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WO2021082520A1 - Procédé de construction de modèle pour robot mou à rigidité variable - Google Patents

Procédé de construction de modèle pour robot mou à rigidité variable Download PDF

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Publication number
WO2021082520A1
WO2021082520A1 PCT/CN2020/100791 CN2020100791W WO2021082520A1 WO 2021082520 A1 WO2021082520 A1 WO 2021082520A1 CN 2020100791 W CN2020100791 W CN 2020100791W WO 2021082520 A1 WO2021082520 A1 WO 2021082520A1
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Prior art keywords
film tube
particles
spherical particles
particle
soft robot
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PCT/CN2020/100791
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English (en)
Chinese (zh)
Inventor
徐丰羽
江丰友
余洪亮
蒋国平
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Nanjing Nanyou Institute Of Information Technovation Co Ltd
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Nanjing Nanyou Institute Of Information Technovation Co Ltd
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/1605—Simulation of manipulator lay-out, design, modelling of manipulator
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1615—Programme controls characterised by special kind of manipulator, e.g. planar, scara, gantry, cantilever, space, closed chain, passive/active joints and tendon driven manipulators

Definitions

  • the invention relates to the technical field of driving travel, in particular to a modeling method of a variable stiffness soft robot.
  • the mechanism needs to have better variable stiffness performance, that is, better flexibility and rigidity.
  • it Before coming into contact with the object, it needs to have good flexibility and be able to realize its own movement through active deformation, so as to better adapt to external objects and obtain a larger contact area.
  • After full contact with the object it needs to have good rigidity to increase the pressure between the objects in contact, and then increase the friction between the objects in contact.
  • Pneumatic structure has good position control performance, but due to the characteristics of its material itself, the stiffness of the mechanism made of it is not high, and the introduction of a blocking system can increase the stiffness of the soft robot to adapt to more applications.
  • the pneumatic drive has the characteristics of fast response, high power density, and high switching speed.
  • the materials constituting the soft robot are usually flexible, the pressure is always maintained at a low level when driven by air pressure, which enables the soft robot to achieve corresponding motions and at the same time has high safety.
  • Variable stiffness is an effective way for soft structures (natural or man-made) to interact with the environment.
  • the inherent flexibility of the software structure deforms itself to adapt to the external environment, and the safe interaction prevents the external environment from damaging the entity. But at the same time, it also needs to strengthen its own rigidity to increase the force applied to the external environment.
  • variable stiffness method based on particle clogging is a more effective method of using vacuum pressure to control stiffness.
  • Particle blockage is to cause a large number of particles to undergo a phase change, transitioning between a fluid state and a solid state. If the particles are placed in a sealing film under normal conditions, due to the large gaps between the particles and the small friction between the particles, they can flow arbitrarily, thus exhibiting a fluid-like behavior. At this time, a large number of particles are wrapped.
  • the sealing film can be changed in any shape. When the air in the sealing film is discharged, a large number of particles are compressed together. At this time, due to the increase of the contact surface pressure between the particles, the friction between the particles rises sharply. At this time, the particles are restricted and cannot flow freely. , So that the filling particles present a solid state, and the sealing film and the particles as a whole show a certain degree of rigidity.
  • variable stiffness software driver software arm and software platform based on blocking mechanism
  • the application is The author discloses a variable stiffness soft drive based on the blocking mechanism, which is mainly composed of a flexible frame, a trachea, an outer flexible layer, a blocking mechanism, a deformable plug and a blocking plug.
  • the blocking mechanism is mainly composed of a supporting frame, an elastic connecting rope, and a large ball. It is composed of particles, small ball particles, tightening spring and sealing film, which can have greater flexibility and rigidity through the principle of variable stiffness.
  • the technical problem to be solved by the present invention is to address the above-mentioned shortcomings of the prior art, and provide a modeling method of a variable stiffness soft robot.
  • the modeling method of the variable stiffness soft robot takes all the filling particles and the film tube in the film tube into consideration. As a whole particle block, the small spherical particles are equivalent to fluid, the film tube is equivalent to a closed space, the sphere-plane Hertz contact model is established, and the locking force is established based on the Hertz contact theory and the Hertz contact model of two spheres. And the model of the locking torque, so as to control the stiffness of the variable stiffness soft robot as required.
  • a modeling method of a variable stiffness soft robot includes the following steps.
  • Step 1 the design of the locking force FL between the filling particles, includes the following steps.
  • Step 11 support frame selection.
  • the support frame in the blocking mechanism is selected as a rhombus frame, and the sealing film is selected as a film tube.
  • the large spherical particles and small spherical particles in the film tube are collectively referred to as filler particles.
  • Step 12 Establish a particle block model.
  • all the filling particles in the film tube are rigid and are restricted as a whole, that is, all the filling particles in the film tube and the film tube, When taken as a whole piece of pellets.
  • Step 13 the design of the locking force FL between the filling particles.
  • the particle block receives an external force
  • the small spherical particles in the filled particles are equivalent to a fluid.
  • the calculation formula of the locking force FL between the filled particles is obtained as follows.
  • P′ is the equivalent pressure in the film tube
  • R 1 is the radius of the diamond-shaped skeleton
  • ⁇ is the sharp apex angle of the diamond-shaped skeleton
  • R 2 is the radius of the large spherical particles
  • ⁇ 1 is the friction coefficient between the small spherical particles and the diamond-shaped skeleton
  • ⁇ 2 is the friction coefficient between small spherical particles and large spherical particles.
  • Step 2 Calculate the equivalent pressure P'in the film tube.
  • the radius of the small spherical particles is much smaller than the radius of the film tube, and the area of the film tube facing the single small spherical particle is small. Therefore, the film tube in contact with the single small spherical particle can be regarded as a flat surface.
  • the sphere-plane Hertz contact model according to the Hertz contact theory and the Hertz contact model of two spheres, the calculation formula for the equivalent pressure P′ in the membrane tube is obtained as follows.
  • R 3 is the radius of the small spherical particles
  • v 1 is the Poisson's ratio of the diamond-shaped framework
  • v 2 is the Poisson's ratio of the small spherical particles
  • E 1 is the Young's modulus of the diamond-shaped framework
  • E 2 is the Young's ratio of the small spherical particles.
  • Modulus P is the vacuum pressure in the film tube.
  • Step 3 Establish the corresponding relationship between the locking force FL and the vacuum pressure P in the film tube. Substituting the equivalent pressure P'in the membrane tube calculated in step 2 into the locking force FL designed in step 1, the corresponding relationship between the locking force FL and the vacuum pressure P in the membrane tube is obtained as shown in the following formula.
  • Step 4 Design the locking torque ML of the particle block.
  • the design formula is shown below.
  • d is the radius of the film tube.
  • step 5 establishing the corresponding relationship between the locking torque M L and the hardness S 1 of the pellets.
  • the corresponding relationship between the Young's modulus value and the Shore hardness value the corresponding relationship between the locking torque M L and the hardness S 1 of the small spherical particles is established as follows.
  • the stiffness of the variable stiffness soft robot is adjusted.
  • step 6 the design of the deformation angle ⁇ of the film tube.
  • the film tube will deform in contact with the small spherical particles, and the deformation angle ⁇ of the film tube is calculated using the following formula.
  • the calculation method of the deformation angle ⁇ of the film tube includes the following steps.
  • Step 61 Calculate the relative radial deformation displacement ⁇ of the thin film tube. According to the sphere-plane Hertzian contact model established in step 2, and then according to the Hertzian contact theory and the two-sphere Hertzian contact model, the relative radial deformation displacement ⁇ of the membrane tube is obtained to satisfy the following calculation formula.
  • Step 62 Establish a corresponding relationship between the deformation angle ⁇ of the membrane tube and the relative radial deformation displacement ⁇ of the membrane tube.
  • the corresponding relationship between the deformation angle ⁇ of the membrane tube and the relative radial deformation displacement ⁇ of the membrane tube is calculated as follows.
  • Step 63 Calculate the deformation angle ⁇ of the film tube. Substituting the relative radial deformation displacement ⁇ of the thin film tube calculated in step 61 into step 62, it is obtained that the deformation angle ⁇ of the thin film tube satisfies the following formula.
  • step 13 according to the static balance equation and Pascal's law, the method of calculating the locking force FL between the filled particles includes the following steps.
  • the particle block includes an upper particle block and a lower particle block, wherein the lower particle block is located on the side of the object to be locked and the bottom is in contact with the object to be locked, and the upper particle is located on the side away from the object to be locked.
  • the locking force of the lower particle block needs to resist the external moment. Therefore, the upper particle block and the lower particle block slide relative to each other in the horizontal direction. According to the static balance equation of the particle block, the locking force F L described as.
  • f L is the friction force of the particle block in the contact area with the diamond-shaped skeleton
  • f P is the static force of the particle block on the locking area
  • f U is the friction force of the lower particle block and the large spherical particles in the horizontal direction.
  • Step 13b f P is calculated.
  • the small spherical particles are equivalent to fluid, and the film tube is equivalent to a closed space.
  • Several small spherical particles are filled in the closed space to form a static fluid model. Then the static force f P applied by the particle block in the horizontal direction of the locking area , Will be provided by the pressure between the particle block and the diamond skeleton, specifically.
  • R 1 is the radius of the rhombus skeleton
  • ⁇ is the apex angle of the rhombus skeleton
  • P′ is the equivalent pressure in the film tube.
  • Step 13c f L is calculated.
  • the frictional force f L of the particle block in the contact area with the diamond-shaped skeleton is.
  • ⁇ 1 is the friction coefficient between the particle block and the diamond-shaped skeleton.
  • Step 13d f U is calculated.
  • the frictional force f U between the lower layer of particles and the large spherical particles in the horizontal direction is.
  • ⁇ 2 is the friction coefficient between small spherical particles and large spherical particles.
  • step 13e the f P , f L and f U calculated in steps 13b, 13c, and 13d are substituted into step 13a respectively to obtain the calculation formula of the locking force FL between the filling particles.
  • the vacuum pressure P in the membrane tube is adjusted by the vacuum pump, and then the stiffness of the variable stiffness soft robot is adjusted.
  • the vacuum pressure P in the membrane tube increases, the deformation angle ⁇ and the locking torque M L of the membrane tube will increase, and the stiffness of the variable stiffness soft robot will increase.
  • the stiffness of the variable stiffness soft robot is adjusted.
  • the radius R 3 of the small ball particle is larger, the locking torque M L is smaller, and the rigidity of the variable-rigidity soft robot will decrease.
  • the stiffness of the variable stiffness soft robot is adjusted.
  • the radius R 1 of the rhombus skeleton is larger, the locking torque M L is larger, and the rigidity of the variable-rigidity soft robot will increase.
  • the stiffness of the variable stiffness soft robot is adjusted.
  • the radius R 2 of the large ball particle is larger, the locking torque M L is larger, and the rigidity of the variable-rigidity soft robot will increase.
  • the invention has the following beneficial effects: the particles are quickly divided into upper and lower layers, and the locking force of the lower layer of particle blocks resists the external moment.
  • the upper and lower layers of particle blocks slide relatively in the horizontal direction.
  • the small spherical particles are equivalent to a fluid
  • the film tube is equivalent to a closed space.
  • the inside of the tube is filled with small spherical particles.
  • the locking force is obtained according to the static balance equation of the particle block.
  • the film area where a single particle is facing If the area is small, it can be regarded as a plane, then the film and particle block are analyzed using the Hertzian contact theory, the sphere-plane Hertzian contact model is established, and the relationship between the hardness of the small ball and the locking torque is obtained.
  • the apex angle and radius of the rhombus skeleton By adjusting the apex angle and radius of the rhombus skeleton, the radius of the large spherical particles, the radius of the small spherical particles, the hardness, the vacuum pressure and other parameters, the required stiffness of the variable stiffness soft robot can be obtained.
  • the model established by the invention is simulated through variable stiffness characteristics, and the simulation result is consistent with the established model, so the reliability is high and it is convenient for popularization and utilization.
  • Figure 1 shows a schematic structural diagram of a blocking mechanism in a variable stiffness soft robot of the present invention.
  • Figure 2 shows a longitudinal cross-sectional view of a blocking mechanism in a variable stiffness soft robot of the present invention.
  • Fig. 3 shows an exploded analysis diagram of the force on the end of the blocking mechanism in a variable stiffness soft robot of the present invention.
  • Figure 4 shows a cross-sectional view of the longitudinal plane where all the large spherical particles connected by the same tightening spring are located.
  • Figure 5 shows a schematic diagram of the force analysis of the lower particle block.
  • Figure 6 shows a schematic diagram of the fluid pressurization model.
  • Figure 7 shows a schematic diagram of the force analysis of the blocking mechanism in the present invention.
  • Figure 8 shows the Hertz model of two balls in contact.
  • Figure 9 shows the particle-plane Hertz contact model of the small spherical particles in contact with the film tube.
  • Figure 10 shows the simplified model diagram of Figure 9.
  • Figure 11 shows the corresponding relationship between the deformation angle ⁇ and the vacuum pressure P.
  • Figure 12 shows the corresponding relationship between the locking torque M L and the vacuum pressure P.
  • Figure 13 shows the corresponding relationship between the locking torque M L and the radius R 3 of the small spherical particles.
  • Figure 14 shows the corresponding relationship between the locking torque M L and the radius R 1 of the diamond skeleton.
  • Figure 15 shows the corresponding relationship between the locking torque M L and the radius R 2 of the large spherical particles.
  • Figure 16 shows the corresponding relationship between the locking torque M L and the hardness S 1 of the pellets.
  • variable stiffness soft robot For details, please refer to the invention patent application filed on August 31, 2017 with the application number CN201710768485.2.
  • the name of the invention is "variable stiffness soft driver, soft arm and software platform based on clogging mechanism.” "This application does not improve the structure of the blocking mechanism itself, but selects the support frame in the blocking mechanism as the diamond-shaped frame 32, and the sealing film as the film tube 31.
  • the large spherical particles 34 and the small spherical particles 35 in the film tube are collectively referred to as filling particles.
  • the elastic connecting rope is selected as a flexible rope 33, and vacuum pressure is provided into the film tube through a vacuum pump 40.
  • the specific structure is shown in Figs. 1 and 2.
  • a modeling method of a variable stiffness soft robot includes the following steps.
  • Step 1 the design of the locking force FL between the filling particles, includes the following steps.
  • Step 11 support frame selection.
  • Step 12 Establish a particle block model.
  • all the filling particles in the film tube are rigid and are restricted as a whole, that is, all the filling particles in the film tube and the film tube, When taken as a whole piece of pellets.
  • Step 13 the design of the locking force FL between the filling particles.
  • the particle block When the particle block receives an external force, the small spherical particles in the filled particles are equivalent to a fluid. According to the static balance equation and Pascal's law, the calculation formula of the locking force FL between the filled particles is obtained as follows.
  • P′ is the equivalent pressure in the film tube
  • R 1 is the radius of the diamond-shaped skeleton
  • ⁇ is the sharp apex angle of the diamond-shaped skeleton
  • R 2 is the radius of the large spherical particles
  • ⁇ 1 is the friction coefficient between the small spherical particles and the diamond-shaped skeleton
  • ⁇ 2 is the friction coefficient between small spherical particles and large spherical particles.
  • the above method for calculating the locking force FL between filled particles according to the static balance equation and Pascal's law includes the following steps.
  • the particle block includes an upper particle block 51 and a lower particle block 52, wherein the lower particle block is located on the side of the object to be locked and the bottom is in contact with the object to be locked, and the upper particle is located on the side away from the object to be locked.
  • the particle block receives an external force F E
  • the locking force of the lower particle block needs to resist the external moment. Therefore, the upper particle block and the lower particle block slide relative to each other in the horizontal direction.
  • the static balance equation of the particle block, then the locking force FL is described as.
  • f L is the friction force of the particle block on the contact area 10 with the diamond-shaped skeleton
  • f P is the static force of the particle block on the locking area 60
  • f U is the horizontal friction between the lower particle block and the large spherical particles. force.
  • Step 13b f P is calculated.
  • the static force f P of the particle block on the locking area can be estimated by the fluid pressure model.
  • the fluid in a confined space exerts pressure on the fluid, can be transferred from the fluid to all directions in the space with the same magnitude.
  • Figure 6 and Pascal's law we can get:
  • the small spherical particles are equivalent to a fluid, and the film tube is equivalent to a closed space, and its interior is filled with small spherical particles, which constitutes a static fluid model as shown in Figure 7.
  • the force applied on each side It can be calculated by the above formula.
  • FN2 is the positive pressure of the particle block on the diamond-shaped skeleton, as shown in Figure 7, R 1 is the radius of the diamond-shaped skeleton, ⁇ is the apex angle of the diamond-shaped skeleton, and P'is the equivalent pressure applied by the particle block to the diamond-shaped skeleton and the big sphere. , Which is the equivalent pressure in the film tube.
  • the above-mentioned diamond-shaped skeleton radius R 1 refers to the radius of the radial large circle in the diamond-shaped skeleton in Fig. 3, which is infinitely close to the radius d of the film tube and can be approximately equal.
  • the apex angle ⁇ of the rhombus skeleton refers to the apex angle on the flexible rope, which is an acute angle.
  • Step 13c f L calculation: the friction force f L of the particle block in the contact area with the diamond-shaped skeleton is:
  • ⁇ 1 is the friction coefficient between the particle block and the diamond-shaped skeleton
  • a 1 is the equivalent area of the contact area between the particle block and the diamond-shaped skeleton.
  • Step 13d the frictional force f U between the lower layer of particles and the large spherical particles in the horizontal direction is:
  • F N1 is the positive pressure of the particle block on the large spherical particle
  • R 2 is the radius of the large spherical particle
  • ⁇ 2 is the friction coefficient between the small spherical particle (filling particle) and the large spherical particle
  • a 2 is the particle block and the large spherical particle. The equivalent area of particle contact.
  • step 13e the f P , f L and f U calculated in steps 13b, 13c, and 13d are substituted into step 13a respectively to obtain the calculation formula of the locking force FL between the filling particles.
  • Step 2 Calculate the equivalent pressure P'in the film tube.
  • Ra is the radius of the ball a in Figure 8
  • R b is the radius of the ball b
  • v a is the Poisson's ratio of the ball a
  • v b is the Poisson's ratio of the ball b
  • E a is the Young's modulus of the ball a
  • E b is b Ball Young's modulus.
  • the radius of the small spherical particle is much smaller than the radius of the film tube, and the area of the film tube facing the single small spherical particle is small. Therefore, the film tube in contact with the single small spherical particle can be regarded as a flat surface.
  • the relative radial deformation displacement of the ⁇ film tube R 3 is the radius of the small spherical particles
  • v 1 is the Poisson's ratio of the diamond-shaped framework
  • v 2 is the Poisson's ratio of the small spherical particles
  • E 1 is the Young's modulus of the diamond-shaped framework
  • E 2 is the Young's modulus of the small spherical particles
  • P is the vacuum pressure in the film tube.
  • Step 3 Establish the corresponding relationship between the locking force FL and the vacuum pressure P in the film tube. Substituting the equivalent pressure P'in the membrane tube calculated in step 2 into the locking force FL designed in step 1, the corresponding relationship between the locking force FL and the vacuum pressure P in the membrane tube is obtained as shown in the following formula.
  • Step 4 Design the locking torque ML of the particle block.
  • the design formula is shown below.
  • d is the radius of the film tube.
  • Step 5 Establish the corresponding relationship between the locking torque M L and the hardness S 1 of the small ball particles.
  • E is the Young's modulus in MPa
  • S is the hardness in accordance with ASTM D2240. This formula is suitable for materials with a hardness of 20 to 80, which is close to the material properties of small spherical particles.
  • the corresponding relationship between the Young's modulus value and the Shore hardness value is established as follows.
  • the stiffness of the variable stiffness soft robot is adjusted.
  • Step 6 the design of the deformation angle ⁇ of the film tube.
  • the film tube When the particle block is subjected to an external force, the film tube will deform in contact with the small spherical particles, and the deformation angle ⁇ of the film tube is calculated using the following formula.
  • the calculation method of the deformation angle ⁇ of the film tube includes the following steps.
  • Step 61 Calculate the relative radial deformation displacement ⁇ of the thin film tube. According to the sphere-plane Hertzian contact model established in step 2, and then according to the Hertzian contact theory and the two-sphere Hertzian contact model, the relative radial deformation displacement ⁇ of the membrane tube is obtained to satisfy the following calculation formula.
  • step 2 the above calculation formula can be obtained, which is only for reference here.
  • Step 62 Establish a corresponding relationship between the deformation angle ⁇ of the membrane tube and the relative radial deformation displacement ⁇ of the membrane tube.
  • Step 63 Calculate the deformation angle ⁇ of the film tube. Substituting the relative radial deformation displacement ⁇ of the thin film tube calculated in step 61 into step 62, it is obtained that the deformation angle ⁇ of the thin film tube satisfies the following formula.
  • the relationship between the locking torque M L and the vacuum pressure P as shown in Fig. 12 is obtained. It can be seen from the figure that the greater the vacuum pressure P, the greater the locking torque M L. Therefore, the stiffness of the mechanism can be controlled by adjusting the vacuum pressure.
  • the relationship between the locking torque M L and the radius R 3 of the small spherical particles shown in Fig. 13 is obtained. It can be seen from the figure that the larger the radius R 3 of the pellets, the smaller the locking torque M L. And as the size of small particles decreases, the decrease of the locking torque M L becomes smaller and smaller under the same size reduction.
  • the relationship between the locking torque M L and the radius size R2 of the large spherical particles shown in Fig. 15 can be obtained. It can be seen that the larger the radius of the large spherical particles, the larger the locking torque M L. And with the increase of the radius of the large spherical particles, the increase of the locking torque M L becomes larger and larger under the same size increment.
  • the invention first theoretically studies and analyzes the principle of variable stiffness of the plugging variable stiffness structure, first simplifying the modeling, and applying the Pascal model and Hertz contact theory to establish the mechanical model of the plugging mechanism, and derive the locking torque and vacuum at the end of the mechanism
  • the relationship between the pressure, the hardness of the small spherical particles and the radius of the large spherical particles The relationship between the stiffness of the mechanism and the degree of vacuum, the radius of the diamond skeleton and the size of the large spherical particles is obtained, and the simulation analysis is performed. It is convenient for the subsequent design of the cavity shape and wall thickness of the driver to have better bending performance and better meet the design requirements.

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  • Engineering & Computer Science (AREA)
  • Robotics (AREA)
  • Mechanical Engineering (AREA)
  • Health & Medical Sciences (AREA)
  • General Health & Medical Sciences (AREA)
  • Orthopedic Medicine & Surgery (AREA)
  • Automation & Control Theory (AREA)
  • Manipulator (AREA)

Abstract

Un procédé de construction de modèle destiné à un robot mou à rigidité variable, comprend : étape 1, la conception d'une force de verrouillage entre des particules de charge ; étape 2, le calcul d'une pression équivalente dans un tube à film mince (31) ; étape 3, la mise en place d'une relation de correspondance entre la force de verrouillage et une pression de vide dans le tube à film mince (31) ; étape 4, la conception d'un couple de verrouillage d'un bloc de particules ; étape 5, la mise en place d'une relation de correspondance entre le couple de verrouillage et une dureté de petites particules sphériques (35) ; et étape 6, le calcul d'un angle de déformation du tube à film mince (31). Le procédé traite toutes les particules de charge (34, 35) dans le tube à film mince (31) et le tube à film mince (31) en tant que bloc de particules intégré, considère les petites particules sphériques (35) comme équivalent à un fluide et le tube à film mince (31) comme équivalent à un espace fermé, et établit un modèle hertzien de contact sphère-plan. Des modèles liés à la force de verrouillage et au couple de verrouillage sont établis selon la théorie de contact de Hertz et un modèle hertzien de contact de deux sphères. De cette manière, l'invention permet de commander la rigidité du robot mou à rigidité variable, et le modèle établi est fiable étant donné que le résultat obtenu par simulation de caractéristique à rigidité variable est conforme au modèle.
PCT/CN2020/100791 2019-10-29 2020-07-08 Procédé de construction de modèle pour robot mou à rigidité variable Ceased WO2021082520A1 (fr)

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CN113319889B (zh) * 2021-06-15 2024-02-23 西北工业大学 用于强化软体刚度的填充颗粒及系列化的应用
CN116818613B (zh) * 2023-06-30 2025-10-28 山东高速集团有限公司 一种颗粒间哈梅克常数的确定方法

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