Optimizing strain energy extraction from multi-beam piezoelectric devices for heavy haul freight cars

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Heavy haul trains used to transport commodities are generally very long and operated by a single individual. Owing to high noise levels from the rolling stock displacement, the driver cannot notice failures in the compartments. It is practically impossible to visually inspect the wagons located far from the locomotive. Sensors that can measure in-train forces may improve the train’s operation, indicating potential failures and preventing accidents and derailments. However, the freight cars employed in most of the railroads are not equipped with electric power sources, making inspections unlikely. Therefore, an energy harvesting system must be developed for the sensors to avoid the need for periodic battery charging or replacement. As a high level of kinetic energy is present in the rolling stock, a vibration energy harvester (VEH) system is an acceptable alternative. Among VEH devices, multi-beam piezoelectric materials used in planar zigzag (PZ) or orthogonal spiral outer fixed (OSo) configurations can be effective alternatives. These can be powered by low-frequency strains readily available in the freight cars. This study investigates the optimum geometries of PZ and OSo aiming to increase the generated power and minimize the structure mass with a focus on their application to ore wagons. Among the optimum solutions, the OSo geometry generates the maximum power, up to 20.93 mW, which is sufficient to feed some critical devices. Conversely, the PZ configurations present the highest energy density, up to 16.595 mW/kg(m s−2)2, which allows for a more suitable solution to be combined in serial and/or parallel pack configurations.

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  1. 1.

    Li C, Luo S, Cole C, Spiryagin M (2018) Bolster spring fault detection strategy for heavy haul wagons. Veh Syst Dyn 56:1604–1621

  2. 2.

    Eckert JJ, Ramos PG, De Oliveira AJS Jr, Da Silva Martins T, Kurka PRG (2019) A dissipated energy model of shock evolution in the simulation of the dynamics of DGM’s of railway compositions. Mech Mach Theory 134:365–375

  3. 3.

    Vineesh KP, Vakkalagadda MRK, Tripathi AK, Mishra A, Racherla V (2016) Non-uniformity in braking in coaching and freight stock in Indian Railways and associated causes. Eng Fail Anal 59:493–508

  4. 4.

    Macucci M, Di Pascoli S, Marconcini P, Tellini B (2016) Derailment detection and data collection in freight trains, based on a wireless sensor network. IEEE Trans Instrum Meas 65:1977–1987

  5. 5.

    Bernal E, Spiryagin M, Cole C (2019) Onboard condition monitoring sensors, systems and techniques for freight railway vehicles: a review. IEEE Sens J 19:4–24

  6. 6.

    Ung C, Moss SD, Vandewater LA, Galea SC, Chiu WK, Crew G (2013) Energy harvesting from heavy haul railcar vibrations. pp 95–8

  7. 7.

    Teodoro ÍP, Eckert JJ, Lopes PF, Martins TS, Santos AA (2019) Parallel simulation of railway pneumatic brake using openMP. Int J Rail Transp.

  8. 8.

    Teodoro ÍP, Ribeiro DF, Botari T, Martins TS, Santos AA (2018) Fast simulation of railway pneumatic brake systems. Proc Inst Mech Eng Part F J Rail Rapid Transit 233:420–430

  9. 9.

    Lopes MV, Eckert JJ, Martins TS, Santos AA (2018) Optimization of EH multi-beam structures for freight car vibration. IFAC-PapersOnLine 51:849–854

  10. 10.

    Moss S, Barry A, Powlesland I, Galea S, Carman GP (2011) A broadband vibro-impacting power harvester with symmetrical piezoelectric bimorph-stops. Smart Mater Struct 20:045013

  11. 11.

    Ju S, Ji C-H (2018) Impact-based piezoelectric vibration energy harvester. Appl Energy 214:139–151

  12. 12.

    Yang Z, Zhou S, Zu J, Inman DJ (2018) High-performance piezoelectric energy harvesters and their applications. Joule 2:642–697

  13. 13.

    Elvin N, Elvin A, Choi DH (2003) A self-powered damage detection sensor. J Strain Anal 38:115–124

  14. 14.

    Clementino MA, Reginatto R, Da Silva S (2014) Modeling of piezoelectric energy harvesting considering the dependence of the rectifier circuit. J Braz Soc Mech Sci Eng 36:283–292

  15. 15.

    Hafezi M, Mirdamadi HR (2019) A novel design for an adaptive aeroelastic energy harvesting system: flutter and power analysis. J Braz Soc Mech Sci Eng 41:9

  16. 16.

    Siang J, Lim MH, Salman Leong M (2018) Review of vibration-based energy harvesting technology: mechanism and architectural approach. Int J Energy Res 42:1866–1893

  17. 17.

    Li Y, Xie C, Quan S, Zen C, Li W (2018) Vibration energy harvesting in vehicles by gear segmentation and a virtual displacement filtering algorithm. Int J Energy Res 42:1702–1713

  18. 18.

    Silleto MN, Yoon S, Arakawa K (2015) Piezoelectric cable macro-fiber composites for use in energy harvesting. Int J Energy Res 39:120–127

  19. 19.

    Wang L, Chen S, Zhou W, Xu T, Zuo L (2017) Piezoelectric vibration energy harvester with two-stage force amplification. J Intell Mater Syst Struct 28:1175–1187

  20. 20.

    Selvan KV, Ali MSM (2016) Micro-scale energy harvesting devices: review of methodological performances in the last decade. Renew Sustain Energy Rev 54:1035–1047

  21. 21.

    Nayak PP, Kar DP, Bhuyan S (2016) Stimulation of piezoelectric devices through bidirectional wireless energy transfer. Int J Energy Res 40:733–738

  22. 22.

    Santos AA, Lopes MV, Gonçalves V, Eckert JJ, Martins TS (2018) Vibration energy harvesting to power ultrasonic sensors in heavy haul railway cars. In: ASME 2018 international mechanical engineering congress and exposition, American Society of Mechanical Engineers, p V06AT08A021

  23. 23.

    Wang X, Chen C, Wang N, San H, Yu Y, Halvorsen E, Chen X (2017) A frequency and bandwidth tunable piezoelectric vibration energy harvester using multiple nonlinear techniques. Appl Energy 190:368–375

  24. 24.

    Xiong X, Oyadiji SO (2015) Modal optimization of doubly clamped base-excited multilayer broadband vibration energy harvesters. J Intell Mater Syst Struct 26:2216–2241

  25. 25.

    Fan K, Tan Q, Zhang Y, Liu S, Cai M, Zhu Y (2018) A monostable piezoelectric energy harvester for broadband low-level excitations. Appl Phys Lett 112:3–8

  26. 26.

    Karami MA, Inman DJ (2009) Vibration analysis of the zigzag micro-structure for energy harvesting. In: Ahmadian M, Ghasemi-Nejhad MN (eds) Proceedings SPIE, vol 7288, pp 728809–728811

  27. 27.

    Karami MA, Inman DJ (2011) Analytical modeling and experimental verification of the vibrations of the zigzag microstructure for energy harvesting. J Vib Acoust 133:11002

  28. 28.

    Karami MA, Inman DJ (2011) Electromechanical modeling of the low-frequency zigzag micro-energy harvester. J Intell Mater Syst Struct 22:271–282

  29. 29.

    Karami MA, Yardimoglu B, Inman DJ (2010) Coupled out of plane vibrations of spiral beams for micro-scale applications. J Sound Vib 329:5584–5599

  30. 30.

    Santos AA, Hobeck JD, Inman DJ (2016) Analytical modeling of orthogonal spiral structures. Smart Mater Struct 25:115017

  31. 31.

    Santos AA, Hobeck JD, Inman DJ (2018) Orthogonal spiral structures for energy harvesting applications: Theoretical and experimental analysis. J Intell Mater Syst Struct.

  32. 32.

    Bai X, Wen Y, Li P, Yang J, Peng X, Yue X (2014) Multi-modal vibration energy harvesting utilizing spiral cantilever with magnetic coupling. Sens Actuators A Phys 209:78–86

  33. 33.

    Yang Z, Wang YQ, Zuo L, Zu J (2017) Introducing arc-shaped piezoelectric elements into energy harvesters. Energy Convers Manag 148:260–266

  34. 34.

    Zhou S, Hobeck JD, Cao J, Inman DJ (2017) Analytical and experimental investigation of flexible longitudinal zigzag structures for enhanced multi-directional energy harvesting. Smart Mater Struct 26:035008

  35. 35.

    Reilly EK, Miller LM, Fain R, Wright P (2009) A study of ambient vibrations for piezoelectric energy conversion. Proc PowerMEMS 2009:312–315

  36. 36.

    Ung C, Moss SD, Chiu WK (2016) Vibration energy harvesting from heavy haul railcar vibrations using a two-degree-of-freedom coupled oscillating system. Proc Inst Mech Eng Part F J Rail Rapid Transit 230:924–934

  37. 37.

    Wu Y, Qiu J, Zhou S, Ji H, Chen Y, Li S (2018) A piezoelectric spring pendulum oscillator used for multi-directional and ultra-low frequency vibration energy harvesting. Appl Energy 231:600–614

  38. 38.

    Lin T, Pan Y, Chen S, Zuo L (2018) Modeling and field testing of an electromagnetic energy harvester for rail tracks with anchorless mounting. Appl Energy 213:219–226

  39. 39.

    Zhang X, Pan H, Qi L, Zhang Z, Yuan Y, Liu Y (2017) A renewable energy harvesting system using a mechanical vibration rectifier (MVR) for railroads. Appl Energy 204:1535–1543

  40. 40.

    Ortiz J, Monje PM, Zabala N, Arsuaga M, Etxaniz J, Aranguren G (2014) New proposal for bogie-mounted sensors using energy harvesting and wireless communications. Proc Inst Mech Eng Part F J Rail Rapid Transit 228:807–820

  41. 41.

    Ung C, Moss SD, Chiu WK, Payne OR, Vandewater LA, Galea SC (2015) In-service demonstration of electromagnetic vibration energy harvesting technologies for heavy haul rail applications. In: Industrial and commercial applications of smart structures technologies 2015, vol 9433. International Society for Optics and Photonics, p 94330Z

  42. 42.

    Moss SD, Hart GA, Burke SK, Carman GP (2014) Hybrid rotary-translational vibration energy harvester using cycloidal motion as a mechanical amplifier. Appl Phys Lett 104:33506

  43. 43.

    Cho JY, Jeong S, Jabbar H, Song Y, Ahn JH, Kim JH, Jung HJ, Yoo HH, Sung TH (2016) Piezoelectric energy harvesting system with magnetic pendulum movement for self-powered safety sensor of trains. Sens Actuators A Phys 250:210–218

  44. 44.

    Abdelmoula H, Sharpes N, Abdelkefi A, Lee H, Priya S (2017) Low-frequency zigzag energy harvesters operating in torsion-dominant mode. Appl Energy 204:413–419

  45. 45.

    Shu LI, Dapino MAJ, Evans PHG, Chen DI, Uanguo QLU (2011) Optimization and dynamic modeling of Galfenol unimorphs. J Intell Mater Syst Struct 22:781–793

  46. 46.

    Zhang J, Hughes WJ, Newnham RE (2001) Modeling and underwater characterization of cymbal transducers and arrays. IEEE Trans Ultrason Ferroelectr Freq Control 48:560–568

  47. 47.

    Kim S-B, Park J-H, Ahn H, Liu D, Kim D-J (2011) Temperature effects on output power of piezoelectric vibration energy harvesters. Microelectron J 42:988–991

  48. 48.

    Abdelkefi A, Yan Z, Hajj MR (2013) Temperature impact on the performance of galloping-based piezoaeroelastic energy harvesters. Smart Mater Struct 22:055026

  49. 49.

    Hobeck JD, Inman DJ (2017) Recursive formulae and performance comparisons for first mode dynamics of periodic structures. Smart Mater Struct 26:55028

  50. 50.

    Essink BC, Hobeck JD, Owen RB, Inman DJ (2015) Magnetoelastic energy harvester for structural health monitoring applications. Act Passiv Smart Struct Integr Syst 2015(9431):943123

  51. 51.

    Ng TH, Liao WH (2005) Sensitivity analysis and energy harvesting for a self-powered piezoelectric sensor. J Intell Mater Syst Struct 16:785–797

  52. 52.

    Timoshenko S, Goodier JN (1986) Theory of elasticity, vol 49. McGraw-Hill book Company, New York

  53. 53.

    Norton RL (2013) Machine design: an integrated approach. Pearson Education, London

  54. 54.

    Salz CRJ, Hoffman M, Westram I, Rödel J (2005) Cyclic fatigue crack growth in PZT under mechanical loading. J Am Ceram Soc 88:1331–1333

  55. 55.

    Anderson TL (1995) Fracture mechanics: fundamentals and applications. CRC Press, Boca Raton

  56. 56.

    Okayasu M, Ozeki G, Mizuno M (2010) Fatigue failure characteristics of lead zirconate titanate piezoelectric ceramics. J Eur Ceram Soc 30:713–725

  57. 57.

    Gen M, Cheng R, Lin L (2008) Network models and optimization: multiobjective genetic algorithm approach. Springer, NewYork

  58. 58.

    Beeby S, White N (2010) Energy Harvesting for Autonomous Systems. Artech House, Norwood

  59. 59.

    Macucci M, Di Pascoli S, Marconcini P, Tellini B (2015) Wireless sensor network for derailment detection in freight trains powered from vibrations. 2015 IEEE international workshop on measurements & networking (M&N), (IEEE) pp 1–6

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The authors thank VALE S. A. and the University of Campinas UNICAMP (Brazil) for sponsoring the research.

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Correspondence to Jony Javorski Eckert.

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Lopes, M.V., Eckert, J.J., Martins, T.S. et al. Optimizing strain energy extraction from multi-beam piezoelectric devices for heavy haul freight cars. J Braz. Soc. Mech. Sci. Eng. 42, 59 (2020).

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  • Strain energy
  • Planar zigzag
  • Orthogonal spiral
  • Genetic algorithm
  • Electromechanical model