On design, modelling, and analysis of a 10‐MW medium‐speed drivetrain for offshore wind turbines

Funding information China Scholarship Council (CSC), Grant/Award Number: 201706050147 Abstract The design of a medium-speed drivetrain for the Technical University of Denmark (DTU) 10-MW reference offshore wind turbine is presented. A four-point support drivetrain layout that is equipped with a gearbox with two planetary stages and one parallel stage is proposed. Then, the drivetrain components are designed based on design loads and criteria that are recommended in relevant international standards. Finally, an optimized drivetrain model is obtained via an iterative design process that minimizes the weight and volume. A high-fidelity numerical model is established via the multibody system approach. Then, the developed drivetrain model is compared with the simplified model that was proposed by DTU, and the two models agree well. In addition, a drivetrain resonance evaluation is conducted based on the Campbell diagrams and the modal energy distribution. Detailed parameters for the drivetrain design and dynamic modelling are provided to support the reproduction of the drivetrain model. A decoupled approach, which consists of global aero-hydro-servo-elastic analysis and local drivetrain analysis, is used to determine the drivetrain dynamic response. The 20-year fatigue damages of gears and bearings are calculated based on the stress or load duration distributions, the Palmgren-Miner linear accumulative damage hypothesis, and long-term environmental condition distributions. Then, an inspection priority map is established based on the failure ranking of the drivetrain components, which supports drivetrain inspection and maintenance assessment and further model optimization. The detailed modelling of the baseline drivetrain model provides a basis for benchmark studies and support for future research on multimegawatt offshore wind turbines.

a simplified predictive pitting model, which is used to estimate the contact fatigue life of gears in the 750-kW drivetrain model. Considering normal operation and parked and transient load cases, a long-term contact fatigue analysis of a planetary rolling element bearing in the 750-kW drivetrain was conducted by Jiang et al. 7 Xing et al 8 studied the dynamics of the 750-KW wind turbine drivetrain supported on a spar-type floating structure, and the dynamic response in the floating wind turbine was compared with that in its equivalent land-based version. Additionally, an offshore gearbox was designed by Nejad et al 9 for the NREL 5MW baseline wind turbine, and they provided detailed descriptions, modelling parameters, and technical data to the public to support research studies for large offshore wind turbines.
However, almost all of these drivetrain models are equipped with the high-speed gearboxes. Very limited studies have been conducted on the medium-speed drivetrains because of the lack of an available reference model. Faced with a reliability problem for the commonly used high-speed drivetrain and a weight issue for the direct-driven drivetrain in the wind turbine upscaling procedure, the medium-speed drivetrain, which is typically composed of a simplified gearbox with only one or two stages and a medium-speed electric generator, is being regarded as a potential alternative in offshore applications. This is because the medium-speed drivetrain could have the advantages of both the high-speed and the direct-driven drivetrain concepts: It could possibly lower the risk of gearbox failure compared with the high-speed drivetrain, while reducing the generator's weight and cost compared with the direct-driven drivetrain. A few applications of the medium-speed drivetrain have been found in large-scale offshore wind turbines in recent years, such as AREVA M 10 Vestas EnVentus V162-5.6 MW, 11 MHI VestasV174-9.5 MW, and V164-10.0 MW. 12 The DTU 10-MW RWT was also proposed to equip with a medium-speed drivetrain, but no related design has been reported in the literature.
The objective of this study is to improve communication and cooperation between various stakeholders to enhance research studies on large-scale offshore wind turbines. To realize this objective, a medium-speed drivetrain is designed for the DTU 10-MW RWT. Detailed design descriptions, including the design basis, loads, criteria, and principles, are presented. Then, a drivetrain numerical model is established via the multibody system modelling method, and the suitability of the modelling parameters is demonstrated via comparative analysis between the developed model and the simplified model that is provided by DTU and by conducting a drivetrain resonance evaluation. Sufficient drivetrain design and dynamic modelling parameters are provided, thereby rending the drivetrain model to be reproducible. Thus, one can replicate the drivetrain model that is utilized in their work to gain insight into the dynamics of 10-MW wind turbines. Moreover, the 20-year drivetrain fatigue damage is calculated using gear and bearing loads that are obtained from the dynamic simulations, the linear fatigue cumulative damage hypothesis, and the long-term environmental condition distributions. Then, a drivetrain vulnerability map is then established by ranking the fatigue damage from the highest to lowest, which supports drivetrain performance assessment and design improvement.

Wind turbine specifications
The DTU 10-MW RWT that serves as the drivetrain design in this study was designed by upscaling the NREL 5 MW reference wind turbine, 13 which is characterized by an efficient lightweight rotor and a medium-speed drivetrain. An overall description of the 10-MW wind turbine is presented in Table 1. The wind turbine was designed for offshore sites with an International Electrotechnical Commission (IEC) class 1A wind climate and is a traditional three-bladed, upwind wind turbine with a variable-speed collective pitch power control system. 1

Drivetrain properties
The general parameters of the drivetrain that were proposed by DTU are listed in Table 2. These parameters are only used for the simplified drivetrain modelling, namely, for the torsional model with one degree of freedom (DOF) in the global analysis. A detailed drivetrain model is not offered by DTU.

Environmental conditions, global response, and local drivetrain response analysis
In this study, the 10-MW wind turbine drivetrain is selected to be supported on a bottom-fixed monopile offshore structure. According to the study of Nejad et al, 14 wave loads have very limited effects on the dynamic response of a drivetrain with this type of offshore structure support.
Thus, in this study, the influences of wave loads on the drivetrain design and on the analysis are neglected, and wind loads are considered to be the only environmental loads. An offshore field in the Northern North Sea is considered as the wind turbine installation site, where hindcast data have been sampled hourly for the wind speed. The long-term 1-hour mean wind speed at 10 m above the average sea level is modelled by a two-parameter Weibull distribution 15,16 : where u is 1-hour mean wind speed at 10 m above the average sea level; a and c are the shape and scale parameters, which are 8.426 and 1.708, respectively. 15 A power law is used to calculate wind speed at hub height: where h hub is the hub height, which is 119 m above the average sea level for this 10-MW reference wind turbine; is the power law exponent, which is assumed to be 0.14 for offshore fields as proposed in the international standard IEC 61400-3. 17 A two-step decoupled analysis approach is employed in this study. First, a global response analysis of the 10-MW wind turbine that is equipped with a simplified drivetrain is conducted using an aero-hydro-servo-elastic dynamic software, namely, SIMA. 18 Then, the rotor forces and moments and the nacelle motions that are obtained from the global analysis are applied to the detailed drivetrain model to conduct a dynamic analysis. Compared with fully coupled analysis approach that solves for the drivetrain's dynamic response in a full wind turbine model, such a decoupled method could realize higher efficiency with less computation time and reasonable accuracy of the numerical results. Detailed descriptions of the decoupled method for the drivetrain response analysis can be found in other studies. 6,19,20

Drivetrain design basis
The 10-MW drivetrain is designed based on the international standard IEC 61400-4. 21 This standard accounts for the wind turbine gearbox design requirements and is applicable for horizontal-axis wind turbines with a power rating in excess of 500 KW in both onshore and offshore fields. The drivetrain design lifetime, design loads, interfaces definition, and specific design codes for the mechanical components are documented in IEC 61400-4, 21 which provide the main guidance and basis for the drivetrain design in this case study.

Drivetrain design loads
According to the descriptions of the wind conditions in the international standards IEC 61400-1 22 and DNVGL-ST- 23  The design load spectra are generated by processing the time series of rotor blade loads that are obtained from the global simulation, which is conducted under normal operational conditions that cover the whole range from the cut-in to cut-out speed. The torque load duration distribution (LDD) is shown in Figure 1, which consists of 64 load bins, and the total duration time is 1.67e5 hours, which corresponds to a 20-year service life with 95% availability of power production. Other nontorque LDDs, which are not presented in this paper, are also considered for the drivetrain design. These nontorque LDDs have limited effects on the sizing of the mechanical components inside the gearbox, while account largely for the main bearing design.

Drivetrain configuration and gearbox layout
Among the currently available geared drivetrain designs, the drivetrain configurations can be divided into three main categories: three-point suspension, two-main-bearing suspension, and integrated drivetrain. Based on industry experiences and a related study 24 on the feasibility of various drivetrain configurations in modern large offshore wind turbines, a four-point support drivetrain configuration with two main bearings and two torque arms is applied in this study.
A conventional high-speed gearbox is typically composed of three stages, namely, one planetary stage and two parallel stages or two planetary stages and one parallel stage, with total transmission ratio of approximately 80:1 to 120:1, while the transmission ratio of the DTU 10-MW medium-speed wind turbine gearbox is 50:1. According to the industry experiences, the medium-speed gearbox is typically designed with one or two stages with the objective of reducing the gearbox failure rate by eliminating the high speed part, which is considered as the main source of gearbox failure. However, according to the study of Schmidt et al, 25  a novel layout such as a power splitting gearbox, a compound, differential or double-helix planetary gearbox, or a combination of them. These novel layouts have enormous potential as they not only realize a high gear ratio but also result in a more compact gearbox with lighter weight and smaller volume, which yields a higher torque or power density compared with the conventional layouts, which was demonstrated in another studies 28,29 of the authors. However, these novel technologies have not been widely used, namely, the applicability of these gearbox concepts may have yet to be reasonably evaluated. This is because there is currently a lack of deep understanding of the dynamic behaviors and reliability of the novel gearbox concepts because of the effects of structure flexibility, stiffness, damping, and multiple source errors. Moreover, the manufacturing, installation, maintenance, and repair procedures of the novel concepts have not been properly estimated. This is because the highly accurate design requirements pose huge difficulties in their manufacturing and assembly, and some of the mechanical components might need to be custom made. In addition, the compact gearbox typically has less available space, which is unfavourable for inspection, maintenance, and repair. Hence, costs have not been estimated accurately.
Compared with the novel gearbox layouts, the conventional three-stage gearbox is more feasible according to many studies on design, dynamic analysis, and cost estimation that have been conducted. As the objective of this study is to provide support for cooperative and comparative studies to facilitate research on the dynamics of 10-MW offshore wind turbines, the conventional three-stage gearbox seems to be more suitable as a baseline model for the present target; thus, this layout is selected to be designed in this study.

Drivetrain component design
The main components of the drivetrain include hub, mainshaft, main bearing, gearbox, coupling, generator, and bedplate. The geometries of the hub, the mainshaft, the coupling, the generator, and the bedplate are designed by referring to the corresponding components in a 2-MW land-based wind turbine, as presented by Wang et al. 30 The basic flow of the gearbox components sizing process is presented in Figure 2. All components are designed based on gearbox design LDD and following the design requirements that are defined in the international standard IEC 61400-4. 21 Gears are designed based on the First, the gearbox initial gear ratio in each stage is set with determined drivetrain information such as the rated torque, the overall speed ratio, and the gearbox configuration. Then, the initial gear size, which is determined by parameters such as the number of gear teeth, the gear modulus, and the face width, is calculated based on the gear load rating. Next, the initial bearing size is selected based on the gear bore diameter and the gear face width constraint. The bearing type selection and arrangements are determined by referring the IEC 61400-4 21 recommendation and the 5-MW offshore wind turbine gearbox design case. 9 The bearing designation is chosen from the bearing database in software KISSsoft 36 with the determined bearing size and type. Next, the initial shaft dimension is designed according to the bearing bore diameter and the gear Four gearbox layout options are proposed and are designed using the gearbox flowchart that is presented above. The design results are presented and compared in Table 3. Compare with the options A and B, a more compact gearbox can be realized by the options C and D. While the option D is slightly smaller and lighter than the option C, it has a higher requirement on the gearbox load-sharing performance. Based on this, the option C is eventually selected in this case study. A detailed analysis is described in the study of Wang et al. 37

Drivetrain numerical modelling
In this study, the wind turbine drivetrain is modelled numerically via a multibody system (MBS) approach. The multibody drivetrain model is composed of various rigid and flexible bodies, which are connected by kinematic constraints. SIMPACK, 38 which is a general-purpose MBS software that is widely used for the kinematics and dynamic analyses of complex mechanical systems, is employed for the drivetrain dynamic In SIMPACK, each gear tooth contact is modelled by a force element, namely, FE 225, and the contact force is composed of stiffness, damping, and friction terms, where the gear meshing stiffness is modelled by a series of spring elements along the line of action, and the stiffness value of each spring element is calculated based on the standard ISO 6336-1. 46 Bearings are modelled by force element FE 43 with a linear force-deflection relationship in SIMPACK. In this paper, the bearing stiffness is represented as a linear diagonal stiffness as follows: where K xx , K yy , and K zz represent the axial, tangential, and radial stiffness, respectively, with units in N/m. The K and K represent pitch and yaw stiffness, respectively, with unit in Nm/rad. The K is 0, because corresponds to rotation direction. The coupling effects between different DOFs are not considered in this study, so the off-diagonal terms are zeros. The bearing stiffness is calculated using the software Romax. 47 The generator is modelled by a proportional-integral velocity controller that is applied on the generator shaft. The velocity controller uses the generator angular velocity that is obtained from the global analysis as a reference; then, the generator torque, which is denoted as T Gen , is calculated via the following equation 9 : where w is the generator angular velocity calculated in the drivetrain model, and w ref is the reference value obtained from global simulation. K P and K I are proportional and integral gain, respectively. In each simulation time step, T Gen is calculated and applied on the generator shaft.

Gear fatigue damage calculation
The long-term gear bending and pitting fatigue damage are calculated in this study. First, the gear tooth contact and bending stresses are calculated by postprocessing the time-varying gear transmitted loads that are obtained from the drivetrain MBS simulation, according to the methods that are proposed in manuals ISO 6336-2 31 and ISO 6336-3, 32 respectively. Then, gear tooth stress bins are created using a stress cycle counting method, as demonstrated in the study of Nejad et al, 48 where the number of gear tooth stress cycles in each stress bin is calculated via the following equation: where n i is the number of stress cycles in the stress bin i, t j is the j-th time duration of the bin i, and w j is the average gear rotational speed (rad/s) in the j-th time duration of bin i. The numbers of stress cycles of the sun and ring gears are multiplied by 5 in the first stage and by 3 in the second stage because they mesh with several planets simultaneously and would encounter several (number of planets) contacts in each rotation.
For each wind speed, the 1-hour short-term gear bending and pitting fatigue damage are calculated according to the Palmgren-Miner linear accumulative damage hypothesis 49 : where u represents the mean wind speed at the tower top height, D(u) is the 1-hour accumulative gear fatigue damage at the wind speed u, n i is the 1-hour number of cycles in stress bin i, and N i is the permissible number of cycles in stress bin i, which is calculated by the gear design SN curve, namely, N i = k · s i −m , in which k and m are SN curve parameters that are calculated based on ISO 6336-2, 31 ISO 6336-3, 32 and ISO 6336-5. 50 Long-term gear fatigue damage can then be calculated by 48 where T is 20-year gearbox design life, f(u) is probability density function of mean wind speed.

Bearing fatigue damage calculation
The bearing fatigue damage is calculated based on the Palmgren-Miner hypothesis. First, bearing basic rating life is calculated according to the load-life relationship, which is established via laboratory tests 34 : where L 10 is the basic rating life, which is expressed units of 10 6 revolutions (r); L 10 is defined as the number of cycles when 10% of the bearings in an identical group incur pitting damage while the remaining 90% bearings operate normally; C is the basic dynamic load rating, namely, the dynamic load that the bearing can withstand if the basic rating life is exactly 10 6 r, which is a specified constant for one bearing; P is the bearing dynamic equivalent load, which is calculated by P = XF r + YF a , where F r and F a are the radial loads and axial loads, respectively, that are experienced by the bearing, and X and Y are dynamic loading factors that are obtained from the bearing standard ISO 281; and a is the bearing life factor: For a ball bearing, a = 3, and for a roller bearing, a = 10 3 . An each wind speed, the 1-hour bearing fatigue damage is calculated according to the linear accumulative damage hypothesis 51 : where D(u) is the 1-hour accumulative bearing fatigue damage at wind speed u; l i is the 1-hour number of load cycles in load P i , where l i , which is associated with P i , is calculated by employing the load cycle counting method, which is the same procedure that is used in the gear stress bin creation; and L i is the permissible number of cycles in load P i , which is calculated via Equation (8).

Drivetrain schematic layout
A schematic diagram of the 10-MW wind turbine layout is presented in Figure 3. According to the layout, the drivetrain is supported by two main bearings to prevent huge nontorque loads from entering the gearbox. A pair of tapered roller bearings are used as the main bearings, which is regarded as a promising application in large offshore turbines. This is because this bearing arrangement has satisfactory system stiffness and high reliability, and the short distance between the two bearings reduces the length of the main shaft, thereby making the drivetrain more compact.
The specifications of the drivetrain model are listed in Table A1 in Appendix A.

Component specifications
The drivetrain component specifications are listed in Appendix A. Table A2 presents the materials that were used in this study for the drivetrain component design. Table A3 lists the detailed gear geometrical specifications in which the gear profile shift coefficients are calculated by software KISSsoft based on the minimum slipping ratio principle. The detailed types, designations, and geometrical specifications of the bearings are listed in Table A4.

MBS model and modelling parameters
The 10-MW drivetrain MBS model that is established using the SIMPACK software is illustrated in Figure 4. The connection relationships between the components in the MBS model and the DOFs of each element are illustrated in the drivetrain topological diagram in Figure B1 in Appendix B. The required parameters, such as the masses and the inertial moments of the components and the bearing modelling stiffness, for the drivetrain numerical modelling are presented in Tables B1 and B2. In this model, the mean contact stiffnesses of the gear pairs in the three stages are 1.4163 × 10 10 , 9.9311 × 10 9 , and 1.0215 × 10 10 N/m, respectively.

Model comparison
Since very limited drivetrain properties have been provided by DTU, many of the drivetrain modelling parameters that are assumed in this detailed model are associated with uncertainties, such as the torsional stiffness and the damping of the drivetrain components. An effective approach, which is proposed in the standard DNVGL-ST- 23 for evaluating the suitability of these parameters, is to compare the first eigenfrequencies between the detailed drivetrain model and the DTU simplified model. The first eigenfrequency of the simplified drivetrain model could be calculated via an equivalent mechanical equation, as specified by Nejad 52 and Oyague, 53 with the essential parameters that are presented in Table 2. Additionally, the first eigenfrequency of the detailed drivetrain model could be obtained by conducting modal analysis in SIMPACK. In the free-free drivetrain mode, the values that are calculated by the detailed and simplified drivetrain models are 3.889 and 4.003 Hz, respectively, and in the free-fixed mode, the values are 0.611 and 0.612 Hz, respectively. The first-order eigenfrequency in the simplified model accords with that in the detailed model, thereby suggesting that the drivetrain MBS modelling parameters could be reasonable.

Resonance analysis of the drivetrain
Although the vibration modes of the drivetrain MBS model are multidimensional, this study focuses only on torsional vibration in which the resonance of the model is most likely to occur under dynamic excitation. The excitation frequencies of the drivetrain include shaft rotation frequencies and gear meshing frequencies that are within the normal operating speed range, which are listed in Table 4.
The natural frequencies that are obtained via modal analysis in SIMPACK are listed in Table 5. Since this analysis focuses on the drivetrain torsional modes, the frequencies that have no torsional mode shape are not listed in this table.
A Campbell diagram is plotted to screen the potential resonance points of the drivetrain model. The horizontal lines in the diagram correspond to natural frequencies and the oblique lines to excitation frequencies. The cross points in the diagram indicate the possible resonances in the    Campbell diagram and modal energy distribution drivetrain model. To make the diagram clear and easy to interpret, the excitation frequencies are separated into three parts, which cover the whole excitation frequency range, and the first part (0-10 Hz), which is shown in Figure 5A, is considered as an example for demonstration in this study.
To further examine the possibility of resonance in this model, modal energy distributions of components that correspond to eigenfrequencies that have cross points with excitation frequencies are plotted. The modal energy calculation method is described in the study of Guo et al. 54 Figure 5B illustrates the modal energy distribution of components that correspond to eigenfrequency f_N2. The kinetic energy is mainly distributed on components st1_carrier and st2_planet2, which are selected based on the critical threshold of 20% energy, as recommended in international standard DNVGL-ST-0361. 23 However, the eigenfrequency f_N2 has a cross point with excitation frequency hss; hence, this frequency will not cause any resonance. The modal energy distribution of the components that correspond to each eigenfrequency is analysed via this approach, and the results demonstrate that resonance will not occur in this drivetrain model within the normal operating range.  Figures C1, C2, and C3, respectively, in Appendix C. Gear fatigue damage Figure D1 in Appendix D plots the gear tooth bending and contact stress bins with the corresponding number of cycles for the first-stage sun gear at the wind speed of 12.6 m/s. The gear pitting and bending fatigue SN curve parameters, as listed in Table D1, are calculated based on the   ISO 6336 standards, with the specified gear material and heat treatment. The 20-year gear tooth bending and pitting fatigue damage throughout   the operating wind speed range, which are calculated via Equations 5 to 7, are presented in Table D2 and illustrated in Figure 6. Four levels, namely, highest, high, low, and lowest, are defined based on the ranking sequence. The pinion gear in the third stage is observed to have both the highest tooth bending and the highest pitting fatigue damage. The primary reason is the large number of cycles that are experienced by this gear.

Drivetrain fatigue damage analysis and vulnerability map
Additionally, the sun gear in the first stage has the highest tooth pitting fatigue damage, which is mainly due to the high tooth contact stress that is caused by the small sun gear tooth curvature. In addition, the lowest gear tooth pitting fatigue damage occurs on the two planetary stage ring gears, which is due to the material resistance for the ring gears being less than those of the other gears.

Drivetrain vulnerability map
Based on the 20-year gear and bearing fatigue damages, a drivetrain vulnerability map is established by ranking those components according to their damage levels, as shown in Figure 8. According to Table D2 and Figure 6, the gear tooth bending fatigue damage is much more severe  The drivetrain vulnerability map ranks components from highest to lowest fatigue damage, which could facilitate drivetrain performance assessment and model optimization. The drivetrain inspection and maintenance costs could be approximated by developing an inspection and maintenance strategy that is based on the vulnerability map. Moreover, one can improve the drivetrain design or enhance its reliability by optimizing the components that have the highest fatigue damage, which could substantially reduce the optimization strategy developing time.
The vulnerability map of the 10-MW drivetrain differs substantially from that of the 5-MW drivetrain that is presented in the study of Nejad et al, 9 which is due to factors such as the wind turbine rating, drivetrain transmission ratio, and mechanical component materials. Hence, the drivetrain fatigue damage will primarily depend on the loads and load cycles that are experienced by the mechanical components and is not closely rated to the drivetrain layout.

CONCLUDING REMARKS
This paper deals with the design, modelling, and analysis of a medium-speed drivetrain for the DTU 10-MW wind turbine. Detailed design and dynamic modelling parameters are provided for public use to facilitate research on the dynamics of 10-MW wind turbines. The main contributions are summarized as follows: • A four-point support drivetrain configuration is selected. Several potential gearbox design layouts for the 10-MW wind turbine case study are proposed. The pros and cons of the conventional gearbox layout and several novel gearbox layouts, such as power splitting gearbox layout and compound, differential or double-helix planetary gearbox layout, are discussed and compared. A conventional three-stage gearbox layout is eventually selected to be designed with the intent of providing a benchmark model for public use.
• A detailed drivetrain design methodology is described. The drivetrain components are designed based on the design loads and criteria that are recommended in relevant international standards, and an iterative process is conducted to optimize the drivetrain design via the considerations of its weight, volume, and load sharing performance.