SAE TECHNICAL 2011-36-0117 PAPER SERIES E Analysis of …static.tongtianta.site/paper_pdf/041f4de4-33ff-11e9-9595... · 2019-02-19 · XX SAE BRASIL International Congress and Exhibition

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SAE TECHNICAL 2011-36-0117 PAPER SERIES E

Analysis of Deformation and Stress Distribution for Spring

Kelen Cristiane Cardoso

Thiago Caetano de Freitas Rudoniel Corrêa Cury

Fabio Nonato de Paula

Eardrum in the Clutch by the Method of Moire Interferometry

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2011-36-0117

Analysis of Deformation and Stress Distribution for Spring Eardrum in the Clutch by the Method of Moire Interferometry

Kelen Cristiane CardosoRudoniel Correa Cury

Thiago Caetano de FreitasFabio Nonato de Paula

Schaeffler Group

Copyright © 2011 SAE International

ABSTRACT

The basic function of the clutch, transmitting torque when running, interrupting the flow of power between the engine and gearbox in the changing gears and stopping and protecting the engine and transmission against overload and dampen vibration transmission. The plateau clutch with spring-membrane is the system used today. The modern clutches are small and save space in the engine compartment reducing the total weight of transmission, minimizing the resistance to rotation of the motor, providing less mechanical losses. The construction and assembly of the membrane spring clutch assembly is very important, since misalignment of reeds could result in chatter or vibration in clutch pedal, along with the hard drive of the pedal, which can also generate a deformation of the components and thus premature wear of the clutch. The displacement of the diaphragm spring clutch actuation promotes a change in the distribution of stress and strain on your profile as well as the components associated with spring, and the misalignment of the reeds causes this distribution is not uniform. The shadow moiré technique can help to assessment the deformation and stresses on the surface of the membrane spring. Conventional techniques of extensimeter and computer simulation (using FEA tools) of the drive spring are used as a basis for comparison between the results obtained by moiré in order to provide a validation of the technique. Replace this description with text.

INTRODUCTION

The car market is known by the big diversity of applications,creating a complex range of requirements for the clutch system, which shows the importance and need of a longer life system, given a clear competitive advantage, both in the series as the replacement market. BRASOLIN [1]

The Clutch is on the most of vehicles powered by combustion engines, but nowadays, the automatic transmission is being widely used by the drive comfort. Because the high cost ismostly used in larger vehicles, on the other hand, shows a consumption fuel increase and performance reduction. Due to the demand for emissions and fuel consumption reduction,

current developments allow integration with hybrid cars (electric & combustion engines), which ensures a long future for the clutches in vehicles.The clutch system is located between the engine and transmission and consists of three basic components: the plateau, the disc and flywheel, where the clutch itself consists of plateau and the disc. Figure 01.

Figure 01: a.) Plateau and b.) Clutch Disc

The clutch is responsible to give the axial power compression needed to transmit the engine torque for the vehicle transmission. It´s also responsible to disconnect physically the engine from the transmission, enabling the driver make the gear changes. Picture 02

Figure 02: a.) Plate spring, b.) Rings, c.)Pressure plate, d.)Diaphragm spring , e.)Plateau and f.) Rivets.


Figure 03: a.) Friction lining, b.) Mating disc, c.) Segmentspring, d.) Rivet, e.) Drive disc, f.) Flange, g.) Pressure spring,h.) Friction bushing, i.) Friction ring, j.) Disk suport, k.)Spacer plate, l.) Plate sprig and m.) Hub.

The basic clutch function is transmit the torque when the vehicle is engaged; stop the power flow between the engine and gear box, in the gear changes and stopped; protect the engine and the transmission against overload and cushion the vibration.

The construction of diaphragm spring and your assembling in the clutch group is very important, because the “fingers” misalignment, could result trepidation or vibration in the clutch pedal, difficulty for the pedal actuation, and may also make the deformation in the components and cause premature damages in the clutch .

The displacement of diaphragm spring during the clutch actuation promotes a distribution changing in the tension and deformation in your profile, as well in the components linked with the spring, and a no uniform distribution is made by the "fingers" misaligned.

The propose of this paper is study by the Moiré Shadow Technique, the qualification of tension and deformation in a diaphragm spring. The Moiré Shadow Technique can help the simulation to determine the deformation, the stress and the pressure distribution on the diaphragm spring surface. The computer simulation of spring action is gonna be used as a basis to compare the obtained results by Moiré technique inorder to validate the study technique in mechanic elements of complex geometry. Strain gages were used to validate the shadow moiré technique .

Technique Shadow Moiré

The perfilometry technique application is of great importance to various industrial segments, mostly in practices and qualitycontrol, mathematical modeling and clinical diagnosis. Within the industry is a powerful tool in manufacturing, quality control, reverse engineering and modeling static and dynamic loads that are submitted to mechanical components.

The optical technique has the benefit of be quick and not have fisic contact. The Moiré´s technique of shadow and projection is the profilometry technique most used , due to its simplicity and speed, and it is reason of frequent studies and various applications.

The moiré´s phenomenon happens when we have two overlapping grids forming fringes, that is the result of the two lines grids combination. This phenomenon is called Moire´s phenomenon or Moire´s effect and the fringes formed are called Moiré´s patterns ou Moiré´s fringes. SCHIAMMARELLA, C. A [2] Mention that the word “moiré” is the French origin and means "watered" . CLOUD, G [3] Mention that D. TOLLENAR in 1975 studying the phenomenon found that the moiré´s fringes are a movement magnificator and could give high sensitivity measurements of relative movement. The same author also mentions that several other authors used to study the phenomenon of displacement, strain and tension. The moiré fringes are produced when overlap two periodic structures, called "grids". (Figure 04)

Figure 04: Moiré fringes produced by two overlapping grids of the same period.

These reticles can be formed with parallel or radial lines, concentric circles or ellipses, or the same points spaced equidistant or not. The most used are made up of lines or stripes (transparent) and dark (opaque), parallel and equidistant. The center of the tracks is called “grid line” and the distance between the centers of grid lines in two continuous stripes is the period or pitch (p) of the reticulum and the inverse of the period and the frequency of reticulum (f), usually given in lines per mm ( millimeters)

The moire fringes considering two reticles, which have spaced equidistant lines, and one (R1 reticle), which has lines parallel to axis y, with period "p1", is overlapped by another (R2reticle) with lines with period "P2" unlike "p1", forming an angle θ between the lines reticulum in two. We noted the appearance of a third grid formed by intersecting lines of the reticle R1 and R2 (Figure 5).

Figure 05: Formation of moire fringes formed by overlapping lattice of parallel lines. Source CLOUD (1988).


In figure 05 has that:

Where:

φ = angle between the fringe moiré and y-axis.

P1 = period of R1

P2 = period de R2

θ= angle between the lines R1 and R2.

Where

Pm= period of the moiré fringe.

An important aspect about the moire fringes formation is that the visualization of these fringe behaves, in most cases, such as sine waves (Figure 06). The light intensity observed is in truth, the average light transmitted through the reticle 1 and 2. Where the light transmitted is maxim , this is the center of the fringes, and where the light transmitted tends to zero, this is the center of the dark fringes

Figure 06: Formation of moire fringes by the transmission of light through two reticulum consisting of parallel lines superimposed. Source CLOUD (1988)

Several techniques based on the moiré phenomenon, are used for measurement of deformation in the plane and outside the plan. Several authors tried to classify the TM, considering the period of the lattice, the formation of fringes and the type of deformation studied.

All Moiré´s techniques can provide the same information and can be interpreted in the same way. The difference between them is on the optical methods used for the formation of moire fringes. In the "Technical Reticulum, " these are analyzed individually and subtracted, resulting in moire standard. In the "Moire Technique" is used the geometric optic system formed by the obstruction of light by two superposed reticulum to explain the formation of moire fringes. While in the "Moire Interferometry", diffraction and interference are the basis of the formation of moire fringes.

For all Moire techniques are necessary two reticles, one follows the contour of the object and is called “reticulum deformed“ and the other stayed intact and is used as reference,and because this is called reticulum undeformed or reference.These two reticulum can mean two reticulum can be physically separated as two records in the same lattice, one before and one after deformation. LINO, A. C. L [6]

The sensitivity of moiré techniques depends mainly on the period of the reticulum, where a shorter period provides greater sensitivity. This sensitivity is desirable for strain measurements in the plane, when has need very small displacement measurement.

SCHIAMMARELLA, C. A. [2] says that the period most commonly used in applications to work with moire, varies between 10 to 40 lines / mm, but higher density line can be used. Fringes produced by low density lines can be observed with the naked eye ordinary light, but for high densities lines, as the effect of diffraction of light becomes dominant, it is necessary to use coherent light.

The Table 01 shows the frequency and the sensitivity of the reticulum of moire used for Geometric plan Moire, Interferometry Moire and Shadow Moiré.

Table 01: Frequency lines for the Moire technique and sensitivity of each one.

.

For the Moiré’s technique of shadow and projection, the angles of illumination and observation in relation to the normal line at moire reticulum are very important . Increasing these angles, or just one, the sensitivity is also increase.

The sensitivity of the Moiré techniques can be increased through various methods such as, fringe interpolation , fringes multiplication and unmet grids

CLOUD, G [3]. Demonstrates the formation of moireshadow´s fringes. The reticulum of model (Rm) follows the topography of the object and this is observed through the reference reticulum (Rr). In some areas the RM lines , from the perspective of the viewer, are under the Rr lines, allowing reflected light transmission by the object's surface, forming the bright fringes. In other areas the Rr lines are aligned with


Rm lines, therefore , no transmission to the viewer of light, thus forming the dark fringes. Figure 7 shows a complete cycle, which goes from clear to dark fringes and dark to bright.

Figure 07: Formation of Moire shadow´s fringes. CLOUD (1988).

MATERIALS AND METHODS

A shadow moiré technique was employed to analyze as well as to qualify the axial deformation imposed to a clutch diaphragm spring. Figure 08 displays the experimental setup selected to carry the tests.

Figure 08: Experiment Setup.

The experimental setup included a vertical hydraulic testing press of 15 ton capacity, a Samsung 7.1 megapixel digital camera equipped with remote control to avoid undesired movement, a white light source, a set of 0.2 mm Ronchi grids and a micrometer. The diaphragm was painted with opaque white color to improve contrast.

Displacements from 0 to 7 mm were imposed to the specimen meanwhile the images were captured at each mm of displacement. Loaded and unloaded diaphragm images were capture sa follows:

The grid was projected on the unloaded diaphragm face, having its image recorded, generating the I1(x,y) image. The image corresponding to 1 mm displacement was named

I2(x,y), following the remaining displacement values generated the images I3(x,y) to I8(x,y). Images were them processed by means of the ImageJ, Hidrisi KilimanjaroSoftware.

Finite elements simulations were carried as well by means of the Abaqus 6.10 software to validate the shadow moiré technique which was the base of this research work

The test was repeated with the same setup shown in Figure 09. Where we used 10 strain gauges, positioned in two fingers of diaphragm spring.

Figure 09: Setup for Strain Gauges reading .

The figure 10 shows how the Strain gauges were bonded in the spring membrane.

1

2,3,4

5

6

7,8,9

10

Figure 10: Diaphragm spring with Strain Gauges application ranked numerically


In the figure 10, the upper fingers have strain gauges numbered the 1 to 5 and the lower fingers, strain gauges numbered 6 to 10.

RESULS AND DISCUSSIONS

Figure 09, 10, 11 and 12 show the grids projected onto the diaphragm spring surface associated to the displacements of 9, 10, 11 and 12 mm respectively. Images were generated in the first ImageJ software processing.

Figure 09: Moiré fringes projected on the diaphragm spring without displacement.

Figure 10: Moiré fringes projected on the diaphragm springwith 2 mm displacement.

Figure 11: Moiré fringes projected on the diaphragm spring with 4 mm displacement.

Figure 12: Moiré fringes projected on the diaphragm spring with 7 mm displacement

The Figures 13, 14 and 15 show the tension distribution of diaphragm spring, through the distribution map of isoclines and isochromatic lines , with displacements of 2mm, 4mm and 7mm.

Figure 13: Isochromatic and isoclines lines with 2mm axial displacement

Figure 14: Isochromatic and isoclines lines with 4mm axial displacement.


Figure 15: Isochromatic lines and isoclines with 7mm axial displacement.

Images 16, 17 and 18,show the simulation result as generated by the Abaqus 6.10 software on a element of the onto the diaphragm spring with 2mm, 4mm and 7mm of displacement.

Figure 16: Diaphragm spring element with displacement of 2mm..

Figure 17: Diaphragm spring element with displacement of 4mm.

Figure 18: Diaphragm spring element with displacement of 7mm..

In the figures 19, 20 and 21, we can see the line differencesbetween the Moiré´s shadow method (a) ABAQUS simulation(b)

a.) b.)

Figure 19: Qualitative stress curves, a) by moiré and b) by the Abaqus software with 2mm of displacement.

a.) b.)



a.) b.)


In the figure 22, we can see the color map processed by Hidrisi software, where can be view the high load regions.

a.) b.)

c.) d.)

Figure 22: Color map generated by the Hidrisi software showing regions of higher load concentration whe a) stands for without displacement, b) for 2mm of displacement, c) for 4mm displacement and d) for 7mm displacement.

The charts 01 to 05 represent the data obtained by the Strain Gauges, where can be view the behavior of deformation in two fingers diaphragm spring.

Chart 01: Strain Gauges reading in positions 1 and 6

DEFORMATION BY STRAIN GAGES

Chart 02: Strain Gauges reading in positions 2 and 7.








Can be checked in the table charts from 01 to 05 that the qualitative behavior of the loads resulting from the displacement of the diaphragm spring through the Strain gages show the same pattern of stress variation when compared with figures 19 to 21.

In the figure 19, the lines of image “a” , are different from the lines image “b” , however when the classification of the loads is checked , can be notice that the gradient of stress show be similar in the same fingers regions off diaphragm spring, in both images. The same occurs when comparing the images a and b, figure 21..

Can be seen in the Figure 20, which in some areas there is an inversion of tension values, between images of Moiré technique and ABAQUS simulation, but in the figure 14 has several fingers with the same behavior shown in Figure 20b.This happen because the material in the ABAQUS simulation, is analyzed a part made of isotropic material ,faithful and geometric according the drawing , on the other hand , in the Moire technique this not occurs because the material can show a anisotropy, and the design have the dimensional tolerances generated in the manufacturing process.

In the figure 22 is shown the load concentration in different areas. In image B can be noted that only the finger on the upper right side show in your edge a region of higher concentration, with increasing fingers displacement. The lower left side fingers start to shown similar behavior.( images c and d ). This suggests that some fingers can deform before others

Still in Figure 22, can be verify that regions of greatest concentration are closer to the edge of the diaphragm spring and showing a intensity growing with increasing displacement in spring. This behavior is also seen in the images of Figures 13 to 15.

CONCLUSIONS

Based on studies and results presented in previous chapters can be concluded that the Shadow s moiré technique is a tool accessible and able to qualify the stress in axial displacements in the clutch diaphragm spring. In the present study is

reflected a comparison between the simulation by ABAQUS 6.10 and the results obtained by Shadow´s moiré technique and the readings made experimentally with the aid of Strain Gages.

It is emphasized as well the importance of photoelastic methods in at studying a material mechanical materials behavior, mainly on anisotropic materials. Moiré method has demonstared reliability with respect to the obtained data which are corresponds to the expaeted behavior. The shadow moiré technique is quite feasible and simple application. This technique can be applied to technical reports, engineering design, quality control and other applications requiring the determination of stress distribution in a complex geometry bodies.

REFERENCES

1. BRAZOLIN, R.T. Desenvolvimento de um método de simulação para avaliação da durabilidade de conjuntos de embreagens para veículos comerciais. 2010. 94p. Dissertação (mestrado em Engenharia Mecânica) –Faculdade de Engenharia Mecânica. Universidade Estadual de Campinas, Campinas.

2. SCHIAMMARELLA, C. A. The moiré method - A review. Experimental Mechanic. V.44, n.8, p.418-433, nov.,1982.

3. CLOUD, G. Optical methods of engineering analysis. Cambridge, Cambridge University Press, 1998.

4. SCHIAMMARELLA, C. A. The moiré method - A review. Experimental Mechanic. V.44, n.8, p.418-433, nov.,1982.

5. LINO, A. C. L. Técnica óptica de moiré visando a aplicação no estudo de superfícies irregulares. 2002. 86p. Dissertação (mestrado em Engenharia Agrícola) –Faculdade de Engenharia Agrícola, Universidade Estadual de Campinas, Campinas.

CONTACT INFORMATION

Kelen Cristiane Cardoso – Schaeffler Brasil – (15) 3335-2100.

[email protected]


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SAE TECHNICAL 2011-36-0117 PAPER SERIES E Analysis of …static.tongtianta.site/paper_pdf/041f4de4-33ff-11e9-9595... · 2019-02-19 · XX SAE BRASIL International Congress and Exhibition