BİLEĞE TAKILAN DOKUNSAL CİHAZ İÇİN SES BOBİNİ AKTÜATÖRÜNÜN MATEMATİKSEL MODELLEMESİ VE FEM TABANLI TASARIM AYARLANMASI

Öz

Ses bobini (voice-coil) aktüatörleri, kompakt yapıları, çift yönlü kontrol edilebilirlikleri ve düzgün kuvvet üretimleri sayesinde dokunsal (haptik) arayüzlerde yaygın olarak kullanılmaktadır. Ancak performansları, elektromanyetik yapılandırmaya ve etkin alan içerisindeki manyetik akı yoğunluğuna güçlü biçimde bağlıdır. Önceki çalışmalarda mekanik tasarım genellikle kapsamlı analizlerden ziyade deneysel gözlemlere dayandırılmıştır. Bu çalışma, CoWrHap adı verilen bileğe takılabilir bir haptik cihaz için özel olarak üretilmiş bir ses bobini aktüatörünün matematiksel modellenmesi ve performans iyileştirme çerçevesini sunmaktadır. Öncelikle, giriş akımı, manyetik akı yoğunluğu ve çıkış kuvveti arasındaki ilişkiyi tanımlayan analitik bir model geliştirilmiştir. Model parametreleri deneysel verilerden elde edilerek etkin manyetik bağlaşım katsayısı ve sürücü devresinin akım doyum sınırları belirlenmiştir. Manyetik akının konuma bağlı uzamsal değişimlerini yakalayabilmek ve alternatif tasarımları değerlendirebilmek amacıyla, ölçülen geometrik ve malzeme özellikleri kullanılarak üç boyutlu bir sonlu elemanlar (FEM) analizi gerçekleştirilmiştir. FEM analizleri, aktüatör ekseni boyunca akı dağılımının düzgün olmadığını göstermiş ve bu doğrultuda yapılan topoloji değişiklikleri sonucunda CoWrHap-2 adlı yeni bir prototip tasarımı elde edilmiştir. Analitik ve sayısal yaklaşımların birleşimi, kuvvet çıktısının doğrusallık ve verimlilik açısından öngörülmesini ve iyileştirilmesini sağlamış; çalışmanın sonuçları, yüksek performanslı bir ses bobini tabanlı haptik cihaz geliştirme potansiyelini ortaya koymuştur.

Anahtar Kelimeler

• Haptik cihazlar
• ses bobini aktüatörleri
• elektromanyetik alan

Destekleyen Kurum

TUBITAK 2232-B programı

Proje Numarası

121C147

Etik Beyan

Yapılan çalışmada araştırma ve yayın etiğine uyulmuştur.

MATHEMATICAL MODELING AND FEM-DRIVEN DESIGN TUNING OF A VOICE-COIL ACTUATOR FOR A WRIST-WORN HAPTIC DEVICE

Öz

Voice-coil actuators are widely used in haptic interfaces due to their compact design, bidirectional controllability, and ability to generate smooth forces. However, their performance strongly depends on the electromagnetic configuration and magnetic flux within the actuation, even though the mechanical design of a prior work was heavily based on experimental observations rather than comprehensive analyses. This study presents a mathematical modeling and enhancement framework for a custom-made voice-coil actuator for a wrist-worn haptic device, named CoWrHap. This paper first presents an analytical model to describe the relationship between input current, magnetic flux density, and output force. The model parameters are identified from experimental data, revealing the effective magnetic coupling coefficient and the current saturation limits of the driver circuit. To capture spatial variations of the magnetic flux and evaluate design alternatives, a three-dimensional finite element method (FEM) simulation is performed using the measured geometric and material properties. The FEM analyses reveal a nonuniform flux distribution along the actuator axis, guiding topology modifications that result in a new prototype design, named CoWrHap-2. The combined analytical and numerical approach enables the prediction and improvement of force output in terms of linearity and efficiency. The results of this study highlight the potential for a high-performance voice-coil haptic device.

Anahtar Kelimeler

• haptic devices
• voice-cail actuation
• electromagnetic field

Destekleyen Kurum

TUBITAK 2232-B program

Proje Numarası

121C147

Etik Beyan

This study complies with the ethical rules of research and publication.

Kaynakça

1. Adeyemi, A., Şen, Ü., Ercan, S. M., & Saraç, M. (2024). Hand Dominance and Congruence for Wrist-Worn Haptics Using Custom Voice-Coil Actuation. IEEE Robotics and Automation Letters, 9(4), 3053. https://doi.org/10.1109/lra.2024.3360815
2. Aliza, A., Zaugg, I., Çelik, E., Stuerzlinger, W., Ortega, F. R., Batmaz, A. U., & Sarac, M. (2024). Eye-Hand Coordination Training: A Systematic Comparison of 2D, VR, and AR Display Technologies and Task Instructions. 2024 IEEE Conference Virtual Reality and 3D User Interfaces (VR), 200. https://doi.org/10.1109/vr58804.2024.00043
3. Chapman, C. E. (1994). Active versus passive touch: factors influencing the transmission of somatosensory signals to primary somatosensory cortex. Canadian Journal of Physiology and Pharmacology, 72(5), 558. https://doi.org/10.1139/y94-080
4. Culbertson, H., Nunez, C. M., Israr, A., Lau, F., Abnousi, F., & Okamura, A. M. (2018). A social haptic device to create continuous lateral motion using sequential normal indentation. 2018 IEEE Haptics Symposium (HAPTICS), 32. https://doi.org/10.1109/haptics.2018.8357149
5. Dominy, N. J. (2009). Evolution of Sensory Receptor Specializations in the Glabrous Skin. Encyclopedia of Neuroscience, 39. https://doi.org/10.1016/b978-008045046-9.00956-6
6. Ercan, S. M., Adeyemi, A., & Saraç, M. (2024). Effects of Rendering Discrete Force Feedback on the Wrist During Virtual Exploration. Lecture Notes in Computer Science, 338. https://doi.org/10.1007/978-3-031-70058-3_28
7. Fahl, J. T., Duvivier, R., Reinke, L., Pierie, J.-P. E. N., & Schönrock-Adema, J. (2023). Towards best practice in developing motor skills: a systematic review on spacing in VR simulator-based psychomotor training for surgical novices. BMC Medical Education, 23(1). https://doi.org/10.1186/s12909-023-04046-1
8. Gaudeni, C., Meli, L., Jones, L. A., & Prattichizzo, D. (2019). Presenting Surface Features Using a Haptic Ring: A Psychophysical Study on Relocating Vibrotactile Feedback. IEEE Transactions on Haptics, 12(4), 428. https://doi.org/10.1109/toh.2019.2938945

9. Hynes, P., & Hashtrudi-Zaad, K. (2013). Evaluation of friction models for haptic devices. In Proceedings of the 2013 IEEE International Conference on Robotics and Automation (ICRA) (pp. 444–449). IEEE. https://doi.org/10.1109/ICRA.2013.6630606
10. Johansson, R. S., & Vallbo, Å. B. (1979). Tactile sensibility in the human hand: relative and absolute densities of four types of mechanoreceptive units in glabrous skin. The Journal of Physiology, 286(1), 283. https://doi.org/10.1113/jphysiol.1979.sp012619
11. Katter, M. (2005). Angular dependence of the demagnetization stability of sintered Nd-Fe-B magnets. IEEE Transactions on Magnetics, 41(10), 3853–3855. https://doi.org/10.1109/TMAG.2005.854872
12. Laffranchi, M., & Caldwell, D. G. (2022). Factors influencing actuator backdrivability in human-centered robotics. Frontiers in Robotics and AI, 9, 1014321. https://doi.org/10.3389/frobt.2022.1014321
13. Lavoie, E. B., Hebert, J. S., & Chapman, C. S. (2025). How a lack of haptic feedback affects eye-hand coordination and embodiment in virtual reality. Scientific Reports, 15(1). https://doi.org/10.1038/s41598-025-10319-0
14. Lorenzis, F. D., Pratticò, F. G., Repetto, M., Pons, E., & Lamberti, F. (2022). Immersive Virtual Reality for procedural training: Comparing traditional and learning by teaching approaches. Computers in Industry, 144, 103785. https://doi.org/10.1016/j.compind.2022.103785
15. Pacchierotti, C., Sinclair, S., Solazzi, M., Frisoli, A., Hayward, V., & Prattichizzo, D. (2017). Wearable Haptic Systems for the Fingertip and the Hand: Taxonomy, Review, and Perspectives. IEEE Transactions on Haptics, 10(4), 580. https://doi.org/10.1109/toh.2017.2689006
16. Palmer, J., Saraç, M., Garza, A. A., & Okamura, A. M. (2022). Haptic Feedback Relocation from the Fingertips to the Wrist for Two-Finger Manipulation in Virtual Reality. 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 628. https://doi.org/10.1109/iros47612.2022.9981392
17. Paredes, P., Ko, R., Aghaseyedjavadi, A., Chuang, J., Canny, J., & Babler, L. (2015). Synestouch: Haptic + audio affective design for wearable devices. 2015 International Conference on Affective Computing and Intelligent Interaction (ACII), 595. https://doi.org/10.1109/acii.2015.7344630
18. Pedram, S., Palmisano, S., Miellet, S., Farrelly, M. C., & Perez, P. (2022). Influence of age and industry experience on learning experiences and outcomes in virtual reality mines rescue training. Frontiers in Virtual Reality, 3. https://doi.org/10.3389/frvir.2022.941225
19. Pezent, E., Macklin, A. S., Yau, J. M., Colonnese, N., & O'Malley, M. K. (2023). Multisensory Pseudo‐Haptics for Rendering Manual Interactions with Virtual Objects. Advanced Intelligent Systems, 5(5). https://doi.org/10.1002/aisy.202200303
20. Postuma, E. M. J. L., Cornelissen, F. W., Pahlevan, M., Heutink, J., & Haan, G. de. (2025). Reduced field of view alters scanning behaviour. Virtual Reality, 29(2). https://doi.org/10.1007/s10055-025-01125-0
21. Sarac, M. (2025). Haptic Relocation Away From the Fingertip: Where, Why, and How. IEEE Transactions on Haptics, 18(3), 470. https://doi.org/10.1109/toh.2025.3581779
22. Saraç, M., Luca, M. D., & Okamura, A. M. (2022). Perception of Mechanical Properties via Wrist Haptics: Effects of Feedback Congruence. 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 620. https://doi.org/10.1109/iros47612.2022.9982079
23. Tanacar, N. T., Mughrabi, M. H., Batmaz, A. U., Leonardis, D., & Sarac, M. (2023). The Impact of Haptic Feedback During Sudden, Rapid Virtual Interactions. 2023 IEEE World Haptics Conference (WHC), 64. https://doi.org/10.1109/whc56415.2023.10224429
24. Toyoda, R., Abegão, F. R., & Glassey, J. (2022). VR-based health and safety training in various high-risk engineering industries: a literature review. International Journal of Educational Technology in Higher Education, 19(1). https://doi.org/10.1186/s41239-022-00349-3
25. Tzolov, D., Bereuter, J., Geissler, M. E., Geissler, R. B., Krause-Jüttler, G., Weitz, J., Distler, M., Oehme, F., Dix, A., & Bechtolsheim, F. von. (2025). Impact of laparoscopic training, haptic feedback and visual haptic latency on virtual fine motor performance. Scientific Reports, 15(1). https://doi.org/10.1038/s41598-025-18862-6
26. Xu, Z., & Zheng, N. (2020). Incorporating Virtual Reality Technology in Safety Training Solution for Construction Site of Urban Cities. Sustainability, 13(1), 243. https://doi.org/10.3390/su13010243
27. Zhang, P., Kamezaki, M., Hattori, Y., & Sugano, S. (2022). A Wearable Fingertip Cutaneous Haptic Device with Continuous Omnidirectional Motion Feedback. 2022 International Conference on Robotics and Automation (ICRA), 8869. https://doi.org/10.1109/icra46639.2022.9812131