A single-axis force sensor based on three nested elastic circular rings

Abstract

The application relates to a single-axis force sensor based on three nested elastic circular rings, which comprises a shell, three elastic circular rings, a bearing, a fixing rod, a support plate, an extrusion piece, side plates, a base, a laser range finder and a main control assembly, the two side plates are fixed as a whole through the base and three support plates; the three elastic circular rings are arranged on the support plates in a nested mode; the bearing is installed at the top of the three elastic circular rings and nests the top of the three elastic circular rings together through the fixing rod, so that the three elastic circular rings are synchronously stressed when external force is loaded; the laser range finder is electrically connected with the main control assembly on the shell to send measurement data to the main control assembly, and the main control assembly calculates the size of the measured external force according to a function relation curve between the external force and the height of the three nested elastic circular rings. The force sensor has the advantages of simple structure, low manufacturing cost, light weight, easy use, high accuracy and reliability in the measurement process.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of force sensors, and particularly relates to a single-axis force sensor based on three nested elastic circular rings. BACKGROUND

[0002] As an important measuring device of basic physical quantities, force sensors play a vital role in various fields such as industry, healthcare and automation. Since force is difficult to measure directly, force sensors usually convert the measured external force into other physical quantities that are easy to measure. For example, displacement type force sensors, resistance type force sensors and capacitance type force sensors. However, these force sensors often have complex structures, more internal components, higher manufacturing process requirements, greater weight, shorter service life and poorer adaptability. In addition, they usually also face the problem of larger measurement error. Some force sensors with smaller measurement error usually have higher cost, which is difficult to meet the needs of the development of society. SUMMARY

[0003] Therefore, the purpose of the present application is to provide a single-axis force sensor based on three nested elastic circular rings, which has simple structure, low manufacturing cost, light weight, easy to use, and shows high accuracy and reliability in the measurement process.

[0004] To achieve the above object, the application adopts the following technical scheme: a single-axis force sensor based on three nested elastic rings, comprising a shell (1), a small elastic ring (4), a middle elastic ring (5), a large elastic ring (6), a bearing (25), a first fixed rod (18), a second fixed rod (20), a third fixed rod (22), a fourth fixed rod (24), a first support plate (12), a second support plate (13), a third support plate (15), a first extrusion piece (3), a second extrusion piece (7), a third extrusion piece (8), a fourth extrusion piece (9), a fifth extrusion piece (17), a sixth extrusion piece (19), a seventh extrusion piece (21), an eighth extrusion piece (23), a first side plate (11), a second side plate (16), a base (14), a laser range finder (10) and a main control component (2), the first side plate (11) and the second side plate (16) are integrated by the base (14) and the first support plate (12), the second support plate (13) and the third support plate (15), the base (14) is installed on the bottom surface in the shell (1), and the shell (1) is used for protecting the internal components; the small elastic ring (4), the middle elastic ring (5) and the large elastic ring (6) are arranged in a nested form on the first support plate (12), the second support plate (13) and the third support plate (15), and the bottoms thereof are fixed by the first fixed rod (18), the second fixed rod (20), the third fixed rod (22) and the second extrusion piece (7), the third extrusion piece (8), the fourth extrusion piece (9), the fifth extrusion piece (17), the sixth extrusion piece (19) and the seventh extrusion piece (21); the three nested small elastic ring (4), middle elastic ring (5) and large elastic ring (6) can change the height of the static configuration under the action of external force, and correspond to different static configuration heights under different external forces; the bearing (25) is installed at the top of the small elastic ring (4), the middle elastic ring (5) and the large elastic ring (6), and the top of the small elastic ring (4), the middle elastic ring (5) and the large elastic ring (6) are nested together by the fourth fixed rod (24) so that the small elastic ring (4), the middle elastic ring (5) and the large elastic ring (6) are synchronously stressed when external force is loaded, and the consistency of height change is ensured; the laser range finder (10) is installed on one side of the first side plate (11) and has a detection direction upward to measure the change of the height of the elastic ring, and the laser range finder (10) is electrically connected with the main control component (2) on the shell (1) to send the measurement data to the main control component (2), and the main control component (2) calculates the size of the measured external force according to the functional relationship curve between the external force and the height of the small elastic ring (4), the middle elastic ring (5) and the large elastic ring (6).

[0005] In a preferred embodiment, the function relationship curve between the external force and the height of the small elastic ring (4), the medium elastic ring (5) and the large elastic ring (6) is calculated by the balance equation of the static configuration of the small elastic ring (4), the medium elastic ring (5) and the large elastic ring (6);

[0006] The small elastic ring (4), the medium elastic ring (5) and the large elastic ring (6) are deformed under the vertical external force, at this time, the coordinate system is established, the bottom of the small elastic ring (4), the medium elastic ring (5) and the large elastic ring (6) is anchored at the origin of the Cartesian coordinate system, and the top of the small elastic ring (4), the medium elastic ring (5) and the large elastic ring (6) is subjected to the pressure or tension on the y-axis; considering the similarity of the three nested elastic rings under tension or pressure in subsequent theoretical analysis, the pressure is taken as an example for theoretical analysis; in the initial state without external force, there is no internal force or torque on the small elastic ring (4), the medium elastic ring (5) and the large elastic ring (6); when the pressure F y =F y1 +F y2 +F y3 is loaded on the top of the ring, the small elastic ring (4), the medium elastic ring (5) and the large elastic ring (6) will generate internal force and torque to balance the pressure; with the action of the pressure, the height of the small elastic ring (4), the medium elastic ring (5) and the large elastic ring (6) will decrease until the system reaches a new equilibrium state, and the energy functional of the right half of the small elastic ring (4), the medium elastic ring (5) and the large elastic ring (6) is represented as:

[0007]

[0008] Where, the bending stiffness K1=EI1, K2=EI2 and K3=EI3 are determined by the elastic modulus E and the moments of inertia I1, I2 and I3, respectively, s1, s2 and s3 represent the arc length of the small elastic ring (4), the medium elastic ring (5) and the large elastic ring (6), the bottom of the small elastic ring (4), the medium elastic ring (5) and the large elastic ring (6) and are the origin of the natural coordinate, θ1(s1), θ2(s2) and θ3(s3) represent the deflection angle of any point on the small elastic ring (4), the medium elastic ring (5) or the large elastic ring (6) relative to the x-axis, θ'1(s1)=dθ1 / ds1, θ'2(s2)=dθ2 / ds2 and θ'3(s3)=dθ3 / ds3 represent the curvature, and represent the internal force in the x direction, and and represent the three components of the pressure loaded on the top of the ring, and where M(πR1) = K1θ1'(πR1), M(πR2) = K2θ2'(πR2) and M(πR3) = K3θ3'(πR3) represent the internal moments at the top of the rings, the constraint in the energy functional represents the symmetry of the elastic circular rings with respect to the y-axis, and the energy functional is reformulated as:

[0009]

[0010] where

[0011]

[0012] Assuming that each circular ring curve undergoes a small virtual deformation, i.e. and Expressing the first variation of W as a function of ξ1, ξ2 and ξ3, which are different small positive parameters, we have

[0013]

[0014] Due to the arbitrariness of η1(s1), η2(s2) and η3(s3), the equilibrium equations for the right half rings are obtained as:

[0015]

[0016]

[0017]

[0018] In addition, the inextensible condition of the rings requires that:

[0019] x1'(s1) = cos θ1(s1), y1'(s1) = sin θ1(s1)

[0020] x'2(s2) = cos θ2(s2), y'2(s2) = sin θ2(s2)

[0021] x'3(s3) = cos θ3(s3), y'3(s3) = sin θ3(s3)

[0022] The differential equation set combines continuity conditions: variables (θ1, θ'1, x1, y1, θ2, θ'2, x2, y2, θ3, θ'3, x3, y3) are continuous along a certain elastic circular ring, and boundary conditions: θ1(0) = 0, y1(0) = 0, x1(0) = 0, x1(πR1) = 0, θ1(πR1) = π, θ2(0) = 0, y2(0) = 0, x2(0) = 0, x2(πR2) = 0, θ2(πR2) = π, θ3(0) = 0, y3(0) = 0, x2(0) = 0, x2(πR3) = 0, and θ3(πR3) = π, by combining the above supplementary conditions, the equilibrium configuration of the three nested elastic circular rings under different external forces can be numerically solved.

[0023] According to the above equation, the relationship between the displacement of the top of the circular ring and the pressure is derived, and the original heights of the small elastic circular ring (4), the medium elastic circular ring (5), and the large elastic circular ring (6) are respectively represented as 2R1, 2R2, and 2R3, due to their nested structure, the top of the small elastic circular ring (4), the medium elastic circular ring (5), and the large elastic circular ring (6) exhibit the same downward displacement under the action of the partial pressure and After numerically solving the equilibrium configuration of the elastic circular ring under the pressure and , the displacement Δy of the top of the circular ring can be calculated:

[0024]

[0025] The relationship between the displacement of the top of the small elastic circular ring (4), the medium elastic circular ring (5), and the large elastic circular ring (6) and the applied pressure and is derived by the equation, and the total pressure can be indirectly measured using the ring top displacement Δy.

[0026] In a preferred embodiment, by changing the bending stiffness of the small elastic circular ring (4), the medium elastic circular ring (5), and the large elastic circular ring (6), the functional relationship between the nested small elastic circular ring (4), the medium elastic circular ring (5), and the large elastic circular ring (6) and the loaded external force can be changed, thereby realizing the adjustment of the measurement range of the force sensor.

[0027] In a preferred embodiment, the main control assembly (2) includes a display screen, the display screen is embedded on one side of the shell (1), and the main control assembly (2) displays the calculated external force on the display screen.

[0028] Compared with the prior art, the present application has the following beneficial effects: the present application provides a single-axis force sensor based on three nested elastic circular rings, which changes its static configuration height under the action of external force, and measures the external force by measuring the height change of the elastic circular ring, which is simple in structure, low in manufacturing cost, light in weight, easy to use, and high in accuracy and reliability during measurement. The installation and calibration process of the sensor is simple, and the measurement range can be changed by adjusting the bending stiffness of the elastic circular ring, so as to adapt to different measurement requirements. In addition, the device has stable structure design, good rollover prevention ability, strong adaptability, high strength, and long service life. BRIEF DESCRIPTION OF DRAWINGS

[0029] Figure 1 is a schematic diagram of the composition structure of the force sensor of the embodiment of the present application.

[0030] Figure 2 is a schematic diagram of the overall structure of the force sensor of the embodiment of the present application.

[0031] Figure 3 is a schematic diagram of the connection structure of the three nested elastic circular rings inside the force sensor in the embodiment of the present application.

[0032] Figure 4 is a force analysis diagram of the three nested elastic circular rings under the action of pressure in the embodiment of the present application.

[0033] Figure 5 is a force analysis diagram of the three nested elastic circular rings under the action of tension in the embodiment of the present application.

[0034] Figure 6 is a function relationship diagram of the displacement change of the three nested elastic circular rings and the external force in the embodiment. DETAILED DESCRIPTION

[0035] The present application will be further described below in conjunction with the drawings and embodiments.

[0036] It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the present application belongs.

[0037] It should be noted that the terms used herein are only for the purpose of describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application; as used herein, the singular form is intended to include the plural form unless the context clearly indicates otherwise, and furthermore, it should be understood that when the terms "comprise" and / or "include" are used in the specification, they indicate the presence of a feature, step, operation, device, component and / or combination thereof.

[0038] As Figures 1-6 shown, the embodiment provides a single-axis force sensor based on three nested elastic rings, including a shell 1, a small elastic ring 4, a middle elastic ring 5, a large elastic ring 6, a bearing 25, a first fixed rod 18, a second fixed rod 20, a third fixed rod 22, a fourth fixed rod 24, a first support plate 12, a second support plate 13, a third support plate 15, a first extrusion 3, a second extrusion 7, a third extrusion 8, a fourth extrusion 9, a fifth extrusion 17, a sixth extrusion 19, a seventh extrusion 21, an eighth extrusion 23, a first side plate 11, a second side plate 16, a base 14, a laser range finder 10 and a main control component 2, the first side plate 11 and the second side plate 16 are integrated by the base 14 and the first support plate 12, the second support plate 13 and the third support plate 15, the base 14 is installed on the bottom surface in the shell 1, and the shell is used for protecting the internal components; the small elastic ring 4, the middle elastic ring 5 and the large elastic ring 6 are arranged in a nested form on the first support plate 12, the second support plate 13 and the third support plate 15, and the bottoms thereof are fixed by the first fixed rod 18, the second fixed rod 20, the third fixed rod 22 and the second extrusion 7, the third extrusion 8, the fourth extrusion 9, the fifth extrusion 17, the sixth extrusion 19 and the seventh extrusion 21; the three nested small elastic ring 4, middle elastic ring 5 and large elastic ring 6 can change the height of the static configuration under the action of external force, and correspond to different static configuration heights under different external forces; the bearing 25 is installed on the top of the small elastic ring 4, the middle elastic ring 5 and the large elastic ring 6, and the top of the small elastic ring 4, the middle elastic ring 5 and the large elastic ring 6 are nested together by the fourth fixed rod 24, so that the small elastic ring 4, the middle elastic ring 5 and the large elastic ring 6 are synchronously stressed when external force is loaded, and the consistency of height change is ensured; the laser range finder 10 is installed on one side of the first side plate 11, and the detection direction thereof faces upward, so as to measure the change of the height of the elastic ring, the laser range finder 10 is electrically connected with the main control component 2 on the shell, so as to send the measurement data to the main control component, and the main control component 2 calculates the size of the measured external force according to the functional relationship curve between the external force and the height of the nested small elastic ring 4, middle elastic ring 5 and large elastic ring 6.

[0039] In the embodiment, the functional relationship curve between the external force and the height of the nested small elastic ring 4, middle elastic ring 5 and large elastic ring 6 is calculated by the balance equation of the static configuration of the three nested elastic rings.

[0040] As Figure 4 , 5As shown, the three nested elastic rings deform under the vertical external force, at this time the coordinate system is established, the bottom of the three rings is anchored at the origin of the Cartesian coordinate system, while their top is subjected to pressure or tension on the y-axis. Considering the similar theoretical analysis for three nested elastic rings under tension or pressure, the pressure is taken as an example of theoretical analysis. Considering the symmetry of the three nested elastic rings with respect to the y-axis, in order to simplify the problem, we will only analyze the configuration of the right half. In the initial state without external force, there is no internal force or torque on the ring. When the pressure is loaded on the top of the ring, the ring will generate internal force and torque to balance this pressure. With the action of pressure, the height of the ring will decrease until the system reaches a new equilibrium state, and the energy functional of the right half of these rings can be expressed as:

[0041]

[0042] where the bending stiffness K1=EI1, K2=EI2 and K3=EI3 are determined by the elastic modulus E and the moments of inertia I1, I2 and I3, respectively, s1, s2 and s3 represent the arc length of the three elastic rings, and the bottom of each ring and is the origin of the natural coordinate, θ1(s1), θ2(s2) and θ3(s3) represent the deflection angle of any point on each ring with respect to the x-axis, θ'1(s1)=dθ1 / ds1, θ'2(s2)=dθ2 / ds2 and θ'3(s3)=dθ3 / ds3 represent the curvature, and represent the internal force in the x direction, and and represent the three components of the pressure loaded on the top of the ring, and represent the internal torque at the bottom of the ring, and M(πR1)=K1θ1'(πR1), M(πR2)=K2θ2'(πR2) and M(πR3)=K3θ3'(πR3) represent the internal torque at the top of the ring, the constraint in the energy functional represents the symmetry of the elastic ring with respect to the y-axis, and the energy functional can be rewritten as:

[0043]

[0044] where,

[0045] ,

[0046] Assuming that each circular curve undergoes a small virtual deformation, i.e. and Taking ξ1, ξ2 and ξ3 as different small positive parameters, the first-order variation of W can be expressed as

[0047]

[0048] Due to the arbitrariness of η1(s1), η2(s2) and η3(s3), the equilibrium equation of the right semi-ring is obtained:

[0049]

[0050]

[0051]

[0052] In addition, the inextensible condition of the ring requires:

[0053] x1'(s1) = cosθ1(s1), y1'(s1) = sinθ1(s1)

[0054] x'2(s2) = cosθ2(s2), y'2(s2) = sinθ2(s2)

[0055] x'3(s3) = cosθ3(s3), y'3(s3) = sinθ3(s3)

[0056] The differential equation set combines the continuity condition that the variables (θ1, θ'1, x1, y1, θ2, θ'2, x2, y2, θ3, θ'3, x3, y3) are continuous along a certain elastic circular ring, and the boundary condition that θ1(0) = 0, y1(0) = 0, x1(0) = 0, x1(πR1) = 0, θ1(πR1) = π, θ2(0) = 0, y2(0) = 0, x2(0) = 0, x2(πR2) = 0, θ2(πR2) = π, θ3(0) = 0, y3(0) = 0, x2(0) = 0, x2(πR3) = 0 and θ3(πR3) = π, and by combining the above supplementary conditions, the equilibrium configuration of the three nested elastic circular rings under different external forces can be numerically solved.

[0057] In this embodiment, the radius of the small elastic circular ring 4 is 2.801 cm, the thickness is 1.13 mm, the width is 2.006 cm, the elastic modulus is 2.05 GPa, the radius of the medium elastic circular ring 5 is 3.599 cm, the thickness is 1.31 mm, the width is 2.007 cm, the elastic modulus is 2.05 GPa, the radius of the large elastic circular ring 5 is 4.399 cm, the thickness is 1.63 mm, the width is 2.008 cm, the elastic modulus is 2.05 GPa, and the overall length of the entire force sensor is 98 mm, the width is 70 mm, and the height is 88 mm.

[0058] According to the above equation, the relationship between the displacement of the top of the circular ring and the pressure can be derived, and the original heights of the three elastic circular rings are represented as 2R1, 2R2 and 2R3, respectively. Due to their nested structure, the top of the three elastic circular rings shows the same downward displacement under the action of the partial pressure and . After numerically solving the equilibrium configuration of the elastic circular ring under the action of the pressure and , the displacement Δy of the top of the circular ring can be calculated:

[0059]

[0060] The relationship between the displacement of the top of the three nested elastic circular rings and the applied pressure and can be derived from the equation. By using the displacement Δy of the top of the ring, the total pressure A similar method is also applicable to the analysis of the tensile force.

[0061] As shown in Figure 6 , the displacement of the top of the three nested elastic circular rings and the applied external force show a nonlinear relationship, and it can be concluded that the pressure measurement range of the force sensor is 0-38N, and the measurement accuracy is 0.69%. The measurement range of the tensile force is 0-83N, and the measurement accuracy is 0.77%.

[0062] By changing the bending stiffness of the three elastic circles, the functional relationship between the three nested elastic circular rings and the applied external force can be changed, and thus the measurement range of the force sensor can be adjusted.

[0063] From the above analysis, it can be seen that the force sensor provided by the present application can accurately measure the external force. When no external force is applied, the carrier 25 is in an initial state, and the laser range finder 10 measures the initial heights of the three nested elastic circular rings. When an external force is applied to the carrier, the heights of the three nested small elastic circular rings 4, the middle elastic circular ring 5 and the large elastic circular ring 6 will change consistently. At this time, the laser range finder 10 measures the heights of the elastic circular rings after the external force is applied, and transmits the changed height data to the main control component 2. The main control component 2 calculates the applied external force according to the nonlinear relationship between the displacement of the top of the three nested elastic circular rings and the applied external force, and displays the calculation result on the display screen of the main control component 2.

[0064] The above merely describes preferred embodiments of the present application, but is not intended to limit the present application to other forms, and any person skilled in the art can make changes or modifications to the above disclosed technical contents into equivalent embodiments with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiments without departing from the technical solution content of the present application and according to the technical essence of the present application still belongs to the protection scope of the technical solution of the present application.

Claims

1. A single-axis force sensor based on three nested elastic tori, characterized in that, The application relates to a height change measuring device, which comprises a shell (1), a small elastic ring (4), a medium elastic ring (5), a large elastic ring (6), a bearing (25), a first fixing rod (18), a second fixing rod (20), a third fixing rod (22), a fourth fixing rod (24), a first supporting plate (12), a second supporting plate (13), a third supporting plate (15), a first extruding piece (3), a second extruding piece (7), a third extruding piece (8), a fourth extruding piece (9), a fifth extruding piece (17), a sixth extruding piece (19), a seventh extruding piece (21), an eighth extruding piece (23), a first side plate (11), a second side plate (16), a base (14), a laser range finder (10) and a main control assembly (2), the first side plate (11) and the second side plate (16) are combined into one through the base (14) and the first supporting plate (12), the second supporting plate (13) and the third supporting plate (15), the base (14) is arranged on the bottom surface in the shell (1), and the shell (1) is used for protecting internal components; the small elastic ring (4), the medium elastic ring (5) and the large elastic ring (6) are arranged on the first supporting plate (12), the second supporting plate (13) and the third supporting plate (15) in a nested mode, and the bottoms of the small elastic ring (4), the medium elastic ring (5) and the large elastic ring (6) are fixed through the first fixing rod (18), the second fixing rod (20), the third fixing rod (22) and the second extruding piece (7), the third extruding piece (8), the fourth extruding piece (9), the fifth extruding piece (17), the sixth extruding piece (19) and the seventh extruding piece (21); the three nested small elastic ring (4), medium elastic ring (5) and large elastic ring (6) can change the height of a static configuration under the action of external force, and correspond to different static configuration heights under different external forces; the bearing (25) is arranged at the top of the small elastic ring (4), the medium elastic ring (5) and the large elastic ring (6), and the top of the small elastic ring (4), the medium elastic ring (5) and the large elastic ring (6) are nested together through the fourth fixing rod (24), so that the small elastic ring (4), the medium elastic ring (5) and the large elastic ring (6) are synchronously stressed when external force is loaded, and the consistency of height change is ensured; the laser range finder (10) is arranged on one side of the first side plate (11) and faces upwards, so as to measure the height change of the elastic ring; the laser range finder (10) is electrically connected with the main control assembly (2) on the shell (1), so as to send the measured data to the main control assembly (2); and the main control assembly (2) calculates the size of the measured external force according to a functional relationship curve between the external force and the height of the small elastic ring (4), the medium elastic ring (5) and the large elastic ring (6).

2. A single-axis force sensor based on three nested elastic circular rings according to claim 1, characterized in that, The functional relationship curve between the external force and the height of the small elastic ring (4), the medium elastic ring (5) and the large elastic ring (6) is calculated through a balance equation of a static configuration of the small elastic ring (4), the medium elastic ring (5) and the large elastic ring (6); The small elastic ring (4), the middle elastic ring (5) and the large elastic ring (6) are deformed under the action of vertical external force, at this time, a coordinate system is established, the bottom of the small elastic ring (4), the middle elastic ring (5) and the large elastic ring (6) is anchored at the origin of the Cartesian coordinate system, and the top of the small elastic ring (4), the middle elastic ring (5) and the large elastic ring (6) is subjected to pressure or tension on the y-axis; considering the similarity of the three nested elastic rings under tension or pressure in subsequent theoretical analysis, the pressure is taken as an example for theoretical analysis; in the initial state without external force, there is no internal force or torque on the small elastic ring (4), the middle elastic ring (5) and the large elastic ring (6); when the pressure = + + is loaded on the top of the ring, the small elastic ring (4), the middle elastic ring (5) and the large elastic ring (6) will generate internal force and torque to balance the pressure; with the action of the pressure, the height of the small elastic ring (4), the middle elastic ring (5) and the large elastic ring (6) will decrease until the system reaches a new equilibrium state, and the energy functional of the right half of the small elastic ring (4), the middle elastic ring (5) and the large elastic ring (6) is represented as: where the bending stiffness , and are determined by the elastic modulus E and the moment of inertia and , and denote the arc length of the small elastic ring (4), the medium elastic ring (5) and the large elastic ring (6), the bottom of the small elastic ring (4), the medium elastic ring (5) and the large elastic ring (6) (s1 = 0), (s2 = 0) and (s3 =0) are the origin of the natural coordinate, (s1), (s2) and (s3) denote the deflection angle of any point on the small elastic ring (4), the medium elastic ring (5) or the large elastic ring (6) relative to the x-axis, = d / d , = d / d and = d / d represent the curvature, , and denote the internal force in the x direction, and , and denote the three components of the load on the ring top pressure, the constraint in the energy functional represents the symmetry of the elastic ring relative to the y-axis, and the energy functional is re-expressed as: In addition, the non-stretching condition of the ring requires that , assuming each circular arc undergoes a small virtual deformation, i.e. + , + and + , with , and as different small positive parameters, the first order variation of W is expressed as Due to the arbitrariness of , and , the balance equation of the right half ring is obtained: ​ Differential equations combined with continuity conditions: variables , , , , , , , , , , , ) are continuous along a certain elastic circular ring, and boundary conditions: , (0) = 0, (0) = 0, (π ) = 0, (π ) = π, , (0) = 0, (0) = 0, (π ) = 0, (π ) = π, , (0) = 0, (0) = 0, (π ) = 0 and (π ) = π, By combining the above supplementary conditions, the equilibrium configuration of three nested elastic circular rings under different external forces can be numerically solved; The relationship between the displacement of the top of the ring and the pressure is derived, and the original heights of the small elastic ring (4), the medium elastic ring (5) and the large elastic ring (6) are respectively represented as 2 , 2 and 2 . Under the action of the partial pressures , and , the tops of the small elastic ring (4), the medium elastic ring (5) and the large elastic ring (6) exhibit the same downward displacement due to their nested structure; after the equilibrium configuration of the elastic ring under the pressures , and is solved numerically, the displacement of the top of the ring, Δy, can be calculated. The relationship between the displacement of the top of the small elastic ring (4), the medium elastic ring (5), the large elastic ring (6) and the applied pressure is derived from the equation, using the ring top displacement Δy, the total pressure can be indirectly measured , and = + + .​ 3. A single-axis force sensor based on three nested elastic circular rings according to claim 2, characterized in that, By changing the bending stiffness of the small elastic ring (4), the medium elastic ring (5) and the large elastic ring (6), the functional relationship between the nested small elastic ring (4), the medium elastic ring (5) and the large elastic ring (6) and the loaded external force is changed, and then the adjustment of the measurement range of the force sensor is realized.

4. A single-axis force sensor based on three nested elastic circular rings according to claim 1, characterized in that, The main control assembly (2) includes a display screen, the display screen is embedded on one side of the shell (1), and the main control assembly (2) displays the calculated external force on the display screen.

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