A weighing system and a nonlinear adjustment method

By adjusting the tilt angle of the beam sensor and using structural adjustment methods such as wedge shims, the nonlinearity problem of the weighing system was solved, the accuracy requirements of the sensor were met, and the measurement accuracy of the weighing system was improved.

CN116481617BActive Publication Date: 2026-01-30METTLER TOLEDO (CHANGZHOU) PRECISION INSTR CO LTD +2
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Patent Information

Application Number
CN202210049395.9
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-01-17
Publication Date
2026-01-30
Estimated Expiration
2042-01-17

AI Technical Summary

Technical Problem

Nonlinearity issues in load cells and weighing systems make it difficult to meet the accuracy requirements of metrological regulations, especially due to structural deformation of resistance strain gauge sensors and nonlinear deviations introduced by system components.

Method used

By adjusting the tilt angle α between the beam sensor and the horizontal or vertical plane, the installation angle of the sensor is optimized to reduce nonlinearity using the finite element model and Kirchhoff's current law, and structural adjustment methods such as wedge shims are adopted.

Benefits of technology

It effectively improves the nonlinear performance of the weighing system, meets the weighing accuracy requirements, and enhances the measurement accuracy of the sensor.

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Abstract

This invention relates to a weighing system and a method for adjusting its nonlinearity. The method for adjusting the nonlinearity of the weighing system includes: the weighing system satisfying a nonlinearity condition where, when the beam sensor is unloaded, the tilt angle formed by the beam sensor and a horizontal or vertical plane is α; obtaining the relationship between the nonlinearity of the weighing system and the tilt angle α based on the nonlinearity condition; and selecting the tilt angle α so that the nonlinearity of the weighing system meets the weighing accuracy requirements. The weighing system and nonlinearity adjustment method proposed in this invention can effectively improve the nonlinearity of the weighing system.
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Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of dynamic weighing, in particular to a weighing system and a non-linear adjustment method. BACKGROUND

[0002] The non-linearity of a weighing sensor or a weighing system is a very important metrological performance index. According to the requirements of metrological regulations, the comprehensive error of the linearity hysteresis of a weighing sensor and a weighing system needs to reach the specified accuracy requirements. If the non-linearity of a weighing sensor or a weighing system is too large, even if other performances such as hysteresis are very good, it is difficult to meet the corresponding accuracy requirements. For a resistance strain gauge type weighing sensor, the influencing factors of its non-linearity mainly include: the structure of the elastic body, the strain gauge, the sensor assembly (such as the pressure head), the bonding surface of the sensor installation, and the non-linearity of the elastic body material, etc. Various influencing factors jointly determine the non-linearity performance of the sensor. The non-linearity of a weighing system depends on the non-linearity of the core component of the weighing sensor and the non-linearity of other related components in the system where the weighing sensor is installed. However, both the weighing system and its core component of the weighing sensor need to meet the corresponding metrological regulation requirements in terms of linearity hysteresis performance.

[0003] Generally, the structural non-linearity of the sensor dominates. Due to the characteristics of the resistance strain gauge type weighing sensor, the weighing signal is derived from the strain gauge strain output caused by the structural deformation of the sensor under load. As the load gradually increases, the deformation of the sensor elastic element will gradually increase. For a beam type resistance strain gauge type sensor, due to the non-linearity of the deformation of the elastic body structure, as the load increases, the change in the strain output caused by the same load increment will change, thereby causing the non-linearity of the output signal of the resistance strain type sensor and leading to weighing errors.

[0004] In the actual design and production of resistance strain type beam sensors, non-linearity of some capacities, especially large capacity sensors, often exceeds the tolerance. The main means to adjust the non-linearity of the sensor is to redesign the structure of the elastic element, but the adjustment of the structure of the elastic element has great limitations. Therefore, in addition to adjusting the structure of the elastic element, it is particularly important to be able to adjust the non-linearity of the weighing sensor.

[0005] For a weighing system containing a resistance strain gauge type weighing sensor, the non-linearity of the weighing sensor itself is only one of the sources of non-linearity of the weighing system. If the weighing sensor meets the requirements of the corresponding accuracy level specified by the metrological regulations, but the non-linearity introduced by the system base and other components is too large, it will also cause the non-linearity of the entire weighing system to exceed the tolerance. SUMMARY

[0006] In view of the above-mentioned problems in the prior art, the present invention proposes a weighing system and a method for adjusting nonlinearity, which can effectively improve the nonlinearity of the weighing system.

[0007] Specifically, this invention proposes a method for adjusting the nonlinearity of a weighing system, wherein the weighing system includes a resistance strain gauge beam sensor, and the adjustment method includes:

[0008] The weighing system satisfies nonlinear conditions, and when the beam sensor is not under load, the tilt angle formed by the beam sensor and the horizontal or vertical plane is α.

[0009] Based on the nonlinear conditions, the relationship between the nonlinearity of the weighing system and the tilt angle α is obtained, and the tilt angle α is selected so that the nonlinearity of the weighing system meets the weighing accuracy requirements of the weighing system.

[0010] According to one embodiment of the present invention, the nonlinear condition includes a nonlinear formula:

[0011]

[0012] Specifically, when the beam sensor is fully loaded, the tilt angle of the elastic element of the beam sensor is β, and when the beam sensor is half-loaded, the tilt angle of the elastic element of the beam sensor is β / 2.

[0013] According to one embodiment of the present invention, the nonlinear condition includes:

[0014] Under the action of the excitation voltage u, according to Kirchhoff's current law, the output voltage of the Wheatstone bridge of the beam sensor can be expressed as:

[0015]

[0016] The initial resistance values ​​of the four resistance strain gauges on the sensor are set to be equal, which is expressed as: R1=R2=R3=R4=R;

[0017] Formula 2 yields:

[0018]

[0019] Under load, the resistance of the strain gauge changes as follows: R+ΔR1; R+ΔR2; R+ΔR3; R+ΔR4;

[0020] The relationship between the resistance change of the strain gauge and its strain is as follows:

[0021]

[0022] Where K is the sensitivity coefficient of the resistance strain gauge, and ε1~ε4 are the strains of the four resistance strain gauges;

[0023] Substituting Formula 4 into Formula 3 yields:

[0024]

[0025] According to the nonlinear definition of the weighing system:

[0026]

[0027] In the finite element model, the tilt angle α between the sensor and the horizontal or vertical plane is changed, and half load and full load are applied to the sensor to obtain the strain ε1~ε4 of the four resistance strain gauges of the sensor under half load and full load. Substitute these strain gauges into Formula 5 to obtain the output under half load and full load at the corresponding tilt angle α, and calculate the nonlinearity at the corresponding tilt angle α according to Formula 6.

[0028] According to one embodiment of the present invention, the selection range of the tilt angle α is -10°≤α<0° or 0<α≤10°.

[0029] The present invention also provides a weighing system, including a resistance strain gauge beam sensor and a mounting part. The weighing system uses the aforementioned adjustment method to set the beam sensor. The mounting end of the beam sensor is fixed in place with the mounting surface of the mounting part so that the beam sensor forms an inclination angle α with the horizontal or vertical plane.

[0030] According to one embodiment of the present invention, the inclination of the mounting end surface is adjusted so that the beam sensor forms an inclination angle α with the horizontal or vertical plane.

[0031] According to one embodiment of the present invention, the inclination of the mounting surface is adjusted so that the beam sensor forms an inclination angle α with the horizontal or vertical plane.

[0032] According to one embodiment of the present invention, the weighing system further includes a wedge-shaped pad disposed between the beam sensor and the mounting portion, so that the beam sensor forms an inclination angle α with the horizontal or vertical plane.

[0033] The present invention provides a weighing system and a method for adjusting nonlinearity, which effectively improves the nonlinearity of the weighing system by adjusting the tilt angle of the beam sensor.

[0034] It should be understood that the above general description and the following detailed description of the present invention are exemplary and illustrative, and are intended to provide further explanation of the present invention. Attached Figure Description

[0035] The accompanying drawings are included to provide a further understanding of the invention; they are incorporated into and constitute a part of this application. The drawings illustrate embodiments of the invention and, together with this specification, serve to explain the principles of the invention. In the drawings:

[0036] Figure 1 A schematic diagram of the force and deformation during installation of a resistance strain gauge beam sensor in the prior art is shown.

[0037] Figure 2 A schematic diagram of the nonlinear variation of a resistance strain gauge beam sensor under different loads and tilt angles is shown.

[0038] Figure 3 A flowchart illustrating a method for adjusting the nonlinearity of a weighing system according to an embodiment of the present invention is shown.

[0039] Figure 4 A schematic diagram of a weighing system according to an embodiment of the present invention is shown.

[0040] Figure 5 A schematic diagram of a weighing system according to another embodiment of the present invention is shown.

[0041] Figure 6 A schematic diagram of a weighing system according to another embodiment of the present invention is shown.

[0042] Figure 7 A schematic diagram of a weighing system according to another embodiment of the present invention is shown.

[0043] Figure 8 A schematic diagram of a weighing system according to another embodiment of the present invention is shown.

[0044] The above figures include the following reference numerals:

[0045] Weighing system 400

[0046] Beam sensor 401

[0047] Installation Department 402

[0048] Installation end 403

[0049] Mounting surface 404

[0050] Bearing end 405

[0051] Bearing section 406

[0052] Wedge gasket 407 Detailed Implementation

[0053] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other.

[0054] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit this application or its application or use. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0055] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0056] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of this application. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following drawings denote similar items; therefore, once an item is defined in one drawing, it need not be further discussed in subsequent drawings.

[0057] In the description of this application, it should be understood that the orientation or positional relationship indicated by directional terms such as "front, back, up, down, left, right", "horizontal, vertical, horizontal" and "top, bottom" is usually based on the orientation or positional relationship shown in the accompanying drawings, and is only for the convenience of describing this application and simplifying the description. Unless otherwise stated, these directional terms do not indicate or imply that the device or element referred to must have a specific orientation or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on the scope of protection of this application; the directional terms "inner" and "outer" refer to the inner and outer contours relative to the outline of each component itself.

[0058] For ease of description, spatial relative terms such as "above," "on top of," "on the upper surface of," "above," etc., are used herein to describe the spatial positional relationship of a device or feature as shown in the figures to other devices or features. It should be understood that spatial relative terms are intended to encompass different orientations in use or operation beyond the orientation of the device as described in the figures. For example, if the device in the figures were inverted, a device described as "above" or "on top of" other devices or structures would subsequently be positioned as "below" or "under" other devices or structures. Thus, the exemplary term "above" can include both "above" and "below." The device may also be positioned in other different ways, rotated 90 degrees, or in other orientations, and the spatial relative descriptions used herein will be interpreted accordingly.

[0059] Furthermore, it should be noted that the use of terms such as "first" and "second" to define components is merely for the purpose of distinguishing the corresponding components. Unless otherwise stated, these terms have no special meaning and therefore should not be construed as limiting the scope of protection of this application. In addition, although the terminology used in this application is selected from commonly known and used terms, some terms mentioned in this application's specification may have been chosen by the applicant according to his or her judgment, and their detailed meanings are explained in the relevant sections of this description. Moreover, this application should be understood not only through the actual terms used, but also through the meaning implied by each term.

[0060] Figure 1 A schematic diagram illustrating the force and deformation during installation of a prior art resistance strain gauge beam sensor is shown. (Reference) Figure 1 Taking a dual-hole parallel beam sensor as an example, Figure 1 The diagram shows the stress and deformation of a dual-hole parallel beam sensor when it is installed at an angle. The beam sensor is installed at an angle α to the horizontal plane. When the beam sensor is fully loaded, the tilt angle of the elastic element due to the deformation caused by the load is β. Therefore, when the beam sensor is half-loaded, the tilt angle of the elastic element is approximately β / 2.

[0061] Figure 2 This diagram illustrates the nonlinear variation of a resistance strain gauge beam sensor under different loads and tilt angles. (Reference) Figure 2 The horizontal axis in the figure reflects the change in load, and the vertical axis reflects the change in nonlinearity. Each curve in the figure represents the relationship between the beam sensor and nonlinearity under different tilt angles α and different load conditions.

[0062] Figure 3A flowchart illustrating a method for adjusting the nonlinearity of a weighing system according to an embodiment of the present invention is shown. As shown, a method for adjusting the nonlinearity of a weighing system is provided. The weighing system includes a resistance strain gauge beam sensor. The adjustment method includes:

[0063] The weighing system satisfies the nonlinear condition. When the beam sensor is not loaded with force, the tilt angle formed between the beam sensor and the horizontal or vertical plane is α.

[0064] Based on the nonlinear conditions, the relationship between the nonlinearity of the weighing system and the tilt angle α is obtained, and the tilt angle α is selected so that the nonlinearity of the weighing system meets the weighing accuracy requirements of the weighing system.

[0065] Preferably, the nonlinear conditions include nonlinear formulas:

[0066]

[0067] Combination Figure 1 As shown, when the beam sensor is unloaded, the tilt angle between the beam sensor and the horizontal or vertical plane is α; when the beam sensor is fully loaded, the tilt angle of the elastic element of the beam sensor is β; and when the beam sensor is half-loaded, the tilt angle of the elastic element of the beam sensor is β / 2.

[0068] The relationship between the nonlinearity of the weighing system and the tilt angle α is obtained according to Formula 1, combined with... Figure 2 As shown, an inclination angle α is selected to ensure that the nonlinearity of the weighing system meets the weighing accuracy requirements of the weighing system.

[0069] Preferably, the nonlinear conditions include:

[0070] Under the action of excitation voltage u, according to Kirchhoff's current law, the output voltage of the Wheatstone bridge of the beam sensor can be expressed as:

[0071]

[0072] The initial resistance values ​​of the four strain gauges on the sensor are set to be equal, which is expressed as:

[0073] R1 = R2 = R3 = R4 = R;

[0074] Formula 2 yields:

[0075]

[0076] Under load, the resistance of the strain gauge changes as follows: R+ΔR1; R+ΔR2; R+ΔR3; R+ΔR4;

[0077] The relationship between the resistance change of a resistance strain gauge and its strain is as follows:

[0078]

[0079] Where K is the sensitivity coefficient of the resistance strain gauge, and ε1~ε4 are the strains of the four resistance strain gauges;

[0080] Substituting Formula 4 into Formula 3 yields:

[0081]

[0082] According to the nonlinear definition of a weighing system:

[0083]

[0084] In the finite element model, the tilt angle α between the sensor and the horizontal or vertical plane is changed. Half load and full load are applied to the beam sensor to obtain the strain ε1~ε4 of the four resistance strain gauges of the beam sensor under half load and full load. Substitute them into Formula 5 to obtain the output under half load and full load at the corresponding tilt angle α. Then, calculate the nonlinearity under the corresponding tilt angle α according to Formula 6.

[0085] Preferably, according to the aforementioned method for adjusting the nonlinearity of the weighing system, the range of the tilt angle α is -10°≤α<0° or 0<α≤10°.

[0086] Figure 4 A schematic diagram of a weighing system according to an embodiment of the present invention is shown. As shown, the present invention also provides a weighing system 400. The weighing system 400 includes a resistance strain gauge beam sensor 401 and a mounting part 402. The weighing system 400 uses the aforementioned adjustment method to set the beam sensor 401. The mounting end 403 of the beam sensor 401 is fitted and fixed with the mounting surface 404 of the mounting part 402 so that the beam sensor 401 forms an inclination angle α with the horizontal or vertical plane. In this embodiment, one end of the beam sensor 401 is set as the mounting end 403, and the bottom surface of the mounting end 403 is fitted and fixed with the top surface of the mounting surface 404 of the mounting part 402. The inclination of the surface of the mounting end 403 of the beam sensor 401 is adjusted so that the beam sensor 401 forms an inclination angle α with the horizontal plane, 0 < α ≤ 10°. The other end of the beam sensor 401 is set as a bearing end 405. The weighing system 400 also includes a bearing part 406 disposed on the bearing end 405. The load-bearing end 405 of the beam sensor 401 loads the object to be weighed through the load-bearing part 406.

[0087] Figure 5A schematic diagram of a weighing system 400 according to another embodiment of the present invention is shown. In this embodiment, one end of the beam sensor 401 is configured as a mounting end 403, and the bottom surface of the mounting end 403 is fixedly fitted to the top surface of the mounting surface 404 of the mounting part 402. The inclination of the mounting surface 404 of the mounting part 402 is adjusted so that the beam sensor 401 forms an inclination angle α with the horizontal plane, 0 < α ≤ 10°. The other end of the beam sensor 401 is configured as a bearing end 405. The weighing system 400 also includes a bearing part 406 disposed on the bearing end 405. The bearing end 405 of the beam sensor 401 loads the object to be weighed through the bearing part 406.

[0088] Figure 6 A schematic diagram of a weighing system 400 according to another embodiment of the present invention is shown. Preferably, the weighing system 400 further includes a wedge-shaped pad 407. The wedge-shaped pad 407 is disposed between the beam sensor 401 and the mounting portion 402, so that the beam sensor 401 forms an inclination angle α with the horizontal or vertical plane. In this embodiment, one end of the beam sensor 401 is configured as a mounting end 403, and the bottom surface of the mounting end 403 is fixed to the top surface of the mounting surface 404 of the mounting portion 402 by the wedge-shaped pad 407 engaging vertically. A suitable wedge-shaped pad 407 is selected so that the beam sensor 401 forms an inclination angle α with the horizontal plane, where 0 < α ≤ 10° or -10° ≤ α < 0°. The other end of the beam sensor 401 is configured as a bearing end 405. The weighing system 400 further includes a bearing portion 406 disposed on the bearing end 405. The bearing end 405 of the beam sensor 401 loads the object to be weighed through the bearing portion 406.

[0089] Figure 7 A schematic diagram of a weighing system 400 according to another embodiment of the present invention is shown. In this embodiment, one end of the beam sensor 401 is configured as a mounting end 403, and the bottom surface of the mounting end 403 is fixedly fitted to the top surface of the mounting surface 404 of the mounting part 402. The inclination of the surface of the mounting surface 404 of the mounting part 402 or the bottom surface of the mounting end 403 is adjusted so that the beam sensor 401 forms an inclination angle α with the horizontal plane, -10°≤α<0°. The other side of the beam sensor 401 is configured as a bearing end 405. The weighing system 400 also includes a bearing part 406 disposed on the surface of the bearing end 405. The bearing end 405 of the beam sensor 401 loads the object to be weighed through the bearing part 406.

[0090] Figure 8A schematic diagram of a weighing system 400 according to another embodiment of the present invention is shown. In this embodiment, one side of the beam sensor 401 is configured as a mounting end 403, and the side of the mounting end 403 is fixedly fitted to the side of the mounting surface 404 of the mounting part 402. The inclination of the mounting surface 404 of the mounting part 402 is adjusted so that the beam sensor 401 forms an inclination angle α with the vertical plane, where 0 < α ≤ 10° or -10° ≤ α < 0°. The other side of the beam sensor 401 is configured as a bearing end 405. The weighing system 400 also includes a bearing part 406 disposed on the surface of the bearing end 405. The bearing end 405 of the beam sensor 401 loads the object to be weighed through the bearing part 406.

[0091] The weighing system and nonlinear adjustment method provided by this invention utilize the structural nonlinearity caused by the large deformation of the beam sensor after weighing deformation, during the process of deformation from zero to maximum deformation, to effectively improve the nonlinearity of the weighing output signal in the weighing system, thereby improving the nonlinearity of the beam sensor and its weighing system to meet the accuracy requirements.

[0092] It will be apparent to those skilled in the art that various modifications and variations can be made to the exemplary embodiments described above without departing from the spirit and scope of the invention. Therefore, it is intended that this invention cover modifications and variations falling within the scope of the appended claims and their equivalents.

Claims

1. A method for adjusting nonlinearity of a weighing system, the weighing system comprising a beam sensor with resistance strain gauges, the method comprising: the weighing system satisfying a nonlinearity condition, the beam sensor forming an inclination angle of α with a horizontal plane or a vertical plane when the beam sensor is not loaded; obtaining a relationship between the nonlinearity of the weighing system and the inclination angle α according to the nonlinearity condition, and selecting the inclination angle α so that the nonlinearity of the weighing system satisfies a weighing accuracy requirement of the weighing system; wherein the nonlinearity condition comprises a nonlinearity formula: wherein β is an inclination angle of an elastic element of the beam sensor when the beam sensor is fully loaded, and β / 2 is an inclination angle of the elastic element of the beam sensor when the beam sensor is half loaded. 2.A method for adjusting nonlinearity of a weighing system, the weighing system comprising a beam sensor with resistance strain gauges, the method comprising: the weighing system satisfying a nonlinearity condition, the beam sensor forming an inclination angle of α with a horizontal plane or a vertical plane when the beam sensor is not loaded; obtaining a relationship between the nonlinearity of the weighing system and the inclination angle α according to the nonlinearity condition, and selecting the inclination angle α so that the nonlinearity of the weighing system satisfies a weighing accuracy requirement of the weighing system; wherein the nonlinearity condition comprises: wherein it is assumed that initial resistances of four resistance strain gauges on the sensor are equal, and is represented as: a conversion formula 2 is obtained: a relationship between a resistance change of the resistance strain gauge and a strain thereof is: formula 4 is obtained by substituting formula 4 into formula 3: the nonlinearity of the weighing system is defined according to:

5. A weighing system comprising a beam sensor with resistance strain gauges and a mounting portion, the weighing system being provided with the beam sensor by using the adjusting method according to any one of claims 1 to 2, a mounting end of the beam sensor being fixedly connected to a mounting surface of the mounting portion so that the beam sensor forms an inclination angle of α with a horizontal plane or a vertical plane. The inclination of the surface of the mounting end is adjusted so that the beam sensor forms the inclination angle of α with the horizontal plane or the vertical plane. Formula 1 ; The inclination of the mounting surface is adjusted so that the beam sensor forms the inclination angle of α with the horizontal plane or the vertical plane. The weighing system further comprises a wedge-shaped gasket, the wedge-shaped gasket being arranged between the beam sensor and the mounting portion so that the beam sensor forms the inclination angle of α with the horizontal plane or the vertical plane. ​ ​ ​ Under the action of an excitation voltage The output voltage of the Wheatstone bridge of the beam sensor can be expressed according to Kirchhoff's current law as: Formula 2; ​ ; ​ Formula 3; Wherein, in the load state, the resistance of the resistance strain gauge changes, which is expressed as: ; ; ; ; ​ , , , Formula 4; where K is a sensitivity coefficient of the resistance strain gauge, ~ is a strain of the four resistance strain gauges. ​ Formula 5; ​ Formula 6; changing the tilt angle a of the sensor with the horizontal plane or vertical plane in the finite element model, applying half load and full load on the sensor, obtaining the strain of the four resistance strain gauges of the sensor under half load and full load respectively into formula 5 to obtain the output under half load and full load corresponding to the tilt angle a, and calculating the nonlinearity under the tilt angle a according to formula 6.​ 3. The method of claim 1, wherein the step of adjusting the non-linearity of the weighing system comprises the step of: The inclination angle a is selected in the range of or .

4. The method of claim 2, wherein the step of adjusting the non-linearity of the weighing system comprises the step of: The inclination angle a is selected in the range of or . ​ 6. The weighing system of claim 5, wherein, ​ 7. The weighing system of claim 5, wherein, ​ 8. The weighing system of claim 5, wherein, ​

Citation Information

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