Wind turbine generator set front rack topological optimization method based on proxy model

Abstract

The invention discloses a wind turbine generator set front rack topological optimization method based on an agent model, and aims to solve the problems of mutual holding between light weight and high reliability of a whole wind turbine generator set and shortened research and development period of the whole wind turbine generator set. In order to achieve the purpose, the minimum flexibility is taken as the target, artificial volume ratio constraint is designed, moments in different directions are applied to the center of the hub to obtain respective topological optimization results, and result characteristics are analyzed. And performing model reconstruction on the front rack, and performing finite element analysis based on the proxy model to determine the structural type and size. The checking result of the ultimate strength and fatigue strength of the optimized structure shows that the topological optimization method has feasibility and effectiveness in the lightweight design of the front rack structure of the wind turbine generator, and the research and development cycle of the product is greatly shortened.

Description

Technical Field

[0001] The invention relates to the technical field of topology optimization of wind turbine sets, and in particular to a method for topology optimization of a front frame of a wind turbine set based on an agent model. Background Art

[0002] Continuum structure topology optimization refers to seeking material distribution layout in a given area to optimize the design goal under certain constraints. In recent years, the capacity of wind turbines has continued to break through the limit, but strength failure events such as tower collapse, bolt breakage, and surface crack initiation of components have occurred occasionally, and the contradiction between lightweight structure and high reliability has become increasingly prominent. In this context, structural innovation tools based on topology optimization have been introduced into the structural design of wind turbines.

[0003] Although topology optimization methods have been successfully applied in the structural design of wind turbine components, the following difficulties and problems still exist: currently, relatively mature stiffness optimization design methods are widely used, but wind turbine structural components must meet strength design requirements. Although stress-constrained and fatigue-constrained topology optimization methods have developed, there are still few successful engineering applications to date; secondly, there are hundreds of design conditions for wind turbines, and their topology optimization is essentially a multi-objective optimization problem. The corresponding large number of finite element analyses will lead to computational difficulties; the topology optimization results are expressed in the form of material stacking, and the conceptual design results are difficult to transform into the final engineering design; the volume ratio is a man-made parameter, and the topology optimization results are expressed in the force transmission path rather than the structural size on the force transmission path. On the basis of a clear force transmission path, a large amount of structural re-analysis is required to finally determine the structural shape and size. Summary of the invention

[0004] The purpose of the present invention is to overcome the shortcomings of the prior art and propose a topology optimization method for the front frame of a wind turbine generator set based on a proxy model to solve the problem that the huge computing power required in the topology optimization process leads to excessively long analysis time, optimize the design cycle of the front frame of the wind turbine generator set, simplify the calculation time, and meet the lightweight design requirements.

[0005] The purpose of the present invention is achieved through the following technical solution: A method for topology optimization of a front frame of a wind turbine generator set based on an agent model, comprising the following steps:

[0006] S1. Determine the load conditions and material properties of the front frame of the wind turbine, perform topology optimization analysis, and obtain topology optimization results;

[0007] S2. Reconstruct the geometric model of the front frame according to the topology optimization results, perform finite element analysis based on the proxy model, iterate until the design structure meets the preset preliminary strength design requirements, and determine the structural type and size;

[0008] S3. Check the structural strength based on the detailed finite element model. If the preset lightweight design requirements of the front frame of the wind turbine generator set are not met, return to step S2 and repeat the iteration until the preset lightweight design requirements of the front frame of the wind turbine generator set are met.

[0009] Further, the step S1 comprises:

[0010] Determine the load conditions and material properties of the front frame of the wind turbine. Based on the variable density method and with the goal of minimum compliance, design an artificial volume ratio constraint to obtain the optimal topology optimization result under a single load.

[0011] Among them, the design load value at the center of the wind turbine hub is calculated based on the wind turbine design software. The load transfer path is: transmitted to the bearing seat through the main shaft, transmitted to the front frame through the flange bolt connection, and the rear frame transmits the weight of the accessories it carries to the front frame through bolts; each extreme load condition includes forces and moments in three directions, and the extreme load condition M is selected. j_max and M j_min The working condition is taken as the loading condition, where j = x, y, z, yz.

[0012] Further, the step S1 comprises:

[0013] The material of the front frame is determined to be QT400, and its yield strength is 220MPa. Based on the wind turbine design software, the area occupied by the front frame is filled with materials. The design area is discretized into N units, and each unit corresponds to a pseudo-density value x in the range of 0 to 1. e , e=1,2,...,N; when x e 0 means the unit is deleted. e When it is 1, it means that the unit is retained. In order to suppress the number of units with intermediate density values, x is established. e and the unit elastic modulus E e The penalty relationship:

[0014]

[0015] Where p is the penalty parameter, which is initially set to 1 and gradually increases with the optimization iterations, and E0 is the elastic modulus of the solid material.

[0016] Further, the step S1 comprises:

[0017] A single load, i.e., the torque in the x, y, and z directions, is used to examine the corresponding force transmission paths. The topology optimization formula with minimum compliance and volume ratio as the constraint is as follows:

[0018] min:c=F T U

[0019]

[0020] KU=F

[0021] 0<ρ min ≤ρ e ≤1

[0022] Where c is the compliance value; V is the optimized structure volume, is the design domain volume; f is the volume ratio that needs to be determined manually; K is the overall stiffness matrix; U is the displacement vector; F is the load vector; ρ min It is the minimum value of cell density and its value is 0.01.

[0023] Further, the step S2 comprises:

[0024] Reconstructing the geometric model of the front frame according to the topology optimization results is a trade-off based on the analysis of different single load topology optimization results; performing finite element analysis based on the proxy model to determine the structural type and size is to use the proxy model to replace the refined model. The proxy model used is to reduce the scale of the finite element model or simplify the solution type by means of low-order unit types and simplified assembly connection relationships. On the basis of retaining the optimal force transmission path, it is quantitatively analyzed through multiple iterations of finite element analysis until the designed structure meets the preset preliminary strength design requirements, determines the specific structural type and structural size, and completes the structural design. At the same time, the refined model results can also be used to correct the results of the proxy model.

[0025] Further, the step S2 comprises:

[0026] The refined model includes refined models of the tower, front frame, rear frame, bearing seat, bolts and bearings, all of which include 6.17 million nodes and 3.39 million units, wherein the front frame is discretized using solid units mainly based on hexahedrons, including 4.5 million nodes and 1.35 million units, the contact relationship between the components connected by bolts is defined, and nonlinear springs are used to simulate bearings; the bottom of the fully constrained tower is loaded in different directions at the center of the hub, and rigid elements are used to achieve load transfer; the proxy model includes proxy models of the tower, front frame, rear frame, bearing seat, bolts and bearings, wherein the front frame proxy model is a low-order solid unit discretized front frame, the front frame proxy model includes 1.08 million nodes and 530,000 units, and the nonlinear contact between the components is simplified to a binding relationship; according to the load condition, the corresponding stress threshold is set for the proxy model, so that the cloud map of the proxy model is close to the cloud map of the refined model.

[0027] Further, the step S3 comprises:

[0028] The strength of the designed structure is checked based on the detailed finite element model according to the preset material safety factor of 1.1. The allowable stress of the front frame material of the wind turbine is 200MPa. The maximum equivalent stress under different extreme working conditions is calculated based on the fine model. If the maximum equivalent stress values ​​under each working condition are all less than the allowable stress, it is judged that the designed front frame structure meets the ultimate strength design requirements; the SN curve of the front frame material QT400 is synthesized, and on this basis, the fatigue strength analysis of the front frame is carried out based on the critical plane method of multi-axial fatigue. The influence of the average stress on fatigue damage is corrected by FKM, and the cumulative fatigue damage distribution of the front frame is obtained. If the cumulative fatigue damage of each part of the front frame structure is less than 1, it indicates that the fatigue strength design requirements are met; if the designed structure does not meet the preset ultimate strength design requirements and fatigue strength design requirements, return to step S2 and repeat the iteration until the preset ultimate strength design requirements and fatigue strength design requirements are met.

[0029] A non-transitory computer-readable medium storing instructions, characterized in that when the instructions are executed by a processor, the steps of the above-mentioned wind turbine front rack topology optimization method based on the agent model are executed.

[0030] A computing device comprises a processor and a memory for storing a program executable by the processor. When the processor executes the program stored in the memory, the above-mentioned method for optimizing the front rack topology of a wind turbine generator system based on an agent model is implemented.

[0031] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0032] The present invention takes the front frame of a wind turbine as the research object, and proposes a structural reanalysis method based on a proxy model on the basis of topology optimization, thereby realizing the rapid iteration of the structural design process; and performs ultimate strength and fatigue strength verification on the optimized structure of the front frame of the wind turbine to ensure its feasibility. Compared with the traditional conventional design process, the research and development cycle of the entire structural design is greatly shortened. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 This is a flow chart of the topology optimization method for the front rack of a wind turbine based on an agent model.

[0034] Figure 2 Schematic diagram of the optimal topology under a single torque.

[0035] Figure 3 Comparison diagram of equivalent stress distribution under refined model and proxy model.

[0036] Figure 4 The comparison diagram of equivalent stress distribution of the wire hole structure under different improvement schemes.

[0037] Figure 5This is a comparison chart of the maximum equivalent stress under different extreme working conditions.

[0038] Figure 6 This is the cumulative fatigue damage distribution diagram of the front frame. DETAILED DESCRIPTION

[0039] The present invention will be further described below in conjunction with specific embodiments.

[0040] Example 1

[0041] See also Figure 1 As shown, the wind turbine front rack topology optimization method based on the proxy model provided in this embodiment includes the following steps:

[0042] S1. Determine the load conditions and material properties of the front frame of the wind turbine, perform topology optimization analysis, and obtain topology optimization results, including:

[0043] First, the load conditions and material properties of the front frame of the wind turbine are determined. The design load value at the center of the wind turbine hub is calculated based on the wind turbine design software. The load transfer path is: transmitted to the bearing seat through the main shaft, transmitted to the front frame through the flange bolt connection, and the rear frame transmits the weight of the accessories it carries to the front frame through bolts; each extreme load condition includes forces and moments in three directions. The extreme load condition M is selected. j_max and M j_min The working condition is taken as the loading condition, where j = x, y, z, yz, and M y_max For example, in all load conditions, the algebraic value of the bending moment in the y direction is the largest. Since the absolute value of the resultant moment in the yoz plane is small, the ultimate strength check can be ignored. yz_min Working conditions; determine that the material of the front frame is QT400, and its yield strength is 220MPa; fill the area occupied by the front frame with materials based on the wind turbine design software, and discretize the design area into N units, each unit corresponds to a pseudo-density value x in the range of 0 to 1 e , e=1,2,...,N; when x e 0 means the unit is deleted. e When it is 1, it means that the unit is retained. In order to suppress the number of units with intermediate density values, x is established. e and the unit elastic modulus E e The penalty relationship:

[0044]

[0045] Where p is the penalty parameter, which is initially set to 1 and gradually increases with the optimization iterations, and E0 is the elastic modulus of the solid material.

[0046] According to the DNV 2016 specification, there are a large number of load conditions for wind turbine structure design, and topology optimization is essentially a multi-objective optimization problem. Generally speaking, the results of multi-condition topology optimization are not a simple superposition of the results of single-condition topology optimization. It has the advantage of coordinating the force transmission paths under different load conditions, but the multi-condition optimization results will also cover up the force transmission paths under a single load. To overcome the above problems, a single load, i.e., the torque in the x, y and z directions, is used to examine the corresponding force transmission paths respectively. The topology optimization with the minimum compliance as the goal and the volume ratio as the constraint is listed as follows:

[0047] min:c=F T U

[0048]

[0049] KU=F

[0050] 0<ρ min ≤ρ e ≤1

[0051] Where c is the compliance value; V is the optimized structure volume, is the design domain volume; f is the volume ratio that needs to be determined manually; K is the overall stiffness matrix; U is the displacement vector; F is the load vector; ρ min It is the minimum value of cell density and its value is 0.01.

[0052] The topology optimization results generally have checkerboard phenomenon and grid dependency problems. In this embodiment, the minimum size is set to eliminate these two types of numerical instability problems. Using the above settings, the topology optimization results under single bending moments in different directions are as follows: Figure 2 As shown, Figure 2 (a) is a single load M x The topology optimization results under the action of Figure 2 (b) is a single load M y The topology optimization results under the action of Figure 2 (c) is a single load M z Topology optimization results under action;

[0053] S2. Reconstruct the geometric model of the front frame based on the topology optimization results, perform finite element analysis based on the proxy model, iterate until the design structure meets the preset preliminary strength design requirements, and determine the structural type and size, including:

[0054] According to common knowledge in this field, the bending moment M y and M z The dominant extreme working condition is usually more dangerous, so the focus here is on Figure 2 (b) and (c) show the force transmission path. Figure 2Taking (b) as an example, the rear bearing seat is transmitted to the top of the tower through the side wall to form a clear force transmission path, and a large hole is formed on the side wall between the front and rear bearing seats, indicating that this area does not bear the bending moment M y Therefore, the reconstruction of the front frame structure needs to make trade-offs based on the analysis of the topology optimization results of different single loads. It is worth noting that the above-mentioned topology optimization adopts a more mature optimization model in theoretical research, that is, the conceptual design scheme under the stiffness maximization goal and volume ratio constraint, but the wind turbine components must focus on meeting the strength design requirements. This requires that on the basis of retaining the optimal force transmission path, the specific structural type and structural size are determined through the finite element analysis results, and finally the strength design requirements are met. Since the topology optimization results are applicable to the conceptual design stage, this process usually requires repeated finite element analysis to achieve the purpose of detailed design;

[0055] Finite element analysis based on proxy model to determine the structural type and size is to use proxy model to replace the refined model. The proxy model used is to reduce the scale of finite element model or simplify the solution type by means of low-order unit type and simplified assembly connection relationship. On the basis of retaining the optimal force transmission path, it is quantitatively analyzed through multiple iterations of finite element analysis until the designed structure meets the preset preliminary strength design requirements, and the specific structural type and structural size are determined to complete the structural design. At the same time, the refined model results can also be used to correct the results of the proxy model;

[0056] The refined model includes the tower, front frame, rear frame, bearing seat, bolt and bearing refined models, all of which include 6.17 million nodes and 3.39 million units, among which the front frame is discretized by solid units mainly based on hexahedrons, including 4.5 million nodes and 1.35 million units, defining the contact relationship between the components connected by bolts, and using nonlinear springs to simulate bearings; the bottom of the tower is fully constrained, loads in different directions are applied at the center of the hub, and rigid elements are used to achieve load transfer. Based on high-performance computing, it takes about 48 hours to complete the calculation of 7 extreme working conditions; the proxy model includes the tower, front frame, rear frame, bearing seat, bolt and bearing proxy model, among which the front frame proxy model is a low-order solid unit discretized front frame, the front frame proxy model includes 1.08 million nodes and 530,000 units, the nonlinear contact between the components is simplified to a bonding relationship, and the total calculation time is shortened to less than 1 hour; with M y_min As an example, the equivalent stress distribution of the refined model and the proxy model is compared. Figure 3 As shown, Figure 3 (a) is the refined model. Figure 3(b) is the proxy model, and the stress thresholds of the cloud map are set to 200MPa and 150MPa respectively. Different stress thresholds need to be adjusted according to different working conditions to make the cloud map of the proxy model as close to the refined model as possible, so as to improve the credibility of the proxy model.

[0057] Depend on Figure 3 It can be seen that although the two types of models have different degrees of refinement, the stress distribution at the dangerous parts is consistent. In fact, the refinement process of the simulation model is only to approximate the real situation to a certain extent. Although the accuracy of the proxy model results is poor, it has the advantage of being able to quickly determine the structural form in the structural concept design stage. The subsequent qualitative evaluation of structural improvements can be carried out on the proxy model to a large extent.

[0058] Taking the improvement of the cable hole structure as an example, the cable hole position was moved outward by 30mm to investigate the y_min and M z_max Two working conditions, based on the proxy model calculation, the equivalent stress distribution before and after the structure improvement is compared. Figure 4 As shown, Figure 4 (a) is the reference structure M z_max Working conditions, Figure 4 (b) The threading hole is moved outward M z_max Working conditions, Figure 4 (c) is the reference structure M y_min Working conditions, Figure 4 (d) The threading hole is moved outward M y_min Working condition, the position of the wire hole can be moved outward to appropriately reduce M z_max The stress level of this dangerous condition, but for M y_min The stress distribution of the working condition has little effect.

[0059] S3, checking the structural strength based on the detailed finite element model, if it does not meet the preset lightweight design requirements of the front frame of the wind turbine generator set, returning to step S2 and iterating repeatedly until the preset lightweight design requirements of the front frame of the wind turbine generator set are met, including:

[0060] According to the preset material safety factor of 1.1, the allowable stress of the front frame material of the wind turbine is 200MPa. Based on the refined model, the maximum equivalent stress under different extreme working conditions is calculated as follows: Figure 5 As shown, in all working conditions, M y_max The maximum equivalent stress value of the working condition is the largest, and the occurrence location is near the rear end wire hole. The maximum equivalent stress values ​​under each working condition are all less than the allowable strength value, and the front frame meets the ultimate strength design requirements.

[0061] According to the DNV2016 certification specification, the SN curve of the front frame material QT400 is synthesized. On this basis, the fatigue strength analysis of the front frame is carried out based on the critical plane method of multi-axial fatigue. The influence of the average stress on fatigue damage is corrected by FKM, and the following is obtained: Figure 6 The cumulative fatigue damage distribution of the front frame is shown in the figure. Except for the bearing seat surface and yaw contact surface, the cumulative fatigue damage of the front frame structure is less than 1, indicating that the fatigue strength design requirements are met. The above limit and fatigue strength verification results further prove the feasibility of the topology optimization method in the lightweight design of the front frame structure.

[0062] Example 2

[0063] This embodiment discloses a non-transitory computer-readable medium storing instructions. When the instructions are executed by a processor, the steps of the wind turbine front rack topology optimization method based on the agent model according to Embodiment 1 are executed.

[0064] The non-temporary computer-readable medium in this embodiment may be a disk, an optical disk, a computer memory, a read-only memory (ROM), a random access memory (RAM), a USB flash drive, a mobile hard disk, or other media.

[0065] Example 3

[0066] This embodiment discloses a computing device, including a processor and a memory for storing a program executable by the processor. When the processor executes the program stored in the memory, the proxy model-based wind turbine front rack topology optimization method described in Example 1 is implemented.

[0067] The computing device described in this embodiment may be a desktop computer, a laptop computer, a smart phone, a PDA handheld terminal, a tablet computer, a programmable logic controller (PLC), or other terminal devices with a processor function.

[0068] The embodiments described above are only preferred embodiments of the present invention and are not intended to limit the scope of implementation of the present invention. Therefore, all changes made according to the shape and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for topology optimization of the front rack of a wind turbine based on an agent model, characterized in that: The following steps are involved: S1. Determine the load conditions and material properties of the front frame of the wind turbine, perform topology optimization analysis, and obtain topology optimization results; S2. Reconstruct the geometric model of the front frame according to the topology optimization results, perform finite element analysis based on the proxy model, iterate until the design structure meets the preset preliminary strength design requirements, and determine the structural type and size; S3. Check the structural strength based on the detailed finite element model. If the preset lightweight design requirements of the front frame of the wind turbine generator set are not met, return to step S2 and repeat the iteration until the preset lightweight design requirements of the front frame of the wind turbine generator set are met.

2. The method for topology optimization of the front frame of a wind turbine generator system based on an agent model according to claim 1, characterized in that: The step S1 comprises: Determine the load conditions and material properties of the front frame of the wind turbine. Based on the variable density method and with the goal of minimum compliance, design an artificial volume ratio constraint to obtain the optimal topology optimization result under a single load. Among them, the design load value at the center of the wind turbine hub is calculated based on the wind turbine design software. The load transfer path is: transmitted to the bearing seat through the main shaft, transmitted to the front frame through the flange bolt connection, and the rear frame transmits the weight of the accessories it carries to the front frame through bolts; each extreme load condition includes forces and moments in three directions, and the extreme load condition M is selected. j_max and M j_min The working condition is taken as the loading condition, where j = x, y, z, yz.

3. The method for topology optimization of the front frame of a wind turbine generator system based on an agent model according to claim 2, characterized in that: The step S1 comprises: The material of the front frame is determined to be QT400, and its yield strength is 220MPa. Based on the wind turbine design software, the area occupied by the front frame is filled with materials. The design area is discretized into N units, and each unit corresponds to a pseudo-density value x in the range of 0 to 1. e , e=1,2,...,N; when x e 0 means the unit is deleted. e When it is 1, it means that the unit is retained. In order to suppress the number of units with intermediate density values, x is established. e and the unit elastic modulus E e The penalty relationship: Where p is the penalty parameter, which is initially set to 1 and gradually increases with the optimization iterations, and E0 is the elastic modulus of the solid material.

4. The method for topology optimization of the front frame of a wind turbine generator system based on an agent model according to claim 3, characterized in that: The step S1 comprises: A single load, i.e., the torque in the x, y, and z directions, is used to examine the corresponding force transmission paths. The topology optimization formula with minimum compliance and volume ratio as the constraint is as follows: min:c=F T U KU=F 0<ρ min ≤ρ e ≤1 Where c is the compliance value; V is the optimized structure volume, is the design domain volume; f is the volume ratio that needs to be determined manually; K is the overall stiffness matrix; U is the displacement vector; F is the load vector; ρ min It is the minimum value of cell density and its value is 0.

01.

5. The method for topology optimization of the front frame of a wind turbine generator system based on an agent model according to claim 1, characterized in that: The step S2 comprises: Reconstructing the geometric model of the front frame according to the topology optimization results is a trade-off based on the analysis of different single load topology optimization results; performing finite element analysis based on the proxy model to determine the structural type and size is to use the proxy model to replace the refined model. The proxy model used is to reduce the scale of the finite element model or simplify the solution type by means of low-order unit types and simplified assembly connection relationships. On the basis of retaining the optimal force transmission path, it is quantitatively analyzed through multiple iterations of finite element analysis until the designed structure meets the preset preliminary strength design requirements, determines the specific structural type and structural size, and completes the structural design. At the same time, the refined model results can also be used to correct the results of the proxy model.

6. The method for topology optimization of the front frame of a wind turbine generator system based on an agent model according to claim 5, characterized in that: The step S2 comprises: The refined model includes refined models of the tower, front frame, rear frame, bearing seat, bolts and bearings, all of which include 6.17 million nodes and 3.39 million units, wherein the front frame is discretized using solid units mainly based on hexahedrons, including 4.5 million nodes and 1.35 million units, the contact relationship between the components connected by bolts is defined, and nonlinear springs are used to simulate bearings; the bottom of the fully constrained tower is loaded in different directions at the center of the hub, and rigid elements are used to achieve load transfer; the proxy model includes proxy models of the tower, front frame, rear frame, bearing seat, bolts and bearings, wherein the front frame proxy model is a low-order solid unit discretized front frame, the front frame proxy model includes 1.08 million nodes and 530,000 units, and the nonlinear contact between the components is simplified to a binding relationship; according to the load condition, the corresponding stress threshold is set for the proxy model, so that the cloud map of the proxy model is close to the cloud map of the refined model.

7. The method for topology optimization of a front frame of a wind turbine generator system based on an agent model according to claim 1, characterized in that: The step S3 comprises: The strength of the designed structure is checked based on the detailed finite element model according to the preset material safety factor of 1.

1. The allowable stress of the front frame material of the wind turbine is 200MPa. The maximum equivalent stress under different extreme working conditions is calculated based on the refined model. If the maximum equivalent stress values ​​under each working condition are all less than the allowable stress, it is judged that the designed front frame structure meets the ultimate strength design requirements; the SN curve of the front frame material QT400 is synthesized, and on this basis, the fatigue strength analysis of the front frame is carried out based on the critical plane method of multi-axial fatigue. The influence of the average stress on fatigue damage is corrected by FKM, and the cumulative fatigue damage distribution of the front frame is obtained. If the cumulative fatigue damage of each part of the front frame structure is less than 1, it indicates that the fatigue strength design requirements are met; if the designed structure does not meet the preset ultimate strength design requirements and fatigue strength design requirements, return to step S2 and repeat the iteration until the preset ultimate strength design requirements and fatigue strength design requirements are met.

8. A non-transitory computer-readable medium storing instructions, characterized in that: When the instruction is executed by the processor, the steps of the wind turbine front rack topology optimization method based on the agent model according to any one of claims 1 to 7 are performed.

9. A computing device comprising a processor and a memory for storing a program executable by the processor, characterized in that: When the processor executes the program stored in the memory, the proxy model-based wind turbine front rack topology optimization method described in any one of claims 1 to 7 is implemented.

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