Lightweight torsion spring optimization design method for robots

Abstract

This invention discloses an optimization design method for lightweight torsion springs used in robots. The method includes the following steps: First, setting design objectives and constraints, with minimizing spring mass as the optimization objective. Constraints include stiffness, maximum stress, torque capacity, and maximum thickness. Then, material selection and topology design are performed, using chromium vanadium steel and designing three sets of symmetrically distributed wave-shaped spring structures. Next, a three-dimensional parametric model is established in a finite element environment, and simulation analysis is conducted to obtain key performance indicators. Further, based on the Latin hypercube sampling method and the Kriging surrogate model, the spring thickness and transition fillet radius are modeled and predicted, and a multi-objective genetic algorithm is used for global optimization to obtain the optimal structural parameters. Finally, physical processing and experimental verification are performed based on the optimization results. This invention can achieve significant weight reduction, reduce stress concentration, and extend service life while ensuring low stiffness and high torque capacity.

Description

Technical Field

[0001] This invention relates to the field of robot component design and optimization technology, specifically to an optimized design method for a lightweight torsion spring used in a robot series elastic actuator. Background Technology

[0002] Series elastic actuators (SEAs) are widely used in rehabilitation robots, wearable robots, and industrial robots due to their advantages such as high safety in human-machine interaction and high accuracy in torque measurement. Torsion springs, as a key component in SEAs, not only transmit torque but also achieve energy buffering and torque detection through their elastic deformation.

[0003] Existing torsion spring designs have the following shortcomings: First, they have excessive stiffness, making it difficult to balance compliance and high load-bearing capacity; second, they lack structural compactness and have a large overall weight, which is not conducive to comfort and lightweight design in wearable scenarios; third, they exhibit significant stress concentration, which can easily cause fatigue damage and shorten service life.

[0004] Please see Figure 1 This diagram illustrates a typical traditional torsion spring structure (e.g., a single- or multi-leaf straight-arm type). As shown, it mainly consists of an inner coil, an outer coil, and several straight or simple arc-shaped spring leaves connecting them. The main drawbacks of this structure are: the force transmission path of the spring leaves is short and direct, resulting in relatively high overall stiffness; to meet torque requirements, a larger cross-sectional dimension (such as thickness) is often required, leading to a larger mass; and at the right-angle or small-arc transition points connecting the spring leaves to the inner and outer coils (circled areas in the diagram), there is a significant geometric abrupt change, which easily leads to stress concentration under load, becoming the initiation point for fatigue cracks, thus affecting service life and reliability.

[0005] Therefore, there is an urgent need for a new torsion spring design method to achieve both low stiffness and high torque load under the premise of lightweight design, while reducing stress concentration and improving reliability. Summary of the Invention

[0006] This invention aims to overcome the problems of large weight, high stiffness, and significant stress concentration in existing torsion spring designs, and provides a systematic optimization design method. This method can achieve significant weight reduction while ensuring the torsion spring has low stiffness and high torque capacity, effectively improve stress distribution, and extend service life, thereby meeting the demanding requirements of high-end robotic applications.

[0007] To address the aforementioned technical problems, this invention provides an optimized design method for lightweight torsion springs used in robots, characterized by comprising the following steps:

[0008] (1) Set design objectives and constraints: The optimization objective is to minimize the mass of the spring, and the constraints are set as follows: stiffness range of 100~200 Nm / rad, maximum equivalent stress not greater than 1320 MPa, rated torque not less than 15 Nm, and thickness not greater than 10 mm.

[0009] (2) Material and topology determination: heat-treated chromium vanadium steel was selected as the spring material, and the topology of the spring was determined to be a wave-shaped spring with three sets of symmetrically distributed leaves.

[0010] (3) Establishment and simulation: Based on the material and topology determined in step (2), a parametric three-dimensional finite element model of the torsion spring is established. Boundary conditions are applied with the inner ring fixed and the outer ring subjected to rated torque. Static simulation analysis is performed to obtain the mass, stiffness and equivalent stress data of the spring.

[0011] (4) Proxy model construction: Taking the spring thickness and the transition fillet radius at the connection between the spring and the inner and outer rings as design variables, the Latin hypercube sampling method is used to generate sample points. Combined with the simulation results of step (3), the Kriging method is used to establish a performance prediction proxy model for spring mass, stiffness and equivalent stress.

[0012] (5) Multi-objective optimization solution: Taking the minimization of spring mass as the objective function and the stiffness, maximum stress and rated torque set in step (1) as constraints, the surrogate model is optimized by using a multi-objective genetic algorithm to obtain the optimal combination of spring thickness and transition fillet radius parameters that satisfy all constraints.

[0013] (6) Physical verification: Based on the optimal parameter combination obtained in step (5), process the torsion spring sample and conduct experimental tests to verify whether its stiffness, maximum stress and hysteresis characteristics meet the design requirements.

[0014] Preferably, in step (2), the chromium vanadium steel is AISI 6150 steel, and the yield strength after heat treatment is 1320MPa.

[0015] Preferably, in step (2), the design range of the transition fillet radius is 2.5~3.5 mm.

[0016] Preferably, in step (4), the Kriging surrogate model needs to be verified for accuracy, wherein the root mean square error of stiffness prediction is no greater than 0.5 Nm / rad.

[0017] Preferably, in step (5), the number of iterations of the multi-objective genetic algorithm is set to 60 generations, and the optimal parameter combination obtained by optimization is: spring thickness 5 mm, transition fillet radius 3.49 mm.

[0018] Preferably, the designed torsion spring is suitable for use in series elastic actuators in rehabilitation robots, wearable robots, and industrial robots.

[0019] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0020] Comprehensive performance optimization is achieved: through systematic "objective-constraint-variable" modeling, and with the help of surrogate models and intelligent optimization algorithms, the optimal design scheme that minimizes the spring mass while meeting the requirements of low stiffness and high load-bearing capacity can be efficiently found under complex multi-constraint conditions.

[0021] Significantly reduced weight and stress: The optimized wave-shaped spring structure combined with the transition rounded corner design significantly reduces the spring mass (up to 0.2289 kg in the example) while ensuring functionality, and makes the stress distribution more uniform. The maximum equivalent stress is far below the material yield limit, which significantly improves fatigue life.

[0022] High design efficiency: By adopting Latin hypercube sampling and Kriging surrogate model, a high-precision prediction model can be built with fewer finite element simulations, replacing the time-consuming direct simulation iteration and greatly shortening the design cycle.

[0023] High practicality: The optimized spring performance was highly consistent with the simulation prediction (stiffness deviation <2%, hysteresis error <1%) through physical experiments, proving the reliability of the method in engineering applications. It is particularly suitable for series elastic actuators in fields such as rehabilitation robots and wearable robots that require lightweight and high compliance. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of an existing torsion spring.

[0025] Figure 2 This is a flowchart of the optimized design method for lightweight torsion springs for robots described in this invention;

[0026] Figure 3 This is an exploded view of the series elastic actuator described in this invention;

[0027] Figure 4 This is a cross-sectional view of the series elastic actuator described in this invention;

[0028] Figure 5 This is a schematic diagram showing the parameters of the torsion spring described in this invention;

[0029] Figure 6 The results of finite element analysis of the torsion spring described in this invention under a torque of 15 Nm are shown.

[0030] Figure 7The graph shows the response of the spring stiffness, equivalent stress, and mass obtained by Kriging fitting of the torsion spring described in this invention.

[0031] Figure 8 The torsion spring described in this invention is obtained through multi-objective optimization iteration curves using a genetic algorithm.

[0032] Figure 9 This is a photograph of a physical sample of the torsion spring described in this invention;

[0033] Figure 10 This is a three-dimensional model diagram of the test bench described in this invention;

[0034] Figure 11 This is a torque-angular displacement characteristic curve of the torsion spring described in this invention;

[0035] Figure 12 This is a comparison diagram of the stiffness and overall performance of the torsion spring described in this invention and existing torsion springs. Specific implementation methods

[0036] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0037] like Figure 2 As shown, the optimization design method for lightweight torsion springs for robots of the present invention includes the following steps: First, setting design objectives and constraints, with minimizing the spring mass as the optimization objective, and constraints including stiffness, stress, and torque bearing range; then, material selection and structural design; next, establishing a finite element model and performing simulation analysis; further, using the Kriging surrogate model to establish performance prediction relationships; then, performing multi-objective optimization through a genetic algorithm; finally, processing prototypes and conducting experimental verification.

[0038] Step S100: The present invention first determines the design objectives and constraints. The optimization objective is to minimize the mass of the torsion spring to achieve a lightweight design. Based on this, the constraints include: stiffness range of 100~200 Nm / rad, maximum stress not exceeding 1320 MPa, rated torque not less than 15 Nm, and thickness not exceeding 10 mm. These indicators combine the comprehensive requirements of low stiffness and high reliability for robotic applications, ensuring that the spring can meet the load-bearing capacity while maintaining sensitive compliance.

[0039] Step S200: In terms of material selection, this invention uses heat-treated chromium-vanadium steel, which has high strength and excellent fatigue performance, making it suitable for manufacturing high-performance springs. In terms of structural design, the spring consists of three sets of symmetrically distributed wave-shaped spring sheets, with rounded transitions at the connections between the spring sheets and the inner and outer coils to avoid stress concentration caused by sharp corners. This structural design not only distributes the load and improves fatigue life but also facilitates processing and forming.

[0040] Step S300: This invention establishes a three-dimensional parametric model of a torsion spring in finite element analysis software. The main design variables of the model are the spring thickness and the fillet radius, which directly affect the spring's mass, stiffness, and stress distribution. In the finite element analysis process, the model is first meshed. Since the spring structure includes wavy springs and rounded transition areas, stress concentration is prone to occur at these locations. Therefore, a finer mesh is used in key areas to improve local calculation accuracy. The overall mesh uses tetrahedral elements to ensure the meshing quality of complex geometric regions. A reasonable number of elements is determined through mesh independence analysis, ensuring high efficiency while maintaining accuracy. Regarding boundary conditions, the inner ring's degrees of freedom are constrained to simulate its fixed connection with the output shaft, while a 15 Nm torque load is applied to the outer ring to simulate the stress state under actual working conditions. In this way, the spring's deformation, stiffness, and stress distribution under rated working conditions can be obtained. Regarding material properties, the model material is heat-treated chromium-vanadium steel, and its elastic modulus, Poisson's ratio, and yield strength are input into the finite element software. To simulate performance under real-world operating conditions, this invention employs a linear statics analysis method. For example... Figure 6 As shown, the simulation results indicate that when a torque of 15 Nm is applied, the maximum equivalent stress of the spring is 911 MPa, which is far lower than the material yield strength of 1320 MPa, and the stiffness is 142.25 Nm / rad, satisfying the design constraints. This result provides an accurate data basis for subsequent surrogate model establishment and optimization design.

[0041] Step S400: To avoid the time and computational costs associated with numerous finite element simulations, this invention employs a surrogate model-based optimization strategy. First, the Latin hypercube sampling method (LHS) is used to generate parameter sample points within the design space. Latin hypercube sampling is an improved random sampling method that divides each variable in the multidimensional parameter space into several equally divided intervals and randomly selects a sample point within each interval, thus ensuring uniform coverage of the entire parameter space in each dimension. Compared to the traditional Monte Carlo method, Latin hypercube sampling can obtain more comprehensive parameter distribution characteristics with the same number of samples, improving modeling efficiency. After obtaining the sample points, finite element simulations are performed on each parameter combination to obtain corresponding performance index data, including stiffness, equivalent stress, and mass. Based on this data, this invention uses the Kriging method to establish a performance prediction surrogate model. The Kriging method is a regression modeling method based on stochastic processes; its core idea is to treat the unknown function as composed of a global trend term and a local random deviation term. By fitting known sample points, the Kriging model can provide predicted values ​​at unsampled points and simultaneously provide an estimate of the prediction error. Compared to multinomial regression or radial basis function models, the Kriging model performs better in handling nonlinear, multimodal problems, and can more accurately capture the complex relationship between reed thickness, corner radius, and performance indicators. After the model is established, this invention also evaluates the accuracy of the surrogate model using cross-validation. The results show that the prediction error is controlled within 5%, meeting the accuracy requirements of optimization calculations. Therefore, the Kriging surrogate model can significantly reduce the number of finite element calculations while ensuring reliability, thus improving overall optimization efficiency.

[0042] Step S500: This invention optimizes the solution based on the surrogate model. To balance design accuracy and computational efficiency, this invention uses a multi-objective genetic algorithm (MOGA) as the optimization method. A genetic algorithm is a stochastic search algorithm based on natural selection and genetic mechanisms. Its core idea is to simulate the biological evolution process, evolving generation by generation in the solution space through selection, crossover, and mutation, ultimately approximating the optimal solution. In multi-objective optimization problems, the genetic algorithm can simultaneously handle multiple contradictory objective functions and obtain a set of Pareto optimal solutions. In the optimization problem of this invention, the optimization objective is to minimize the spring mass while satisfying the following constraints: stiffness maintained between 100 and 200 Nm / rad, maximum stress not exceeding the material yield strength, and rated torque not less than 15 Nm. By embedding the Kriging surrogate model into the iterative process of the genetic algorithm, the performance under different combinations of design variables can be quickly calculated. During the optimization process, the population is first initialized, generating several sets of design variables as initial solutions. Subsequently, a selection operator is used to retain individuals with high fitness, a crossover operator is used for information exchange, and a mutation operator is used to increase the diversity of solutions to avoid getting trapped in local optima. After each iteration, the algorithm evaluates candidate solutions based on the fitness function and gradually converges towards the Pareto front. Figure 8 As shown, after multiple iterations, the spring's mass gradually decreases, and its stiffness and stress gradually stabilize, exhibiting a clear convergence trend. The final optimal solution is: spring thickness 5 mm, corner radius 3.49 mm, with a spring mass of 0.2289 kg, stiffness of 142.25 Nm / rad, and maximum stress of 911 MPa. These design parameters achieve significant weight reduction while satisfying all constraints. Through the above optimization process, this invention significantly improves optimization efficiency while maintaining computational accuracy, avoiding extensive finite element simulation calculations, and verifying the feasibility and superiority of a multi-objective optimization strategy based on genetic algorithms in the design of torsion springs for robots.

[0043] Step S600: The present invention performs physical machining of the torsion spring based on the optimized design parameters. The material is heat-treated chromium vanadium steel plate. First, the spring structure is formed by CNC cutting and machining, then subjected to high-temperature quenching and low-temperature tempering to obtain the required strength and toughness. Finally, precision milling is used at the connection between the spring and the inner and outer rings to ensure a smooth transition of the rounded corners, thereby effectively reducing stress concentration. After machining, the spring is shot-peened to further improve fatigue life. The machined sample is installed on a dedicated test bench for loading experiments. The test bench mainly consists of a loading mechanism, a torque sensor, an angular displacement sensor, and a data acquisition system. In the experiment, the inner ring of the spring is fixedly connected to the output shaft, and the outer ring is subjected to progressively increasing torque loads, while the angular displacement and torque change data are recorded in real time. The experimental conditions are consistent with the working conditions in the finite element analysis, i.e., the rated torque is 15 Nm. Furthermore, the present invention compares the performance of the optimized design sample with that of a traditional torsion spring to ensure that the torsion spring has a lower overall stiffness while maintaining its rated load capacity, making it more suitable for the compliant control requirements of robots.

[0044] The following is an appendix to the instruction manual. Figure 3 - Appendix Figure 12 Detailed explanation:

[0045] like Figure 3 and Figure 4 As shown, the torsion spring of the present invention is applied in a series elastic actuator. The inner ring is fixedly connected to the output shaft, and the outer ring is connected to the adapter plate by bolts. It can realize torque transmission between the drive unit and the load, and realize torque detection and energy buffering through elastic deformation.

[0046] Figure 3 The exploded view clearly illustrates the specific assembly relationship of the torsion spring (identified as a key component in the figure) designed in this invention within the series elastic actuator (SEA). As shown, the torsion spring, as the core elastic element, has its inner ring fixed to the output shaft (or load-side shaft) via a keyway or interference fit; its outer ring is connected to an adapter plate (or drive ring) via multiple circumferentially distributed bolts, which in turn connects to the output end of the motor drive unit (not fully shown in the figure). This assembly method clearly defines the position of the torsion spring in the power transmission chain: it is connected in series between the drive unit and the final load.

[0047] Figure 4 for Figure 3The cross-sectional view of the component further reveals its internal structure. The figure clearly shows that when the drive unit (such as a motor) is running, torque is transmitted to the outer coil of the spring via an adapter plate, forcing the outer coil to twist relative to the fixed inner coil. At this time, the wave-shaped spring connecting the inner and outer coils undergoes elastic bending deformation, thereby storing or releasing energy and achieving buffering. Simultaneously, by measuring this relative torsion angle using a high-precision sensor (such as an encoder), the transmitted torque value can be indirectly and accurately calculated based on the spring's stiffness characteristics. This figure visually illustrates the working principle of SEA in achieving "elastic series connection" and "torque measurement" through spring deformation.

[0048] like Figure 5 As shown, this invention establishes a parametric model of a torsion spring. The main design variables in the model are the spring thickness and the fillet radius, which directly affect the spring's stiffness, stress distribution, and mass.

[0049] A parametric 3D model of a lightweight torsion spring is presented, with two geometric parameters highlighted as key design variables: spring thickness t and transition fillet radius R.

[0050] Spring thickness t: refers to the dimension of the three sets of symmetrical wave-shaped springs that make up the spring in the normal direction. This parameter directly and significantly affects the spring's torsional stiffness (the larger t is, the greater the stiffness), mass (the larger t is, the greater the mass), and bending section modulus (affecting the stress level).

[0051] Transition fillet radius R: Specifically refers to the radius of the smooth arc transition area designed to eliminate sharp corners at the intersection of each corrugated spring leaf and its connected inner ring support and outer ring connection. This parameter is key to controlling the degree of stress concentration (the larger the R, the more moderate the stress concentration), and it also slightly affects the effective length of the spring leaf, thus having a certain impact on the overall stiffness.

[0052] By establishing a parametric model with t and R as variables, the dimensions can be easily modified and a series of simulations can be performed, laying the foundation for subsequent optimization design.

[0053] like Figure 6 As shown, finite element analysis was performed under a torque of 15 Nm. The results show that the maximum equivalent stress of the spring is 911 MPa, which is lower than the material yield strength of 1320 MPa, and the stiffness is 142.25 Nm / rad, which meets the predetermined design target.

[0054] This figure presents the equivalent stress distribution contour plot calculated using finite element method software for a spring model with a certain initial design parameters (e.g., t=6mm, R=3mm) after applying a rated torque load of 15 Nm (boundary conditions: inner ring fixed, torque applied to outer ring). Different colors in the figure represent different stress levels. It can be clearly observed that:

[0055] Stress concentration area: The maximum stress (usually shown as a red area in the diagram) does not occur in the middle of the reed, but precisely at the transition fillet designed in step S2. This verifies that the fillet is the most critical part of the stress distribution.

[0056] Stress level: The figure shows that the maximum equivalent stress in this example is approximately 911 MPa. This value is significantly lower than the yield strength of the selected chromium vanadium steel after heat treatment (1320 MPa), indicating that the design has a sufficient safety margin.

[0057] Stress distribution trend: The stress decreases rapidly from the area of ​​maximum value at the rounded corners towards the center of the spring, and the distribution conforms to the bending theory of elastic beams. At the same time, the stress distribution of the three sets of springs is basically symmetrical, proving the rationality of the structural design.

[0058] Performance output: Based on this simulation, the spring stiffness was calculated to be 142.25 Nm / rad, which meets the preset constraint condition of 100~200 Nm / rad. This figure provides key initial performance data before optimization.

[0059] like Figure 7 As shown, this invention uses Latin hypercube sampling to generate combinations of design variables and establishes a Kriging surrogate model based on finite element results to obtain the response relationships of stiffness, stress, and mass. The surrogate model allows for rapid prediction of performance under different parameter combinations, significantly reducing the overhead of direct simulation calculations.

[0060] This figure, presented in the form of a two-dimensional or three-dimensional response surface, illustrates a performance prediction surrogate model built using the Kriging interpolation method based on sample data obtained through Latin hypercube sampling (LHS). The figure typically contains three subplots or a combined surface plot, representing, individually or collectively, the following:

[0061] The relationship between spring stiffness (K) and spring thickness (t) and fillet radius (R).

[0062] The relationship between maximum equivalent stress (σ_max) and t and R.

[0063] The relationship between spring mass (M) and t (mass is mainly affected by thickness and is not sensitive to R).

[0064] These response plots visually reveal the complex nonlinear mapping relationship between design variables and performance indicators. For example, the surface trend of stiffness K increasing sharply with thickness t is clearly visible, as well as the "valley" shape of maximum stress σ_max decreasing with corner radius R. These models enable rapid and relatively accurate prediction of spring performance under arbitrary (t, R) combinations without the need for time-consuming and laborious finite element calculations, making them a core tool for efficient optimization iteration.

[0065] like Figure 8 As shown, this invention utilizes a multi-objective genetic algorithm to optimize design variables. During the optimization process, the spring mass gradually decreases, and the stress and stiffness tend to stabilize. The final optimal design parameters are a spring thickness of 5 mm and a corner radius of 3.49 mm. At this point, the spring mass is 0.2289 kg, the stiffness is 142.25 Nm / rad, and the maximum stress is 911 MPa.

[0066] This figure shows the convergence record of the multi-objective genetic algorithm (MOGA) optimization process. The horizontal axis represents the number of iterations (or the number of function evaluations), and the vertical axis typically represents the tracking curves of the objective function value (spring mass M) and key constraint indicators (such as the stiffness K and maximum stress σ_max of the current optimal solution).

[0067] From the diagram, we can observe that:

[0068] Mass convergence process: The curve representing the spring's mass shows an overall decreasing trend and eventually stabilizes as the number of iterations increases. This indicates that the algorithm is effectively searching for lighter design solutions.

[0069] Performance constraint satisfaction: The curves representing stiffness and stress may fluctuate greatly in the early stages of the iteration, but as optimization progresses, they are gradually "pulled back" and stabilized within the preset constraint range (for example, the stress is below the horizontal line of 1320 MPa in the zone where the stiffness is 100-200 Nm / rad).

[0070] Algorithm Effectiveness: The convergence process of the curve demonstrates the global search capability and effectiveness of the genetic algorithm in solving such multivariable, nonlinearly constrained optimization problems. Ultimately, the algorithm finds the optimal solution or Pareto front that minimizes the mass while satisfying all constraints.

[0071] like Figure 9 As shown, a torsion spring prototype was fabricated based on the optimization results, and the prototype structure is consistent with the design model.

[0072] This image shows a photograph of a lightweight torsion spring manufactured using precision machining (such as wire EDM and CNC milling) and after heat treatment and shot peening, based on the optimal design parameters (t=5.0 mm, R=3.49 mm) obtained from the optimization algorithm. The image clearly shows:

[0073] Structural consistency: physical sample and Figure 5 The three-dimensional model shown perfectly matches the design intent, featuring three sets of symmetrically distributed wave-shaped reeds.

[0074] Key feature: The large-radius rounded corners at the connection between the reed and the inner and outer rings are smooth and uniform, which is a physical realization of reducing stress concentration.

[0075] Lightweight appearance: with Figure 2 Compared to the traditional structure shown, this prototype is more sophisticated and compact, intuitively demonstrating the results of lightweight design.

[0076] like Figure 10 As shown, this invention constructs a three-dimensional model of the test bench and installs a torsion spring within it for loading experiments. The experimental conditions are consistent with the design conditions, which verifies the effectiveness of the optimized design method.

[0077] This figure shows a 3D model of a test bench specifically designed to verify the spring performance of this invention. The test bench typically includes the following core components:

[0078] Base and support frame: Provide a rigid foundation.

[0079] Servo motors or actuators: used to apply precise and controllable rotational torque or angle.

[0080] High-precision torque sensor: connected in series at the drive end, used to directly measure the input torque.

[0081] High-precision rotary encoder (or angle sensor): used to accurately measure the relative torsional angular displacement between the inner and outer coils of a spring.

[0082] Specialized clamps: used to reliably fix the inner and outer rings of the spring, ensuring that the load application method is consistent with the boundary conditions in the finite element simulation (inner ring fixed, outer ring subjected to torsion).

[0083] This test bench model demonstrates the scientific rigor and precision of the verification experiment, providing hardware support for obtaining reliable torque-angular displacement data.

[0084] like Figure 11 As shown, the experimentally measured torque-angular displacement characteristic curve is basically consistent with the finite element prediction results. The test results show that the stiffness deviation is less than 2% and the hysteresis error is less than 1%, and the performance meets the design requirements.

[0085] This figure, through the superposition and comparison of experimental data and simulation results, strongly verifies the accuracy and effectiveness of the optimization design method. The horizontal axis represents angular displacement (unit: rad), and the vertical axis represents torque (unit: Nm). The figure contains two main curves:

[0086] Finite element prediction curve: The theoretical torque-angular displacement relationship line obtained by simulation calculation based on the optimized parameter model is usually a straight line (linear segment), and its slope is the predicted stiffness value (142.25 Nm / rad).

[0087] Experimental test curve: Figure 9 The physical sample was installed at Figure 10 On the test bench, a load-unload test was conducted, and the torque-angular displacement relationship curve was actually collected and plotted by sensors. Due to minute factors such as internal friction of the material and assembly clearance, the experimental curve will form a narrow hysteresis loop.

[0088] Comparison results: The loading segment (or average line) of the experimental curve perfectly coincides with the straight line predicted by the finite element method. Calculations show that the deviation between the actual stiffness value obtained from fitting the experimental data and the predicted value is less than 2%. Simultaneously, the area enclosed by the hysteresis loop is very small, and the calculated hysteresis error is less than 1%. These two key indicators fully demonstrate the high accuracy and reliability of the entire process from design and simulation to manufacturing.

[0089] like Figure 12 As shown, the stiffness of the torsion spring described in this invention is compared with that of existing torsion springs. The design of this invention achieves significantly low stiffness characteristics while maintaining load-bearing capacity.

[0090] By comparing overall performance, the torsion spring designed in this invention has a weight reduction of about 30%, a more uniform stress distribution, and a significantly improved fatigue life, and its overall performance is superior to existing designs.

[0091] This figure uses both bar charts and radar charts (spider web diagrams) to compare the spring and... Figure 2 The existing technology springs shown were compared and analyzed in a comprehensive quantitative manner.

[0092] The bar chart comparison (such as stiffness comparison) clearly shows that, under the premise of bearing the same rated torque (15 Nm), the stiffness value of the spring of the present invention is significantly lower than that of the traditional spring, thus achieving better compliance.

[0093] Radar chart performance comparison: The multiple axes of the radar chart represent key performance indicators such as mass, stiffness, maximum stress, fatigue life, and power density. By normalizing the various properties of the two springs and plotting them on the chart, the performance can be clearly seen.

[0094] The spring of this invention has significant advantages in terms of mass (lightweight), maximum stress (low stress concentration), and fatigue life.

[0095] It also achieved excellent levels in terms of stiffness (low stiffness) and load-bearing capacity (torque).

[0096] As shown in the overall outline, the comprehensive performance area of ​​the spring of this invention is much larger than that of traditional springs, and it comprehensively and evenly improves the key performance of torsion springs.

[0097] In summary, the optimized design method of this invention can effectively solve the problems of large weight, high stiffness and stress concentration in existing torsion springs, and achieve comprehensive performance of low stiffness, high torque and lightweight, and has wide application value.

Claims

1. An optimized design method for lightweight torsion springs used in robots, characterized in that, Includes the following steps: (1) Set design objectives and constraints: The optimization objective is to minimize the mass of the spring, and the constraints are set as follows: stiffness range of 100~200 Nm / rad, maximum equivalent stress not greater than 1320 MPa, rated torque not less than 15 Nm, and thickness not greater than 10 mm. (2) Material and topology determination: heat-treated chromium vanadium steel was selected as the spring material, and the topology of the spring was determined to be a wave-shaped spring with three sets of symmetrically distributed leaves. (3) Establishment and simulation: Based on the material and topology determined in step (2), a parametric three-dimensional finite element model of the torsion spring is established. Boundary conditions are applied with the inner ring fixed and the outer ring subjected to rated torque. Static simulation analysis is performed to obtain the mass, stiffness and equivalent stress data of the spring. (4) Proxy model construction: Taking the spring thickness and the transition fillet radius at the connection between the spring and the inner and outer rings as design variables, the Latin hypercube sampling method is used to generate sample points. Combined with the simulation results of step (3), the Kriging method is used to establish a performance prediction proxy model for spring mass, stiffness and equivalent stress. (5) Multi-objective optimization solution: Taking the minimization of spring mass as the objective function and the stiffness, maximum stress and rated torque set in step (1) as constraints, the surrogate model is optimized by using a multi-objective genetic algorithm to obtain the optimal combination of spring thickness and transition fillet radius parameters that satisfy all constraints. (6) Physical verification: Based on the optimal parameter combination obtained in step (5), process the torsion spring sample and conduct experimental tests to verify whether its stiffness, maximum stress and hysteresis characteristics meet the design requirements.

2. The optimized design method for a lightweight torsion spring for robots according to claim 1, characterized in that, In step (2), the chromium vanadium steel is AISI 6150 steel, and its yield strength after heat treatment is 1320 MPa.

3. The optimized design method for a lightweight torsion spring for robots according to claim 1, characterized in that, In step (2), the design range of the transition fillet radius is 2.5~3.5 mm.

4. The optimized design method for a lightweight torsion spring for robots according to claim 1, characterized in that, In step (4), the Kriging surrogate model needs to be verified for accuracy, wherein the root mean square error of stiffness prediction is no greater than 0.5 Nm / rad.

5. The optimized design method for a lightweight torsion spring for robots according to claim 1, characterized in that, In step (5), the number of iterations of the multi-objective genetic algorithm is set to 60 generations, and the optimal parameter combination obtained by optimization is: spring thickness 5 mm, transition fillet radius 3.49 mm.

6. The optimized design method for a lightweight torsion spring for a robot according to any one of claims 1 to 5, characterized in that, The designed torsion spring is suitable for series elastic actuators in rehabilitation robots, wearable robots and industrial robots.

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