A theoretical model used for determining the stiffness of composite leaf springs with a main spring and an auxiliary spring

  • 27 Accesses


The stiffness characteristics of composite leaf springs with a main spring and an auxiliary spring directly affect the handling stability and riding comfort of automobiles and finally determine its application value. In order to achieve precise calculation for the stiffness characteristics of composite leaf springs with a main spring and an auxiliary spring, a theoretical model, which is verified by finite element simulation and related test results, was established by using the mechanics of composite materials and finite difference method. Then, the design parameters that influence the stiffness of the composite leaf spring with a main spring and an auxiliary spring were analyzed to provide a guide for the stiffness matching and optimization of this kind of composite leaf springs. The proposed theoretical model is suitable for parametric modeling and programming, which not only considers the detail features of the spring and the anisotropy of composite material, but also guarantees the speed and the accuracy of the calculation process. This paper also provides a new numerical method for calculating the stiffness of composite structures with arbitrary section shape or complex material composition.

This is a preview of subscription content, log in to check access.

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

Subscribe to journal

Immediate online access to all issues from 2019. Subscription will auto renew annually.

US$ 99

This is the net price. Taxes to be calculated in checkout.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13


  1. 1.

    Rajendran I, Vijayarangan S (2001) Optimal design of a composite leaf spring using genetic algorithms. Comput Struct 79:1121–1129

  2. 2.

    Ke J, Shi W-K, Qian C, Li G-M, Yuan K (2015) Prediction and matching design method for stiffness of composite leaf spring. J Zhejiang Univ (Eng Sci) 49:2103–2110

  3. 3.

    Yang A, Sun Y, Wu X, Si X, Si L, Ding R et al (2015) Development and verification of the composite leaf spring for a heavy tractor. Automot Eng 37:1221–1225

  4. 4.

    Jancirani J, Assarudeen H (2015) A review on structural analysis and experimental investigation of fiber reinforced composite leaf spring. J Reinf Plast Compos 34:95–100

  5. 5.

    Subramanian C, Senthilvelan S (2010) Effect of reinforced fiber length on the joint performance of thermoplastic leaf spring. Mater Des 31:3733–3741

  6. 6.

    Subramanian C, Senthilvelan S (2011) Joint performance of the glass fiber reinforced polypropylene leaf spring. Compos Struct 93:759–766

  7. 7.

    Deshmukh BB, Jaju SB (2011) Design and analysis of glass fiber reinforced polymer (GFRP) leaf spring. In: 4th international conference on emerging trends in engineering and technology, ICETET 2011, 18–20 November 2011. Hotel Le Meridien, IEEE Computer Society, Mauritius, pp 82–87

  8. 8.

    Yinhuan Z, Ka X, Zhigao H (2011) Finite element analysis of composite leaf spring. In: 6th international conference on computer science and education, ICCSE 2011, 3–5 August 2011. IEEE Computer Society, Singapore, pp 316–319

  9. 9.

    Soner M, Tanoglu M, Guven N, Karaagac M, Akyali R, Aksoy O et al (2012) Design and fatigue life comparison of steel and composite leaf spring. SAE 2012 World Congress and Exhibition, 24–26 April 2012. SAE International, Detroit

  10. 10.

    Carello M, Airale AG, Ferraris A, Messana A, Sisca L (2017) Static design and finite element analysis of innovative cfrp transverse leaf spring. Appl Compos Mater 24:1493–1508

  11. 11.

    Gopalakrishnan T, Raja M, Prakash VMJ, Gnanavel C (2017) Design and fabrication of E-glass/carbon/graphite epoxy hybrid composite leaf spring. In: Chandrasekaran M, Arun S (eds) International conference on emerging trends in engineering research

  12. 12.

    Wang H, Hui L, Ding X, Lu Z, Wang D, Wang S et al (2017) Design and preparation of basalt-fiber reinforced composite leaf spring. Eng Plast Appl 45:65–69

  13. 13.

    Hameed MI, Alazawi DA, Hammoudi ZS (2018) Finite element analysis of steel and composite leaf springs under static loading. In: 1st international scientific conference of engineering sciences—3rd scientific conference of engineering science, ISCES 2018, 10–11 January 2018. Institute of Electrical and Electronics Engineers Inc., Diyala, pp 181–185

  14. 14.

    Jenarthanan MP, Ramesh Kumar S, Venkatesh G, Nishanthan S (2018) Analysis of leaf spring using carbon/glass epoxy and EN45 using ANSYS: a comparison. Mater Today Proc 5:14512–14519

  15. 15.

    Oztoprak N, Gunes MD, Tanoglu M, Aktas E, Egilmez OO, Senocak C et al (2018) Developing polymer composite-based leaf spring systems for automotive industry. Sci Eng Compos Mater 25:1167–1176

  16. 16.

    Qian C, Shi W, Chen Z, Yang S, Song Q (2017) Fatigue reliability design of composite leaf springs based on ply scheme optimization. Compos Struct 168:40–46

  17. 17.

    Shi W, Qian C, Chen Z, Song Q, Yang S (2017) Establishment of theoretical model of composite leaf springs by using the mechanics of composite materials. J Reinf Plast Compos 36:1316–1326

  18. 18.

    Ekbote T, Sadashivappa KS, Abdul Budan D (2012) Optimal design and analysis of mono leaf composite spring by finite element analysis. In: 1st international conference on advances in engineering, science and management, ICAESM-2012, 30–31 March 2012. IEEE Computer Society, Nagapattinam, pp 41–46

  19. 19.

    Ismaeel LMA (2015) Optimization and static stress analysis of hybrid fiber reinforced composite leaf spring. Adv Mater Sci Eng 2015:1–13

  20. 20.

    Ke J, Shi W, Qian C, Yuan K, Li G (2015) A multi-objective optimization for composite leaf springs using genetic algorithms. J Xi’an Jiaotong Univ 49:102–108

  21. 21.

    Rajesh S, Bhaskar GB, Subash R, Pazhanivel K, Sagadevan SS (2017) Optimization of composite leaf spring design using response surface methodology. Rom J Mater 47:98–105

  22. 22.

    Subramanian C, Senthilvelan S (2011) Short-term flexural creep behavior and model analysis of a glass-fiber-reinforced thermoplastic composite leaf spring. J Appl Polym Sci 120:3679–3686

  23. 23.

    Wang J, Li Z, Jiang Q (2013) The analysis of composite leaf spring by finite element method and experimental measurements. FISITA 2012 World Automotive Congress, 27–30 November 2012, vol 7. Springer, Beijing, pp 823–829

  24. 24.

    Papacz W, Tertel E, Frankovsky P, Kurylo P (2014) Analysis of the fatigue life of composite leaf springs. Appl Mech Mater 611:346–351

  25. 25.

    Rajesh S, Bhaskar GB (2014) Response of composite leaf springs to low velocity impact loading. In: 2014 international conference on computational intelligence and advanced manufacturing research, ICCIAMR 2014, 2–3 May 2014. Trans Tech Publications Ltd. Chennai, pp 47–50

  26. 26.

    Krall S, Zemann R (2015) Investigation of the dynamic behaviour of CFRP leaf springs. Procedia Eng 100:646–655

  27. 27.

    Venkatesan M, Gandhi VCS, Janarthan E (2015) Performance analysis of composite leaf spring in a defence sumo vehicle. J Eng Sci Technol 10:680–691

  28. 28.

    Rajesh S, Bhaskar GB, Venkatachalam J, Pazhanivel K, Sagadevan S (2016) Performance of leaf springs made of composite material subjected to low frequency impact loading. J Mech Sci Technol 30:4291–4298

  29. 29.

    Shi W, Qian C, Ke J, Gao B, Li G, Yuan K (2016) Prediction and analysis for the modal of a composite leaf spring in a light bus. J Vib Shock 35:139–144

  30. 30.

    Banka H, Muluka R, Reddy V (2017) Fabrication and experimental analysis of epoxy-glass fiber composite leaf spring. In: SAE international conference on advances in design, materials, manufacturing and surface engineering for mobility, ADMMS 2017, 19 July 2017, July ed. SAE International, Chennai

  31. 31.

    Belevi M, Kochan C (2017) Experimental investigation of fiber reinforced composite leaf springs. Mater Test 59:853–858

  32. 32.

    Shi W, Qian C, Song Q, Gao B, Ke J, China SAE (2017) Damping analysis and test research of a composite leaf spring in a light bus. In: Proceedings of Sae-China Congress 2016: Selected Papers, pp 327–341

  33. 33.

    Singh H, Brar GS (2018) Characterization and investigation of mechanical properties of composite materials used for leaf spring. Mater Today Proc 5:5857–5863

  34. 34.

    Rausch J, Mäder E (2010) Health monitoring in continuous glass fibre reinforced thermoplastics: tailored sensitivity and cyclic loading of CNT-based interphase sensors. Compos Sci Technol 70:2023–2030

  35. 35.

    Papacz W, Frankovsky P, Kostka J, Kottfer D (2017) Monitoring of damage of the composite leaf spring using methods of acoustic emission. In: 55th international scientific conference on experimental stress analysis 2017, EAN 2017, 30 May–1 June 2017. Technical University of Kosice, Novy Smokovec, pp 648–657

  36. 36.

    Jamadar NI, Kivade SB, Pedada SR (2018) Detection and quantification of crack in composite mono leaf spring by vibration parameters. J Inst Eng (India) Ser C 99:589–598

  37. 37.

    Jamadar NI, Kivade SB, Raushan R (2018) Failure analysis of composite mono leaf spring using modal flexibility and curvature method. J Fail Anal Prev 18:782–790

  38. 38.

    Jamadar NI, Kivade SB, Tati P (2018) Prediction of residual fatigue life of composite mono leaf spring based on stiffness degradation. J Fail Anal Prev 18:1516–1525

  39. 39.

    Hou JP, Cherruault JY, Nairne I, Jeronimidis G, Mayer RM (2007) Evolution of the eye-end design of a composite leaf spring for heavy axle loads. Compos Struct 78:351–358

  40. 40.

    Kumar MS, Vijayarangan S (2007) Analytical and experimental studies on fatigue life prediction of steel and composite multi-leaf spring for light passenger vehicles using life data analysis. Mater Sci Medzg 13:141–146

  41. 41.

    Kumar MS, Vijayarangan S (2007) Static analysis and fatigue life prediction of steel and composite leaf spring for light passenger vehicles. J Sci Ind Res 66:128–134

  42. 42.

    Cherruault JY, Hou JP, Jeronimidis G, Mayer R, Chvojan J (2010) Testing of fiber composite leaf spring for heavy axle loads. J Thermoplast Compos Mater 24:111–132

  43. 43.

    Liu R, Zhen R, Tang B (1993) Theoretical calculations and experimental verifications of gradually variable rigidity leaf springs. Automob Technol 11:12–15

  44. 44.

    Kim S, Moon W, Yoo Y (2002) An efficient method for calculating the nonlinear stiffness of progressive multi-leaf springs. Int J Veh Des 29(4):403–422

  45. 45.

    Shi WK, Liu C, Chen ZY, He W, Zu QH (2016) Efficient method for calculating the composite stiffness of parabolic leaf springs with variable stiffness for vehicle rear suspension. Math Probl Eng 2016:1–12

Download references


The authors acknowledge the financial support of the National Natural Science Foundation of China (Grant No. 51775514), the Zhejiang Natural Science Outstanding Youth Fund of China (Grant No. LR18E050001) and the Zhejiang Natural Science Youth Fund of China (Grant No. LQ20E050001).

Author information

Correspondence to Zhenyu Wu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Technical Editor: João Marciano Laredo dos Reis.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ke, J., Qian, C., Wu, Z. et al. A theoretical model used for determining the stiffness of composite leaf springs with a main spring and an auxiliary spring. J Braz. Soc. Mech. Sci. Eng. 42, 58 (2020) doi:10.1007/s40430-019-2138-4

Download citation


  • Composite
  • Stiffness
  • Leaf spring
  • Finite element method
  • Finite difference method