I. Definition of Hysteresis Sensitivity Using the above graph as a model, the definition of hysteresis is introduced: the horizontal axis represents the load, and the vertical axis represents the sensitivity output. When testing the characteristics of a sensor, the rated load is generally divided into five equal parts, and the load is applied step-by-step from 0 to 100%, with the corresponding output values ​​read. Connecting the five reading points forms a smooth curve, which is the thick solid line in the figure, called the loading curve, also known as the progress curve. The corresponding data at the 75% point is calculated using the linear interpolation method. A straight line is drawn between the zero point and the 75% point, as shown in the dotted line in the figure. This straight line is called the ideal straight line. The error between the loading curve and the ideal straight line is called the nonlinear error. The load is then gradually reduced from 100% to 0 in five equal parts, with the corresponding data read. Connecting these five sets of data forms a smooth curve, which is the thick dashed line in the figure, called the unloading curve, also known as the return curve. The error between the unloading curve and the loading curve is called the hysteresis error. Hysteresis error reflects one of the main indicators of sensor accuracy. The magnitude of the error directly affects the measurement accuracy, so various factors affecting hysteresis must be strictly controlled during the sensor manufacturing process. Simultaneously, it is also necessary to ensure that factors affecting hysteresis are minimized under different sensor installation conditions. The following details some factors affecting hysteresis. II. Analysis of Factors Affecting Hysteresis 1. Raw Material Elastomer: Due to the complexity of its internal microstructure, any metallic material, when subjected to external force, generates micro-strain between tiny grains. After the external force disappears, the micro-strain disappears as well, but whether it completely disappears and returns to its original state varies significantly between different materials. In Figure 1, we can see that the strain curve ε1 during loading does not coincide with the strain curve ε2 during unloading. The difference Δ = ε2 - ε1 is called hysteresis. The magnitude of this difference mainly depends on the stability and uniformity of the material's composition, and the metallographic structure after heat treatment. As a key component of the weighing sensor, the elastomer has even more stringent requirements in this regard. Different heat treatment methods can be used to improve the elastic limit and reduce hysteresis. Currently, the commonly used material in the domestic market is 40CrNiMoA, which can achieve ideal comprehensive mechanical properties after proper heat treatment. Strain Gauge: The typical structure of a metal strain gauge consists of a sensitive grid, a substrate, a coating layer, and leads. In sensor applications, the strain of an elastic body is converted into a change in resistance through the resistance strain effect of the sensitive grid. Due to the inherent hysteresis of the material, the strain gauge itself also exhibits hysteresis. Currently, world-renowned strain gauge manufacturers fully consider self-compensation for hysteresis in their manufacturing processes, minimizing its impact on sensor applications. Therefore, this factor must be considered when selecting a strain gauge. Sealant: A large amount of sealant is used in the sensor production process, primarily for fixing circuitry and sealing. Superficially, the sealant is relatively soft after curing, and its strength relative to the elastic body is almost negligible. However, for small-range products, this must be considered. In small-range products, the deformation zone is relatively weak, and the influence of sealant thickness increases significantly. Figure 2 shows the relationship between hysteresis and range when the sealant layer thickness is constant. The approximate functional relationship is: Y = K * e - Xa Where: Y—sensor hysteresis; K—hysteresis after complete sealant curing; Xa—sensor rated load. Figure 3 shows the relationship between hysteresis and sealant layer thickness when the range is constant. The approximate functional relationship is: Y = K * (1 - e - Xb) Where: Y — sensor hysteresis; K — hysteresis after complete curing of the sealant; Xb — sealant thickness. Different qualities of sealant exhibit different characteristics. If the hardness of the sealant layer changes over time, the hysteresis of the product will also change. Therefore, when selecting sealant, it is essential to choose one with stable properties after curing. 2. Installation Conditions Installation conditions refer to two aspects. First, the boundary conditions of the load cell when installing special accessories (such as the base of a bridge sensor). The influence of these boundary conditions is analyzed in detail in the magazine "Weighing Instruments," where surface condition and installation torque are the most significant influencing factors, which will not be elaborated upon here. Second, the installation conditions at the application site of the load cell. Based on research and analysis with customers of different applications, the following factors affect the hysteresis of the sensor or the entire machine: surface condition, contact area, installation torque, bolt strength, and bearing surface hardness. These influencing factors are sometimes misdiagnosed as poor sensor quality. Surface condition: This refers to the quality of the contact surface between the weighing platform and the sensor, such as roughness and parallelism. An excessively rough surface can cause the fastening bolts to loosen and affect performance over time. Excessive parallelism can cause unnecessary force on the sensor after loading, directly affecting product accuracy and failing to reflect the sensor's true accuracy. Some companies, in order to reduce costs, simply cut steel plates of a certain thickness to the appropriate size and weld them onto the weighing platform without any processing. While this may not cause problems initially, the accuracy will deteriorate over time. Contact area: This refers to the fixed contact area between the sensor and the weighing platform. As shown in Figure 4, (a) the contact area is too small, and (b) the contact area is too large. Different companies' products have slightly different contact area sizes due to variations in structure and manufacturing processes. Therefore, this must be determined during sensor production and defined in detail in the sensor's installation and operation manual to ensure customers can install and use it under optimal conditions. Refer to Vistedia's 3410 product and mark the installation control lines on the sensor, as shown in Figure 4(c). Installation Torque: The relationship between installation torque and hysteresis of bridge-type sensors was previously discussed in the magazine *Weighing Instruments*. Under the condition of a fixed contact surface, the greater the installation torque, the smaller the hysteresis. Similarly, the installation torque directly affects the actual accuracy of the product when the sensor is installed on different devices. Sensors are classified into six main categories according to their different force-bearing structures: single-point, cantilever beam, bridge, "S" type, spoke type, and column type. The influence of installation torque varies for products with different structures. For example, for cantilever beam sensors, the optimal hysteresis is achieved with an installation torque of 100 Nm. Too much or too little torque will worsen the hysteresis (the optimal installation torque value varies between different companies and must be determined experimentally). The hysteresis of spoke-type sensors is more sensitive to installation torque, so it is essential to install them according to the manufacturer's installation and operation instructions to ensure product quality. Bolt Strength: The strength of the bolts affects the same aspect as the installation torque. If the strength is insufficient, the tightening force will loosen after a period of use, thus affecting accuracy. Mounting Surface Hardness: Taking a cantilever beam load cell as an example, because the contact surface at its fixed end is small, if the hardness is too low, the load-bearing fulcrum will shift with the number of uses during operation, as shown in Figure 5. The load-bearing fulcrum shifts from point a to point b, resulting in varying degrees of change in accuracy. The influencing factors described above are directly related to the sensor and are easy to understand. However, there are other factors that seem unrelated to the sensor but still affect its accuracy. These include the strength of the weighing platform, the robustness of the foundation, and dust and water resistance. The Influence of Weighing Platform Strength: Taking a platform scale as an example, four cantilever beam load cells are typically used and installed at the four corners, as shown in Figure 6(a). Figure 6(b) shows a simplified side view and force model of the platform scale. If the strength of the weighing platform is insufficient, it can cause the center of the platform to sag, as shown in Figure 6(d). This result will cause the sensor to be affected by lateral forces. Furthermore, the magnitude of the lateral force increases with the weight of the measured object, but the increase is non-linear. Using Figure 6(c) as a simplified model, the relationship between the sensor's force and load can be estimated using the following formula: F = G/2cosα = G/2cos(G·L²/4·E·I) Where: F—Force on the sensor's load end; G—Load on the weighing platform; E—Stiffness of the weighing platform; L—Distance between the sensor's fixed end and the center of the weighing platform; I—Moment of inertia of the weighing platform; α—Angle of force and deformation of the weighing platform. From the formula, it can be seen that if the weighing platform is strong enough, deformation can be ignored, i.e., α = 0, cosα = 1, therefore F = G/2. If the strength of the weighing platform is poor, the angle α increases with the load, thus worsening the non-linearity between F and G. In practical applications, there are two types of mounting feet: fixed feet (Figure 6(e)) and movable feet (Figure 6(f)). The structure of a fixed foot consists of a screw, a base, and vibration-damping rubber. The movable feet consist of a screw, steel ball, base, and anti-slip pad. If the platform scale's mounting feet are fixed, the load-bearing structure must also consider the impact of changes in the fulcrum after the feet tilt, as shown in Figure 7(b). Using movable feet can reduce the negative impact caused by foot deformation. Besides the platform scale itself, insufficient strength of the truck scale platform not only affects the product's accuracy but also its calibration. The influence of the foundation: Here, the foundation refers to the mounting foundation of the truck scale or rail scale's sensors. For example, a truck scale with a load capacity of eighty tons typically uses six or eight load cells. The sensors are fixed to the foundation's embedded parts via the base. The contact area of ​​a single sensor is approximately 250 cm², with a pressure per unit area of ​​0.40–0.58 kN/cm². If the foundation is not solid, after a period of use, changes in the foundation will prevent the sensor's characteristics from being fully realized. The conditions will differ significantly from those during initial installation and calibration. The effects of dust and water: These two factors have no effect under good maintenance conditions, but special attention should be paid to weighing instruments used outdoors, such as truck scales and rail scales. Let's take truck scales in cement plants or mines as an example to illustrate their impact: Cement plant environments are generally harsh, with heavy trucks frequently passing through. The dust carried by these trucks is mostly composed of cement, which accumulates over time on exposed sensor surfaces and in the gaps between components. After the rainy season or in humid environments, the dust on the sensor surface or in the gaps between components hardens, making previously moving components fixed. If the components are in the sensor's deformation-sensitive area, the sensor's linearity and hysteresis will significantly deteriorate. On the other hand, water or moisture mainly corrodes the sensor surface, causing changes in the contact points. Especially for products containing components, rust can cause the components to "rust" together with the sensor, affecting accuracy. We once encountered a special case: a customer installed an 80t truck scale around June in the summer, using six 30t bridge-type sensors, in a northern location. During installation, on-site personnel scratched the sealing strip in the middle of the sensor without making any improvements before calibration and delivery. In November, the user reported inaccurate weighbridge data; morning measurements were significantly lower than midday measurements by 8-10 tons, leading to suspicion of a problem with the sensor's temperature compensation. Multiple analyses failed to pinpoint the issue. Given the morning conditions, it was suggested the user heat the sensor with a hot air blower; the problem disappeared after half an hour. It was later discovered that the deformation gap of the sensor with the scratched sealing strip was filled with water. In the morning, it was solid ice, while at midday it was water. This meant that in the morning, the solid ice in the deformation gap prevented the sensor from deforming under stress, resulting in a very low output for that sensor and affecting the output results. Experienced manufacturers would employ appropriate protective measures to address the impact of dust, such as adding a sealing cover and applying a suitable amount of grease to the surface. The aforementioned factors, to varying degrees, will affect the accuracy of the weighbridge; these should be avoided during foundation construction and installation to ensure stable performance over long-term use.