Skip to main content
SpringerLink
Log in

Dynamic characteristics and generation mechanism of windscreen frameless wiper blade oscillations

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Oscillations generated by the windscreen frameless wiper blades during operation will cause unwanted noise and scraping defects, which is a problem that manufacturers need to address. However, the generation mechanism of oscillations is unclear, and the systematic research and development scheme for wiper blades is absent. In this paper, a closed-loop scheme of wiper blade structural design and performance prediction is proposed to solve the problem of oscillations. A sectional linkage model of the wiper system and a stability discriminant were proposed to explain the deep-seated causes of oscillations and explore the critical influencing parameters. Transient structural simulation based on hyperelastic neoprene material and friction exponential decay model was performed to investigate the wiper blade’s nonlinear dynamic behavior and verify the proposed theory’s reliability. The results indicate that the generation mechanism of oscillations can be explained as the instability of the wiper blade due to the excitation of negative friction characteristics. The wiper operates in three conditions, namely slip, stick and skim, each with different dynamic behavior and prerequisites. In a wiping cycle, the periods of slip and stick are closely related to the stability of the wiper blade, while the period of skim is stochastic. The oscillation time, absolute integral of acceleration, and average normal force can be adopted as the indicators of oscillation intensity. Based on the stability discriminant, the critical parameters affecting the oscillation intensity were obtained, which can be adopted in the optimization design of the wiper blade.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

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
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Abbreviations

W :

Strain energy potential function

\(\mu _{1i}, \alpha _i\) :

Hyperelastic material constants

\(D_k\) :

Incompressibility parameter

\(\lambda _{a,b,c}\) :

Principal elongation parameters

\(\mu _\textrm{e}\) :

Friction coefficient characterized by the exponential decay model

\(\mu _\textrm{s}\) :

Friction coefficient characterized by the Stribeck model

\(v_\textrm{rel}\) :

Horizontal relative velocity of the blade lip tip relative to the windscreen

Mu:

Static coefficient of friction in the exponential decay model

Fact:

Ratio of static to dynamic coefficients of friction in the exponential decay model

DC:

Decay coefficient in the exponential decay model

\(\textrm{co}_1\) :

Static coefficient of friction in the Stribeck model

\(\textrm{co}_2\) :

Dynamic coefficient of friction in the Stribeck model

\(\textrm{co}_3\) :

Decay coefficients in the Stribeck model

\(l_0\) :

Customized representative length

T :

Dimensionless representative time

t :

Wiper system motion time

\(l_1\) :

Length of the upper linkage, which represents the length of the blade body

\(l_2\) :

Length of the upper linkage, which represents the length of the blade lip

\(l_{G_1}\) :

Distances from the midpoint of the blade neck to the centroid of the blade body

\(l_{G_2}\) :

Distance from the boundary between the blade body and lip to the centroid of the blade lip

\(I_1\) :

Moment of inertia of the blade body rotating around an axis passing through its centroid and perpendicular to the cross section of the wiper system

\(I_2\) :

Moment of inertia of the blade lip rotating around an axis passing through its centroid and perpendicular to the cross section of the wiper system

\(\rho \) :

Density of neoprene rubber

\(m_1\) :

Mass of the blade body

\(m_2\) :

Mass of the blade lip

\(k_0\) :

Elastic coefficient of the vertical spring at the support side equated by the blade head, spring beams and holder reinforcements

\(c_0\) :

Viscous coefficient of the vertical spring at the support side equated by the blade head, spring beams and holder reinforcements

\(c_1\) :

Viscous coefficient of the torsion spring at the blade neck

\(c_2\) :

Viscous coefficient of the torsion spring at the midpoint of the boundary between the blade body and lip

\({\widetilde{\varphi }}\) :

Critical rotation angle of the blade body when it just touches the blade shoulder

\(\varphi _1\) :

Rotation angle of the blade body around the midpoint of the blade neck

\(\varphi _2\) :

Rotation angle of the blade lip around the midpoint of the boundary between the blade body and lip

\(k_{\varphi _1}\) :

Elasticity coefficient of the equivalent torsion spring at the centroid of the blade neck

\(k_M\) :

Elastic coefficient of the equivalent torsion spring at the blade neck when the blade body is in contact with the blade shoulder

\(k_m\) :

Elastic coefficient of the equivalent torsion spring at the blade neck when the blade body is not in contact with the blade shoulder

\(k_{\varphi _2}\) :

Elasticity coefficient of the equivalent torsion spring at the boundary between the blade body and lip

\(M_{\varphi _1}\) :

Restoring moment at the blade neck

\(m_{a,b,c}\) :

Dimensionless coefficients related to mass

\(m_{{\varphi _1},{\varphi _2}}\) :

Dimensionless moments of inertia

S :

Horizontal displacement of the windscreen relative to the blade head

\(h_\textrm{d}\) :

Push-down distance of the support side

\(V_\textrm{s}\) :

Velocity amplitude of the horizontal motion of the windscreen in sinusoidal form

\(f_\textrm{s}\) :

Frequency of velocity change of the windscreen moving horizontally in sinusoidal form

\(\emptyset \) :

Initial phase of the velocity of the windscreen moving horizontally in sinusoidal form

\(\lambda _\textrm{N}\) :

Normal force of the blade lip tip in contact with the windscreen

\(\lambda _\textrm{T}\) :

Friction between the blade lip tip and the windscreen

J :

Jacobian matrix

\(\lambda _{1,2}\) :

Eigenvalues of the Jacobian matrix J

\(\chi _1\) :

Parameter in eigenvalues, which is also the stability discriminant

\(\chi _2\) :

Parameter in eigenvalues

\(\chi _2\) :

Parameter in eigenvalues

\({\Delta t}\) :

Oscillation time

H :

Maximum overshoot

AIA:

Absolute integral of acceleration

\({\lambda _\textrm{N}}_\textrm{avr}\) :

Average normal force in the reversal position

References

  1. Okura, S., Sekiguchi, T., Oya, T.: Complete 3D dynamic analysis of blade reversal behavior in a windshield wiper system. SAE Papers. (2003). https://doi.org/10.4271/2003-01-1373

  2. Lee, S.H., Kim, Y.H., Sung, J., Shin, K.C., Oh, J.H.: Investigation of the contact force distribution and dynamics behaviour of an automobile windshield wiper blade system. Proc. Inst. Mech. Eng. 227(7), 1040–1052 (2013). https://doi.org/10.1177/0954407012474136

    Article  Google Scholar 

  3. Fuji, Y., Yamaguchi, T.: Dynamic characteristics measurements of a car wiper blade. JSME Int J. Ser. C 49(3), 799–803 (2007). https://doi.org/10.1299/jsmec.49.799

    Article  Google Scholar 

  4. Lancioni, G., et al.: Dynamics of windscreen wiper blades: squeal noise, reversal noise and chattering. Int. J. Non-Linear Mech. 80, 132–143 (2016). https://doi.org/10.1016/j.ijnonlinmec.2015.10.003

    Article  Google Scholar 

  5. Lee, H.I.: A study on the attenuation of flip-over vibration in the flat blade windshield wiper. Trans. Korean Soc. Noise Vib. Eng. 22(10), 974–984 (2012). https://doi.org/10.5050/KSNVE.2012.22.10.974

    Article  Google Scholar 

  6. Awang, I.M., et al.: Complex eigenvalue analysis of windscreen wiper chatter noise and its suppression by structural modifications. Veh. Struct. Syst. 1, 24–29 (2009). https://doi.org/10.4273/ijvss.1.1-3.03

    Article  Google Scholar 

  7. Grenouillat, R., Leblanc, C.: Simulation of chatter vibrations for wiper systems. SAE Technical Paper 1 (2002). https://doi.org/10.4271/2002-01-1239

  8. Suzuki, R., Yasuda, K.: Analysis of chatter vibration in an automotive wiper assembly. Int. J. Jpn. Soc. Mech. Eng. 41, 616–620 (1998). https://doi.org/10.1299/jsmec.41.616

    Article  Google Scholar 

  9. Goto, S., Takahashi, H., Oya, T.: Clarification of the mechanism of wiper blade rubber squeal noise generation. JSAE Rev. 22(1), 57–62 (2001). https://doi.org/10.1016/S0389-4304(00)00095-3

    Article  Google Scholar 

  10. Shun, C.C., Hai, P.L.: Chaos attitude motion and chaos control in an automotive wiper system. Int. J. Solids Struct. 41(13), 3491–3504 (2004). https://doi.org/10.1016/j.ijsolstr.2004.02.005

    Article  MATH  Google Scholar 

  11. Min, D., Jeong, S., Yoo, H.H., et al.: Experimental investigation of vehicle wiper blade’s squeal noise generation due to windscreen waviness. Tribol. Int. 80, 191–197 (2014). https://doi.org/10.1016/j.triboint.2014.06.024

    Article  Google Scholar 

  12. Xiong, Z., Deng, K., Liu, Z., et al.: The finite volume element method for a parameter identification problem. J. Ambient Intell. Hum. Comput. 6, 533–539 (2015). https://doi.org/10.1007/s12652-014-0238-7

    Article  Google Scholar 

  13. Unno, M., et al.: Analysis of the behavior of a wiper blade around the reversal in consideration of dynamic and static friction. J. Sound Vib. 393, 76–91 (2017). https://doi.org/10.1016/j.jsv.2017.01.018

    Article  Google Scholar 

  14. Turner, J.D.: On the simulation of discontinuous functions. J. Appl. Mech. 68(5), 751–757 (2001). https://doi.org/10.4271/2015-01-0106

    Article  MATH  Google Scholar 

  15. Baumgarte, J.: Stabilization of constraints and integrals of motion in dynamical systems. Comput. Methods Appl. Mech. Eng. 1(1), 1–16 (1972). https://doi.org/10.1016/0045-7825(72)90018-7

    Article  MATH  Google Scholar 

  16. Deleau, F., Mazuyer, D., Koenen, A.: Sliding friction at elastomer/glass contact: Influence of the wetting conditions and instability analysis. Tribol. Int. 42(1), 149–159 (2009). https://doi.org/10.1016/j.triboint.2008.04.012

    Article  Google Scholar 

  17. Vola, D., Raus, M., Martins, J.A.C.: Friction and instability of steady sliding: squeal of a rubber/glass contact. Int. J. Numer. Methods Eng. 46, 1699–1720 (1999). https://doi.org/10.1002/(SICI)1097-0207(19991210)46:10<1699::AID-NME720>3.0.CO;2-Y

    Article  MATH  Google Scholar 

  18. Stein, G.J., Zahoranský, R., Múčka, P.: On dry friction modelling and simulation in kinematically excited oscillatory systems. J. Sound Vib. 311(1–2), 74–96 (2008). https://doi.org/10.1016/j.jsv.2007.08.017

    Article  Google Scholar 

  19. Sheng, G.: Friction-Induced Vibrations and Sound: Principles and Applications. CRC Press, London (2007)

    Google Scholar 

  20. Denny, M.: Stick-slip motion: an important example of self-excited oscillation. Eur. J. Phys. 25(2), 311 (2004). https://doi.org/10.1088/0143-0807/25/2/018

    Article  MATH  Google Scholar 

  21. Rouzic, J., et al.: Friction-induced vibration by Stribeck’s law: application to wiper blade squeal noise. Tribol. Lett. 49(3), 563–572 (2013). https://doi.org/10.1007/s11249-012-0100-z

    Article  Google Scholar 

  22. Farivar, F., Shoorehdeli, M.A., Manthouri, M.: Improved teaching–learning based optimization algorithm using Lyapunov stability analysis. J. Ambient Intell. Hum. Comput. 13, 3609–3618 (2022). https://doi.org/10.1007/s12652-020-02012-z

    Article  Google Scholar 

  23. Ambikapathy, B., Krishnamurthy, K.: Analysis of electromyograms recorded using invasive and noninvasive electrodes: a study based on entropy and Lyapunov exponents estimated using artificial neural networks. J. Ambient Intell. Hum. Comput. (2018). https://doi.org/10.1007/s12652-018-0811-6

    Article  Google Scholar 

  24. Nakano, K.: Two dimensionless parameters controlling the occurrence of stick-slip motion in a 1-DOF system with Coulomb friction. Tribol. Lett. 24(2), 91–98 (2006). https://doi.org/10.1007/s11249-006-9107-7

    Article  Google Scholar 

  25. Zolfagharian, A., et al.: Unwanted noise and vibration control using finite element analysis and artificial intelligence. Appl. Math. Model. 38, 2435–2453 (2014). https://doi.org/10.1016/j.apm.2013.10.039

    Article  MATH  Google Scholar 

  26. Stenti A, Vanderostyne K, Hauser F.: A mechatronic approach to reduce wiper system reversal noise: development of a multi-objective optimization tool (2012)

  27. Zhe, Y., Qin, W., Hou, Q., et al.: Dynamic analysis of wiper system and noise prediction of blade reverse. SAE Technical Papers 1 (2015). https://doi.org/10.4271/2015-01-0106

  28. Mizokami, M., Akuto, T., et al.: A fundamental study on the reversal behavior of an automobile wiper blade. ASME Int. Mech. Eng. Congr. Expo. (2009). https://doi.org/10.1115/IMECE2009-11038

    Article  Google Scholar 

  29. Cadirci, S., Ak, E.S., Selenbas, B., Gunes, H.: Numerical and experimental investigation of wiper system performance at high speeds. J. Appl. Fluid Mech. 10(3), 861–870 (2017). https://doi.org/10.18869/ACADPUB.JAFM.73.240.26527

    Article  Google Scholar 

  30. Goto, S., Takahashi, H., Oya, T.: Investigation of wiper blade squeal noise reduction measures. SAE Paper 1 (2001). https://doi.org/10.4271/2001-01-1410

  31. Tang, S., Zhang, G., Yang, H., et al.: A data-driven approach to use 1D data for 3D nonlinear elastic materials modeling. Comput. Methods Appl. Mech. Eng. 357, 112587 (2019). https://doi.org/10.1016/j.cma.2019.112587

    Article  MATH  Google Scholar 

  32. Hong, J.G., Won, H.I., Kim, H.R., et al.: Squeal noise reduction of an automobile wiper blade. Trans. Korean Soc. Noise Vib. Eng. 24(5), 374–380 (2014). https://doi.org/10.5050/KSNVE.2014.24.5.374

    Article  Google Scholar 

  33. Hou, Q., Qin, W., Yu, Z., et al.: Analysis of windshield wiper reversal impact and its suppression by structural design. SAE Technical Paper (2015). https://doi.org/10.4271/2015-01-0108

  34. Galvanetto, U.: Non-linear dynamics of multiple friction oscillators. Comput. Methods Appl. Mech. Eng. 178(3–4), 291–306 (1999). https://doi.org/10.1016/j.ijnonlinmec.2018.12.004

    Article  MATH  Google Scholar 

  35. Pfeiffer, F.G., Foerg, M.O.: On the structure of multiple impact systems. Nonlinear Dyn. 42, 101–112 (2005). https://doi.org/10.1007/s11071-005-1910-4

    Article  MATH  Google Scholar 

  36. Lancioni, G., Stefano, L., Ugo, G.: Non-linear dynamics of a mechanical system with a frictional unilateral constraint. Int. J. Non-Linear Mech. 44(6), 658–674 (2009). https://doi.org/10.1016/j.ijnonlinmec.2009.02.012

    Article  Google Scholar 

  37. Guo, J., Chen, Y., Lai, G., et al.: Neural networks-based adaptive control of uncertain nonlinear systems with unknown input constraints. J. Ambient Intell. Hum. Comput. (2021). https://doi.org/10.1007/s12652-020-02582-y

    Article  Google Scholar 

  38. Rigatos, G., Siano, P., Zervos, N.: An approach to fault diagnosis of nonlinear systems using neural networks with invariance to Fourier transform. J. Ambient Intell. Hum. Comput. 4, 621–639 (2013). https://doi.org/10.1007/s12652-012-0173-4

    Article  Google Scholar 

  39. Sugita, M., Yabuno, H., Yanagisawa, D.: Bifurcation phenomena of the reversal behavior of an automobile wiper blade. Nonlinear Dyn. 69(3), 1111–1123 (2012). https://doi.org/10.1007/s11071-012-0332-3

    Article  Google Scholar 

  40. Leine, I.R., Nijmeijer, H.: Dynamics and Bifurcations of Non-smooth Mechanical Systems. Springer Science and Business Media, Berlin (2013)

    MATH  Google Scholar 

  41. Dankowicz, H., Nordmark, A.: On the origin and bifurcations of stickslip oscillations. Physica D 136, 280–302 (2000). https://doi.org/10.1016/S0167-2789(99)00161-X

    Article  MATH  Google Scholar 

  42. Peng, Z., Yu, W., Wang, J., et al.: Dynamic analysis of seven-dimensional fractional-order chaotic system and its application in encrypted communication. J. Ambient Intell. Hum. Comput. 11, 5399–5417 (2020). https://doi.org/10.1007/s12652-020-01896-1

    Article  Google Scholar 

  43. Gupta, V., Mittal, M., Mittal, V.: Chaos theory: an emerging tool for arrhythmia detection. Sens. Imaging 21(1), 1–22 (2020). https://doi.org/10.1007/s11220-020-0272-9

    Article  Google Scholar 

  44. Gupta, V., Mittal, M.: QRS complex detection using STFT, chaos analysis, and PCA in standard and real-time ECG databases. J. Inst. Eng. India Ser. B 100, 489–497 (2019). https://doi.org/10.1007/s40031-019-00398-9

    Article  Google Scholar 

  45. Gupta, V., Mittal, M., Mittal, V.: Chaos theory and ARTFA: emerging tools for interpreting ECG signals to diagnose cardiac arrhythmias. Wirel. Pers. Commun. 118, 3615–3646 (2021). https://doi.org/10.1007/s11277-021-08411-5

    Article  Google Scholar 

  46. Gupta, V., Mittal, M., Mittal, V.: R-peak detection using chaos analysis in standard and real time ECG database. IRBM 40(6), 341–354 (2019). https://doi.org/10.1016/j.irbm.2019.10.001

    Article  Google Scholar 

  47. Gupta, V., Mittal, M., Mittal, V.: R-peak detection based chaos analysis of ECG signal. Analog Integr. Circ. Sig. Process 102, 479–490 (2020). https://doi.org/10.1007/s10470-019-01556-1

Download references

Acknowledgements

The authors would particularly like to thank the reviewers for their positive and constructive comments.

Funding

The authors have not received any funding.

Author information

Authors and Affiliations

  1. School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, 200444, China

    Yunyuan Li & Jingjing Xu

Authors
  1. Yunyuan Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jingjing Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Yunyuan Li or Jingjing Xu.

Ethics declarations

Conflicts of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

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

Appendix A: Coefficients in the equations

Appendix A: Coefficients in the equations

The coefficients in (10) are expressed as follows:

$$\begin{aligned} \begin{aligned}&a_0(\varphi _1)=m_{\varphi _1}-m_al_1^*\sin ^2{\varphi _1}\\&a_1(\varphi _1)=-m_al_1^*\cos {\varphi _1}\sin {\varphi _1}\\&a_2=c_1^*+c_2^*\\&a_3(\varphi _1,\ \varphi _2)=\left( k_{\varphi _1}^*(\varphi _1,\ \varphi _2)\right) +m_{\varphi _2}\\&b_0(\varphi _1,\ \varphi _2)=m_c\cos {(\varphi _1-\varphi _2})-m_al_2^*\sin {\varphi _1}\sin {\varphi _2}\\&b_1(\varphi _1,\varphi _2)=m_c\sin {\left( \varphi _1-\varphi _2\right) }-m_al_2^*\cos {\varphi _2\sin {\varphi _1}}\\&b_2=-c_2^*\\&b_3=-m_{\varphi _2}\\&d_1(\varphi _1)=m_a{{\ddot{S}}}^*\cos {\varphi _1}-{\lambda _\textrm{N}}^*l_1^*\sin {\varphi _1}+{\lambda _\textrm{T}}^*l_1^*\cos {\varphi _1} \end{aligned} \nonumber \\ \end{aligned}$$
(A.1)

And the coefficients in (11) are expressed as follows:

$$\begin{aligned}{} & {} a_4(\varphi _1,\ \varphi _2)=m_c\cos {(\varphi _1-\varphi _2})-m_bl_1^*\sin {\varphi _1}\sin {\varphi _2}\nonumber \\{} & {} a_5(\varphi _1,\ \varphi _2)=m_c\sin {\left( \varphi _1-\varphi _2\right) }-m_bl_1^*\cos {\varphi _1\sin {\varphi _2}} \nonumber \\{} & {} a_6=-c_2^*\nonumber \\{} & {} a_7=-m_{\varphi _2}\nonumber \\{} & {} b_4(\varphi _2)=m_{\varphi _2}-m_bl_2^*\sin ^2{\varphi _2}\nonumber \\{} & {} b_5(\varphi _2)=-m_bl_2^*\cos {\varphi _2}\sin {\varphi _2}\nonumber \\{} & {} b_6=c_2^*\nonumber \\{} & {} b_7=m_{\varphi _2}\nonumber \\{} & {} d_3(\varphi _2)=m_b{{\ddot{S}}}^*\cos {\varphi _2}-{\lambda _\textrm{N}}^*l_2^*\sin {\varphi _2}+{\lambda _\textrm{T}}^*l_2^*\cos {\varphi _2} \nonumber \\ \end{aligned}$$
(A.2)

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, Y., Xu, J. Dynamic characteristics and generation mechanism of windscreen frameless wiper blade oscillations. Nonlinear Dyn 111, 3053–3079 (2023). https://doi.org/10.1007/s11071-022-08030-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-022-08030-0

Keywords

Search

Navigation