Improvement of the calculation methodology for elastic elements of load-cell sensors using the finite element method
DOI:
https://doi.org/10.15276/opu.1.73.2026.11Keywords:
finite element method, stress-strain state, elastic element, force meter, equivalent stress, structural geometryAbstract
Ensuring high accuracy in calibrating force-measuring sensors and weighing systems is a critical task in modern instrumentation. This significant limitation stems from the omission of the object’s geometric features. In this paper, an improved method for calculating the real elastic element of a force meter is proposed, which effectively overcomes this gap through numerical simulation. Mathematically, the problem is formulated as a general matrix equation for static elasticity that accounts for the elastomer’s geometry and clamping conditions. The numerical implementation of the model was performed using the finite element method in the ANSYS software package, based on ten-node spatial tetrahedra with a quadratic displacement approximation, ensuring high accuracy in regions with a large stress gradient. The simulation results showed that the structure has a high stiffness, generating minimal linear displacements in the stiffening ribs, which is a necessary condition for the stable operation of strain gauges and preserving the linearity of the output signal. The main scientific result is the determination of the full spatial stress-strain state by fixing the maximum equivalent stress at the Huber-Mises criterion in the contact zone between the cylinder and the base, thereby ensuring the structure’s static strength. The analysis demonstrated significant non-uniformity in the stress distribution along the height of the cylindrical part, confirming the physical correctness of the stress-concentration calculation. The developed methodology provides a reliable basis for the precision design and modernization of elastic elements of force meters as operating loads change, significantly reducing the need for expensive full-scale laboratory testing.
References
1. Kamble, V. A., & Gore, P. N. (2012). Use of FEM and photo elasticity for shape optimization of S type load cell. Indian Journal of Science and Technology, 5(3), 2384–2389. DOI: 10.17485/ijst/2012/v5i3.24.
2. Rogge, N., et al. (2025). Investigations on anelastic effects in electrical discharge machined titan grade 2 flexures for the use in precision force instruments. Technisches Messen, 92(6), 243–250. DOI: 10.1515/teme-2025-0020.
3. Gavrilenkov, S. I., Gavrushin, S. S., & Godzikovskiy, V. A. (2017). System for multicriteria design of strain gauge load cells having axis symmetrical elastic elements. Engineering Journal: Science and Innovation, (1), 1–10. DOI: 10.18698/2308-6033-2017-1-1578.
4. Robinson, G. M. (1997). Finite element modelling of load cell hysteresis. Measurement, 20(2), 103–107. DOI: 10.1016/S0263-2241(97)00010-8.
5. Liang, Q., et al. (2016). Design and analysis of a sensor system for cutting force measurement in machining processes. Sensors, 16(1), 70. DOI: 10.3390/s16010070.
6. Kalai, D. M., et al. (2016). Parametric optimization of rectangular beam type load cell using Taguchi method. International Journal of Computer Engineering In Research Trends, 3(11), 596–601.
7. Oblasova, I., Timofeeva, E., & Shiryaeva, N. (2022). Implementation of an integro-differential model of a singularly loaded rod by the finite element method. Lecture Notes in Networks and Systems, 424, 301–315. DOI: 10.1007/978-3-030-97020-8_28.
8. Wang, X., & Tao, W. (2024). Optimization of elastomer structure parameters of load cell based on ANSYS. Journal of Sensor Technology and Application, 12(3), 391–398. DOI: 10.12677/jsta.2024.123042.
9. Rogge, N., et al. (2025). Investigations on anelastic effects in electrical discharge machined titan grade 2 flexures for the use in precision force instruments. Technisches Messen, 92(6), 243–250.
10. Zhenjie Zhang, & Wansheng Cheng. (2026). Optimization of a strain gauge load cell using an improved Mayfly algorithm. Measurement, 260, Article 119855. DOI: 10.1016/j.measurement.2025.119855.
11. Liu, L., et al. (2025). Design and application of a new high-performance flexible six-axis force/torque sensor for massage therapy. Measurement, 243, Article 116312. DOI: 10.1016/j.measurement.2024.116312.
12. Osypiuk, R., Piskorowski, J., & Kubus, D. (2016). A method of improving the dynamic response of 3D force/torque sensors. Mechanical Systems and Signal Processing, 68–69, 366–377. DOI: 10.1016/j.ymssp.2015.07.007.
13. Pu, M., et al. (2022). Theory and application of an optimal design method for capacitive six-axis force/torque sensors. Measurement, 203, Article 112009. DOI: 10.1016/j.measurement.2022.112009.
14. Zhang, Z., & Cheng, W. (2026). Optimization of a strain gauge load cell using an improved Mayfly algorithm. Measurement, 260, Article 119855. DOI: 10.1016/j.measurement.2025.119855.
15. Park, M., Bok, B.-G., Ahn, J.-H., & Kim, M.-S. (2018). Recent Advances in Tactile Sensing Technology. Micromachines, 9(7), Article 321. DOI: 10.3390/mi9070321.
