reducing propagation of structure-borne noise in...

Reducing propagation of structure-borne noise in transmissions

S. Sanzenbacher1, M. W. Bouraui2, Prof. Dr.-Ing. B. Bertsche2 1 University of Stuttgart, Institute of Machine Components Pfaffenwaldring 9, D-70569, Stuttgart, Germany e-mail: [email protected] 2 University of Stuttgart, Institute of Machine Components Pfaffenwaldring 9, D-70569, Stuttgart, Germany

Abstract Gear pairs under load cause vibrations in transmissions that are propagated as structure-borne noise. In this paper, different possibilities to abate the physical transmission fundamentals of structure-borne noise are described. To reduce the propagation, a ring between the bearing outer ring and the housing is used. Some designs of the rings derived from these principals are also introduced here. In finite element computations, the designs are pre-validated and later on evaluated by manufacturing and mounting them by means of a test transmission.

1 Introduction

Due to increasing customer requirements and current developments, an important goal in passenger car development is to decrease transmission noises, e.g. in an electric car the engine noise is scarcely audible. Therefore, transmission noises have come into the focus of attention.

Excitation phenomena of transmission noises can be divided into five categories (Table 1).

Transmission noise Cause

1/ Whine

Vibration of gearwheels under load: meshing impact, parametrically excited vibration and rolling contact noise

2/ Rattling/Clattering

Vibration of loose parts, caused by torsional vibration of the power train: idler gears synchronizer rings

3/ Clunk Knocking noise during initial loading of components with clearance (gearwheels, joints, shaft-hub connection etc.)

4/ Shifting noise Scraping and grating of the selector teeth when the synchromesh is not functioning properly

5/ Bearing noise Running noise of rolling bearings; especially when they are damaged

Table 1: Transmission noises and their causes [1]

Loose parts, like synchronizer rings or idler gears entail rattle noises. Torsional vibrations of the input shaft, caused by irregularities in the engine speed, excite loose parts to reach their clearance boundaries and cause impacts. Different possibilities are known to minimise these noises like minimising backlash

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and restricting centre distance tolerances as well as to unlink the torsional vibration of the engine from the transmission [1]. Sudden load changes cause clunk noises if components of the transmission knock against each other. Shifting noises are entailed by not properly working shifting elements. Bearing noises occur especially in cases of damage.

The most significant transmission noise is whining. Not only because of its absolute loudness but also because its tonal characteristic has it been described as annoying by customers. Whining noises are caused by gear pairs driven under load. From the toothing, the excited structure-borne noise waves are transferred to the housing by means of gear wheel bodies, shafts and bearings. From there they are either transmitted to attached parts (by structure-borne noise) or radiated as air-borne noise.

In this paper, a newly developed component is presented. It belongs to the acoustic transmission path and its purpose is to reduce the propagation of structure-borne noise. The element that is used is a ring between the bearing outer ring and the housing. It has been chosen because it is one of the last parts in the structure-borne noise transmission path inside the gearbox. Additionally, the load in this part is primarily static and no other functions have to be fulfilled. Different physical principals were considered for the design of the ring and transferred into real design proposals.

To determine the real potential, a testing transmission was designed, built up and mounted on a testing bench. The most promising designs will be tested and compared to a non-optimised ring.

2 Excitation and propagation of transmission noises

As described in the introduction, whining is the most significant transmission noise that appears when a gear pair is driven under load. By definition, one of the main functions of a transmission is the conversion of torque and speed. The main component in this case is the gear stage whose purpose it is to transmit rotation and torque from the input to the positively locking output shaft. During this transfer process three types of excitations occur that may be divided into parametrical excitation, displacement excitation and shock excitation.

2.1 Parametrical excitation

Normally, involute profiles are used for gears in passenger car transmissions. With this profile type, the rotation is transmitted uniformly from the input to the output shaft in load-free cases. Additionally, these profiles can be produced easily and cost-effective, and are insensitive to centre distance fluctuation [2]. Under load, the driving and the driven gear wheel as well as the shafts and the housing are being deformed, the deformation consisting of driving wheel deformation, driven wheel deformation and Hertzian flattening of the tooth flanks [2]. Depending on the meshing position, the rigidity of a straight spur gear pair varies as shown in figure 1a.

cscscγ cγ

a) turning travel

c

b)εγ p εγ pt

toot

h rig

idity

toot

h rig

idity

c

turning travel Figure 1: Overall tooth rigidity pattern cs, meshing rigidity cγ (average value of cs over time). a) straight

spur gearing; b) helical gearing [2]

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As one or two tooth pairs are in contact alternately, the overall rigidity cS results from a superposition of the individual tooth pair rigidity c of all tooth pairs in contact. If two pairs of teeth are in contact, the rigidity reaches its maximum. During the phase of only one tooth pair in contact, the highest rigidity is reached if the levers of both teeth are nearly similar. In case of tip or root contact, the rigidity decreases. figure 1b shows the tooth rigidity of a helical gear pair. There is less variation compared to straight spur gears. One reason is the more sinusoidal characteristic of the rigidity of one pair of teeth, the other reason is the contact ratio. Normally, in helical cut gear pairs always more than two tooth pairs are in contact. Therefore, the absolute value of rigidity varies less than in straight spur gearings.

In a first approximation the characteristic of gear pair rigidity can be described by a sine function. The equation (1) illustrates the relation between the frequency of this function, called gear mesh frequency fmesh in Hz, the operating speed n in rpm and the number of teeth z.

zn

fmesh 60 (1)

2.2 Displacement excitation

Even in unloaded condition derivations from an ideal flank lead to variations in the law of gears. They can occur as tooth trace deviation or as deviations from an ideal involute profile. They result either from manufacturing imperfections or are part of the tooth design.

In most cases, tooth design is a complicated optimization problem. Even a gear pair which has been optimised concerning its load-carrying capacity may produce unfavourable noise. The load case significantly influences the behaviour of gear pairs. Under different load and speed conditions deformation of teeth, shafts, and housing vary. Therefore, tooth contact conditions change as well. For an automotive transmission a high torque range is requested. Different types of drivers as well as different driving situations (e.g. up-hill driving) generate varying speed and torque demands.

2.3 Shock excitation

A third phenomenon of excitation is shock excitation. Under load the driving 2 and driven 2’ teeth are deformed as shown in figure 2. Consequently, the unloaded tooth 3 gets in contact with tooth 3’. Due to these modified engagement conditions the teeth knock against each other. These meshing impacts can also be caused by pitch errors.

The excitation arising from this phenomenon is periodic and pulse-like. Profile corrections, such as tip or root relief, or accurate manufacturing, can reduce or even eliminate this type of excitation.

gearwheel 2

gearwheel 1

driven

driving

base cir

cle 2

base cir

cle 1

E

f

AC

1

2

2´

f´

3´

3

Figure 2: Meshing impact resulting from deformed teeth [2]

VEHICLE NOISE AND VIBRATION (NVH) 4009

2.4 Propagation of structure-borne noise

Only a small share of vibrational energy caused by tooth contact is radiated inside the gearbox housing as air-borne noise. A large part of the excitations are propagated by gear bodies, shafts and bearings as structure-borne noise. One part is transmitted to the gearbox housing and radiated as air-borne noise. Another part is transmitted to other attached parts by structure-borne noise. The propagation path of the excitation is shown in figure 3, the small and thin arrows symbolizing air-borne noise, the bold ones structure-borne noise.

Figure 3: Acoustic transmission path of a gearbox

Vibrations and waves in solid bodies are commonly known as structure-borne noise. The propagation results from stress and strain deformation of the solid body and can be described by a vector of velocity and a stress tensor. Relevant wave types that occur can be classified by their form of propagation [3]. Basic types are longitudinal and transversal waves. Wave types that can be combined of those two base types are called quasilongitudinal waves, bending waves, torsional waves, and Rayleigh waves. The most important type in technical acoustics are bending waves. The amplitudes of the vibrations occur orthogonal to the direction of propagation and are easily excited due to minimal resistance against exciting forces.

In technical components, structure-borne noise waves are modified during propagation. The waves are reflected, diffracted, and spread at the edges of components, at geometrical discontinuities, or due to changes in media. Structure-borne noise waves are reflected in the same way as optical or electro-magnetic waves. In a two-dimensional case, an impinging longitudinal wave causes both, a longitudinal and a transversal wave (figure 4a). Similarly, an impinging transversal wave causes a transversal and a longitudinal wave (figure 4b). In case of diffracting, e.g. at interfaces between two kinds of media, the waves are partly reflected and partly transferred to the second medium at a different angle (figure 4c). In both cases transversal and longitudinal waves occur.

L1

L2T2

ΘL ΘL

ΘT

T1

T2

L2 ΘT ΘT

ΘL

L1

L2

T2

ΘL1

ΘL1

ΘT1

ΘT2 Θ

L2

L3

T3

medium 1 medium 2

a) c)b)

Figure 4: Reflection and diffraction of structure-borne noise waves. a) reflexion of longitudinal waves; b)

reflexion of transversal waves; c) diffraction of longitudinal waves


Due to material damping and absorption processes, the amplitudes of the waves decrease. Based on these facts, concepts to reduce the propagation of structure-borne sound are developed and presented in this paper.

3 Possibilities to reduce structure-borne noise

In transmission development, two methods to diminish structure-borne noise caused by gear pairs under load are known. As primary influences all possibilities to affect the excitation are described, such as optimisations of the geometry of the teeth (e.g. tip or root relief to lessen pulse excitation). As described in chapter 2.2, these optimisations only work for special load and speed conditions and are often uneconomic. Secondary influences include all design possibilities to affect propagation of structure-borne noise with the aim to reduce the radiation of sound.

In this work, only secondary ways to affect structure-borne noise are examined. Therefore, different concepts are considered, such as increasing the mechanical impedance, attenuation, and damping.

3.1 Mechanical impedance

Mechanical impedance is a measure of the resistance for a structure to exciting forces and moments [4], with F̂ and v̂ as the effective values of the exciting force and the vibration velocity, respectively.

v

FZ

ˆ

ˆ (2)

The overall impedance of a body depends on its input impedance, transfer impedance and output impedance, input impedance having the greatest influence on the acoustic behaviour. This can be increased by mass concentration at the input area. Thus, quite frequently problems arise from the function of the component, e.g. changes in dynamic behaviour due to a modified moment of inertia.

3.2 Attenuation

As described in chapter 2.4, excitations affect propagation of transversal waves, longitudinal waves or a combination of both in a solid body. If those waves impinge any kind of discontinuity they are reflected, diffracted, and spread. By systematically integrated discontinuities in the sound transmission path, reflection and interference progresses can be excited. Discontinuities can either be realized as geometrical discontinuities (e.g. holes or slots), an additional mass, or elastic interlayers.

3.3 Damping

Damping in technical acoustic is understood as a process that is characterised by the transformation of sound energy into any other form of energy, e.g. heat. Therefore, structure-borne noise energy is absorbed or dissipated. Damping mechanisms are classified into inner material damping, joint patch damping, and damping by vibration absorbers.


4 Design approaches to reduce propagation of structure-borne noise

This paper deals with the possibilities to reduce the propagation of transmission noises. To be able to analyze the potential of different design approaches to minimise the propagation of structure-borne noise, a testing transmission, shown in figure 5 was developed. In this single-stage transmission that is driven via an input shaft (1), torque and speed are changed by a gear stage (2) and passed to the output via an output shaft (3). The design modifications to abate structure-borne noise will be integrated in the adapter ring (4) between the bearing outer ring and the housing. This component was chosen because it is one of the last parts in the structure-borne noise transmission path inside the gearbox. Additionally, the load case in this ring is predominantly static and no other functions, such as converting torque or sealing, have to be fulfilled. Therefore, the design approach can be developed with few limitations.

3

1

4

2

1 input shaft2 gear stage

3 output shaft 4 adapter ring

Figure 5: Testing transmission

In a first step, the design approaches for the ring are developed analytically. To be able to compare the different designs Finite Element (FE) models of the designs were built. The ring is mounted in a fixed plate and excited concentrically by an alternating sinusoidal force. As described in chapter 2, a gear pair under load excites parametrically excited forces that can be approximately described by a sine function where the amplitude of the force F is F̂ . The exciting frequency f varies from 16 Hz to 10 kHz.

)π2sin(ˆ)( ftFtF (3)

The reaction of the modified design to the excitation is measured as acceleration at nodes on the inner and outer surface of the ring. To evaluate the acoustic characteristics, two specific values are used. In this case, the transfer function and the insertion loss.

The transfer function T(f) is calculated as quotient of output aout(f) and input ain(f) acceleration [5].

)(

)()(

fa

fafT

in

out (4)


The insertion loss ΔLa directly describes the efficiency of a design approach compared to a non-optimised ring. Therefore, the effective value of acceleration of the optimised ring âopt and the not-optimised ring â0 are used.

0ˆ

ˆlog20

a

aL opt

a (5)

Results given by the FE-calculation can only be used to compare the different designs. In reality the values can vary tremendously. To prove the real potential, experimental results are invaluable.

4.1 Geometrical discontinuities

To affect the transmission of structure-borne noise, geometrical discontinuities can be integrated into a component by removing material in order to reflect, diffract and to spread the waves. The crucial parameters for the discontinuities are: geometry, frequency and distance to the excitation point. Basically, they can be differentiated into four categories: flat, convex, concave, and circular or elliptic. All relevant shapes can be separated into those four base geometries. The propagation of structure-borne noise can be described as wave fronts moving through solid bodies. Impinging a discontinuity the waves are reflected as transversal and longitudinal waves, as described in chapter 2.4.

In a first step an analytical approach is used to analyze the propagation of structure-borne noise in a body with geometrical discontinuities integrated. Therefore, some simplifications have to be made:

Only circular waves radiated from a punctual sound source are considered. All other types of wave fronts are sectionally approximated by circular waves.

Ideal reflection

Variation effects, effects due to roughness and deviation from the ideal form are neglected.

Loss of oscillation amplitude is neglected

The simplest form of reflection occurs if the discontinuity is flat, but enforcing local interference is extremely difficult with these kinds of geometries. The lengths of structure-borne noise waves are very large in comparison to the dimension of components used in a normal automotive transmission. If destructive interference should be used to abate structure-borne noise, other kinds of geometries are an alternative. For example, convex and concave discontinuities, as shown in figures 6a and 6b.

a) b)

c)

Figure 6: Convex (a), concave (b) and circular (c) discontinuities

Convex discontinuities can be used to distribute the energy on wide areas. Concave discontinuities, with a curve radius smaller than the distance to the sound source, lead to high energy concentrations. Circular discontinuities, as shown in figure 6c, belong to the category of convex discontinuities. With decreasing


diameter the effect of spreading is increased, therefore, these kinds of discontinuities can be used to distribute energy over large areas. Larger diameters can, if combined suitably, effect the concentration of structure-borne noise energy.

Based on the described reflection progresses, the design of the adapter ring is acoustically optimised. One aspect to be considered is that mass and stiffness parameters should not be reduced too much. Otherwise the input impedance of the component is too small to improve the acoustic behaviour. A simple design approach is shown in figure 7a. Eight larger holes affect destructive interference, material damping a reduction of vibration energy. Small alternating collocated holes are integrated to abate the propagation of vibration energy. Another design approach that includes slot-shaped discontinuities is shown in figure 7b. The advantage of these kinds of discontinuities is that the transmission path for structure-borne noise can be significantly extended and material damping can reduce the vibration energy.

M1.1 M1.2

Figure 7: Geometrical discontinuities a) holes (M 1.1); b) slots (M1.2)

To compare these design approaches FE-calculations were made. In figure 8, the transfer values and insertion losses for a non-optimised ring (M0), the ring with holes (M1.1), and the ring with slots (M1.2) are shown. As described in chapter 2.1 the frequency range of interest is based on the number of teeth, which, in this case, is 25. With a maximum input speed of 6000 rpm, the gear mesh frequency is mainly about 2500 Hz with the first harmonic frequency at roughly 5000 Hz.

frequency [Hz]

inse

rstio

n lo

ss [d

B]

-5

-4

-3

-2

-1

0

1

2

3

4

5

0 2000 4000 6000 8000 10000

M1.1M1.2

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

0 2000 4000 6000 8000frequency [Hz]

trans

fer v

alue

[-]

M1.1 M0M1.2

10000

Figure 8: Transfer value a) and insertion loss b) for a ring with holes (M1.1) and a ring with slots (M1.2)


The transfer values for model M1.1 and M1.2 are less than that of the original model M0. Due to interference phenomena, the insertion loss of model M1.1 is greater than zero, i.e. the structure-borne noise is increasing. Model M1.2 achieves a reduction of noise level in the lower frequency range of about 3 dB.

4.2 Visco-elastic interlayers

Another possibility to reduce the propagation of structure-borne noise is to use insulating layers. An important pre-condition in this case is a complete decoupling of the primary vibrating structure. Problems that occur are mainly concerning the stiffness of the component. One aspect is the decreasing load capacity, another aspect are displacements due to the flexibility of elastic materials. To minimise the displacement, the thickness of the interlayer should be as small as possible and the effective area, i.e. the bearing surface, should be as large as possible.

Theoretically elastic interlayers can be imagined as springs. To minimise the spring stroke under the same load conditions the springs can be arranged in parallel. Two constructive proposals are shown in figure 9. Model M2.1 uses ring shaped interlayers. By this means, the effective area is enlarged to about five times its size and the displacement is reduced in equal measure. Model M2.2 is an optimised model concerning assembly. Furthermore, due to the bevel, the shear load increases and will, thus, strengthen the insulation property.

M2.1 M2.2

Figure 9: a) Ring with ring shaped elastic interlayers (M2.1); b) optimised ring (M2.2)

4.3 Resonators and vibration absorbers

Geometrical discontinuities or elastic interlayers have a wide band effect on the propagation of structure-borne noise. Using resonators or vibration absorbers can result in damping a specific frequency. They are made of an additional spring-mass system that is applied to the vibration system. If appropriate mechanical properties are chosen, a significant amount of vibration energy can be eliminated. Vibration absorbers oscillate phase-shifted or in antiphase to the exciting force, converting vibration energy into heat. Resonators are fixed as an exposed beam at the vibrating body. Those free-standing structures are easily excited, especially by bending vibration waves, the most important waves in the propagation of structure-borne noise. If damping materials are mounted on the surface of these structures, vibration energy is converted into another, acoustically uninteresting, kind of energy. Both types have in common that in case of efficient use, they have to be actuated near their eigenfrequencies. For a known frequency they can be aligned to this by their geometrical properties like length and thickness. However, running these components near their eigenfrequencies results in unfavourably high loads on the component. Therefore, precise dimensioning is required.

One of the simplest forms of resonators is shown in figure 10. The bending beams are produced by milling. With the vibration of the beams, a lot of vibration energy can be withdrawn. Without any further damping nearly all the converted energy is radiated as air-borne noise.


M3.1 A

A

A-A

Figure 10: Resonator design approach (M3.1)

To estimate the potential of this structure, FE-calculations were made. As indicated in figure 11, the transfer value and insertion loss of the optimised ring show decreasing acceleration amplitudes. In the characteristic of both curves belonging to model M3.1, peaks occur that can be traced back on the eigenfrequencies of the small beams.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

0 2000 4000 6000 8000frequency [Hz]

trans

fer v

alue

[-]

M0M3.1

10000

frequency [Hz]

inse

rstio

n lo

ss [d

B]

-70

-60

-50

-40

0

10

0 2000 4000 6000 8000 10000

M3.1

-30

-20

-10

Figure 11: Transfer value a) and insertion loss b) for a resonator ring (M3.1)

If the radiation of air-borne noise is considered undesirable, three-layered systems can be mounted on the ring as an additional component. Manufacturing these components is relatively simple. Moreover, they can easily be replaced in case of failure. These parts are designed to be operated at or near their eigenfrequencies, which entails high demands on the used materials. Another advantage is that they can be adjusted very easily to the necessary frequency range. In figure 12, one design proposal is shown (M3.2). By the thickness of the tree-layered plates l and by the variation of width d of the slots in the plate, the eigenfrequency of the component can be affected.


dM3.2

l

Figure 12: Resonator including multi-layers (M3.2)

5 Bench testing

The Institute of Machine Components runs a testing bench to perform service life functionality, functional, and reliability tests in the field of drive technology. Components as well as complete transmissions or other parts of the drive-train can be tested with this testing bench. The electric torque change device consists of two asynchronous machines as shown in figure 13. The maximal power of the input machine is 300 kW with a nominal torque of 704 Nm at 4475 rpm, and a maximum speed of 8000 rpm. The output machine works as a generator with a maximum power of 460 kW, a nominal torque of 1484 Nm at 2960 rpm, and a maximum speed of 8000 rpm. A specific characteristic of this testing bench is the very low moment of inertia (0.31 kgm²) of the input machine that allows a realistic replication of rotational discontinuities in combustion engine torque. The machine bed is mounted on membrane air-suspensions to decouple the testing bench from the building.

input machine output machine

machine bed

testing transmission

incremental encodercoupling

accelerometer Figure 13: Testing bench

The testing transmission is mounted between the two machines and connected by two elastic and torsional rigid couplings to compensate offset.

The actuation of the testing bench works via a control software. The operator can decide on the control mode, in this case regulation of torque at the input shaft and regulation of speed at the output shaft.


5.1 Testing conditions

To simulate different exciting sources with the testing transmission, the use of different gear pairs is possible. As described in chapter 2.1 the excitation of straight spur gears differs from helical gears. For this testing transmission, two different gear pairs were designed. One spur-, the other helical-toothed. For both variants the driving and driven gears have the same number of teeth to be able to compare the results. They are fixed on the shafts by using a key connection. The used oil is a common manual transmission fluid. The housing is made of aluminium, again a commonly used material for transmission housings.

Incremental encoders with 10,000 counts per revolution are mounted on the input and output shafts. This allows high-precision measuring of the state of speed and the irregularity of speed occurring, among other things, due to the varying gear-pair stiffness. Accelerometers are assembled to various spots on the housing surface to measure the amplitudes of acceleration. These values serve as the basis for the comparison of design variants of the rings.

5.2 Speed run up of the testing transmission

The dynamic behaviour of a drive system can be evaluated by a power-spectral-density of a machine. In this case, the power level of acceleration measured during a speed run up within 20 seconds and constant load is plotted over frequency and time as shown in figure 14. The acceleration of the gearbox housing was measured by an accelerometer mounted on the surface of the housing. In this configuration straight spur gears are used and the adapter ring is non-optimised. The level of acceleration LP is calculated by equation (6) where a1 is the acceleration and a0 is the reference value of 1·10-6m/s² which is a common value to calculate the level of sound acceleration.

dBa

aLP

0

1log20 (6)

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 00

5

1 0

1 5

2 0

gear mesh frequency

1st harmonic

2nd harmonic

3rd harmonic

frequency [Hz]

time

[s]

leve

l of a

ccel

erat

ion

[dB

]

8 0

9 0

1 0 0

1 1 0

1 2 0

Figure 14: Power-spectral-density of a run-up of the testing transmission

In the plot the gear mesh frequency fmesh, dependent on the number of teeth is clearly visible as a straight line with zero as the origin and the gradient given by the speed of the shafts. After 20 seconds an input speed of roughly 1400 rpm is reached. With a number of teeth of z = 25, the gear mesh frequency


fmesh = 585 Hz is calculated as given in equation (1). The other lines that are visible in this plot are the respective harmonic frequencies of the gear meshing frequency.

6 Conclusion

The acoustical optimisation of passenger car transmissions is an important aim in automotive industry. One of the most annoying noises in automotive transmissions is whining, a noise that occurs when gear pairs are driven under load. During the past few years, the main focus of research was on minimising the excitation by optimising the shape and surface of the gears. However a gear pair can only be perfectly designed and developed for one special load case. The criteria for the optimisation of acoustics are not always in line with the criteria for the optimising of load capacity of gears. Hence, the aspect of excitation cannot be neglected completely.

This paper deals with the possibility to abate structure-borne noise caused by excitations of a tooth contact. Different design approaches for a component that is part of the structure-borne noise transmission path are analyzed and evaluated. This requires the physical basics of wave propagation in solid structures to be examined. Based on existing mechanisms, different designs were developed. They were classified into three different categories. The rings belonging to the first category all include geometrical discontinuities. The expected minimization of sound propagation is rather low but the manufacturing of the parts quite easy. In the second category elastic interlayers are included. The expected improvement by these rings is significantly higher, especially with lower frequency ranges. Resonators and vibration absorbers compose the third group. The potential of these designs is considered the most effective way to abate propagation of structure-borne noise. A problem is that these components are expensive to manufacture. To determine the different designs, FE-calculations were made.

To identify the real potential of the different designs a testing transmission was developed. It was mounted on a special testing bench to be driven under specified load and speed conditions. On the surface of the gearbox housing, accelerometers were fixed to measure the level of acceleration at which the structure-borne sound is transmitted to the gearbox housing.

In a further step the different design proposals will be manufactured and mounted on the testing transmission. Measurements of the housing acceleration will be used to compare the different designs to a non-optimised ring. Another future prospect will be the improvement of the FE model to pre-validate the different designs. First of all, a more realistic calculation of the excitation is required. To meet this requirement a multi-body model of the transmission was developed that will be able to simulate the parametrical, geometrical, and shock excitation occurring at the gear stage. The exciting forces calculated in the multi-body system will then be applied to a FE-model of the testing transmission to calculate the acceleration of the housing. These values can be directly compared to the data established by the accelerometers that were mounted on the gear-box housing. With these improved models it will be possible to improve the design proposals of the rings or to create new principles to abate the propagation of structure-borne noise.

References

[1] H. Naunheimer, B. Bertsche, J. Ryborz, W. Novak, Automotive Transmissions, Springer, Berlin (2011).

[2] G. Niemann, H. Winter, Maschinenelemente Band II, Springer, Berlin (1983)

[3] M. Heckel, H. A. Müller, Taschenbuch der Technischen Akustik, Springer, Berlin (1994)

[4] L. Cremer, M. Heckel, Structure-Borne Sound, Springer, Berlin (2005)

[5] A. Schmidt, Impedanzelement, Forschungsvereinigung Antriebstechnik e.V., Forschungsvorhaben Nr. 522, Abschlussbericht, TU Clausthal, Institut für Maschinenwesen (1997)


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