OF SYMBOLS
m Element mass
r Radial distance from centre ω Rotational speed
Tm Melting temperature
Nmax Maximum operating speed
σmax Maximum allowable stress
σy Yield strength
σut Ultimate tensile strength
σr Radial stress
σt Tangential stress
σVM Von Mises equivalent stress
σp Bearing stress
E Modulus of elasticity µ Friction coefficient
α Thermal expansion coefficient
ρ Density
υ Poisson ratio
Dr Maximum calculated outer diameter
Fr Reaction force
Pm Lathe motor power
FA Axial cutting force
FH Resultant cutting force
FC Tangential cutting force
xxii List of symbols
V Cutting speed
ECT Equivalent chip thickness CFA Chip flow angle
CEL Chip edge length
f Feed rate
Q Metal removal rate Kp Power constant
Kc Specific cutting force
C Feed factor W Tool wear factor
e Machine tool efficiency factor
L Length
A Cross sectional area
KB Bearing stress distribution concentration factor
