Force measuring device based on height change of three deformable round elementsTechnical Field
The invention relates to the technical field of force measurement, in particular to a force measuring device based on height change of three deformable round elements.
Background
With advances in technology and improvements in the living standard of people, there is an increasing demand for high performance force measuring devices. These devices have found wide application in a number of fields including industrial automation, medical diagnostics, food production, biomechanics, etc. Common force measuring devices include magnetic induction force measuring devices, piezoelectric force measuring devices, optical fiber force measuring devices and the like. Although these force measuring devices perform well in certain scenarios, challenges remain in terms of accuracy, weight, and cost. Current force measuring devices typically rely on complex sensor systems or mechanical structures to achieve force measurement, which not only results in a device of high weight, but also makes manufacturing and maintenance costs prohibitive, limiting their use in a wider range of fields. Furthermore, some high precision force measuring devices, while capable of providing reliable measurement results, have complex structures that make the operation and maintenance process cumbersome.
Disclosure of Invention
In view of the above, the present invention aims to provide a force measuring device based on the height change of three deformable round elements, which provides a force measuring solution with high precision, light weight and economical efficiency through a unique design, and significantly improves the practicability and popularity of the force measuring device.
In order to achieve the aim, the force measuring device based on the height change of three deformable round elements comprises a shell (1), a first deformable round element (9), a second deformable round element (10), a third deformable round element (11), a load bearing unit (18), a first connecting plate (3), a second connecting plate (4), a third connecting plate (5), a fourth connecting plate (6), a fifth connecting plate (7), a first plate pair (13), a second plate pair (14), a third plate pair (15), a fourth plate pair (16), a fifth plate pair (17), a bottom plate (12), a laser distance meter (8) and a display control module (2), wherein the bottoms of the first deformable round element (9), the second deformable round element (10) and the third deformable round element (11) are fixed on the bottom plate (12) after being rotated, and the bottoms are firmly fixed through the fourth connecting plate (6), the fifth connecting plate (7) and the first plate pair (13) and the second plate pair (14), the first deformable round element (9), the second deformable round element (10) and the third deformable round element (11) are subjected to static external force change, the load bearing unit (18) is arranged at the top of the first deformable round element (9), the second deformable round element (10) and the third deformable round element (11) and is integrated with the first connecting plate (3), the second connecting plate (4), the third connecting plate (5) and the third plate pair (15), the fourth plate pair (16) and the fifth plate pair (17) through the first connecting plate, the second connecting plate, the third connecting plate (5) and the third plate pair (15) so as to ensure that the first deformable round element (9), the second deformable round element (10) and the third deformable round element (11) are stressed synchronously under the action of different external forces, so that the consistency of the height change is maintained, the laser range finder (8) is arranged at one side of the shell (1) and the detection direction of the laser range finder is upward so as to measure the height change of the first deformable round element (9), the second deformable round element (10) and the third deformable round element (11), the laser range finder (8) is electrically connected with a display control module (2) on the shell so as to ensure that the real-time function between the first deformable round element (9) and the second deformable round element (11) can be electrically connected with the display control module (2) according to the measured real-time deformation curve, the magnitude of the external force is calculated and determined.
In a preferred embodiment, the functional relationship between the external force and the heights of the first deformable circular element (9), the second deformable circular element (10) and the third deformable circular element (11) is obtained by solving three deformable circular element static balance equations;
The first deformable round element (9), the second deformable round element (10) and the third deformable round element (11) deform under the action of vertical external force, the first deformable round element (9), the second deformable round element (10) and the third deformable round element (11) all follow a theoretical model between the external force and the top displacement of the round elements, a coordinate system is established at the moment, the bottom of the first deformable round element (9), the second deformable round element (10) and the third deformable round element (11) is fixed at the origin of the Cartesian coordinate system, the top is stressed by pressure or pulling force on the y axis, the pressure is taken as an example of theoretical analysis when the deformable round elements are stressed by the following theoretical analysis, the first deformable round element (9), the second deformable round element (10) and the third deformable round element (11) are not affected by internal force or torque in the initial state without the external force, and when the pressure is appliedThe first (9), the second (10) and the third (11) deformable circular elements generate internal forces and torques to balance the pressure when the top of the circular elements, the heights of the first (9), the second (10) and the third (11) deformable circular elements decrease with the application of the pressure until the system reaches a new balance state, and the energy functions of the right half parts of the first (9), the second (10) and the third (11) deformable circular elements are expressed as:
Wherein i=1, 2,3 respectively represent the first deformable circular element (9), the second deformable circular element (10) and the third deformable circular element (11), the bending stiffness Ki＝EIi of the first deformable circular element (9), the second deformable circular element (10) and the third deformable circular element (11) is the elastic modulus, Ii is the corresponding moment of inertia, i=1, 2,3 respectively determined by the elastic modulus and the moment of inertia, s1,s2 and s3 respectively represent the arc length of the first deformable circular element (9), the second deformable circular element (10) and the third deformable circular element (11), and the bottoms of the first deformable circular element (9), the second deformable circular element (10) and the third deformable circular element (11) are respectively provided with the elastic modulus and the moment of inertiaAndIs the origin of natural coordinates, the deflection angles of any point on the first deformable round element (9), the second deformable round element (10) and the third deformable round element (11) relative to the x axis are respectively expressed by theta1(s1),θ2(s2) and theta3(s3), and theta'i(si)＝dθi/dsi (i=1, 2, 3) represents curvature, and the component of the internal force along the x direction is expressed byAndRepresenting the three components of the pressure applied to the top of the first (9), second (10) and third (11) deformable circular elements, respectivelyAndThe internal moment at the bottom of the first deformable round element (9), the second deformable round element (10) and the third deformable round element (11) is represented byThe internal moment at the top is represented by M (pi Ri)＝Kiθ'i(πRi) (i=1, 2, 3), the constraints in the energy functional represent the symmetry of the first (9), second (10) and third (11) deformable circular elements with respect to the y-axis, and finally the energy functional is restated as:
in the formula,I.e.Where ζ1,ξ2 and ζ3 are different small positive parameters, the first order variation of W is denoted as:
considering any of η1(s1),η2(s2) and η3(s3), the derivation of the equilibrium equation for the right half of the first (9), second (10) and third (11) deformable circular elements is as follows:
wherein i=1, 2,3, and in addition, the deformable circular element satisfies the non-stretchable condition
xi′(si)＝cosθi(si),yi′(si)＝sinθi(si)
Firstly, taking into consideration a differential equation set and continuity conditions, wherein the continuity conditions comprise that a variable (θ1,θ'1,x1,y1,θ2,θ'2,x2,y2,θ3,θ'3,x3,y3); is continuous on the first deformable round element (9), the second deformable round element (10) and the third deformable round element (11), and furthermore, the boundary conditions ：θi(0)＝0,yi(0)＝0,xi(0)＝0,xi(πRi)＝0,θi(πRi)＝π(i＝1,2,3), are met, and the balance states of the first deformable round element (9), the second deformable round element (10) and the third deformable round element (11) are numerically solved by integrating the continuity conditions;
Deriving the relationship between the top displacement of the first (9), second (10) and third (11) deformable circular elements and the applied pressure according to the above equation, the initial heights of the first (9), second (10) and third (11) deformable circular elements being 2R1,2R2 and 2R3 respectively, and the differential pressure due to their connection structureAndThe top of the first (9), second (10) and third (11) deformable circular elements are displaced downwards in the same way, and the displacement deltay of the top of the first (9), second (10) and third (11) deformable circular elements is further calculated by numerically solving the first (9), second (10) and third (11) deformable circular elements under these partial pressures:
Wherein i=1, 2,3;
Deriving the displacement and the applied pressure of the top of the first (9), second (10) and third (11) deformable circular elementsAndThe relation between the first (9), second (10) and third (11) deformable circular elements is determined indirectly by measuring the displacement of the top of the circular elements, and the total pressure is calculated indirectly by accumulating the pressures exerted by the first (9), second (10) and third (11) deformable circular elements due to the same displacement of the top of the first (9), second (10) and third (11) deformable circular elementsA similar method is also suitable for analyzing the tension.
In a preferred embodiment, the bending stiffness of the deformable circular elements is adjusted, so that the top displacement of the first deformable circular element (9), the second deformable circular element (10) and the third deformable circular element (11) can be changed as a function of the applied external force, and the adjustment of the measuring range of the force measuring device is realized.
In a preferred embodiment, the display control module (2) comprises a display screen, the display screen is embedded in one side of the housing, and the display control module displays the calculated external force value on the display screen.
Compared with the prior art, the invention has the following beneficial effects:
(1) The force measuring device is based on the principle that the static configuration height of three deformable round elements can be changed under the action of external force to realize the measurement of the external force, has the advantages of simple structure, low manufacturing cost, light weight and easy operation, and shows higher accuracy and reliability in the measuring process.
(2) In order to accommodate different measuring ranges, the force measuring device allows for manufacturing by adjusting the dimensional parameters of the three deformable circular elements or using materials with a larger modulus of elasticity. This flexibility enables the device to meet a variety of measurement requirements.
(3) The force measuring device has excellent structural stability and long service life. The method has high repeatability, strong environmental adaptability and simple and convenient installation and replacement process. These characteristics make the device very durable and easy to maintain in practical applications.
Drawings
FIG. 1 is a schematic view of the constitution of a force measuring device according to an embodiment of the present invention;
FIG. 2 is a schematic view of the overall structure of a force measuring device according to an embodiment of the invention;
FIG. 3 is a schematic view of the connection structure of the first deformable circular element, the second deformable circular element and the third deformable circular element inside the force measuring device according to the embodiment of the present invention;
FIG. 4 is a graph showing force analysis of a first deformable circular element, a second deformable circular element, and a third deformable circular element under pressure in an embodiment of the present invention;
FIG. 5 is a diagram showing the force analysis of the first, second, and third deformable circular elements under tension in an embodiment of the present invention;
FIG. 6 is a plot of the change in displacement of the first deformable circular element, the second deformable circular element, and the third deformable circular element as a function of external force in an embodiment.
Detailed Description
The invention will be further described with reference to the accompanying drawings and examples.
It should be noted that the following detailed description is illustrative and is intended to provide further explanation of the application. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It should be noted that the terms used herein are merely used to describe specific embodiments and are not intended to limit exemplary embodiments in accordance with the present application, and as used herein, singular forms are intended to include plural forms unless the context clearly indicates otherwise, and furthermore, it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they refer to the presence of features, steps, operations, devices, components and/or combinations thereof.
As shown in fig. 1 to 6, the present embodiment provides a force measuring device based on a height change of three deformable circular elements, comprising a housing 1, a first deformable circular element 9, a second deformable circular element 10, a third deformable circular element 11, a load bearing unit 18, a first connecting plate 3, a second connecting plate 4, a third connecting plate 5, a fourth connecting plate 6, a fifth connecting plate 7, a first plate pair 13, a second plate pair 14, a third plate pair 15, a fourth plate pair 16, a fifth plate pair 17, a bottom plate 12, a laser range finder 8 and a display control module 2, wherein the bottoms of the first deformable circular element 9, the second deformable circular element 10 and the third deformable circular element 11 are fixed on the bottom plate after being rotated by a specific angle, and are ensured to be firmly fixed by the fourth connecting plate 6, the fifth connecting plate 7, the first plate pair 13 and the second plate pair 14; the first, second and third deformable round elements 9, 10 and 11 can change the height of their static configuration under the action of external force and correspond to different static configuration heights under the action of different external force, the load bearing units 18 are arranged on the tops of the three deformable round elements and are integrated into a whole through the first, second and third connecting plates 3, 4, 5 and the third, fourth and fifth plate pairs 15, 16 and 17 to ensure that the first, second and third deformable round elements 9, 10 and 11 can synchronously bear force when the external force is applied, thereby keeping the consistency of the height change, the laser range finder 8 is arranged on one side of the shell 1 and the detection direction is upward, the laser range finder 8 is electrically connected with the display control module 2 on the shell to transmit real-time measurement data to the display control module, and the display control module 2 calculates and determines the magnitude of the external force according to a predetermined functional relation curve between the external force and the heights of the first deformable round element 9, the second deformable round element 10 and the third deformable round element 11.
In this embodiment, the functional relationship between the external force and the heights of the first, second and third deformable circular elements 9, 10, 11 is obtained by solving the static balance equation of the first, second and third deformable circular elements 9, 10, 11;
As shown in fig. 4 and 5, the first deformable circular element 9, the second deformable circular element 10 and the third deformable circular element 11 deform under the action of a vertical external force, and a coordinate system is established at this time because each deformable circular element follows a theoretical model between the external force and the displacement of the top of the circular element, the bottom of the first deformable circular element 9, the second deformable circular element 10 and the third deformable circular element 11 is fixed at the origin of the cartesian coordinate system, and the top is subjected to a compressive force or a tensile force on the y axis. In view of a similar theoretical analysis, for a deformable circular element, when subjected to a tensile or compressive force, a compressive force is taken as a case of the theoretical analysis. While considering the symmetry of the deformable circular element with respect to the y-axis, we only studied the configuration of the right half thereof in order to simplify the analysis. In an initial state without external forces, the three deformable circular elements are not affected by internal forces or torques. When pressure is appliedAt the top of the circular elements, three deformable circular elements will generate internal forces and torques to balance the pressure. As pressure is applied, the height of the circular element will decrease until the system reaches a new equilibrium state. At this time, the energy functional of the right half of the three deformable circular elements can be expressed as:
Where i=1, 2,3 represents three deformable circular elements. The bending stiffness Ki＝EIi (E is the elastic modulus, Ii is the corresponding moment of inertia, i=1, 2, 3) of each deformable circular element is determined by the elastic modulus and moment of inertia, respectively. s1,s2 and s3 represent the arc lengths of three circular elements, the bottom of each circular elementAndIs the origin of the natural coordinates. The deflection angle of any point on each circular element relative to the x-axis is expressed in terms of θ1(s1),θ2(s2) and θ3(s3), respectively, θ'i(si)＝dθi/dsi (i=1, 2, 3) represents the curvature, and the component of the internal force in the x-direction is defined byAndRepresenting the three components of the pressure applied to the top of the circular element asAndThe internal moment of the bottom of the circular element is defined byThe internal torque at the top is represented by M (pi Ri)＝Kiθ'i(πRi) (i=1, 2, 3). The constraints in the energy functional reflect the symmetry of the circular element with respect to the y-axis. Finally, the energy function can be restated as:
in the formula,Assuming that each circular element curve undergoes a slight virtual deformation, i.eWhere ζ1,ξ2 and ζ3 are different small positive parameters, the first order variation of W can be expressed as:
Considering any of η1(s1),η2(s2) and η3(s3), the derivation of the equilibrium equation for the right half of the three deformable circular elements is as follows:
where i=1, 2,3. Furthermore, the deformable circular element satisfies the non-stretchable condition
xi′(si)＝cosθi(si),yi′(si)＝sinθi(si)
The equilibrium configuration of the three deformable circular elements under the action of different external forces can be solved numerically by combining the following conditions. First, consider a set of differential equations and continuity conditions, which include that the variables (θ1,θ'1,x1,y1,θ2,θ'2,x2,y2,θ3,θ'3,x3,y3) should be continuous on each deformable circular element. In addition, boundary conditions ：θi(0)＝0,yi(0)＝0,xi(0)＝0,xi(πRi)＝0,θi(πRi)＝π(i＝1,2,3), are also required to be satisfied, and by integrating the conditions, the equilibrium states of the three deformable circular elements can be solved numerically;
in this embodiment, the radius of the third deformable circular element 11 is 2cm, the thickness is 0.62mm, the width is 1.6cm, the elastic modulus is 2.75GPa, the radius of the second deformable circular element 10 is 3cm, the thickness is 0.94mm, the width is 1.8cm, the elastic modulus is 2.75GPa, the radius of the first deformable circular element 9 is 4cm, the thickness is 1.26mm, the width is 2cm, the elastic modulus is 2.75GPa, the overall length of the entire force sensor is 120mm, the width is 100mm, and the height is 120mm.
From the above equation, the relationship between the deformable circular element top displacement and the applied pressure can be deduced. The initial heights of the three deformable circular elements were 2R1,2R2 and 2R3, respectively. Due to their connection structure, at partial pressureAndThe same downward displacement of the top of these deformable circular elements occurs under the influence of (a). By numerically solving the deformable circular element under these partial pressures, the displacement Δy of the top of the deformable circular element can be further calculated:
Where i=1, 2,3.
The displacement of the top of the three deformable circular elements and the applied pressure can be deduced by equationsAndThe relationship between them, and thus, by measuring the displacement of the top of the circular element, the applied pressure can be determined indirectly. Since the displacement of the tops of the three deformable circular elements is the same, the total pressure can be calculated indirectly by summing the pressures to which the three deformable circular elements are subjectedA similar method is also suitable for analyzing the tension.
As shown in fig. 6, the displacement of the top of the three deformable circular elements and the applied external force show a nonlinear relationship, and the pressure measurement range of the force sensor can be obtained to be 0-18N, the measurement precision is 1.9%, the measurement range of the pulling force is 0-26N, and the measurement precision is 1.7%.
By changing the bending stiffness of the elastic circle, the functional relation between the first deformable circular element 9, the second deformable circular element 10 and the third deformable circular element 11 and the loaded external force can be changed, so that the adjustment of the measuring range of the force measuring device can be realized.
From the analysis, the force measuring device provided by the invention can accurately measure the external force. When no external force is applied, the load bearing unit 18 is in the original state, and the laser rangefinder 8 measures the initial heights of the first deformable circular element 9, the second deformable circular element 10, and the third deformable circular element 11. When an external force is applied to the load bearing unit, the heights of the first, second and third deformable circular elements 9, 10, 11 change uniformly. At this time, the laser rangefinder 8 measures the height of the deformable circular element after the external force is applied, and transmits the changed height data to the display control module 2, and the display control module 2 calculates according to the nonlinear relationship between the displacement of the top of the three deformable circular elements and the applied external force, thereby determining the applied external force, and displaying the calculation result on the display screen of the display control module 2.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the invention in any way, and any person skilled in the art may make modifications or alterations to the disclosed technical content to the equivalent embodiments. However, any simple modification, equivalent variation and variation of the above embodiments according to the technical substance of the present invention still fall within the protection scope of the technical solution of the present invention.