Gearbox Modeling And Load Simulation Of A Baseline . - NREL
Gearbox Modeling and LoadSimulation of a Baseline 750-kWWind Turbine Using State-of-theArt Simulation CodesF. OyagueTechnical ReportNREL/TP-500-41160February 2009
Gearbox Modeling and LoadSimulation of a Baseline 750-kWWind Turbine Using State-of-theArt Simulation CodesF. OyaguePrepared under Task No. WER8.2001National Renewable Energy Laboratory1617 Cole Boulevard, Golden, Colorado 80401-3393303-275-3000 www.nrel.govNREL is a national laboratory of the U.S. Department of EnergyOffice of Energy Efficiency and Renewable EnergyOperated by the Alliance for Sustainable Energy, LLCContract No. DE-AC36-08-GO28308Technical ReportNREL/TP-500-41160February 2009
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Executive SummaryThe wind energy industry continually evolves, and industry professionals have streamlinedgearbox design to a consensus configuration. This configuration and its design iteration haveexisted for many years; consequently, design and manufacturing flaws have been minimizedsequentially. Regardless of the maturity of the gearbox design and design process, however, mostwind turbine downtime is attributed to gearbox-related issues. Moreover, gearbox replacementand lubrication accounts for 38% of the parts cost of the entire turbine.Several hypotheses have been offered to explain gearbox failure, including the absence of anumber of load cases relevant to the design process; the transfer of nontorsional loads betweenthe different components of the drivetrain; the lack of a uniform standardization of bearing-lifeanalysis calculations; and poor communication between wind turbine designers, gearboxsuppliers, and bearing providers.This report discusses determining a method for revealing the missing loading conditions thatshould be factored into the gearbox-design process. This objective is achieved by development ofa number of analytical models that sequentially increase in complexity, and which are capable ofreproducing the dynamical behavior of the internal components of the drivetrain. Additionally,the parameters obtained from these models are correlated with the gearbox-design process.Importantly, the models developed are offered freely to improve communication and to openinformation-sharing avenues between manufacturers and designers involved in the non-verticaldesign process.The models reveal that the level of complexity does not greatly affect torsional behavior.Furthermore, models of higher complexity are capable of providing important insight into theloading conditions for the bearings of the gearbox, and still account for loads generated by geartooth interactions.i
AcknowledgementsI would like to thank my primary supervisor Professor Dr. Dipl.-Ing. Martin Kühn, my secondarysupervisor Dipl.-Ing. Stefan Hauptmann, and my COMMAS supervisor Professor Dr.-Ing. BerndKröplin, for arranging the integration of the COMMAS Masters Program with the EndowedChair of Wind Energy (SWE), and thus allowing me the opportunity to participate in cuttingedge research.Thanks also go to Chief Engineer Sandy Butterfield, my external supervisor, who allowed me theopportunity to research and write this report at the National Renewable Energy Laboratory(NREL), and who provided constant advice and guidance; and to Ed Hahlbeck, Don McVittie,and Brian McNiff, who shared their expertise in the gearbox-design process and the wind turbineindustry, and gave me valuable advice.I thank INTEC GmbH for providing the multibody system code SIMPACK, which madepossible the development of the progressive models used in this report.Last, but not least, I thank my family and friends for their ever-constant support and guidance.Specifically, I would like to acknowledge Maria Christina and Marnix Vanderplas, whogenerously provided the financial support that enabled me to produce this report.ii
Table of ContentsSymbols . viList of Figures. viiiIntroduction. 1Motivation. 1Problem Definition. 2Approach. 3Wind Turbine Configurations . 4Overview. 4Horizontal Axis Drivetrain . 5Modular Drivetrain . 5Integrated Drivetrain . 6Partially Integrated Drivetrain. 7Direct Power Train . 7Drivetrain Configuration Comparison . 8Modular Drivetrain Components . 9The Low-Speed Shaft . 9Couplings. 10Gearbox . 10Parallel Shaft Gearbox . 11Planetary Gearbox. 11Brakes . 13Aerodynamic Brakes. 13Mechanical Brakes. 14Generator . 14Control Systems . 14Pitch Control. 15Stall Control. 15Pitch Control Versus Stall Control . 15Gears . 16Fundamental Law of Gearing . 16Gear Types . 17Spur Gears . 17Helical Gears . 18Involute Gear Tooth Nomenclature . 18Gear Failure Modes. 19Wear . 19Moderate and Excessive Wear . 20Abrasion . 20Tip Root Interference . 21Surface Fatigue. 21Micropitting. 21Macropitting . 22Spalling. 22Crushing . 23iii
Plastic Flow . 23Fracture. 23Bearings . 24Bearings Failure Modes . 24Gear and Bearing Failures in Wind Turbines . 25Simulations Using FAST AD. 26Multibody System Simulations . 27Simulation with SIMPACK . 28Force Element Description . 29SIMPACK Force Element FE:12, . 29Torsion-Spring Suspension (Force Law Based on the Joint State Quantities). 29SIMPACK Force Element FE:14, Gearbox with Elastic Transmission. 29SIMPACK Force Element FE:225, Component Force Element . 29Simulation Theoretical Input Parameters . 30Shaft Torsional Stiffness. 30Mechanical Interaction . 30Hooke’s Law . 31Shear Strain Relationship . 31Torsional Deflection of a Circular Shaft . 32Torsional Free Vibration. 33Torsional Free Damped Vibration . 34Logarithmic Descent. 34Gear Mesh Simplified Stiffness . 36Mesh Stiffness Calculation Input Parameters . 37Blade Inertia. 37Effective Inertia and Stiffness. 38Progressive Stage Description. 40Turbine Description . 40Stage 1. Simplified Complete Drivetrain Model . 40Data Acquisition and Validation . 42Stage 2. Simplified Rotor and Generator with Multiple-Stage Gearboxes. 47Mesh Stiffness . 49Shaft Stiffness. 49Inertias . 50Data Acquisition and Validation . 50Stage 3. Multiple-Stage Gearboxes with Contact Element Implementation . 51Mesh Stiffness . 54Shaft Stiffness. 54Inertias . 54Data Acquisition and Validation . 54Stage 4. Multiple-Stage Gearboxes with Contact Element Implementation and BearingStiffness. 55Special Consideration for Bearings . 57Validation and Parameter Acquisition. 57iv
FAST Model Description. 58FAST Input Parameters . 58Blade Characteristics . 58Tower Properties . 58Generator Models . 58FAST Generated Load Cases. 59Model Comparison. 61Drivetrain Design Process . 66Pre-Design Process . 66Gearbox Design Process . 66Vertically Integrated Design Process. 67Load Case Predictions . 67Analysis and Iteration. 67Gear Design . 67Driving Load Cases . 68Reiteration and Refinements . 68Vibration Analysis. 68Controls . 68Non–Vertically Integrated Design Process. 69Develop Rotor and System Loads . 69Drivetrain Definition . 69Drivetrain Specification. 69Initial Design Review . 69Design Selection. 69Prototype and Testing. 69Comparison of Drivetrain Design Processes . 70Multistage MBS and the Design Process. 71Conclusions and Final Remarks . 72Future Work. 74References. 76Appendix:. 78Aerodynamic Simulation. 78One-Dimensional Momentum Theory. 78Ideal Wind Turbine with Wake Rotation. 78Blade Element Theory . 79v
SymbolsbccClCdDdADringDSunEGhIaIm, JIpkKkeqktlLlsmm εγWith of cross-sectional area [m]Airfoil cord length [m]Damping coefficient [N/m/sec]Lift coefficient [-]Drag coefficient [-]Drag force [N]infinitesimal element [-]Ring gear diameter [m]Sun gear diameter [m]Young’s modulus [N/m2]Shear modulus of elasticity [N/m2]Height of the cross-sectional [m]Area moment inertia [m4]Mass moment of inertia [kg m2]Polar moment of inertia [m4]Spring constant [Nm/rad]Stiffness [Nm/rad]Equivalent stiffness [Nm/rad]Torsional stiffness [Nm/rad]Length of rod under torsion [m]Lift force [N]Airfoil span [m]Mass [kg]Mass flow rate [kg/sec]Mechanical advantage [-]Gear ratio [-]Velocity ratio [-]High-speed shaft angular velocity [-]Low-speed shaft angular velocity [-]Period of oscillation [sec]Angular velocity input [rad/sec]Angular velocity output [rad/sec]Pitch radius of input gear [m]Pitch radius of output gear [m]Radius of rod under torsion [m]Maximum beam deflection [m]Rotor thrust [N]Incoming wind velocity [m/s]Outgoing wind velocity [m/s]Undisturbed fluid velocity [m/sec]Density [kg/m3]Stress [N/m2]Strain [-]Shear strain deformation [rad]vi
τφTωnƒn x x xζδαShear stress [N/m2]Angle of torsional deflection [rad]Applied torque [N/m]Undamped natural frequency [rad/sec]Undamped natural frequency [HZ]Acceleration [m/sec2]Velocity [m/sec]Position [m]Damping ratio [-]Logarithmic descent [-]Rotation around the X axis [-]vii
List of FiguresFigure 1. Downtime hours accumulated from 2003 to 2007 for wind turbines operating inGermany . 1Figure 2. Vertical axis turbine . 4Figure 3. Horizontal axis turbine . 5Figure 4. Modular drivetrain configuration . 6Figure 5. Integrated drivetrain from Wind World W-2700 . 7Figure 6. Partially integrated drivetrain . 7Figure 7. Enercon direct power train . 8Figure 8. Planetary stage components . 12Figure 9. Planetary stage components rotational direction. 13Figure 10. Rudimentary gear set. 16Figure 11. Involute tooth profile. 18Figure 12. Involute tooth nomenclature. 19Figure 13. Moderate tooth wear. 20Figure 14. Excessive tooth wear . 20Figure 15. Gear-tooth abrasion . 21Figure 16. Tooth interference damage . 21Figure 17. Surface fatigue micropitting . 22Figure 18. Surface fatigue macropitting . 22Figure 19. Surface fatigue spalling . 23Figure 20. Plastic flow failure. 23Figure 21. Gear-tooth fracture . 24Figure 22. Surface fatigue on bearing raceway . 25Figure 23. Adhesive wear produced by overheating . 25Figure 24. Absolute and relative coordinates . 28Figure 25. FE:12 spring damper . 29Figure 26. FE:225 point of contact . 30Figure 27. Stress versus strain representative curves. 31Figure 28. Shear deformation . 32Figure 29. Logarithmic reduction . 35Figure 30. Gear tooth deflection . 37Figure 31. Blade mass discretization . 38Figure 32. Two-stage representative drivetrain . 39Figure 33. Equivalent one-stage drivetrain with single stiffness and inertia. 39Figure 34. Graphic representation of equivalent stiffness . 40Figure 35. Stage 1 graphical representation. 41Figure 36. Topology of constrained model. 42Figure 37. Topology of unconstrained model. 42Figure 38. Experimental data and secondary frequency response. 44Figure 39. True response (left) and collected response (right) . 45Figure 40. Experimental data and simulated response. 46Figure 41. Stage 1 simulated response with refined integration time step . 46Figure 42. Stage 2 graphical representation. 47Figure 43. Planetary stage topology. 48viii
Figure 44. Subsequent gearbox stages topology. 49Figure 45. Stage 2 model simulated response with fine integration time step . 51Figure 46. Stage 3 graphical representation. 52Figure 47. Topology of planetary stage with FE:225 . 53Figure 48. Topology of subsequent gearbox stages with FE:225. 53Figure 49. Stage 3 model simulated response with fine integration time step . 55Figure 50. Bearing stiffness representation . 56Figure 51. Planetary stage with added degrees of freedoms and force constraints . 57Figure 52. FAST AD generator models. 59Figure 53. FAST AD simulated braking maneuver and event description. 59Figure 54. Planet carrier displacement under braking event. 60Figure 55. Axial displacement under bre
Area moment inertia [m. 4] I. m, J . Mass moment of inertia [kg m. 2] I. p . Polar moment of inertia [m. 4] k . Spring constant [Nm/rad] K . Stiffness [Nm/rad] k. eq . Equivalent stiffness [Nm/rad] k. t . Torsional stiffness [Nm/rad] l . Length of rod under torsion [m] L . Lift force [N] l
1 Simulation Modeling 1 2 Generating Randomness in Simulation 17 3 Spreadsheet Simulation 63 4 Introduction to Simulation in Arena 97 5 Basic Process Modeling 163 6 Modeling Randomness in Simulation 233 7 Analyzing Simulation Output 299 8 Modeling Queuing and Inventory Systems 393 9 Entity Movement and Material-Handling Constructs 489
Harmonic gearbox have smaller backlash but a very high price, while a planetary gearbox have a higher load carrying capacity, a better coefficient of efficiency and a significantly lower price, all for the same overall dimensions. Because of this, it would be reasonable to use a planetary gearbox instead of a harmonic gearbox. Figure 5.
Field test: torque and modal characterization. Planet bearing calibration. Trunnion stiffness characterization. Phase 1. Dyno Gearbox 1: run-in and instrumentation checkout. Field Gearbox 1: loads, responses, events. Dyno Gearbox 2: run-in, limited non-torque loading. Phase 2. Dyno Gearbox 2: extensive Non-Torque Loads (NTL), dynamics, HSS .
REDUCTION GEARBOX FINNØY REDUCTION GEARBOX The gearbox range covers input powers from 250 kW and up to 12 000 kW. They are divided into 3 model types: - SINGLE STAGE REDUCTION GEARBOX, with vertical or horizontal offset - GXU REDUCTION GEARBOX - TWIN
Gearbox Modeling and Load . Technical Report . Simulation of a Baseline 750-kW . NREL/TP-500-41160 . February 20
box casing is an important parameter to be taken into account while designing. In order to assess the strength, of the gearbox casing, a step by step approach is adopted. It was statically analyzed using simulation software Ansys. The strength of the gearbox casing's hooks and bolts has important during the lifting off and fixing the gearbox .
the gearbox; (1) experimental modal analysis and representation of the test gearbox using only a (2) dynamic vibration measurements during oper- limited number of modes. ation. In the experimental modal analysis, modal parameters, such as system natural frequencies For the dynamic study of the gearbox vibra-
Floor Joist Spans 35 – 47 Floor Joist Bridging and Bracing Requirements 35 Joist Bridging Detail 35 10 psf Dead Load and 20 psf Live Load 36 – 37 10 psf Dead Load and 30 psf Live Load 38 – 39 10 psf Dead Load and 40 psf Live Load 40 – 41 10 psf Dead Load and 50 psf Live Load 42 – 43 15 psf Dead Load and 125 psf Live Load 44 – 45
