A dynamic photo-elasticity based method for ...

A dynamic photo-elasticity based method for Squeak & Rattle noises analysis Thomas Gardin1,2 , François Gautier1 , Charles Pézerat1 1

Laboratoire d’Acoustique de l’Université du Maine, UMR CNRS 6613, Av. O. Messiaen, 72085 Le Mans, France 2 Faurecia Automotive Seats, Caligny technical center, 61100 Caligny, France

Abstract: Recent progress in the field of noise reduction in automotive cockpits, combined with the emergence of new electrical cars, emphasizes other kinds of noises that were masked in the past. These are commonly named Squeak and Rattle noises and are qualified as very disturbing for end user perception. Hence, these noises are potentially very harmful in regards to perceived quality of automotive systems. A methodology based on photo-elasticity is proposed to investigate contacts induced by multiple random impacts. An academic set-up has been developed for representing Squeak and Rattle noises found in industrial context. Using a high speed camera coupled with an optical photo-elastic set-up allows a stress and strain field evolution visualization with time, yielding useful data for the complete understanding of the observed phenomenon.

that are inherent to complex structure. These noises show a great impact on perceived automotive quality, and are direct indicators given to final users of the vehicle build quality and durability. This consequently leads car manufacturers to unwanted quality issues and program over cost. Some surveys estimate that Squeak & Rattle issues represent over 10% of the total warranty claims. Squeaks and Rattles are also reported as the third major concern of final customers after three months of ownerships [3]. One can easily imagine that new advances in terms of noise reduction in automotive cabins tends to potentially increase these figures. Statistical data gathered on various vehicles [4] shows sub-system responsibility. As shown in fig.1 automotive seat systems remain one of the major inducers of Squeak & Rattle issues.

Keywords: Squeak noise, rattle noise, photo-elasticity. 1. Introduction Noises that can be found in an automotive cockpit are generally induced by these three classes of noise sources: - Aero-dynamical noise, increasing with car speed - Road/tyre contact noise, depending on road profile - Engine noise, depending on engine regime Because subsequent progress as been performed in the field of noise reduction of these three following classes, a fourth class has began to appear with more and more importance. Figure 1: Squeak & Rattle issues in automotive subsystems

This fourth class of noises found inside automotive cabins are today mostly divided into two main families. Those caused by loose elements potentially impact others, generally modelled as normal contacts are called Rattle noises [2]. On a the other hand, noise caused by elements in friction are called Squeak noises, and are modelled as tangential contacts [5]. Both of these two noises mostly appear under dynamic solicitation (e.g. forced road surface excitation) and are characterized by their random behaviour. They are due to unwilling contact or free play,

Until today, most of the tests which are carried out to detect squeak and rattle issues on automotive systems are based on the subjective assessments using a four-post test bench, a vibration shaker or road tests. And because squeak and rattle mechanisms of appearance are very difficult to simulate using finite element analysis, due to 1

the wide range of causes and the complexity of these phenomena, only a few studies of squeak and rattle model has been reported using computer aided engineering [1].

adhesives. Use of a circular polariscope allows visualization of isochromatics which corresponds to the points where the difference in the first and second principal stress remains constant. Thus they are the lines which join the points with equal maximum shear stress magnitude. As shown fig.2, a circular polariscope is composed of two polarisers and two quarter wave plates.

In parallel, development of optical based methods dedicated to vibrations measurement have grown up in the last decades. Methods such as laser Doppler vibrometry allow punctual vibrations measurements, and full field displacement measurements are today achieved using numerical holography (speckle interferometry) allowing high spatial resolution [8].

A full field approach such as photo-elasticity is therefore proposed to analyse rattle and squeak process of appearance. This method, initially developed in the beginning of the twentieth century, falls into abeyance due to the development of CAE analysis, however it has multiple advantages: - Photo-elasticity is easy to carry out and can be easily deployed in situ on sub-assembly such as seat systems in order to determine precisely where impacts leading to rattle noise occur on the seat structure. - Photo-elasticity is also not invasive, so that, no perturbations are given to the observed phenomenon, which Figure 2: Circular polariscope in transmission configuration are potentially very sensitive to any external influences. Furthermore, dynamic configuration made possible by the use of a high speed camera, is also helpful to visualize phenomena evolution with time and can help to understand how an impact can influence others.

Considering the polariscope, incident natural light is po−→ larised along the axis of polarisation Xp as −→ (1) E = a0 cos(ωt).Xp .

Firstly, in this paper, a short description of the principle of photo-elasticity is proposed. Then an experimental set-up using dynamic photo-elasticity is introduced. Experimental results are finally discussed using some theoretical assumptions.

When entering the quarter wave plate, projection of the ray is performed along its two axis as − →0 − →0 E = a0 sin(ωt).X − a0 cos(ωt).Y . (2) After projection and several developments, we finally ob→ − tain the light components along the principal strain axis X → − and Y of the considered specimen → − → − π π E = a0 sin(ωt + − β). X − a0 cos(ωt + − β). Y . (3) 4 4

2. Photo-elasticity 2.1 Principle This experimental optical based method allows strain and stress distribution visualization in material and can determine the principal axis of stress and strain directions. Photo-elasticity is based on the accidental birefringent properties of some materials, meaning that isotropic material becomes anisotropic and birefringent when submitted to a stress. Birefringent axis of the considered parts becomes principal axis of strain when the part is stressed.

The angle quoted β is the angle between the principal strain axis and the vertical and horizontal axis. Same projections and developments are then performed on the second part of the polariscope, leading to the following expression of the obtained light intensity −→ − → when the two polarisers are crossed (Xa = −Yp )

Photo-elasticity can be performed in transmission, using a transparent birefringent material, but can also be with: performed in reflection. To do so, the birefringent material is directly bonded on the studied structure using reflective 2

φ I = 4a20 sin2 ( ), 2

φ=

2πδ . λ

(4)

(5)

The parameter δ is the optical delay introduced by the birefringent specimen and directly depends upon principal strain difference ε1 and ε2 as δ = eK(ε1 − ε2 ).

(6)

In a circular polariscope, light intensity becomes zero when δ = 0, δ = 1λ, δ = 2λ. In general, δ = N λ, where N is the isochromatic fringe order. 2.2 Experimental set-up The first objective of the experimental set-up presented in fig.8 is to perform dynamic photo-elasticity. To do so, a circular polariscope is coupled with a high speed camera Figure 4: Fringe pattern observed at the beginning of an (Phantom V 5.1) which is set at 4380 images per seconds. impact (t=0,005 s.) A squared transparent photo-elastic plate (250x250x2 mm) with clamped boundary conditions is considered. A layer of reflective compound is applied on the outer face for light reflection allowing use of the polariscope in a reflective configuration.

Figure 5: Fringe pattern observed at the intermediate phase of an impact (t=0,016 s.)

Figure 3: Experimental set-up used

A monochromatic source such as HE-Ne laser with a wavelength of λ = 630nm is used and diffracted with a microscope lens. The considered plate is randomly impacted on its outer face. The process is filmed simultaneously on the output of the polariscope analyser in order to visualize evolution with time of isochromatics during several impact occurrences. 2.3 Results The three pictures here are extracted from a complete video containing multiple impacts. These three pictures fo- Figure 6: Fringe pattern observed at the end of interaction cus on the evolution with time of a single impact of 0, 07s. between impactor and impacted (t=0,029 s.) duration which is representative from all others. 3

The evolution with time of isochromatics fringe shape indicates that boundary conditions of the plate have an remains always the same: first loop shapes are observed important role in the evolution of its flexural motion field, as shown in fig.4, moving to circular fringes as in fig.5, leading to a non axi-symmetrical stress distribution. which then get back to the loops fringe shapes shown in This first phase is then followed by a brief transient one fig.6. where the motion field is locally axi-symmetrical. TheoretiHence, strain field evolution induced by the impact can cal calculation corroborates this phase only. This symmetry in then lost at the end of the impact, leading to another be decomposed as follows: - A first state at t=0,005 s., given in fig.4, corresponds to non axi-symmetrical stress distribution. the beginning of the impact. Fringe pattern shapes appear One can also denotes that no modifications of the orias loops. - A second phase at t=0,016 s., given in fig.5, corre- entations of the fringes is observed during the first and the sponds to an intermediate phase of the impact, fringe pat- third phases, meaning that there are no modifications of terns are circular shaped. the principal stress and strain axis during the whole impact - A last phase t=0,029s., appearing as not so different process. from the first one, fringe shapes can also be described as 4. Conclusion loops and vanish until the end of the whole considered impact (t = 0, 07s.). An easy to carry out and not invasive method is here proposed to dynamically analyse rattle noise processes of appearance. However, sensitivity of this method has to be In the first phase of the impact shown in fig.4, obtained improved in order to measure very low forced impacts that isochromatics are not axi-symmetrical, meaning that stress can lead to rattle noise. field is also not. Although this study focuses mainly on rattle phenomena. This method can also be deployed regarding friction In order to check the relevance of this experimental reissues leading to squeak noise radiation. sult, a theoretical calculation of fringe pattern obtained in 3. Discussion

the case of an infinitely extended plate submitted to a lateral load is proposed. A detailed development is given in the appendix. Isochromatics are plotted fig.7, an axisymmetrical distribution is clearly generated.

This study also yielded that impact phenomena consequences can be controlled using boundary conditions of the impacted structure which directly influences the structure of the obtained stress and strain field distribution. 5. Acknowledgements The authors would like to thank all the mechatronic team of the research department of Faurecia Automotive Seating. All measurements described in this paper were performed at ENSIM (Ecole Nationale Superieure d’Ingenieurs du Mans) which is gratefully acknowledged. 6. Appendix Some theoretical assumptions, needed in the discussion paragraph are here developed. Let’s first consider a homogeneous isotropic plate of constant rigidity D, subjected to a lateral load P . The governing equation of flexural motion of this plate, is based on Kirchoff’s classical small deflection theory [7]. Equation for thin plate is

Figure 7: Theoretical fringe computation

D∇4 w = D∇2 ∇2 w = P,

(7)

in which

Because stress distribution obtained in the first phase is not axi-symmetrical, this means that the plate can not be considered as an infinite extended one. This should

∇4 ≡

4

∂4 ∂4 ∂4 + 2 + , ∂x4 ∂x2 ∂y 2 ∂y 4

(8)

is the biharmonic operator. A particular solution, obtained from 7 and relevant to an infinite extended plate which is subjected to a concentrated force can be written as [9] w(O, r) =

P r2 Ln(r), 8πD

2D ((1 − ν)εr + νεθ + νεz 1 − 2ν   σ = 2D ((1 − ν)ε + νε + νε θ r z θ 1 − 2ν    σr =

(9)

where O is considered as the point of application of the load, r is the point where the deflection is calculated and D is the flexural rigidity defined here as D=

Eh , 12 − (1 − ν)

(12)

Light intensity emerging from a polariscope can be plotted using the principal strain calculated above and equation 4. In our considered case, circulated fringes are awaited as shown in fig.7.

(10)

7. References

with E Young’s modulus, h plate thickness, ν Poisson’s coefficient.

[1] L. Desvard. Modélisation des bruits parasites à l’interieur d’un habitacle automobile. PhD thesis, INSA Lyon, 2009. [2] L. Desvard, N. Hamzaoui, and J.M. Duffal. Modeling and characterization of rattle noise encountered in an automotive environment. Journal of the Acoustical Society of America, 123(5):3453, 2008. Figure 8: Thin infinite plate and notations

[3] F. Kavarana and B. Rediers. Squeak and Rattle-State of the Art and Beyond. Sound and Vibration, 35(4):56– 65, 2001.

Knowing the plate motion equation (9), thus, the longitudinal components of displacements can be calculated ∂w z ∂w using the following equation u = −z and v = − ∂r r ∂θ [6]. Partial derivation of the motion equation 9 is done. Strain of the impacted plate are then given by  ∂u  εr = −z    ∂r   1 ∂v u (11) + εθ =  r ∂θ r      γ = 1 ∂u + r ∂ v , rθ r ∂θ ∂r r

[4] E. Y. Kuo. Up-front body structural designs for squeak and rattle prevention. SAE International, 2003. [5] B. Laulagnet. Acoustique du contact & des machines. Habilitation à diriger des recherches, INSA Lyon, 2008. [6] A. W Leissa. Vibration of plates. Storming Media, 1969. [7] A. E.H Love. A treatise on the mathematical theory of elasticity. University Press, 1920.

∂v ∂u = 0 and = 0 in our considered case, leading with ∂θ ∂r to γrθ = 0. εr and εθ are considered as principal strain directions that can consequently be used in equation (4).

[8] P. Picart, E. Moisson, and D. Mounier. Twinsensitivity measurement by spatial multiplexing of digitally recorded holograms. Applied optics, 42(11):1947– 1957, 2003.

Principal stress can then be calculated using generalized Hooke’s law

[9] S. Timoshenko and S. Woinowsky-Krieger. Theory of plates and shells. McGraw-Hill New York, 1959.

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