Viscoelasticity-based curved pneumatic muscle mechanism modeling method

Abstract

The invention discloses a viscoelasticity-based curved pneumatic muscle mechanism modeling method, which comprises the following steps of: (1) considering a curved pneumatic muscle to be composed of a plurality of infinitesimal elements, performing stress analysis on the infinitesimal elements, and establishing a force balance equation; (2) analyzing the linear pressure of the woven mesh pipe on the elastic hose, and establishing the relationship between the linear pressure and the tensile force of the woven wire; (3) establishing a stress-strain relation of the pneumatic muscle based on a linear viscoelasticity theory; (4) analyzing the balance relation among the air pressure, the circumferential stress and the braided wire tension; (5) establishing a geometrical relationship between the radial displacement and the inner diameter, the circumferential strain, the axial strain, the lift angle of the braided wire and the bending angle; and (6) calculating the model. According to the method, the hysteresis and creep characteristics of the curved pneumatic muscle are described by adopting the linear viscoelastic constitutive relation, a complete mechanism model of the curved pneumatic muscle is established, and a theoretical basis is provided for design, control and optimization of the curved pneumatic muscle.

Description

Technical Field

[0001] The present invention belongs to the field of flexible actuator modeling, and specifically relates to a modeling method for a bending-type pneumatic muscle mechanism based on viscoelasticity. Background Art

[0002] As a new type of flexible actuator, the bending pneumatic muscle is driven by the air pressure input externally. Its process is like the muscle movement of the human body, and it has the advantages of light weight, high force-to-weight ratio, good flexibility, etc., and has broad application prospects in the fields of robots, medical devices, bionic devices, etc. However, the dynamic characteristics of the pneumatic muscle are complex, and its hysteresis and creep characteristics bring great challenges to accurate modeling.

[0003] Traditional modeling methods usually adopt linear elastic or hyperelastic constitutive relations, but this method cannot accurately reflect the hysteresis characteristics shown by the pneumatic muscle during the air pressure loading and unloading processes. In addition, most of the existing models are for axial pneumatic muscles, and there is less research on the modeling of bending pneumatic muscles, which is difficult to meet the actual application requirements. Summary of the Invention

[0004] To solve the above problems, the present invention discloses a modeling method for a bending-type pneumatic muscle mechanism based on viscoelasticity, and innovatively uses viscoelastic theory to describe the hysteresis and creep characteristics of the bending-type pneumatic muscle, so as to achieve accurate modeling of the bending-type pneumatic muscle.

[0005] To achieve the above object, the technical solution of the present invention is as follows:

[0006] The modeling method for a bending-type pneumatic muscle mechanism based on viscoelasticity includes the following steps:

[0007] (1) Regarding the bending-type pneumatic muscle as being composed of multiple micro-elements, performing a force analysis on the micro-elements, and establishing a force balance equation;

[0008] (2) Analyzing the linear pressure of the braided net tube on the elastic hose, and establishing the relationship between the linear pressure and the braided wire tension;

[0009] (3) Based on linear viscoelastic theory, establishing the stress-strain relationship of the pneumatic muscle, and introducing the Boltzmann superposition principle to consider the stress relaxation effect;

[0010] (4) Analyzing the balance relationship among the air pressure, the circumferential stress, and the braided wire tension;

[0011] (5) Establishing the geometric relationship among the radial displacement, the inner diameter, the circumferential strain, the axial strain, the braided wire lead angle, and the bending angle;

[0012] (6) Model solution.

[0013] The beneficial effects of the present invention are:

[0014] The method for mechanism modeling of a bending-type pneumatic muscle based on viscoelasticity according to the present invention adopts a linear viscoelastic constitutive relation, and can accurately characterize the hysteresis characteristics exhibited by the pneumatic muscle during air pressure loading and unloading; a complete mechanism model of the bending-type pneumatic muscle is established, which can accurately predict the bending angle of the pneumatic muscle under different air pressures; the model parameters have clear physical meanings, facilitating practical applications and parameter identification; and it provides a theoretical basis for the design, control, and optimization of the bending-type pneumatic muscle. Description of the Drawings

[0015] Figure 1 It is a schematic diagram of the bending-type pneumatic muscle;

[0016] Figure 2 It is a schematic diagram of the force analysis of the microelement;

[0017] Figure 3 It is a schematic diagram of the linear pressure analysis;

[0018] Figure 4 It is a schematic diagram of the air pressure balance. Detailed Embodiments

[0019] The present invention will be further clarified below in conjunction with the drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and not to limit the scope of the present invention.

[0020] As shown in the figure, the method for mechanism modeling of a bending-type pneumatic muscle based on viscoelasticity according to the present invention includes the following steps:

[0021] (1) The bending-type pneumatic muscle is regarded as being composed of multiple microelements, the force analysis of the microelement is carried out, and a force balance equation is established:

[0022] Axial stresses σ1 are applied on both axial sides, circumferential stresses σ2 are applied on both circumferential sides, a distributed air pressure P is applied on the inner wall, and a linear pressure P of the braided net tube is applied on the outer wall e , as Figure 2 shown. Since the radial deformation is much smaller than the circumferential deformation and the axial deformation, the radial stress is ignored, and it is considered that the wall thickness th of the elastic hose is fixed. The inner diameter of the microelement is R, the axial bending radius is R bend , the circumferential bending angle is dθ, and the axial bending angle is From the force balance of the microelement in the vertical direction, it can be obtained that:

[0023]

[0024] (2) Analyze the linear pressure of the braided net tube on the elastic hose, and establish the relationship between the linear pressure and the braided wire tension:

[0025] The bending pneumatic muscle consists of an elastic hose and a braided network tube. The braided network tube is attached to the surface of the elastic hose to restrict its movement. The braided network tube is woven from multiple threads, and the braided threads are helically wound. The pressure P exerted by the braided network tube on the elastic hose e can be obtained by calculating the linear pressure of a single braided thread on the elastic hose , where T is the tension of the thread. Let the helix angle of the braided thread be α, then the component of the tension on the braided thread in the circumferential direction is Tcosα, and the linear pressure is denoted as as Figure 3 shown. From the balance of the vertical components of the pressure of the braided thread on the elastic hose and the vertical component of the tension, we can obtain:

[0026]

[0027] (3) Based on the linear viscoelastic theory, establish the stress-strain relationship of the pneumatic muscle, and introduce the Boltzmann superposition principle to consider the stress relaxation effect.

[0028] Use the linear viscoelastic constitutive relationship to accurately model the hysteresis phenomenon of the pneumatic muscle. The difference between the linear viscoelastic constitutive relationship and the linear elastic constitutive relationship or the hyperelastic constitutive relationship is that the shear modulus G and the bulk modulus K are no longer constant, but change with time, that is, σ = f(ε, t). According to the Boltzmann superposition principle, when the air pressure changes, the linear viscoelastic constitutive relationship is:

[0029]

[0030] where G ∞ , K ∞ are the shear modulus and bulk modulus when time t approaches infinity. t0 is the initial time. G(t) and K(t) are represented by the generalized Maxwell model, that is:

[0031]

[0032] where G ∞ , G1, τ G , K ∞ , K1 and τ K are the viscoelastic material parameters to be optimized.

[0033] (4) Analyze the balance relationship among air pressure, circumferential stress and braided thread tension. The air pressure, circumferential stress σ2 and braided thread tension are in balance in the normal direction of the longitudinal section, as Figure 4 shown, and the force balance formula is as follows:

[0034]

[0035] where is the circumferential stress at the circumferential angles of 0 degrees and 180 degrees, l0, lθ＝π and l θ＝π / 2 are the lengths at circumferential angles of 0°, 180°, and 90°.

[0036] (5) Establish the geometric relationships between the radial displacement and the inner diameter, circumferential strain, axial strain, braid angle, and bending angle.

[0037] For step (5), it includes the following sub-steps:

[0038] (5.1) Establish the geometric relationship between the radial displacement and the inner diameter. When the bending-type pneumatic muscle moves, the radius of the elastic hose changes with the air pressure. The radius before deformation is denoted as R0, and the inner diameter R after deformation can be calculated using the radial displacement at a circumferential angle of 180°. That is:

[0039]

[0040] (5.2) Establish the geometric relationship between the radial displacement and the circumferential strain. The geometric relationship is: where ε2 is the circumferential strain.

[0041] (5.3) Establish the geometric relationship between the radial displacement and the axial strain. Compared with the elastic hose, the elastic deformation of the braided tube can be ignored. Therefore, the length of the braided wire is fixed and denoted as BL. When the pneumatic muscle bends, the length l and the inner diameter R change continuously, but the length of the braided wire remains unchanged. Then:

[0042]

[0043] where n is the number of winding turns of the braided wire, is the axial strain at a circumferential angle of 90°.

[0044] (5.4) Establish the geometric relationship between the radial displacement and the braid angle. Since the length of the braided wire remains unchanged, the mesh of the braided tube always maintains a rhombus structure and the side length of the rhombus remains unchanged. Let the initial braid angle of the braided wire be α0, and the braid angle becomes α after the braided tube elongates. Then:

[0045] cosα = cosα0(1 + ε2)

[0046] According to step (5.2), there is a geometric relationship between the radial displacement u3 and the circumferential strain ε2. Therefore, there is also a geometric relationship between the radial displacement u3 and the braid angle α.

[0047] (5.5) Establish the geometric relationship between the radial displacement and the bending angle. The geometric relationship is: where β is the bending angle, is the axial strain at a circumferential angle of 180°.

[0048] (6) Model solution. Apply air pressure loading and unloading cycles to the bending pneumatic muscle 10 times, and record the input air pressure and bending angle data. The parameters to be optimized in step (3) are obtained through iterative optimization using the nonlinear least squares algorithm with this set of experimental data. Solve the equations established in steps (1) to (5) to obtain the relationship between the bending angle of the pneumatic muscle and the input air pressure.

[0049] It should be noted that the above content only illustrates the technical idea of the present invention and cannot be used to limit the protection scope of the present invention. For those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can still be made, and these improvements and refinements all fall within the protection scope of the claims of the present invention.

Claims

1. A modeling method for the mechanism of bending pneumatic muscles based on viscoelasticity, characterized in that: It includes the following steps: (1) Regarding the bending pneumatic muscle as being composed of multiple micro-elements, analyzing the forces acting on the micro-elements, and establishing a force balance equation; (2) Analyzing the linear pressure of the braided network tube on the elastic hose, and establishing the relationship between the linear pressure and the tension of the braided wire; (3) Based on the linear viscoelastic theory, establishing the stress-strain relationship of the pneumatic muscle, and introducing the Boltzmann superposition principle to consider the stress relaxation effect; (4) Analyzing the balance relationship among the air pressure, the circumferential stress, and the tension of the braided wire; (5) Establishing the geometric relationship between the radial displacement and the inner diameter, the circumferential strain, the axial strain, the helix angle of the braided wire, and the bending angle; (6) Solving the model.

2. The modeling method of the bending-type pneumatic muscle mechanism based on viscoelasticity according to claim 1, characterized in that: The specific content of step (1) is as follows: Axially, it is subjected to axial stress σ1 on both sides, circumferentially, it is subjected to circumferential stress σ2 on both sides, the inner wall is subjected to distributed gas pressure P, and the outer wall is subjected to the linear pressure P of the braided network tube e , the wall thickness th of the elastic hose is fixed and unchanged; the inner diameter of the microelement is R, and the axial bending radius is R bend , the circumferential bending angle is dθ, and the axial bending angle is From the force balance of the microelement in the vertical direction, it can be obtained that:

3. The method for modeling the bending-type pneumatic muscle mechanism based on viscoelasticity according to claim 1, wherein: The specific content of step (2) is as follows: The braided network tube is formed by braiding multiple wires, and the braided wires are spirally wound; the pressure P exerted by the braided network tube on the elastic hose e is obtained by calculating the linear pressure of a single braided wire on the elastic hose where T is the tension of the wire. Let the helix angle of the braided wire be α, then the component of the tension on the braided wire in the circumferential direction is Tcosα, and the linear pressure is denoted as From the balance of the vertical component of the pressure of the braided wire on the elastic hose and the vertical component of the tension, we get:

4. The method for modeling the bending-type pneumatic muscle mechanism based on viscoelasticity according to claim 1, characterized in that: The specific content of step (3) is as follows: Using the linear viscoelastic constitutive relationship to accurately model the hysteresis phenomenon of the pneumatic muscle; the shear modulus G and the bulk modulus K in the linear viscoelastic constitutive relationship change with time, that is, σ = f(ε, t); according to the Boltzmann superposition principle, when the air pressure changes, the linear viscoelastic constitutive relationship is: where G ∞ , K ∞ are the shear modulus and bulk modulus when time t approaches infinity, t0 is the initial time, and G(t), K(t) are represented by the generalized Maxwell model, i.e.: Among which G ∞ , G1, τ G , K ∞ , K1 and τ K are viscoelastic material parameters to be optimized.

5. The method for modeling the bending-type pneumatic muscle mechanism based on viscoelasticity according to claim 1, wherein: The specific content of step (4) is as follows: The air pressure, the circumferential stress σ2, and the tension of the braided wire are in balance in the normal direction of the longitudinal section, and the force balance formula is as follows: wherein are the circumferential stresses at circumferential angles of 0 degrees and 180 degrees, and l0, l θ＝π , l θ＝π / 2 are the lengths at circumferential angles of 0 degrees, 180 degrees, and 90 degrees.

6. The method for modeling the bending pneumatic muscle mechanism based on viscoelasticity according to claim 1, wherein: Step (5) includes the following sub-steps: (5.1) Establish the geometric relationship between the radial displacement and the inner diameter: When the bending pneumatic muscle moves, the radius of the elastic hose changes with the air pressure; the radius before deformation is denoted as R0, and the inner diameter R after deformation is calculated using the radial displacement with a circumferential angle of 180 degrees, that is: Namely: (5.2) Establishing the geometric relationship between the radial displacement and the circumferential strain: where ε2 is the circumferential strain; (5.3) Establishing the geometric relationship between the radial displacement and the axial strain: The length of the braided wire is fixed and represented by BL; when the pneumatic muscle bends, the length l and the inner diameter R change continuously, but the length of the braided wire remains unchanged, so there is: where n is the number of winding turns of the braided wire, is the axial strain at the circumferential angle of 90 degrees; (5.4) Establishing the geometric relationship between the radial displacement and the helix angle of the braided wire: Because the length of the braided wire remains unchanged, the mesh of the braided network tube always maintains a rhombus structure and the side length of the rhombus remains unchanged; let the initial helix angle of the braided wire be α0, and the helix angle becomes α after the braided network tube stretches, then there is: cosα = cosα0(1 + ε2) According to step (5.2), there is a geometric relationship between the radial displacement u3 and the circumferential strain ε2, so there is also a geometric relationship between the radial displacement u3 and the helix angle α of the braided wire; (5.5) Establishing the geometric relationship between the radial displacement and the bending angle: where β is the bending angle, is the axial strain at the circumferential angle of 180 degrees.

7. The method for modeling the bending-type pneumatic muscle mechanism based on viscoelasticity according to claim 4, characterized in that: The specific content of step (6) is as follows: (6.1) Conducting 10 cycles of air pressure loading and unloading on the bending pneumatic muscle, recording the input air pressure and bending angle data, and the parameters to be optimized in step (3) are obtained by iterative optimization using the non-linear least squares algorithm through this set of experimental data.

8. The method for modeling the bending pneumatic muscle mechanism based on viscoelasticity according to claim 7, characterized in that: The specific content of step (6) is as follows: (6.2) Solving the equations established in steps (1) to (5) to obtain the relationship between the bending angle of the pneumatic muscle and the input air pressure.

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