Dynamic measurements of elastomer elements

Transcription

1 Dynamic measrements of elastomer elements Michael M. Winler Cologne University of Applied Sciences aclty of Atomotive Systems and Prodction Institte of Atomotive Engineering NVH.ab Ttor: Prof. Dr.-Ing. K. Becer Smmary: The paper describes the process of preliminary tests for dynamic measrements of elastomer elements and the identification of their dynamic transfer stiffness. The aim of these preliminary tests is to clarify whether the existing test setp flfils the reqirements of the cstomer. In the second step of the testing it is clarified how exact the test setp and the test procedre meet the norms DIN pren ISO 846- and -.. INTRODUCTION The cstomers decision for bying a vehicle depends largely on emotions. These emotions are basically inflenced by the sensations sbjectively perceived by the cstomer. This and the additional fact of a strong competition reslt for the atomobile manfactrers in the need to strengthen their development efforts in the fields of visal, aditory and tactile appearance of their vehicles to the cstomer. Big efforts to improve the optical design are made in the field of visal perception since the beginning of atomobile development. This applies for both, the oter appearance of the vehicle and the design of the interior. The fields of aditory and tactile perception on the other hand come in the focs of the atomobile development in recent times. Today this development field is called NVH (Noise Vibration Harshness). Noise stands for the aditory aspect and vibration for the tactile aspect. Harshness describes combined effects of aditory and tactile perceptions. A major part of the sond and vibrations in a vehicle is made by systems e.g. the engine or chassis parts, which transfer excitations from street to car body. To redce the nwanted sonds and vibrations the power train and its components and chassis parts are lined elastically to the car body by elastomer elements. or the design of the elastomer elements the mechanical transfer behavior mst be determined by characteristic qantities. The determination of static qantities is mandatory, bt not enogh becase the transfer behavior of elastomer elements is amongst others related to the excitation freqency. or this reason an often sed characteristic qantity is the dynamic stiffness. In this paper the dynamic stiffness is determined by a test rig.. BASICS The behavior of mechanical strctres and ths also of elastomer elements can be described by dint of the system theory. inpt transference otpt I (ω ) H (ω ) O(ω ) igre : System theory

2 The transfer fnction H (ω ) characterizes the relation between inpt and otpt. It is a complex qantity. I( ω ) H ( ω ) = O( ω ) H ( ω ) O( ω ) I ( ω ) trans fer fnction otpt (system response) inpt (excitation) () If the excitation and the response of a system are nown, the transfer behavior can be determined. The data for the excitation and the system response are measred in terms of physical qantities. In Table examples of transfer fnctions are listed. dynamic flexibility dynamic stiffness mechanical admittance mechanical impedance inertance virtal mass Table : Transfer fnctions displacement displacement speed speed accelerartion acceleration X X X & X& X & X&& The dynamic stiffness is divided into dynamic inpt stiffness and dynamic transfer stiffness. The dynamic inpt stiffness is the ratio of inpt and inpt displacement, whereas the dynamic transfer stiffness is the ratio of otpt and inpt displacement. elastomer element inpt inpt displacement otpt otpt displacement igre : Inpt / otpt qantities According to igre the balance of s can be described by the following eqations. =,, =, and, + and, +,,, elastomer element is fixed the opposite side (i.e. respectively dynamic transfer stiffness - or passive elastomer elements applies becase of the dynamic inpt stiffness, if the reciprocity = ), =, each at = and () (3) The matrices notation of the eqations () and (3) can be seen in eqation (4). = [ ] (4) General case (six oscillation directions) If the s and oscillations are represented by six orthogonal components for each side (three translatory and three rotatory), the elastomer element can be specified as -pol [4]. The dimensions of the stiffness matrix are x. The stiffness matrix can be ct into for matrices containing 6x6 elements. [] = [ ], [, ] [, ] [ ] [ ] and, [ ] [ ] and [ ],,,, stiffness stifness (5) matrices of the dynamic inpt matrices of the dynamic transfer

3 Special case (one oscillation direction) In case of one oscillation direction the dynamic stiffness matrix is redced to the matrix shown in eqation (6)., [], = (6),, In the following the focs is pt on the ynamic transfer stiffness. The nit of d, the dynamic transfer stiffness is Newton per millimeter. As mentioned above the dynamic transfer stiffness is an important qantity to characterize the mechanical vibration behavior of elastomer elements. ( ω) = ( ω ) ( ω ) X ( ω ) ( ω ) X ( ω ) dynamic transfer stiffness otpt (system response) inpt displacement (excitation) (7) There are different standardized methods for the determination of the dynamic transfer stiffness by rig testing. In this paper the direct method (see []) is the bacgrond for the measrements. 3. TEST SETUP The rig consists of Measring and analysis eqipment Excitation system Concrete bloc and gibbet Test object Measring and analysis eqipment The measring and analysis eqipment has as hardware a standard compter and a VXI- and analysis the front-end. or measring software PAK is sed. orces and accelerations are measred by two sensors. On the inpt side of the test object s and accelerations are m easred by an impedance sensor. On the otpt side the is measred by a mono axial sensor. Excitation system The measring and analysis software PAK offers the possibility to generate different signals by a waveform generator for the excitation of test objects. or the measrements described in this paper, the sed excitation signals are white noise, band noise and sinsoidal signals. The excitation signal, which is generated by the wave form generator, is transferred to the amplifier by the VXI-front-end. The amplifier controls an electro-dynamic shaer. The electro- voltage adjsted. That dynamic shaer is means the operator can only adjst the otpt voltage of the amplifier bt not accelerations or displacements. Accelerations and displacements are reslts of the systems behavior and the adjsted voltage. The operator is only able to inflence the accelerations and displacements indirectly. The electrodynamic shaer is lined to the impedance sensor by a so called stinger (igre 3). igre 3: Stinger or exact measring data the stinger mst transfer the excitation axial and free of transversal s into the test strctre. Becase of this, the stinger is thin, long and made of carbon fiber. The opportnity of this linage is the high axial stiffness and the low transversal and rotational stiffness [3]. Concrete bloc and gibbet The mass of the conc rete bloc is nearly.5 g. The great mass of the concrete bloc restrains it to vibrate with the test strctre. The gibbet is to hang p the electro dynamic shaer. The shaer is lined to the gibbet by for spring elements. With the help of this elastic monting it is possible to shift the eigenfreqencies of the oscillating shaer into a low freqency range, which is otside the interesting freqencies. The gibbet is not monted direct at the concrete bloc bt on a separate

4 steel plate. This avoids nwanted bypass transmissions. Test object The test object is located between the impedance sensor and the sensor. or the measrements mentioned in this paper are sed steel springs, hexagonal and ring-shaped elastomer elements as test objects. 5 impedance sensor on the inpt side. Above the impedance sensor is monted a cylindrical steel body. The fnction of the steel body is to apply a preload by its selfweight. The thereby generated preload is abot Newton. The preload avoids a complete nloading of the steel spring, which wold lead to bad reslts. The steel spring is gled together with a small alminm dis which is screwed into the sensor. In igre 6 and igre 7 the two sed steel springs are shown. They have different stiffness s as can be seen by the different wire diameters and the nmbers of windings. 3 6 ig. 6: Hard spring 4 igre 4: Test setp : Measring and analysis eqipment; : Electrodynamic shaer and stinger; 3: Amplifier 4: Concrete bloc; 5: Gibbet ; 6: Test object and sensors 4. SPRING TEST SETUP AND MEASUREMENTS At begin of the preliminary tests the general accracy of the reslts for the dynami c transfer stiffness, determined with the above described test setp shall be demonstrated. A possibility to do this is to mae dynamic measrements of components with nown static stiffness. The measred dynamic transfer stiffness has to correspond with the static stiffness for freqencies near zero Hertz []. In the present test steel springs are sed for this. The steel springs with nown static stiffness are measred dynamically. The steel spring is fixed in the rig between the sensor on the otpt side and the igre 5: Spring test setp ig. 7: Soft spring The measrements are made with different excitation signals and voltages. The best reslts are prodced at measrements with white noise and five Volts. The correlation of the measred reslts and the nown static stiffness is shown in Table. or the comparison the dynamic transfer stiffness at 45 Hz is chosen. Becase resonances occr below this freqency it is not possible to se lower freqencies. By this comparison the general correctness of the measred reslts can be demonstrated. Table : Comparison of static stiffness and measred dynamic stiffness Soft spring Hard spring static stiffness 8.5 N/mm 73. N/mm dynamic measrement 8.9 N/mm 8.6 N/mm at 45 Hz

5 5. HEXAGONA EASTOMER EEMENT TEST SETUP AND MEASUREMENTS The qality of rig measrements is often negatively inflenced by additional components lie bracets or monts. or this reason a test setp is chosen which has hardly any additional components. The test object has also a simple geometry. It is a hexagonal elastomer element (igre 8). The measred reslts constitte the best possible ones for this test rig. The test setp for the hexagonal elastomer element is basically the same lie the test setp for the steel springs. Merely the cylindrical steel body and the steel spring are replaced by the elastomer element, which is screwed between two cylindrical alminm blocs. Becase of omitting the cylindrical steel body there is no preload attached to the test object. The elastomer element itself consists of two metal diss on which setscrews are monted and the elastomer material between the metal diss. The elastomer element is vlcanized to the metal diss. White noise is sed for excitation to get a smooth excitation at a wide freqency range. In igre 9 the reslt of the measrement is shown. There is no distrbance or nsteadiness at the whole freqency range for the dynamic transfer stiffness. igre 8: Hexagonal elastomer element & test setp Sch distrbances may occr by resonances of addition components. This shows the high potential of this test se tp in comparison to conventional rbber mont testing machines which are sally limited to freqencies arond Hz. dynamic transfer stiffness / N/mm freqency / Hz igre 9: Dynamic stiffness of hexagonal elastomer element 6. RING-SHAPED EASTOMER EEMENT The aim of the first two testing steps is to demonstrate the appropriateness of the test rig for dynamic measrements on elastomer elements. The following third step of the preliminary test is to clarify whether the reqirements of the cstomer regarding the displacement can be flfilled. or these measrements ring-shaped elastomer elements are sed (igre ). 6. TEST SETUP RING-SHAPED EASTOMER EEMENT There are two different test setps, a test setp for radial measrements (igre ) and one for axial measrements (igre ). or measrements in axial direction a preload abot Newton is attached. As mentioned before the preload is generated by a cylindrical steel body, which is monted between the stinger and the impedance sensor. or measrements in radial direction no preload is reqired. The U-shaped bracet is made of alminm. It is sed to mont the elastomer element. The acceleration sensor at the otpt side and the three axial acceleration sensor at the inpt side are sed for the measrements in chapter 6.3. The ring shaped elastomer

6 element consists of an inner and an oter part. The inner part is a metal tbe and the oter part is made ot of elastomer. Both parts are vlcanized together. igre : Ring-shaped elastomer element - pictre and CAD drawing 6. RING-SHAPED EASTOMER EEMENT MEASUREMENTS The reqirements of the cstomer are 5 µm constant displacements for the interesting freqency range. Becase of the voltage reglated electro dynamic shaer is it not possible to adjst constant displacements on a direct way. The only possibility to achieve this is to se a sinsoidal signal of one freqency for excitation. With this signal it is possible to adjst the wanted displacement by the voltage. One after another measrement the target displacement can be adjsted for different freqencies. On that way it is possible to get a constant displacement for different freqencies. In present case the measrements are made in Hz steps. In a first step the maximm possible displacements for each freqency step are measred. As reslt of these measrements occrred that it is not possible to achieve the reqired 5 µm constant displacement becase of the capability of the amplifier. In Table 3 the maximm achievable displacements for radial and axial measrements are listed. The comparison of the measred displacements at the test rig with data from in-vehicle testing shows that the test rig is capable to operate the monts at the same displacement levels as in the vehicle. Table 3: Maximm displac igre &: Ring-shaped element radial/axial test setp As conclsion the test rig is able to reach the real in vehicle displacem ents and according to this it flfills the reqirements. The cstomer reqirement of a constant displacement over the whole freqency range is realized with displacements of 8 µm for radial measrement and respectively.9 µm for axial measrem ents. The reslts of these measrements are shown below. dynamic tra nsf er stiffn ess / N/mm µm constant displacement measred by Hz steps freqency / Hz igre 3: Ring-shaped elastomer element, dynamic transfer stiffness, radial excitation dynamic transfer stiffness / N/mm 5 4 3,9 µm constant displacement measred by Hz steps freqency / Hz igre 4: Ring-shaped elastomer element, dynamic transfer stiffness, axial excitation ement for sinsoidal excitation freqency / Hz displacement radial ,3 8,6 8,4 8,5 /µm axial 4 8, 7, 9,7 8,9,7,,88

7 6.3 MAIN CRITERIA OR THE ACCORDANCE WITH DIN pren ISO 846- The norm DIN pren ISO 846- and - describe procedres for measrements of elastomer elements. or the cstomer the accordance of the measrements with the norm is a very important point. By this means the cstomer is able to compare res lts w hich are measred on different test rigs. The DIN no rm basica lly contains for criteria to chec the capability of a test rig to measre dynamic stiffness. These are the freqency criterion, the measrem ent criterion, the excitation acceleration criterion and the linearity criterion. or the measrements to chec the criterion a band noise excitation at a freqency range of 5 Hz - 5 Hz is sed. The maximm possible voltage is cased by the linearity criterion, eqation (&). It is.9 Volt for radial and.7 Volt for axial measrements. reqency criterion The freqency criterion compares the inpt side acceleration with the otpt side acceleration. The measrements for dynamic transfer stiffness are only valid for freqencies which flfill the following eqation. a a, = db (8) a a acceleration level inpt side acceleration level otpt side A reason for a too small level difference, can be an insfficient stiffness difference of the test object and the grond plate (concrete bloc) []. In igres 5 and 6 the reslts for the measrements in radial and axial direction are compared. The criterion is met the whole interesting freqency range. celeration level / db difference of ac minimm difference regarding DIN specification db 6 4 freqency / Hz acceleration level / db acceleration level inpt side acceleration level otpt side 6 4 freqency / Hz igre 5: Ring-shaped elastomer element, freqency criterion, radial excitation difference of acceleration level / db minimm difference regarding DIN specification db 6 4 freqency / Hz acceleration level / db acceleration level inpt side acceleration level otpt side 6 4 freqency / Hz igre 6: Ring-shaped elastomer element, freqency criterion, axial excitation

8 mass / g max mass between otpt side elastomer element and sensor regarding DIN spec. mass for this test setp 8g ot of DIN specification. 6 4 freqency / Hz igre 7: Ring-shaped elastomer element, measrement criterion, radial excitation mass / g max mass between otpt side elastomer element and sensor regarding DIN spec. mass for this test setp 78g ot of DIN specification. 6 4 freqency / Hz igre 8: Ring-shaped elastomer element, measrement criterion, axial excitation orce measrement criterion Between the sensor at the otpt side and the otpt side of the elastomer element are monted additional components lie the U-shaped bracet. These additional components have a mass. If the addition of these masses is too big, the reslts of the measred are falsified. To avoid a falsification the norm specifies a maximm weight for this mass. Becase of the freqency dependency of the measred data the maximm allowed weight is also freqency dependent. m,6* g (9) a m a Mass between otpt side elastomer element and sensor orce level otpt side Acceleration level otpt side The igres 7 and 8 show clearly, that the mass m is too big. This applies for both, axial and radial measrements. Excitation acceleration criterion acing symmetry of the excitation or the bondary conditions and the test object properties may generate distrbing vibrations, which are different to the wanted excitation direction. These distrbances can case a high and nwanted vibration response at particlar freqencies []. Corresponding to the norm, measrements are only valid, if eqation () is flfilled. az ax,y az a x,y Acceleration level in excitation Accelerarion level cross to excitation direction 5 db direction () The evalation of the measred reslts regarding the excitation acceleration criterion is shown in igres 9 and. The igres obviosly display that the criterion is not flfilled all over the interesting freqency range. A reason can be a bad shaer orientation above the elastomer element or a bended stinger.

9 e of acceleration level / db differenc minimm difference regarding DIN specification 5 db ot of DIN specification 6 4 freqency / Hz acceleration level / db in excitation direction cross to excitation direction 6 4 freqency / Hz igre 9: Ring-shaped elastomer element, excitation acceleration criterion, radial excitation, cross direction difference of acceleration level / db minimm difference regarding DIN specification 5 db ot of DIN specification 6 4 freqency / Hz acceleration level / db in excitation direction cross to excitation direction 6 4 freqency / Hz igre : Ring-shaped elastomer element, excitation acceleration criterion, axial excitation, cross direction inearity criterion In the norm ISO 846 the definitions of the dynamic transfer stiffness and the measrement procedres for its determination act on the assmption of linear models for the vibration behavior of elastomer elements. In practice the elastomer elements show only nearly linear behavior []. The fnction of the eqations () and () is to define the validation of the measred reslts for the dynamic transfer stiffness in dependence to the level of the excitatory vibrations. A - B db A B i = A < 5, db /3 - ovtave - spectrm B second /3 - ovtave - spectrm difference of dynamic transfer stiffness dynamic transfer inpt stiffness acceleration () () signal The igres and 3 show the measred reslts evalated with the linearity criterion. igre displays the evalation with the linearity criterion for a measrement with.9 Volt and. Volt in radial direction. In several measrements with different voltages it is identified that the linearity criterion is jst flfilled for.9 Volt. Only at one freqency band the difference of the dynamic transfer stiffness exceed the assigned maximm vale by. db. igre shows the reslts for the axial excitation direction. In axial direction is the otcome of a mltiplicity of measrements that for a maximm voltage of.7 Volt nearly linear behavior can be expected. 7. CONCUSIONS The preliminary tests show that the test rig and the test procedre are applicable for

10 ence of acceleration level / db differ 5 5 minimm difference regarding DIN specification db 6 4 freqency / Hz diff. of dynamic stiffness level / db minimm difference regarding DIN specification,5 db ot of DIN specification 6 4 freqency / Hz igre : Ring-shaped elastomer element, linearity criterion, radial excitation db difference of acceleration level / 5 5 minimm difference regarding DIN specification db 6 4 freqency / Hz diff. of dynamic stiffness level / db minimm difference regarding DIN specification,5 db 6 4 freqency / Hz igre : Ring-shaped elastomer element, linearity criterion, axial excitation dynamic measrements at elastomer elements. The measrement reslts are repeatable and fit basically with the expectations. Bt there are still some improvements necessary to flfill the reqirements of the DIN pren ISO 846- and -. These improvements are the redction of the bracet mass as well as the avoidance of exceeding accelerations cross to the excitation direction. REERENCES [] Norm DIN pren ISO 846-:5 Acostics and vibration - aboratory measrement of vibro-acostic transfer properties of resilient elements - Part : Principles and gidelines [] Norm DIN pren ISO 846-:5 Acostics and vibration - aboratory measrement of vibro-acostic transfer properties of resilient elements - Part : Direct method for determination of dynamic stiffness of resilient spports for translatory motion [3] Døssing, O.: Strtren prüfen. Teil : Mechanische Beweglicheits-Messngen Nærm: Brüel & Kjær, 988 [4] Verheij, J. W.: Mltipath sond transfer from resiliently monted shipboard machinery. Dissertation, Technische Universität Delft, TNO Institte of Applied Physics, Delft, 98