Stiffness-variable joint scale law and load-response speed multi-objective optimization method

Abstract

The present application relates to a variable stiffness joint scale law and load-response speed multi-objective optimization method, belonging to the field of robot joint design. In view of the problems that the output torque and dynamic performance of the existing variable stiffness joint are difficult to balance, the components are redundant, and the size and cost are high, a maximum torque and moment of inertia scaling model of a brushless DC motor, a differential gear, an electromagnetic spring and a harmonic reducer is established to form a joint overall scale law; the NSGA-III algorithm is used to optimize the parameter combination with the maximum output torque and resonance frequency as the target. After optimization, the joint output torque reaches 50.2Nm, the resonance frequency is increased to 382.3Hz, the diameter is reduced by 15mm, and the length is reduced by 8.3mm, which significantly improves the power density and dynamic performance.

Description

Technical Field

[0001] This invention belongs to the field of robot joint design and relates to a multi-objective optimization method for variable stiffness joint scaling law and load-response speed. Background Technology

[0002] In recent years, the application of robots has become increasingly widespread, placing higher demands on their output and dynamic performance. Robots with variable stiffness characteristics are widely used. By adjusting the actuator output through stiffness changes, more complex outputs can be achieved, enabling them to adapt to more complex environments. High torque density, power density, energy efficiency, and torque control fidelity are all important characteristics of robots. Variable stiffness integrated designs with high power density, high dynamic performance, and a wider range of stiffness changes are superior. The appropriate combination of motors, reducers, differential gears, and electromagnetic springs is crucial for variable stiffness joints, including torque requirements, dynamic performance requirements, and reduction ratio distribution. A suitable combination can simultaneously meet the requirements of output torque and dynamic performance, allowing for effective utilization of each component, reducing energy efficiency losses, and simultaneously reducing the overall size of the joint and lowering costs. Optimization of material layout and reducer selection ensures the best performance of the integrated robot system. A more comprehensive design approach is adopted for the joint transmission system to improve the dynamics of collaborative robots. Summary of the Invention

[0003] In view of this, the purpose of this invention is to provide a scaling law for variable stiffness joints and a multi-objective optimization method for load-response speed. By deriving scaling laws for maximum output torque and moment of inertia from calculations of each part, and performing multi-objective optimization on relevant parameters, the optimal dimensions of the variable stiffness joint can be selected for different output torque and dynamic performance requirements. Alternatively, for different variable stiffness joint size requirements, the optimal combination of parameters can be calculated to determine the output torque and dynamic performance. Parameter combinations can be selected based on the varying proportions of output torque and dynamic performance requirements.

[0004] To achieve the above objectives, the present invention provides the following technical solution: A multi-objective optimization method for variable stiffness joint scaling law and load-response speed includes the following steps: S1: Establish scaling law models for the maximum output torque and moment of inertia of the brushless DC motor, differential gear, electromagnetic spring, and harmonic reducer in the variable stiffness joint, respectively. S2: Based on the scaling law model of the brushless DC motor, differential gear, electromagnetic spring and harmonic reducer, a global scaling law model of the variable stiffness joint is generated by coupling. S3: Establish a multi-objective optimization model with the maximum output torque and dynamic performance parameters of the variable stiffness joint as the optimization objectives; S4: The NSGA-III algorithm is used to solve the multi-objective optimization model to obtain the parameter combination that satisfies the constraints; S5: Determine the size of the variable stiffness joint and the reduction ratio configuration based on the optimized parameter combination.

[0005] Furthermore, in S1: The maximum output torque of the brushless DC motor is proportional to the square of the motor diameter and the length, and the moment of inertia is proportional to the fourth power of the motor diameter and the length. The maximum output torque of the differential gear is proportional to the square of the gear diameter, the length, and the reduction ratio; the moment of inertia is proportional to the fourth power of the gear diameter, the length, and the reduction ratio. The maximum output torque of the electromagnetic spring is proportional to the cube of the spring diameter and its length. The maximum output torque of the harmonic reducer is proportional to the cube of the reducer diameter, and the moment of inertia is proportional to the fourth power of the reducer diameter, the length, and the square of the reduction ratio.

[0006] Furthermore, the reduction ratio function of the differential gear is: in, This is the differential gear reduction ratio.

[0007] Furthermore, in S2, the conditions for coupling to generate the overall scaling law model include: The axial lengths of the differential gear and the electromagnetic spring are equal; The output end of the planetary carrier of the differential gear is connected to the input shaft of the harmonic reducer.

[0008] Furthermore, in step S3, the dynamic performance parameter is the resonant frequency, and its expression is:

[0009] In the formula, The moment of inertia of the motor. The inertia at the joint output end. For joint stiffness, This represents the overall reduction ratio.

[0010] Furthermore, the total moment of inertia satisfy:

[0011] in, The moment of inertia of the differential gear. The moment of inertia of the harmonic reducer. For differential gear reduction ratio, This refers to the reduction ratio of the harmonic reducer.

[0012] Furthermore, in S4, the constraints include: The diameter range of the variable stiffness joint is 90~110mm; The output torque of the harmonic reducer shall not be less than 50 Nm; The differential gear reduction ratio ranges from 2.5 to 6, and the harmonic reducer reduction ratio ranges from 30 to 100.

[0013] Furthermore, in S5, the parameter combinations include: Length and diameter of a brushless DC motor; The length, diameter, and reduction ratio of the differential gear; The length and diameter of the electromagnetic spring; The length, diameter, and reduction ratio of the harmonic reducer.

[0014] Furthermore, the optimized reduction ratio of the harmonic reducer is 100, and the optimized reduction ratio of the differential gear is 2.5.

[0015] A variable stiffness joint system, using the parameter combination optimized by the method described above, includes: A brushless DC motor, whose output shaft is connected to the sun gear of a differential gear; Differential gear, with its internal gear coupled to the electromagnetic spring rotor, planetary carrier connected to the input shaft of the harmonic reducer; The harmonic reducer uses a rigid wheel as the joint output end.

[0016] The beneficial effects of this invention are as follows: For robot joints, the output requirements of the actuators vary under different loads and dynamic performance requirements, making it extremely important to design joints that meet these requirements under different conditions. This invention addresses a novel variable stiffness joint for robots, deriving a scaling law that enables the computational selection of variable stiffness joints. This invention derives the scaling laws for the motor, differential gear, electromagnetic spring, and harmonic reducer within the variable stiffness joint, integrating these components into a unified whole and applying it to the entire variable stiffness joint. Furthermore, a multi-objective optimization method is employed to optimize relevant parameters, selecting parameters such as the size and transmission ratio of the variable stiffness joint under different maximum output torque and dynamic performance requirements.

[0017] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0018] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein: Figure 1 This is a schematic diagram of the overall structure of a variable stiffness joint. Figure 2 This is a schematic diagram of a variable stiffness joint. Figure 3 This is a schematic diagram of the motor structure; Figure 4 A visualization of the maximum continuous output torque of a brushless DC motor; Figure 5 A visualization of the moment of inertia of a brushless DC motor; Figure 6 This is a schematic diagram of a differential gear structure; Figure 7 A visualization of the maximum continuous output torque of the differential gear; Figure 8 A visualization of the moment of inertia of a differential gear; Figure 9 This is a schematic diagram of an electromagnetic spring structure; Figure 10 A visualization of the output torque of an electromagnetic spring; Figure 11 This is a schematic diagram of a harmonic reducer. Figure 12 A visualization of the maximum continuous output torque of harmonic reducers with different reduction ratios; Figure 13 A visualization of the moment of inertia of a harmonic reducer; Figure 14 A flowchart for solving multi-objective optimization problems using the NSGA-III algorithm; Figure 15 The optimized result for NSGA-III is shown in the figure. Detailed Implementation

[0019] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0020] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0021] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0022] This invention addresses a novel variable stiffness joint for robots. It derives scaling laws for the maximum output torque and moment of inertia of a brushless DC motor, differential gear, electromagnetic spring, and harmonic reducer with respect to diameter, length, and reduction ratio. These scaling laws for each component are then integrated to form the scaling law for the variable stiffness joint. Typically, we aim for the maximum output torque of a joint to be as large as possible while minimizing the moment of inertia to ensure good dynamic performance. However, these two conditions cannot be simultaneously met. Therefore, this invention also performs multi-objective optimization of the scaling law. Using NSGA-III, with the maximum output torque and moment of inertia of the variable stiffness joint as objective functions, relevant parameters are optimized. Comparison with the results and parameters before optimization verifies the accuracy of the optimization process. This provides assistance for subsequent selection of variable stiffness joint dimensions and transmission ratios under different conditions, enabling a balance between maximum output torque and dynamic performance during selection, allowing for choices based on different priorities.

[0023] This invention addresses a novel variable stiffness joint for robots, proposing a method for selecting the optimal combination of a motor, differential gear, electromagnetic spring, and reducer. By calculating and deriving scaling laws for maximum output torque and moment of inertia for each component, and performing multi-objective optimization of relevant parameters, the optimal dimensions of the variable stiffness joint can be selected for different output torque and dynamic performance requirements. Alternatively, for different variable stiffness joint size requirements, the optimal combination of parameters can be calculated to determine the output torque and dynamic performance. The parameter combination can be selected based on the varying proportions of output torque and dynamic performance requirements.

[0024] Figure 1 This is the overall structural diagram of the variable stiffness system. Figure 2This is a schematic diagram of a variable stiffness joint. A brushless DC motor provides the power source for the variable stiffness joint. The sun gear of the differential gear is connected to the motor output shaft. An electromagnetic spring is coupled to the differential gear to achieve variable stiffness of the entire joint. The planetary carrier of the differential gear is connected to the harmonic reducer to form the entire variable stiffness joint. The rigid wheel of the harmonic reducer realizes the power output.

[0025] 1. Scaling Law This section derives the scaling laws for maximum output torque and moment of inertia for motors, differential gears, electromagnetic springs, and harmonic reducers.

[0026] 1.1 Motor A brushless DC motor was selected as the power source for the novel variable stiffness joint of the robot, where the required length in the scaling law was... and diameter like Figure 3 As shown.

[0027] 1.1.1 Maximum Torque The formula for calculating the average electromagnetic torque of a brushless DC motor is given in formula (1). Under the rated operating conditions and when the motor is running stably, the average electromagnetic torque of the brushless DC motor is the same as the rated torque. The rated torque is approximated by the average electromagnetic torque, and its relationship with length and diameter is explored. The expression for the average electromagnetic torque is: (1) (2) (3) (4) In the formula, The motor utilization factor (torque generated per unit volume of effective material). The winding coefficient of the phase winding, For electromagnetic load, The amplitude of the air gap magnetic flux density. The stator core diameter (cm) is the diameter of the stator core. Calculate the length (cm) of the stator core. The number of turns in series per phase. The average winding current, The outer diameter of the motor. For coefficients, The coefficients of the back electromotive force waveform function are the average values ​​within the state angle. These are the effective value coefficients of the back electromotive force waveform function within the state angle. The coefficients representing the relationship between the back electromotive force coefficient and the equivalent resistance of the equivalent winding and the back electromotive force coefficient of a single-phase winding are given.

[0028] Assumption Based on motor utilization factor By replacing the relevant parameters in the expression for average electromagnetic torque to represent the average electromagnetic torque of the motor, we can obtain the following from formula (1): (5) Formula (5) represents the linear relationship between the motor length and diameter and the average electromagnetic torque. Based on the relationship between the average electromagnetic torque and the rated output torque of the motor, Formula (5) can be used to approximate the linear relationship between the motor length and diameter and the maximum output torque of the motor. Figure 4 By displaying catalog data of Maxon brushless DC motors, the scaling law in formula (5) is verified. The purple, red and green dots represent the catalog data of Maxon brushless DC motors in three cases: closed tail, open rotor tail, and tail with fan. The three lines shown in the figure for different cases provide the best design solution according to the proposed scaling law.

[0029] 1.1.2 Moment of inertia The moment of inertia of a cylinder about its axis of rotation is given by the following formula: (6) From formula (6), where the outer diameter and length of the cylinder about its axis of rotation are respectively represented by the rotor diameter and length, the moment of inertia of the motor can be expressed as: (7) In the formula, The diameter of the motor rotor. Rotor length Assumption , According to formula (7), the moment of inertia of the motor can be written as: (8) Figure 5 The visualization of the moment of inertia of the brushless DC motor is shown in the figure. By comparing the moment of inertia values ​​extracted from the Maxon brushless DC motor catalog, the scaling law of the moment of inertia of the brushless DC motor with respect to the moment of inertia (i.e., ...) is derived from Equation (8). Figure 5 The red line in the figure accurately reflects the moment of inertia of different brushless DC motors.

[0030] 1.2 Differential Gear Figure 6 This is a structural diagram of a differential gear, showing the length of the differential gear required in the scaling law. and diameter .

[0031] 1.2.1 Maximum Output Torque For differential gears, the expression for the maximum contact stress on the tooth surface is: (9) In the formula It is the elasticity coefficient. Node region coefficient, It is the overlap coefficient. It is the load factor, for multi-stage transmissions, It is a single-stage transmission ratio. This is the first-stage transmission ratio. For the maximum contact stress, For maximum output torque, , , For the length of the differential gear, It is a series.

[0032] From formula (9), , For a single-stage differential gear, the maximum output torque can be expressed as: (10) Compare formula (10) with the output torque of a single-stage gear in the Maxon gearbox catalog, such as... Figure 7 As shown, formula (10) can better reflect the changing trend.

[0033] 1.2.2 Moment of Inertia From formula (6), the moment of inertia of a single-stage differential gear can be expressed as: (11) Compare Formula 11 with the moment of inertia of a single-stage gear in the Maxon gearbox catalog, such as... Figure 8 As shown, formula (11) can better reflect the trend of change.

[0034] 1.3 Electromagnetic Spring Electromagnetic springs, such as Figure 9 As shown, it consists of four parts: stator, rotor, stator coil, and rotor magnet. In the overall structure, the internal gear of the differential gear serves as the electromagnetic spring rotor, permanent magnets are bonded to the outer surface of the differential gear as rotor magnets, and copper wire is wound around the stator as stator coils. The differential gear and electromagnetic spring are coupled to form a whole and interact with each other during operation. The length of the electromagnetic spring according to the scaling law is also shown in the figure. and diameter .

[0035] The electromagnetic spring and differential gear are coupled, based on the torque distribution relationship. (12) In the formula, For planetary carrier torque, The torque on the sun gear, The torque on the internal gear. The radius of the sun gear, The radius of the internal gear is given.

[0036] From formula (12), the maximum torque required for the electromagnetic spring is... for: (13) In the formula This is the differential gear reduction ratio.

[0037] The peak force generated by the coupling between the coil and the permanent magnet in an electromagnetic spring can be expressed as: (14) (15) (16) (17) (18) In the formula, This represents the number of permanent magnets. The number of turns of the coil. For coil current, The air gap magnetic flux density is... For axial thickness, The thickness of the permanent magnet. The flux density coefficient, The slope of the demagnetizing characteristic. is the leakage flux coefficient. It is the Carter coefficient. It is the permeability coefficient. It is the remanent magnetic field strength. It is the magnet fraction. It is a toothed opening. It is the polar distance. It is the slot spacing at the air gap. It is the effective air gap with the Carter coefficient.

[0038] The total current of the electromagnetic spring is calculated by calculating the area of ​​the winding. (19) In the formula, This represents the maximum current that can pass through a single winding hole. The number of coil turns. The maximum current that a single conductor can carry. For current density, These are the simplified constant coefficients.

[0039] (20) From (20), the diameter of the electromagnetic spring can be expressed as: (twenty one) In the formula, The diameter of the electromagnetic spring. This is the proportionality coefficient.

[0040] The equation for calculating the torque in an electromagnetic spring is: (This equation is derived from the equation of ... (twenty two) Substituting formulas (19), (21), and (14) into formula (22), we can obtain the maximum torque generated by the coupling between the energized coil and the permanent magnet in the electromagnetic spring as follows: (twenty three) From formula (23), the relationship between the torque of the electromagnetic spring and its diameter and length can be obtained: (twenty four) Compare formula (24) with the electromagnetic spring torque simulated using Maxwell 2D, as follows: Figure 10 As shown, formula (24) can better represent the relationship between the output torque of the electromagnetic spring and the size.

[0041] 1.4 Harmonic Reducer Harmonic reducers, such as Figure 11 As shown, it consists of three parts: a wave generator, a flexible wheel, and a rigid wheel.

[0042] In harmonic drive, a wave generator is typically used as the input. Connected to the input shaft, the wave generator generates and controls the deformation of the flexspline's gear ring. Composed of an elliptical cam and a thin-walled flexible bearing, it enables controllable elastic deformation of the flexspline. The flexspline has a gear ring on its open end that deforms as the wave generator rotates. The rigid gear is a rigid internal gear. As the wave generator rotates continuously, the deformation of the flexspline constantly changes, causing the meshing state between the flexspline and the rigid gear to continuously change—engaging, disengaging, re-engaging…—a cyclical process that achieves rotation and transmits motion and power. Figure 11 The image shows the length required in the scaling law. and diameter .

[0043] 1.4.1 Torque According to Timofeyev et al., the relationship between maximum output torque and the thickness of the flexible wheel rim below the tooth tip is as follows: (25) In the formula, The diameter of the pitch circle. This represents the durability limit.

[0044] Not greater than ,right Take the maximum value. Therefore, formula (25) can be expressed as: (26) From formula (26), the maximum output torque of the harmonic reducer can be expressed as: (27) The pitch circle diameter is related to the total diameter of the harmonic reducer, therefore... Furthermore, the maximum continuous output torque of the harmonic reducer can be expressed as: (28) Formula (28) shows the maximum continuous output torque at different reduction ratios as follows: Figure 12 As shown, when compared with the data of the harmonic reducer catalog under the corresponding reduction ratio, formula (28) can better reflect the changing trend.

[0045] 1.4.2 Moment of Inertia According to formula (6), the moment of inertia of the harmonic reducer can be expressed as: (29) In the formula This refers to the reduction ratio of the speed reducer.

[0046] Compare formula (29) with the moment of inertia of harmonic reducers in the harmonic reducer catalog, such as... Figure 13 As shown, formula (29) can better reflect the trend of change.

[0047] 1.5 Overall Scaling Law of Variable Stiffness Joints The scaling of each part is integrated based on the connections and relationships between them to form a scaling law for a novel variable stiffness joint of the robot. For torque, the length of the differential gear is calculated and compared with the length of the electromagnetic spring. The relevant parameters of the differential gear and the electromagnetic spring are adjusted. While meeting the torque requirements of the electromagnetic spring, increasing the diameter of the differential gear increases the required length of the electromagnetic spring and decreases the required length of the differential gear. When the two lengths are equal, the required length of the coupled model is minimized, ensuring the minimization of dimensions.

[0048] 2. Multi-objective optimization To improve the coordination of variable stiffness joint structure and output torque and dynamic performance, reduce the loss and waste of each component at rated output torque, reduce redundancy, and increase power density, the NSGA-III algorithm is used for multi-objective optimization of the scaling law of robot variable stiffness joint.

[0049] 2.1 Objective Function Using the maximum output torque and resonant frequency of the variable stiffness joint as objective functions, we find the maximum value of both and optimize other parameters to improve the space utilization and power density of the variable stiffness joint, which can achieve good dynamic performance while meeting the output torque requirements.

[0050] 2.1.1 Maximum Output Torque The maximum output torque is the minimum torque of the motor, differential gear, and reducer at the reducer output terminal. (30) (31) The maximum output torque at the reducer end is: (32) 2.1.2 Resonant Frequency The resonant frequency of a robot joint can be expressed as: (33) (34) In the formula, The moment of inertia of the motor. The inertia at the joint output end. For joint stiffness, The total reduction ratio, For the output torque of the reducer, To input the angle, To output the angle, For differential gear reduction ratio, This refers to the reduction ratio of the speed reducer.

[0051] Higher resonant frequencies allow for greater control bandwidth, thereby enhancing dynamic performance. Therefore, one of the optimization goals is to increase the resonant frequency of variable stiffness joints.

[0052] The total moment of inertia of the variable stiffness joint is the sum of the motor, differential gear, and harmonic reducer. The interaction between the electromagnetic spring and the differential gear is electromagnetic, introducing no new moment of inertia and ensuring superior dynamic performance. The total moment of inertia is: (35) The total reduction ratio of the variable stiffness joint is: (36) Substituting formulas (34) to (36) into formula (33), we get: (37) 2.2 Design Parameters and Constraints The variable stiffness joint harmonic reducer is designed with an output torque of 50 Nm. Based on the output torque, the harmonic reducer, differential gear, electromagnetic spring, and brushless DC motor were selected for design. The main initial design parameters are listed in Table 1, and the range of variation of these design parameters is constrained.

[0053] Table 1

[0054] 2.3 Solving the Optimization Model Optimization is performed using the NSGA-III algorithm. The flowchart for using the NSGA-III algorithm is as follows: Figure 14 As shown, after repeated convergence tests, the final algorithm parameters were determined. Algorithm 1 introduces the steps of using the NSGA-III algorithm.

[0055]

[0056] The initial design parameters for the variable stiffness joint calculated an output torque of 50 Nm. Through multi-objective optimization of the variable stiffness joint, a set of multi-objective optimization results were obtained, such as... Figure 15 As shown, when the output torque is 50.2 Nm, the resonant frequency is 382.3 MHz. Table 2 gives the value range of the design variables, the initial design, and the optimal design values ​​at this point. After optimizing the relevant parameters, under the same output torque, the diameter of the variable stiffness joint is reduced by 15 mm, and the motor length is reduced by 8 mm. Since the differential gear and electromagnetic spring are coupled, after optimization, their lengths are the same, and the axial dimension after coupling is also greatly reduced. The length of the electromagnetic spring is reduced by 5 mm, the length of the differential gear is reduced by 4 mm, and the diameter of the differential gear is reduced by 21.3 mm. This indicates that in the initial design, there was a significant waste in the torque output of the differential gear. The length of the harmonic reducer increased by 4.7 mm. For the overall size of the variable stiffness joint, the diameter is reduced by 15 mm, and the length is reduced by 8.3 mm. Since the initial design resonant frequency was 262 MHz, the optimized design increases the resonant frequency, resulting in better dynamic performance. For situations with higher dynamic performance requirements, a portion of the output torque can be sacrificed to meet the dynamic performance requirements. Similarly, for situations with lower dynamic performance requirements, a portion of the resonant frequency can be sacrificed to achieve a larger output torque.

[0057] Table 2

[0058] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A multi-objective optimization method for variable stiffness joint scaling law and load-response speed, characterized in that: Includes the following steps: S1: Establish scaling law models for the maximum output torque and moment of inertia of the brushless DC motor, differential gear, electromagnetic spring, and harmonic reducer in the variable stiffness joint, respectively. S2: Based on the scaling law model of the brushless DC motor, differential gear, electromagnetic spring and harmonic reducer, a global scaling law model of the variable stiffness joint is generated by coupling. S3: Establish a multi-objective optimization model with the maximum output torque and dynamic performance parameters of the variable stiffness joint as the optimization objectives; S4: The NSGA-III algorithm is used to solve the multi-objective optimization model to obtain the parameter combination that satisfies the constraints; S5: Determine the size of the variable stiffness joint and the reduction ratio configuration based on the optimized parameter combination.

2. The variable stiffness joint scaling law and load-response speed multi-objective optimization method according to claim 1, characterized in that: In S1: The maximum output torque of the brushless DC motor is proportional to the square of the motor diameter and the length, and the moment of inertia is proportional to the fourth power of the motor diameter and the length. The maximum output torque of the differential gear is proportional to the square of the gear diameter, the length, and the reduction ratio; the moment of inertia is proportional to the fourth power of the gear diameter, the length, and the reduction ratio. The maximum output torque of the electromagnetic spring is proportional to the cube of the spring diameter and its length. The maximum output torque of the harmonic reducer is proportional to the cube of the reducer diameter, and the moment of inertia is proportional to the fourth power of the reducer diameter, the length, and the square of the reduction ratio.

3. The variable stiffness joint scaling law and load-response speed multi-objective optimization method according to claim 2, characterized in that: The reduction ratio function of the differential gear is: in, This is the differential gear reduction ratio.

4. The variable stiffness joint scaling law and load-response speed multi-objective optimization method according to claim 1, characterized in that: In S2, the conditions for coupling to generate the overall scaling law model include: The axial lengths of the differential gear and the electromagnetic spring are equal; The output end of the planetary carrier of the differential gear is connected to the input shaft of the harmonic reducer.

5. The variable stiffness joint scaling law and load-response speed multi-objective optimization method according to claim 1, characterized in that: In S3, the dynamic performance parameter is the resonant frequency, and its expression is: In the formula, For the moment of inertia of the motor, The inertia at the joint output end. For joint stiffness, This represents the overall reduction ratio.

6. The variable stiffness joint scaling law and load-response speed multi-objective optimization method according to claim 5, characterized in that: The total moment of inertia satisfy: in, The moment of inertia of the differential gear. The moment of inertia of the harmonic reducer. For differential gear reduction ratio, This refers to the reduction ratio of the harmonic reducer.

7. The variable stiffness joint scaling law and load-response speed multi-objective optimization method according to claim 1, characterized in that: In S4, the constraints include: The diameter range of the variable stiffness joint is 90~110mm; The output torque of the harmonic reducer shall not be less than 50 Nm; The differential gear reduction ratio ranges from 2.5 to 6, and the harmonic reducer reduction ratio ranges from 30 to 100.

8. The variable stiffness joint scaling law and load-response speed multi-objective optimization method according to claim 1, characterized in that: In S5, the parameter combinations include: Length and diameter of a brushless DC motor; The length, diameter, and reduction ratio of the differential gear; The length and diameter of the electromagnetic spring; The length, diameter, and reduction ratio of the harmonic reducer.

9. The variable stiffness joint scaling law and load-response speed multi-objective optimization method according to claim 8, characterized in that: The optimized reduction ratio of the harmonic reducer is 100, and the optimized reduction ratio of the differential gear is 2.

5.

10. A variable stiffness joint system, characterized in that: The method employs the optimized parameter combination as described in any one of claims 1 to 9, including: A brushless DC motor, whose output shaft is connected to the sun gear of a differential gear; Differential gear, with its internal gear coupled to the electromagnetic spring rotor, planetary carrier connected to the input shaft of the harmonic reducer; The harmonic reducer uses a rigid wheel as the joint output end.

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