Cylindrical and cylindrical weighing sensors are widely used in large electronic weighing instruments of various structures due to their simple and compact structure, small size, large measuring range and light weight. The geometric shapes of the elastic element and the protective shell are simple cylindrical and cylindrical, which are easy to process with high size and shape accuracy. The elastic element has high stiffness, high natural frequency and fast dynamic response. The loading and bearing boundary can be designed into double planes, one plane and one sphere, and double spheres. The cylindrical and cylindrical elastic elements with the same cross-sectional area have the same stiffness for pure axial loads, but the elastic element with cylindrical structure has a larger moment of inertia, so it has better anti-bending ability and is mostly used in large electronic hook scales. From the design principle of the elastic element of the weighing sensor, although the cylindrical and cylindrical elastic elements have very outstanding characteristics, their inherent linearity is poor and they are prone to rotation errors, which are also very fatal. Therefore, it is necessary to make good structural design and nonlinear compensation of the elastic element, protective shell, and pressure head bottom pad, and control the rotation error to achieve a higher accuracy level. The main factors that cause nonlinear errors in cylindrical and drum weighing sensors are:
(1) Area effect. When the elastic element is subjected to tensile and compressive loads, the cross-sectional area of the strain zone changes, resulting in nonlinearity in the P-σ relationship;
(2) Poisson's ratio effect. That is, the axial and circumferential strains of the elastic element differ greatly, causing the change in resistance of a certain bridge arm in the bridge to not match the reverse change in resistance of the adjacent bridge arm, resulting in nonlinear errors in the bridge;
(3) Material properties. The stress-strain relationship is mainly the error of the elastic element material. When the strain degree is high, its stress-strain relationship is not completely linear, and the hysteresis, creep and elastic modulus are not ideal constants. When the load increases, the nonlinearity also increases;
(4) The influence of the welded sealing diaphragm. It is mainly the nonlinear sealing die's shunt effect on the load. That is, when the ambient temperature changes, the welded diaphragm and the shell form an over-static structure, and internal stress is generated due to the incoordination of deformation. The change in shell size causes the gas pressure in the sealing cavity to change, causing the temperature drift of the weighing sensor. The rotation error of cylindrical and cylindrical elastic elements is a function of additional non-measured strains, and its influencing factors are:
(1) The influence of the geometric errors of the cylindrical and cylindrical elastic elements, the pressure head that introduces the load, and the bottom pad that bears the load.
It is mainly caused by the different strains in each direction caused by the concentricity, symmetry, and parallelism.
(2) The additional strain caused by the working characteristics of the resistance strain gauge and the positioning error of the resistance strain gauge on the elastic element. In the past, the nonlinear error of cylindrical and cylindrical weighing sensors was mainly analyzed theoretically, and the conclusions were roughly the same: the inherent nonlinear error of the weighing sensor itself (including elastic elements, resistance strain gauges, and bridge circuits) is generally small and has little effect on accuracy; the strain gradient of the elastic element strain zone and the positioning deviation of the resistance strain gauge have a great influence on nonlinearity, and reducing this value can greatly reduce the nonlinear error; the size of the elastic element, pressure head, and bottom pad has an impact on the strain gradient of the strain zone, and unreasonable structural design will lead to large nonlinear errors, etc., without breaking out of the traditional theoretical analysis model. The design and calculation of modern weighing sensor structure should use mathematical analysis to establish mathematical models of various characteristics, analyze and calculate related errors through mathematical fitting formulas, and lay a theoretical foundation for nonlinear compensation technology. To this end, it is necessary to master the structural characteristics of cylindrical and cylindrical elastic elements, the influence of non-ideal loading (such as eccentric load, lateral load), and physical variables (such as temperature, pressure, vibration) on nonlinearity. This paper analyzes the errors caused by the area effect of the strain area of cylindrical and cylindrical elastic elements, the nonlinear error of the bridge circuit caused by the Poisson's ratio of metal materials, the nonlinear error caused by the load shunt effect of the welding sealing diaphragm, and the rotation loading error caused by the positioning deviation of the resistance strain gauge by establishing mathematical models and mathematical analysis methods.
2. Nonlinear error caused by area effect
The high-order effects caused by the area effect, the bridge arms of the bridge and similar geometric parameter changes are typically: when the temperature changes by 60℃, the impact amount is 0.1~0.2%. However, their influence on the output of the weighing sensor is difficult to distinguish from other errors caused by temperature, so the output change with temperature caused by the combined effect of all these effects must be compensated.
Usually, the height to diameter ratio of cylindrical and cylindrical elastic elements is H/D=3~5. Since cylindrical and cylindrical structures are also affected by the secondary effect caused by non-axial force components, measures must be taken to separate the axial load from the output generated by the non-axial component. Affected by the area effect, the stiffness of the elastic element increases continuously when subjected to compressive loads, while the stiffness of the elastic element decreases continuously when subjected to tensile loads. This argument is based on the assumption that the elastic modulus remains constant and is independent of the simultaneous density changes. However, in fact, the elastic modulus increases slightly when subjected to compressive loads and decreases slightly when subjected to tensile loads, resulting in a more serious area effect. Although this change in the elastic modulus is so small that it is difficult to detect it in general material performance tests, its impact is still significant from the accuracy level of modern resistive strain weighing sensors. Even without considering the change of the elastic modulus with stress, we can at least estimate the nonlinear error caused by the area change. When the axial strain of a cylindrical elastic element changes by 100με, the nonlinearity caused by the area change is about 0.003%, which is considerable and cannot be ignored. In contrast, the volume of bending and shear elastic elements is generally equal when subjected to equal tensile and compressive stresses, and there is no area effect, so the inherent linearity is good. However, the inherent linearity of cylindrical and cylindrical elastic elements is very poor, so nonlinear compensation must be performed to achieve a higher level of accuracy.