A performance optimization method for a wind power blade drop-type fatigue test mechanism

Abstract

The application discloses a wind power blade floor type fatigue test mechanism performance optimization method and relates to the technical field of wind power blades. On the basis of deduced Jacobian matrix, end output force model and dynamic torque, the dexterity performance index and the end output force performance index of the fatigue test mechanism are constructed and performance analysis is conducted, then each rod length parameter is taken as a design variable, and a multi-objective optimization method is used to solve an optimal structure parameter combination considering motion dexterity and loading capacity. The fatigue test mechanism can have higher stability, better controllability and stronger loading capacity in fatigue test.

Description

Technical Field

[0001] This invention relates to the field of wind turbine blade technology, and more specifically to a method for optimizing the performance of a ground-mounted fatigue testing mechanism for wind turbine blades. Background Technology

[0002] As wind turbine blades continue to evolve towards larger and more flexible designs, traditional fatigue testing equipment is increasingly unable to meet their loading requirements, making the upgrading and innovation of testing equipment a research hotspot. In recent years, using a parallel five-bar linkage to replace the traditional exciter for blade fatigue loading has been considered a feasible and promising new approach.

[0003] For fatigue testing mechanisms for wind turbine blades, the feasibility of the test is primarily limited by the mechanism's end-effector force capability. Only when the mechanism can continuously output a stable and controllable excitation force that meets the target bending moment requirements within the effective working space can the feasibility and reliability of the fatigue test be guaranteed. Since fatigue testing requires the long-term, stable application of periodic loads that meet test requirements within a defined operating range, the mechanism's end-effector force capability and motion transmission performance directly determine the feasibility and stability of the test. However, combinations of rod length dimensions significantly alter the mechanism's transmission characteristics, end-effector force level, and distribution pattern, simultaneously affecting the torque and power requirements of the drive joints. To enable the fatigue testing mechanism to possess higher stability, better controllability, and stronger loading capacity in fatigue testing, it is necessary to further conduct systematic performance evaluation and structural parameter optimization research based on the theoretical model established by the novel fatigue loading device for wind turbine blades. Summary of the Invention

[0004] The purpose of this invention is to provide a performance optimization method for a ground-mounted fatigue testing mechanism for wind turbine blades, which enables the fatigue testing mechanism to have higher stability, better controllability, and stronger loading capacity in fatigue tests.

[0005] The technical solution of the present invention is as follows: This invention provides a performance optimization method for a ground-mounted fatigue testing mechanism for wind turbine blades. Based on the derived Jacobian matrix, end-effector force model, and dynamic torque, it constructs and analyzes the dexterity and end-effector force performance indices of the fatigue testing mechanism. Then, using the length parameters of each link as design variables, a multi-objective optimization method is employed to solve for the optimal combination of structural parameters that balances motion dexterity and loading capacity. The method includes the following steps: S1: Analyze the working space of the ground-mounted fatigue testing mechanism for wind turbine blades to evaluate the overall motion performance of the mechanism within its theoretically achievable range; S2: Construct a local dexterity index for the fatigue testing mechanism to reflect the performance characteristics of the mechanism in fatigue loading tasks; S3: Establish the mapping relationship between the end output force of the fatigue testing mechanism and the torque of the driving joint; S4: Introduce the singular value decomposition method to construct an evaluation index for end-output force performance, so as to quantitatively characterize the output force capability of fatigue testing mechanisms; S5: Evaluation of the end-effector output force performance of a floor-mounted fatigue testing mechanism; S6: Construct a multi-objective optimization model for the size parameters of the fatigue testing mechanism and set constraints. Use the NSGA-II multi-objective optimization algorithm to solve the problem and obtain the Pareto optimal solution set that satisfies the working condition constraints. Furthermore, in some embodiments of the present invention, in step S1 above, the concept of operable workspace is used to characterize the workspace. That is, under the premise of satisfying closed-loop geometric feasibility and assembly branch consistency, operability constraints such as singularity avoidance are introduced to eliminate the Jacobian matrix degeneration and the configuration corresponding to its neighborhood, thereby obtaining a relatively stable end reachable region that can be used for actual loading and subsequent performance evaluation, and calculating the complete operable space and effective workspace.

[0006] Furthermore, in some embodiments of the present invention, in step S2 above, the local dexterity performance index of the fatigue testing mechanism is constructed based on the condition number of the velocity Jacobian matrix, and the corresponding dexterity analysis is carried out.

[0007] Furthermore, in some embodiments of the present invention, in step S5 above, the evaluation of the end-effector output force performance of the floor-mounted fatigue testing mechanism is more comprehensive in characterizing the fatigue loading capacity of the mechanism under adverse working conditions because biaxial loading involves motion and force transmission in multiple directions simultaneously. This is because biaxial loading involves motion and force transmission in multiple directions, resulting in more complex dynamic coupling and higher torque requirements for the drive joints. Based on this, the end-effector output force performance of the mechanism in the complete working space and the effective working space corresponding to the fatigue testing conditions are analyzed and compared. Through a comprehensive evaluation at both working space levels, the overall output capacity of the mechanism within its theoretically achievable range and its force transmission characteristics under fatigue testing conditions can be revealed.

[0008] Furthermore, in some embodiments of the present invention, in step S6 above, the task and working condition requirements of the fatigue testing mechanism are clarified, design variables are set, and then a multi-objective optimization model of the mechanism size parameters is constructed and constraints are set using the constructed local dexterity index and the end output force performance evaluation index as objective functions. Subsequently, the NSGA-II multi-objective optimization algorithm is used to solve the problem and obtain the Pareto optimal solution set that satisfies the working condition constraints. Finally, the solution set is analyzed to provide a basis for determining the optimal combination of mechanism link length parameters and their engineering values.

[0009] Compared with the prior art, the embodiments of the present invention have at least the following advantages or beneficial effects: 1. Under the premise of satisfying the constraints, the present invention achieves this by appropriately reducing the base spacing. And increase the length of the driven rod At the same time, maintain the length of the active rod. Stability can improve the condition number distribution of the Jacobian matrix within the effective workspace, thereby enhancing the dexterity of the mechanism and having a positive effect on the end-effector output capability.

[0010] 2. In view of the requirement that fatigue tests need to apply cyclic loads stably for a long time within the effective working space, this invention establishes two performance evaluation indicators: dexterity and end-effector output force, and conducts performance distribution evaluation under the constraints of the effective working space and typical working conditions.

[0011] 3. Through trade-off analysis and mechanism explanation of the optimization results, this invention determines the optimal combination of structural parameters that balances high dexterity and high output force. Compared with the original design, the optimized rod length parameters improve dexterity and end-effector output force, revealing the influence of key rod length parameters on dexterity and end-effector output force, and realizing the transformation of mechanism from empirical size design to performance-driven optimization design. Attached Figure Description

[0012] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0013] Figure 1 This is a diagram showing the complete operable workspace of the floor-mounted fatigue testing mechanism in an embodiment of the present invention. Figure 2 This is a diagram showing the effective working space of the floor-mounted fatigue testing mechanism in an embodiment of the present invention. Figure 3 This is a heat map showing the local dexterity of the floor-mounted fatigue testing mechanism in an embodiment of the present invention. Figure 4 This is a contour map showing the local dexterity of the floor-mounted fatigue testing mechanism in an embodiment of the present invention. Figure 5 This is a heat map of the local end-effector output force index of the floor-mounted fatigue testing mechanism in an embodiment of the present invention. Figure 6 This is a contour map of the local end-effector output force index of the floor-mounted fatigue testing mechanism in an embodiment of the present invention; Figure 7 This is a flowchart of the multi-objective optimization design in an embodiment of the present invention; Figure 8This is a schematic diagram illustrating the optimization principle of the NSGA-Ⅱ algorithm in an embodiment of the present invention. Figure 9 This is a comparison diagram of local dexterity before and after optimization in an embodiment of the present invention; Figure 10 This is a heatmap showing the difference in dexterity before and after optimization in an embodiment of the present invention; Figure 11 This is a comparison diagram of the local end output force before and after optimization in an embodiment of the present invention; Figure 12 This is a heat map showing the difference in output force before and after optimization in an embodiment of the present invention. Detailed Implementation

[0014] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Where specific conditions are not specified in the embodiments, conventional conditions or conditions recommended by the manufacturer shall apply. Reagents or instruments whose manufacturers are not specified are all conventional products that can be purchased commercially.

[0015] It should be noted that the term "comprising," or any other variation thereof, is intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes it.

[0016] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0017] The features and performance of the present invention will be further described in detail below with reference to embodiments.

[0018] Example 1 This invention provides a method for performance optimization of a ground-mounted fatigue testing mechanism for wind turbine blades, comprising the following steps: S1: Analyze the working space of the ground-mounted fatigue testing mechanism for wind turbine blades to evaluate the overall motion performance of the mechanism within its theoretically achievable range; S2: Construct a local dexterity index for the fatigue testing mechanism to reflect the performance characteristics of the mechanism in fatigue loading tasks; S3: Establish the mapping relationship between the end output force of the fatigue testing mechanism and the torque of the driving joint; S4: Introduce the singular value decomposition method to construct an evaluation index for end-output force performance, so as to quantitatively characterize the output force capability of fatigue testing mechanisms; S5: Evaluation of the end-effector output force performance of a floor-mounted fatigue testing mechanism; S6: Construct a multi-objective optimization model for the size parameters of the fatigue testing mechanism and set constraints. Use the NSGA-II multi-objective optimization algorithm to solve the problem and obtain the Pareto optimal solution set that satisfies the working condition constraints. Furthermore, in some embodiments of the present invention, in step S1 above, the concept of operable workspace is used to characterize the workspace. That is, under the premise of satisfying closed-loop geometric feasibility and assembly branch consistency, operability constraints such as singularity avoidance are introduced to eliminate the Jacobian matrix degeneration and the configuration corresponding to its neighborhood, thereby obtaining a relatively stable end reachable region that can be used for actual loading and subsequent performance evaluation, and calculating the complete operable space and effective workspace.

[0019] Specifically, in the above embodiments, the complete operable space and effective workspace are calculated, with the following constraints: Joint constraints: (1) Institutional reachability conditions: (2) Singularity constraints: To ensure the stability of motion / force transmission of the mechanism during fatigue loading, this embodiment of the invention uses singularity avoidance as one of the key constraints of a complete operable workspace.

[0020] Singular configurations of parallel mechanisms are generally categorized into three types: When the speed mapping relationship is Input side matrix A rank deficiency occurs, that is When the mechanism is in a type I singularity, the movement of the driven joint is difficult to be effectively transmitted to the end in certain directions, resulting in a decline in motor ability.

[0021] When the constraint side matrix An order deficiency occurs. At this time, the mechanism is in a Type II singularity, with end-effector degradation and the possibility of uncontrolled motion and a significant decrease in load-bearing capacity.

[0022] when and When both conditions are met, it is classified as a Type III singularity. Calculation is based on joint space rule sampling. , Then, singular and neighboring configurations are eliminated to obtain an operable workspace for subsequent performance evaluation and optimization.

[0023] During fatigue testing of wind turbine blades, the displacement amplitude of the loading point is relatively limited. The loading point typically reciprocates within a small range around the target loading trajectory and does not cover the complete operable workspace of the mechanism under full joint stroke. Based on the displacement amplitude of the fatigue test loading point and the continuous operability requirements of the mechanism, the effective workspace of the fatigue test corresponding to the range of the drive joints is defined in the joint space as follows.

[0024] (3) The constraints on the mechanism's reachability and singularity avoidance are the same as above. This allows us to obtain the effective operational workspace of the fatigue testing mechanism.

[0025] Furthermore, in some embodiments of the present invention, in step S2 above, the local dexterity performance index of the fatigue testing mechanism is constructed based on the condition number of the velocity Jacobian matrix, and the corresponding dexterity analysis is carried out.

[0026] Specifically, the positive velocity solution for the mechanism reference point C is: (4) according to Drive joint speed With the final velocity at point C The relationship shows that: (5) If there is a speed deviation in the drive Then the terminal velocity will also deviate. , becomes: (6) By subtracting equations (4) and (6), we can obtain: (7) Taking the L2 norm of both sides of the above equation, we get: (8) Similarly, We can obtain: (9) Will and Substituting and rearranging, we can obtain the boundary of the relative error as: (10) In the formula, The condition number of the Jacobian matrix can be obtained by using... express.

[0027] According to the spectral norm: (11) In the formula, for The largest eigenvalue, for The smallest eigenvalue; for The maximum singular value, for The smallest singular value.

[0028] Therefore, the condition number of the velocity Jacobian matrix can be expressed as: (12) condition number The condition number, ranging from 1 to positive infinity, is a typical indicator for measuring the numerical stability of the velocity Jacobian matrix. In engineering applications, the reciprocal of the condition number is usually used as an indicator of the dexterity performance of a mechanism, with a value ranging from [0,1]. The closer the reciprocal of the condition number is to 1, the higher the dexterity of the mechanism; when its value equals 1, the mechanism is in its optimal dexterity state. Conversely, the closer the reciprocal of the condition number is to 0, the worse the dexterity of the mechanism, indicating that the mechanism is in or close to a singular configuration.

[0029] Based on this, the local dexterity index of the floor-mounted fatigue testing mechanism is defined as follows: (13) Furthermore, in some embodiments of the present invention, in step S3 above, a mapping relationship is established between the end-effector output force of the fatigue testing mechanism and the torque of the drive joint. The external force on the end effector and the torque generated by the drive joint are correlated through the transpose of the Jacobian matrix. This relationship can reflect the mechanical transmission characteristics and amplification law of the mechanism under different postures.

[0030] Specifically, its basic expression is as follows: (14) In the formula, Indicates the active joint torque of the mechanism; This represents the force in the x and y directions at point C. Jacobi represents speed The transpose of .

[0031] When the active joint torque of the mechanism is known At that time, the force exerted by the end of the mechanism on the outside can be determined, which can be obtained from equation (14): (15) In the formula: (16) Finally to and for: (17) Furthermore, in some embodiments of the present invention, in step S4 above, a singular value decomposition method is introduced to construct an end-effector output force performance evaluation index to quantitatively characterize the output force capability of the mechanism. Based on the relevant formulas derived in step S3 above, the output force vector of the mechanism's end in the Cartesian coordinate system and the driving torque vectors of the two active joints are as follows: (18) Based on the end-effector force mapping relationship given by equation (17), under a given configuration, the end-effector force components can be expressed as a linear combination of the active joint torques: (19) In the formula, , It is a function of the mechanism configuration and dimensional parameters, and its expression is derived from the mechanism geometric relations and force Jacobian, as detailed in equation (17).

[0032] Equation (19) can be transformed into matrix form as follows: (20) In the formula: (twenty one) matrix It can be called the force Jacobian correlation matrix under this configuration, which represents the force response generated at the end of a unit joint torque input under the current configuration.

[0033] Considering the maximum allowable torque of the drive system is and Constraints are typically given in component form, as follows: (twenty two) Since the rated driving torque upper limits of the active joints in fatigue testing mechanisms may differ, directly performing end-effector force performance analysis within the original torque space would prevent comparisons of the impact of different joint capabilities on the results on the same scale. Therefore, an input normalization weighting matrix, i.e., a weighting matrix, is introduced.

[0034] (twenty three) After weighting the input torque, a weighted input vector is defined. for: (twenty four) In the formula, Each component is a dimensionless quantity normalized to its own upper limit. and for: (25) To obtain a unified set of input constraints that facilitates subsequent analysis, the constraint set is transformed from component inequalities into L2 norm sphere constraints: (26) The above formula represents all input torques that satisfy the upper limit constraint, which are enveloped in the weighted space as a sphere with a unit L2 norm.

[0035] From equation (24), we can obtain: (27) Substituting equation (27) into equation (20), we obtain the end force mapping under the normalized input constraint as follows: (28) In the formula, It is an equivalent force mapping matrix that takes into account the upper limit of torque. Its column vectors actually correspond to the contribution of each joint to the end output force under the rated upper limit scale.

[0036] For matrix Singular value decomposition can be performed to obtain and They respectively represent matrices The maximum and minimum singular values.

[0037] Based on the geometric meaning of linear mapping, under constraints Below, the reachable set of the end-output force is an ellipse, with the following principal axis lengths: (29) In the formula, This represents the maximum force that the end effector can output in the most advantageous direction under the current posture. This is the minimum output force. Therefore, and The maximum and minimum output force capabilities of the fatigue testing mechanism in this position are described respectively.

[0038] Use alone Using the final output force indicator as a metric can easily overestimate the mechanism's output capability in unfavorable directions, while using it alone... This approach can easily lead to overly conservative evaluations, resulting in overly large mechanism dimensions and drive capabilities. Using only one indicator as a performance evaluation metric is insufficient to comprehensively reflect the overall performance of the mechanism in that pose. Therefore, to comprehensively reflect the overall output force level of the end effector in all directions, its average value is defined as the local end effector output force index. Physically, it represents the average output force capability of the end effector in all directions under the current pose, and its formula is: (30) Furthermore, in some embodiments of the present invention, in step S5 above, the evaluation of the end-effector output force performance of the floor-mounted fatigue testing mechanism is more comprehensive in characterizing the fatigue loading capacity of the mechanism under adverse working conditions because biaxial loading involves motion and force transmission in multiple directions simultaneously. This is because biaxial loading involves motion and force transmission in multiple directions, resulting in more complex dynamic coupling and higher torque requirements for the drive joints. Based on this, the end-effector output force performance of the mechanism in the complete working space and the effective working space corresponding to the fatigue testing conditions are analyzed and compared. Through a comprehensive evaluation at both working space levels, the overall output capacity of the mechanism within its theoretically achievable range and its force transmission characteristics under fatigue testing conditions can be revealed.

[0039] Furthermore, in some embodiments of the present invention, in step S6 above, the task and working condition requirements of the fatigue testing mechanism are clarified, design variables are set, and then a multi-objective optimization model of the mechanism size parameters is constructed and constraints are set using the constructed local dexterity index and the end output force performance evaluation index as objective functions. Subsequently, the NSGA-II multi-objective optimization algorithm is used to solve the problem and obtain the Pareto optimal solution set that satisfies the working condition constraints. Finally, the solution set is analyzed to provide a basis for determining the optimal combination of mechanism link length parameters and their engineering values.

[0040] Example 2 This embodiment is based on Embodiment 1; please refer to the following for details. Figures 1-12 .

[0041] like Figure 1 As shown, the workspace of a parallel mechanism refers to the set of all poses that the end effector can reach in Cartesian space under given input constraints. For the working conditions required by the fatigue testing mechanism, the concept of an operable workspace is used to characterize the workspace. That is, under the premise of satisfying closed-loop geometric feasibility and assembly branch consistency, further operability constraints such as singularity avoidance are introduced to eliminate Jacobian matrix degeneration and its corresponding neighborhood configurations, thereby obtaining an end-effector reachable region with relatively stable motion / force transmission performance that can be used for actual loading and subsequent performance evaluation. Based on the above method, the complete operable workspace within the entire joint stroke range and the effective operable workspace within the joint range of the fatigue testing condition can be given respectively. The complete operable workspace is the end-effector reachable region obtained after comprehensively considering closed-loop geometric feasibility, assembly branch selection, and singularity avoidance constraints. This invention obtains the complete operable workspace of the mechanism by eliminating the configurations corresponding to Jacobian matrix degeneration (singular and near-singular). This result reflects the maximum reachability of the mechanism within the entire joint stroke range and can be used to verify the rationality of the mechanism's dimensional parameters and overall reachability. Since the floor-mounted fatigue testing mechanism adopts a floor-mounted base arrangement and the motion area of ​​the loading point is located above the base, the actual testing process does not involve the spatial range of the negative half-axis of the y-axis. Therefore, this invention only analyzes the working space of the positive half-axis of the y-axis.

[0042] like Figure 2 As shown, this invention employs a numerical method of discrete sampling using a regular grid in the joint space to solve the workspace: uniform discrete sampling is performed within the allowable range of the driving joint, and the end-effector position point set is obtained through forward kinematic mapping. Simultaneously, constraints such as geometric feasibility, assembly branching, and singularity avoidance are applied for screening, thereby directly constructing an operable workspace. Figure 2 (a) is the set of points in the effective workspace. Figure 2 (b) A comparison of the superimposed effective workspace and the complete workspace. As shown in the figure, the effective workspace is concentrated in the core area within the complete workspace. This effective space is defined based on the displacement requirements of the actual fatigue test. This range fully covers the motion trajectory required for the fatigue test and effectively avoids the possibility of collinearity of connecting rods during the movement of the floor-mounted fatigue testing mechanism. Operating within this effective workspace ensures the overall system stability during actual fatigue testing.

[0043] like Figure 3 As shown, based on the workspace analysis in step S1 and the construction of local dexterity indices in step S2, the dexterity performance analysis of the floor-mounted fatigue testing mechanism under the initial design parameters will be conducted from two levels: firstly, the dexterity distribution within the entire workspace, used to evaluate the overall motion performance of the mechanism within its theoretically reachable range; secondly, the dexterity performance within the effective workspace under fatigue testing conditions, reflecting the performance characteristics of the mechanism in the fatigue testing task. Through the above two parts of analysis, the dexterity level of the mechanism in the entire reachable workspace and the effective workspace under fatigue testing conditions can be comprehensively revealed. Figure 3 (a) illustrates the dexterity distribution of the floor-mounted fatigue testing mechanism within its complete workspace. This workspace, determined by the mechanism's kinematic constraints, reflects all possible poses of the end effector within its theoretically reachable range. Colors in the figure, from cool to warm, represent dexterity from low to high, and their values ​​are characterized by the reciprocal of the condition number of the velocity Jacobian matrix. As can be seen from the figure, the mechanism exhibits a high level of dexterity overall within the workspace; however, dexterity decreases significantly near the workspace boundary and in local singular neighborhoods, indicating poor motion and force transmission performance in these areas.

[0044] Figure 3(b) This section demonstrates the dexterity distribution of the floor-mounted fatigue testing mechanism within its effective workspace under fatigue testing conditions. This workspace is determined by factors such as the blade's geometric characteristics, fatigue loading amplitude, and loading trajectory, reflecting the actual range of motion of the end effector during the fatigue test. Compared to the complete workspace, this effective workspace is primarily distributed in areas of higher dexterity, with its overall dexterity level significantly better than that of the workspace boundaries and low-dexterity areas. This indicates that, with appropriate structural parameter configuration, the mechanism can maintain good motion transmission performance and control stability within the effective workspace, further validating the feasibility and rationality of applying this mechanism to wind turbine blade fatigue testing.

[0045] contrast Figure 3 As can be seen from (a) and (b), although there are certain low-dexterity areas in the complete workspace, these areas are not involved in the effective workspace. During the test, the mechanism mainly operates within the effective workspace with higher dexterity, thereby effectively improving the motion transmission performance of the mechanism while meeting the fatigue loading capacity requirements.

[0046] like Figure 4 As shown, Figure 4 (a) shows the contour distribution of dexterity for the floor-mounted fatigue testing mechanism within its complete workspace. It can be seen that the contour lines are relatively flat within the workspace, but become significantly denser near the workspace boundary and in local singular neighborhoods, indicating drastic changes in dexterity and significant performance degradation in these areas. This result is consistent with... Figure 3 (a) The distribution pattern reflected by the dexterity heatmap is consistent with that in the complete workspace, further verifying the overall trend of dexterity change.

[0047] Figure 4 (b) illustrates the distribution of dexterity contour lines within the effective workspace. Compared to the complete workspace, this contour distribution is more concentrated and primarily located in the higher dexterity range. The overall shape is continuous and smooth, without any obvious abrupt changes. This indicates that during fatigue loading, the mechanism mainly operates in a work area with high dexterity and relatively gentle changes, which is beneficial for maintaining stable motion transmission performance and improving the system's control accuracy.

[0048] comprehensive Figure 4 As shown in (a) and (b), although there are certain low-dexterity regions and regions with large dexterity gradient changes within the complete workspace, these regions are not involved in the effective workspace under fatigue loading conditions. In comparison, the dexterity contour distribution within the effective workspace is more reasonable and stable, providing a good foundation for subsequent performance optimization design under working condition constraints.

[0049] like Figure 5 As shown, based on the local end-effector output force performance index established in step S4, this section selects the drive joint torque data obtained from the previous dynamic simulation under biaxial fatigue test conditions to evaluate the end-effector output force performance of the mechanism. Since biaxial loading involves motion and force transmission in multiple directions simultaneously, its dynamic coupling relationship is more complex, and the drive joint torque requirement is higher, which can more fully characterize the fatigue loading capability of the mechanism under adverse conditions. Based on this, the end-effector output force performance of the mechanism in the complete workspace and the effective workspace corresponding to the fatigue test conditions are analyzed and compared respectively. Through comprehensive evaluation at both workspace levels, the overall output capability of the mechanism within its theoretically achievable range and its force transmission characteristics under fatigue test conditions can be revealed, providing a reliable performance evaluation basis for subsequent structural parameter optimization. Figure 5 The distribution of the end-effector average output force of the floor-mounted fatigue testing mechanism under different workspace constraints is shown. Figure 5 (a) A heatmap of the end-effector average output force of the mechanism within the complete theoretical workspace is presented. This workspace, defined by the kinematic constraints of the mechanism, encompasses all theoretically attainable, but not all, end-effector poses used for actual fatigue loading. As shown in the figure, the end-effector average output force exhibits a significant non-uniform distribution within the complete workspace. Particularly near the workspace boundary and singular neighborhoods, the mechanism's output force capability decreases significantly, thus noticeably weakening the overall average output force level. Although higher output force peaks can be obtained at some local poses, these high-output force regions constitute a limited proportion and are insufficient to reflect the mechanism's actual fatigue loading capability.

[0050] In comparison, Figure 5 (b) The distribution of the average end-effector output force within the effective workspace under fatigue loading conditions is presented. This effective workspace only covers the pose range involved in the actual fatigue test. It can be seen that within the effective workspace, the overall level of the average end-effector output force is significantly improved, the low-output force region is significantly reduced, and the output force distribution is more concentrated and continuous, indicating that the mechanism possesses a more stable and reliable force output capability under actual operating conditions. Therefore, analyzing the output force performance based on the effective workspace is of greater practical engineering significance in fatigue loading performance evaluation and subsequent structural parameter optimization.

[0051] like Figure 6 As shown, Figure 6 Contour lines depicting the average output force index at the end of the circuit under different workspace conditions are presented to further reveal the spatial variation of output force performance. Figure 6(a) It can be seen that the contour lines of the average output force at the end effector are relatively dispersed within the complete workspace, and the high output force region exhibits local and relatively isolated characteristics, mainly concentrated within a limited range inside the workspace; while near the boundary of the workspace and in the singular neighborhood, the output force level at the end effector decreases rapidly, and the contour lines are significantly denser, indicating that the force transmission performance in this region is highly sensitive to changes in the end effector pose. Figure 6 As shown in (b), within the effective workspace corresponding to the loading condition, the contour lines of the average output force at the end of the mechanism are more regular and continuous, and the high output force region is distributed in a band-like pattern along the loading trajectory, with relatively uniform spacing between the contour lines. This indicates that under actual fatigue loading conditions, the output force performance of the mechanism's end of the mechanism changes more smoothly with pose, which is beneficial for achieving long-term, stable cyclic load application. This result further verifies the necessity and rationality of introducing fatigue loading condition constraints and conducting evaluations based on the effective workspace during the analysis of end-effector output force performance and structural parameter optimization.

[0052] like Figure 7 As shown, according to Figure 7 The process involves multi-objective optimization. First, the tasks and working conditions of the fatigue testing mechanism are defined. Second, design variables are set. Then, based on the dexterity and end-effector performance indicators established in the previous section as objective functions, a multi-objective optimization model for the mechanism's dimensional parameters is constructed and constraints are set. Subsequently, the NSGA-II multi-objective optimization algorithm is used to solve the problem and obtain the Pareto optimal solution set that satisfies the working condition constraints. Finally, the solution set is analyzed to provide a basis for determining the optimal combination of the mechanism's link length parameters and their engineering values.

[0053] like Figure 8 As shown, the optimization process of the NSGA-II algorithm is as follows: 1. The initial random size is parental population and generate the same size offspring population ; 2. The parent population With offspring population The merged result is of size A mixed population. Then, a non-dominated sorting strategy was used to sort populations of size... The mixed population is stratified to obtain each non-dominated level; and the crowding distance of individuals within each level is calculated to characterize the distribution density of solutions in the target space. Based on this, the individuals in the population are reordered by combining the non-dominated level and the crowding distance. 3. Based on the ranking results of non-dominance level and crowding distance, perform environment selection, prioritizing the retention of individuals with lower dominance levels (better) and larger crowding distances, and constructing an environment of [scale value missing]. The new generation of parental population; 4. In Based on this, iterative propagation is performed using genetic operators: parent individuals are determined by selection operators, and then crossover and mutation operations are performed to generate individuals of a scale of [missing information]. The new generation of offspring population ; 5. Repeat steps 2 to 4 until the preset maximum number of iterations is reached or the convergence criterion is met, and finally obtain a stable Pareto optimal solution set and its corresponding Pareto front.

[0054] like Figure 9 As shown in the figure, the local dexterity of the optimized scheme and the initial scheme is compared in the effective working space using a heatmap. Compared with the initial scheme, the overall level of dexterity distribution is improved after optimization. In particular, in the areas where low dexterity was concentrated, the color shifts from low value areas to medium and high value areas, indicating that the overall distribution of the Jacobian matrix condition number in the working space tends to improve. In particular, the minimum local dexterity increases from 0.2054 to 0.3060, indicating that the balanced optimization not only improves the average transfer performance but also effectively enhances the transfer capability at the most unfavorable pose, thereby improving the overall availability and robustness of the mechanism in the effective working space.

[0055] like Figure 10 As shown, this is a heatmap of the dexterity difference before and after optimization. The results show that the local dexterity difference is positive in most areas, but a slight negative gain of -0.05 occurs in some areas. This is because the end-effector force index affects the structural parameters during multi-objective optimization, causing a certain decrease in dexterity in local areas. According to step S1, the main working area of ​​the mechanism on the y-axis is approximately 1000 mm to 1200 mm, within which dexterity is improved. Therefore, the overall balancing scheme significantly improves the end-effector force level while also improving the overall dexterity level, especially in the worst-case area.

[0056] like Figure 11 As shown, the output force index of the local end of the mechanism is given. A comparison of the distribution within the effective workspace. As shown in the figure, the distribution patterns before and after optimization are basically the same. However, compared to the unoptimized scheme, the optimized scheme shows an overall upward shift in the local end-effector output force index, with a more pronounced high-value area, indicating that the mechanism has a stronger force output capability after optimization. The balanced scheme significantly improves the end-effector output force capability within the effective workspace while ensuring the mechanism's motion transmission performance, especially providing significant reinforcement to areas with low output force.

[0057] like Figure 12As shown, a heatmap of the difference is presented. The graph shows that the difference is generally positive within the effective workspace, indicating that the balancing optimization scheme achieves a general end-effector force gain within the effective workspace. This gain exhibits significant spatial non-uniformity, with more pronounced increases in the upper and lateral regions of the workspace, while the increase is relatively smaller in the lower region near the boundary. These results demonstrate that the balancing scheme not only improves the overall output force level but also addresses the weaker end-effector force areas of the original scheme, thereby resulting in a more abundant distribution of force output capability within the effective workspace.

[0058] Example 3 The optimization toolbox of MATLAB software was used to optimize the fatigue testing mechanism based on the multi-objective optimization model and constraints established in Example 1, and the Pareto front solution set of the two objective functions, global dexterity and end-effector force index, was obtained. The parameter settings of the NSGA-II optimization algorithm are shown in Table 1.

[0059] Table 1

[0060] Based on the obtained Pareto front, 13 compromise solutions of moderate arc length were uniformly extracted from the front, and extreme solutions at both ends were added, resulting in 15 representative solutions. The structural parameters of the mechanism before and after optimization, along with their corresponding objective function values, are presented to compare the magnitude and pattern of parameter adjustment and performance improvement under multi-objective optimization, as shown in Table 2. This result not only intuitively reflects the impact of structural parameter changes on indicators such as dexterity and end-effector force, but also provides a quantitative basis for subsequent mechanism size selection. It is important to emphasize that the Pareto front solution set reveals the trade-off relationships between various objectives, providing more targeted design references and optimization decision support for scheme selection under different engineering preferences and constraints.

[0061] Table 2

[0062] As shown in Table 2, under the constraints of effective workspace and link length, the optimization algorithm obtained a set of continuously distributed Pareto optimal solutions. The 10th set of data represents the selected compromise solution, and this set is the focus of the analysis. The dexterity index of the optimized mechanism is also analyzed. When the value increases from 0.635 to approximately 0.721, the end-output force index... The value gradually decreased from 13732.17 N to 12416.66 N, indicating that improving the dexterity of the mechanism requires sacrificing some output force. Meanwhile, the geometric parameters in the table show a clear pattern of change along the Pareto front: with increasing dexterity... Increase The overall diameter increased from 879.06 mm to 931 mm. It gradually decreased from 743.99 mm to 619.70 mm, while The dimensionless parameter changes consistently from 1352.56 mm to 1432.30 mm. This trend indicates that the optimization process, by redistributing the link length ratios, makes the mechanism's configuration distribution within the effective working space more reasonable, providing a basis for selecting and determining representative solutions.

[0063] Table 3 shows the comparison between the optimal dexterity and the result before optimization, indicating that the motion transmission performance of the mechanism has been significantly improved.

[0064] Table 3

[0065] As can be seen from Table 3, the dexterity index The value increased from 0.685 to 0.721, an increase of 5.26%. Meanwhile, the end-effector output force performance index... The increase from 11673.05 N to 12416.66 N, representing a 6.37% improvement, indicates that the solution did not sacrifice output power for increased dexterity, but rather achieved simultaneous improvement in both performance aspects.

[0066] Optimized structural parameters, such as base spacing The length of the active rod was reduced from 1000 mm to 931 mm, a decrease of 6.90%. The length of the driven rod remains basically unchanged. The length increased to 1432.30 mm, an increase of 5.08%. The change in rod length indicates that, under the premise of satisfying the constraints, appropriately reducing... and increase At the same time, maintain Stability can improve the condition number distribution of the Jacobian matrix within the effective workspace, thereby enhancing the dexterity of the mechanism and having a positive effect on the end-effector output force. Although this result achieves maximum dexterity without reducing output force compared to the performance under the original design parameters, the improvement in output force is relatively limited. Considering the priority requirement for load output force under fatigue loading conditions, a more balanced scheme that better balances dexterity and output force will be further selected from the Pareto solution set as the final design.

[0067] Table 4 shows the comparison results of parameters before and after optimal optimization of the end output force.

[0068] Table 4

[0069] As shown in Table 4, under the premise of satisfying the constraints, the output force capacity index of the mechanism's end effector is... The increase from 11673.05 N to 13732.17 N, a rise of 17.64%, indicates that this parameter combination significantly enhances the load output margin of the mechanism within its effective workspace. However, while increasing the output force, this solution sacrifices some motion transmission performance, affecting the dexterity index. The value decreased from 0.685 to 0.635, a drop of 7.30%, indicating a decline in the overall transmission performance of the mechanism.

[0070] The corresponding structural parameters have also changed significantly: The diameter decreased from 1000 mm to 879.06 mm, a reduction of 12.09%. The diameter increased from 620 mm to 743.99 mm, an increase of 20%. The length was reduced to 1352.56 mm, a small change of approximately 0.77%. However, this change altered the distribution balance of the Jacobian matrix singular values ​​within the workspace, reducing the motion transmission performance of some configurations and thus impacting the dexterity index. The parameters showed a certain degree of reduction. This indicates that the parameter combination is more biased towards the extreme loading requirements dominated by output force capability. In order to balance the mobility and force transmission performance during fatigue testing, it is still necessary to select a more balanced optimization scheme that comprehensively weighs dexterity and output force from the Pareto solution set as the final design.

[0071] As can be seen from the Pareto frontier, the global dexterity metric With end output force index There is a clear trade-off: when a higher output force capability is desired, the dexterity of the mechanism will decrease to varying degrees, and vice versa. Considering the primary requirement of stable and sufficiently large cyclic loads for wind turbine blade fatigue testing, while also taking into account the relatively good motion transmission performance of the mechanism within the effective working space, this invention selects a scheme that significantly increases output force while maintaining or even improving dexterity. The structural parameters of the selected balanced optimization scheme are shown in Table 5.

[0072] Table 5

[0073] In summary, the embodiments of the present invention provide a performance optimization method for a ground-mounted fatigue testing mechanism for wind turbine blades, which enables the fatigue testing mechanism to have higher stability, better controllability, and stronger loading capacity in fatigue tests.

[0074] The embodiments described above are some, but not all, embodiments of the present invention. The detailed description of the embodiments of the present invention is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

Claims

1. A method for performance optimization of a ground-mounted fatigue testing mechanism for wind turbine blades, characterized in that, Based on the derived Jacobian matrix, end-effector force model, and dynamic torque, the dexterity performance index and end-effector force performance index of the fatigue testing mechanism are constructed and their performance is analyzed. Then, using the length parameters of each link as design variables, a multi-objective optimization method is used to solve for the optimal combination of structural parameters that balances motion dexterity and loading capacity. The process includes the following steps: S1: Analyze the working space of the ground-mounted fatigue testing mechanism for wind turbine blades to evaluate the overall motion performance of the mechanism within its theoretically achievable range; S2: Construct a local dexterity index for the fatigue testing mechanism to reflect the performance characteristics of the mechanism in fatigue loading tasks; S3: Establish the mapping relationship between the end output force of the fatigue testing mechanism and the torque of the driving joint; S4: Introduce the singular value decomposition method to construct an evaluation index for end-output force performance, so as to quantitatively characterize the output force capability of fatigue testing mechanisms; S5: Performance evaluation of the end-effector output force of a floor-mounted fatigue testing mechanism; S6: Construct a multi-objective optimization model for the dimensional parameters of the fatigue testing mechanism and set constraints. Use the NSGA-II multi-objective optimization algorithm to solve the model and obtain the Pareto optimal solution set that satisfies the working condition constraints.

2. The performance optimization method for the ground-mounted fatigue testing mechanism for wind turbine blades according to claim 1, characterized in that, In step S1, the concept of operable workspace is used to characterize the workspace. That is, under the premise of satisfying closed-loop geometric feasibility and assembly branch consistency, operability constraints such as singularity avoidance are introduced to eliminate the Jacobian matrix degeneration and the configuration corresponding to its neighborhood, thereby obtaining the end reachable region with relatively stable motion / force transmission performance that can be used for actual loading and subsequent performance evaluation, and calculating the complete operable space and effective workspace.

3. The performance optimization method for the ground-mounted fatigue testing mechanism for wind turbine blades according to claim 1, characterized in that, In step S2, the local dexterity performance index of the fatigue testing mechanism is constructed based on the condition number of the velocity Jacobian matrix, and the corresponding dexterity analysis is carried out.

4. The performance optimization method for the ground-mounted fatigue testing mechanism for wind turbine blades according to claim 1, characterized in that, In step S6, the task and working condition requirements of the fatigue testing mechanism are clarified, design variables are set, and then a multi-objective optimization model of the mechanism size parameters is constructed with the constructed local dexterity index and the end output force performance evaluation index as objective functions and constraints are set. Subsequently, the NSGA-II multi-objective optimization algorithm is used to solve the problem and obtain the Pareto optimal solution set that satisfies the working condition constraints. Finally, the solution set is analyzed to provide a basis for determining the optimal combination of mechanism link length parameters and their engineering values.

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