Effect of Decompression Hole Structure Design on Stress Inhomogeneity of Stainless Steel Base Force Transducers

In order to reduce the stress inhomogeneity of the stainless steel base force transducer, the force transducer structure with decompression holes of different depths and different hole morphologies is designed in this paper and compared with the traditional force transducer structure without decompression hole design. According to the finite element analysis theory, the stress inhomogeneity level under different pressures and different structures is tested using a simulation platform. When a flat-bottomed hole is used and the depth of the decompression hole is 7 mm, the stress inhomogeneity of the inner ring of the force measurement structure is 32.77% of the original scheme, and the stress inhomogeneity of the outer ring is 90.12% of the original scheme. The simulation results show that the use of a suitable decompression hole structure can help to reduce the stress inhomogeneity of the force measurement structure. This work provides a new idea in the field of sensor optimization.


Introduction
In the process of new energy vehicle battery system pressure monitoring, the detection of battery expansion force is very important because the abnormal state of the battery often causes changes in the battery expansion force [1][2][3][4].Battery expansion force monitoring is often carried out using elastomer pressure sensors [5].However, force sensors using different substrates with different processes have different force measurement results.Wearable force sensors usually use new materials (e.g., highly flexible carbon composite conductors [6], soft magnetic powders [7], etc.), new processes [8], etc. in a way to optimize their performance, and place emphasis on the portability, accuracy, and even comfort of the sensors.This type of sensor often has the disadvantages of high cost and poor reliability.In contrast, the design of industrial force sensors tends to use relatively mature materials (e.g., stainless steel [9]) as the substrate material, and relatively mature processes (e.g., thick-film technology [10]) as the optimization process to unfold.Therefore, industrial force sensors usually have the advantages of low cost and high reliability.However, such sensors still suffer from the phenomenon of uneven stress in the force measurement structure, while at the same time, there are few academic reports on the macro-optimization of force measurement sensor structures.
Therefore, this paper proposes a macro-optimization structural optimization method to develop stainless steel-based force transducers with decompression holes of different depths and different morphologies, by optimizing the structural parameters of the decompression holes, in order to achieve the reduction of the stress inhomogeneity of the force measurement structure.

Design of Force Transducer Structure and Material Parameters
The force transducer designed in this study utilizes the following geometries: force platform, connection body, strain detector body, wire extraction holes, and limit structures.The force measuring platform is cylindrical with a diameter of 68 mm and a height of 10 mm; the connecting body is cylindrical with a diameter of 27 mm and a height of 6 mm, and it has been processed with rounded corners; the strain detecting body is a concave table structure with a diameter of 68 mm; and the extraction holes and limit structures are located on top of the strain detecting body.Its specific structure is shown in figure 1.For material selection, 304 annealed stainless steel was chosen as the substrate material in this study.In terms of material properties, stainless steel has the advantages of low cost and easy processing compared with new materials such as organic polymers and titanium alloys.In terms of processing, heat treatment, as a mature metal processing process, can be a good help for all mechanical properties related to stainless steel materials.Such material selection helps the smooth development of subsequent research.

Optimized Parameter Design of Force Transducer
The optimization scheme is mainly designed for the strain detecting body by excavating several decompression holes in the strain detecting body relatively far away from the geometric center.This study focuses on the effects of different decompression hole depths (D) and decompression hole cone angles (A) on the strain inhomogeneity of the force measurement structure.Specifically, the depth of the decompression holes in this study was chosen to be 3 mm, 5 mm and 7 mm for the study, while the cone-top angles of the decompression holes were chosen to be 118 degrees and 0 degrees for the study.This study is carried out using the control variable method, and all the parameters are kept consistent except those being discussed.The specific optimized parameters are shown in table 1.

Simulation Process Design for Force Transducers
In order to simulate the stress change process in the strain detecting body, UG 12.0 FEM software was chosen for this study.The entire experimental body was loaded with 304 annealed stainless steel as the simulation material.A 3D tetrahedral mesh with a single side size of 5 mm was used for the delineation, which is much smaller than the conventional stress region to ensure the accurate portrayal of the stress distribution.Since the pressure detection used in new energy vehicles is mostly monitored by fixing the sensors outside the battery box, fixed constraints are applied to the whole model in this study in order to simulate the actual working conditions.Although there may be uneven pressure inside the battery when a short-circuit or other fault occurs inside the battery, the battery case can homogenize the pressure inside the battery, and the force sensor is in direct contact with the case, which makes its working condition approximate to accepting a uniform load.Therefore, this study focuses on analyzing the behavior of the strain transducer under a uniform load.In addition, strains usually spread from the centre outwards and the stability of the centre is particularly important.Therefore, this simulation focuses on the stress variations at the centre point, the inner ring (within 5 mm from the centre) and the outer ring (within 10 mm from the centre).
In order to compare the data changes before and after the optimization of the sensor structure, a total of five force measurement structure schemes were designed.These schemes were simulated and tested under loads of 1000N, 5000N, 10000N, 50000N and 100000N, and a large number of data points were collected, aiming to fully prove the feasibility of the optimized schemes.Figure 2 shows the strain representation of the variant schemes.

Force Process of Force Transducer
For force transducers, the force process can be divided into three stages.First, in the first stage, the load begins to be applied to the force measuring platform, the force measuring platform is under pressure, the center position of the deformation occurs slightly, and produce stress; then, in the second stage, the load on the force measuring platform is increasing, the deformation range and degree of gradual expansion, and downward conduction; finally, in the third stage, the detection platform by the upper connecting body of the squeeze, the deformation of the slight deformation occurs, and accordingly, the generation of strain.After the deformation of the force measurement structure under different loads, the linearity of the force measurement results can be evaluated according to the center sampling point, the average value of the inner circle sampling point, and the average value of the outer circle sampling point, and it is found that the force measurement platform has excellent linearity.The test results are shown in figure 3.

Definition of Key Parameters of Stress Inhomogeneity
In order to characterize the level of bottom stress uniformity of the force transducer throughout the loading process, the concepts of relative inhomogeneity (R) and absolute inhomogeneity (S) are introduced in this study.In order to differentiate between inner-ring strain inhomogeneity and outerring strain inhomogeneity, this study defines them differently.The inner-circle strain inhomogeneity is defined as the variance of the bottom inner-circle strain group, while the outer-circle strain inhomogeneity is the variance of the bottom outer-circle strain group.
The equations for the absolute inhomogeneities    and    are as follows where I in    denotes the inner circle group (Inner), k denotes the number of the variant program, k=0,1,2,3 ......12; O in    denotes the outer circle group (Outer), k denotes the number of the variant scheme, k=0,1,2,3 ......12; n denotes the number of samples of the current variant scheme in the current sampling group;   denotes the sampling value of the current sample; ̅ denotes the mean value of the current sample group; The equations for the relative inhomogeneities    and    are as follows I in    denotes the inner circle group (Inner), k denotes the number of the variant program, k=0,1,2,3 ......12; O in    denotes the outer circle group (Outer), k denotes the number of the variant program, k=0,1,2,3 ......12;

Effect of Decompression Hole Depth Design on Stress Inhomogeneity
In order to investigate the effect of the depth of the decompression hole on the inhomogeneity of the force measuring structure, three variants of the scheme (1, 2, and 3) were selected in this study, with the dimensions of the decompression holes from the center point being 3 mm, 5 mm, and 7 mm, respectively.According to the different loads, the samples were sampled for inhomogeneity in five sampling groups (1000N, 5000N, 10000N, 50000N, and 100000N) , and the following results were obtained.Taking variant scheme III as an example, through the analysis of absolute inhomogeneity plots and relative inhomogeneity comparison plots, it is found that the stress inhomogeneity performance of variant scheme III is better than that of the original scheme in most of the sampling groups.Especially in the low load condition (1000N, 5000N), the inner ring stress non-uniformity of variant scheme III performs well, which is only 25.98% and 26.65% of the original scheme.At the same time, the schemes with other hole depths are included in the discussion.The results show that the reduction of stress non-uniformity by the decompression hole is optimized when the decompression hole depth is 7 mm.This indicates that too small decompression hole depth may lead to insufficient decompression effect.Therefore, a relatively large decompression hole depth should be selected in practical engineering applications.In addition, it is also necessary to pay attention to the effect of decompression hole depth on the structural strength, so as to avoid selecting too large a hole depth that leads to a decrease in structural reliability.A comparison of the variant and ontology scenarios is shown in figure 4. The effect of decompression hole depth on relative inhomogeneity is shown in figure 5.

Effect of Decompression Hole Pore Morphology Design on Stress Inhomogeneity
In order to investigate the effect of decompression hole morphology on the inhomogeneity of the force measurement structure, two variants of the scheme (1 and 4) were chosen in this study, with a cone angle at the top of the decompression hole of 118° and 0°, respectively.The samples were sampled for inhomogeneity at five sampling groups (1000N, 5000N, 10000N, 50000N, 100000N) according to different loads and the following results were obtained.The simulation results show that the flatbottomed hole scheme exhibits better stress inhomogeneity compared to the tapered-bottomed hole scheme, all other conditions being equal.The stress inhomogeneity of the inner rim of the flat bottom hole scheme is 80.72% of that of the tapered bottom hole scheme and the stress inhomogeneity of the outer rim is 83.38% of that of the tapered bottom hole scheme.The effect of cone top angle on stress inhomogeneity is shown in figure 6.
However, it needs to be considered that the flat-bottomed hole solution has higher machining cost requirements and is more prone to machining defects.Therefore, in practical engineering applications, it is also necessary to comprehensively consider the economic applicability to determine the final program.

Conclusions
The design of the decompression hole of a stainless steel-based force transducer is an important factor affecting the stress non-uniformity of this transducer.This study aims to reduce the stress inhomogeneity by optimizing the design of decompression holes from several angles.This study focuses on simulation from two perspectives: depth and morphology of the decompression holes.The results show that these two factors have a certain effect on the stress inhomogeneity of the force transducer.In specific engineering applications, manufacturers also need to consider the processing cost, system reliability and other factors to choose a suitable optimization scheme to achieve a balance between measurement accuracy and economic cost.
Briefly, in this study, the optimal scheme is the variant scheme III.This scheme utilized eight decompression holes with a distance of 16 mm between the decompression holes, a hole diameter of 6 mm, a hole depth of 7 mm, and a top cone angle of 118°.This scheme showed a superior level of stress inhomogeneity, with an average inhomogeneity of only 32.77% of the original scheme for the inner ring and 90.12% of the original scheme for the outer ring.

Figure 1 .
Figure 1.Three-dimensional diagram of the force transducer.

Figure 2 .
Figure 2. Demonstration of the strain of the variant scheme.|

Figure 3 .
Figure 3. Linearity of the force measuring structure at different sampling points under different loads.

Figure 4 .
Figure 4. Comparison of relative inhomogeneity between variant scheme 3 and the body scheme.

Figure 5 .
Figure 5.Effect of decompression hole depth on relative inhomogeneity.

Figure 6 .
Figure 6.Effect of cone top angle on stress inhomogeneity.

Table 1 .
Optimized structural parameter design.