DEVELOPMENT You will find

andinDamping theVibration figures mentioned this article in the German issue of ATZ 12/2002 beginning on page 1082.

Systembetrachtung zu alternativen Drehschwingungsdämpfern im Pkw-Antriebsstrang

System Considerations Concerning

Alternative Torsion Vibration Dampers in Automobile Drive Trains In addition to the transmission of torque, reduction in vibration for the prevention of drive noise, in particular gear chatter, has greatly increased in importance for clutch systems in cars in the past years. This is particularly the case because on the one hand the unsteadiness of rotational speed has increased in modern engine designs, such as direct injection Diesel or Gas engines, and on the other hand the excitability of gear chatter and noise emission has likewise increased in modern gear boxes due to light-weight construction and low viscosity gear oils. An article of ZF Sachs AG.

Sachs has two systems available which are very well established on the market: the conventional clutch system with a torsion damper integrated in the clutch disc for less torsional-vibration-critical vehicles, and the clutch with a grease filled dual-mass flywheel for more torsional-vibration-critical vehicles. However, for reasons of cost and construction space, it is often not possible to realize the technical necessary function of the dual-mass flywheel in vehicles in the lower or medium price segment. Therefore at ZF Sachs AG a systematic search for alternatives to the already established vibration decoupling systems is being carried out, which should offer a cost advantage with acceptable functioning.

pects have to be taken into account. Often it is a good idea to consider particularly those systems in more detail which were initially assessed rather critically with regard to their operation or design. Here it is important to carefully analyze the operational principle fully at an early stage of development, so that the weaknesses of the system can be recognized before the costly and time consuming construction of prototypes. Finally, the essential system parameters for the construction of prototypes should be predetermined by means of a computer simulation in order to be able to minimize the necessary number of experiments for the verification of its functioning in the vehicle. The individual steps will be explained below in more detail and be illustrated by means of examples.

2 Systematic Search for Alternatives

2.1 Categorizing Existing Solutions

In the systematic search for an alternative vibration decoupling system, several as-

During the search for new approaches, a high degree of abstract physical consideration is chosen, so that systems are consid-

1 Introduction

By Reinhard Feldhaus and Hartmut Bach

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ered which would otherwise be overlooked if only the design properties were regarded. As the first step, already-known solutions can be analyzed using criteria defined by the developer and then entered into a system for generating a solution tree. It will already be apparent at this stage that for some branches of this tree there are no examples for their realization. However, it is not unusual that precisely these branches contain the potential for innovative future solutions. Such a solution tree with known solutions and open “blank zones” is shown in Figure 1. The known mechanical vibration decoupling systems in the car drive train, which do not require external energy, can be subdivided into two groups. The first group only includes systems with two degrees of freedom of motion. All the variants in this group are distinguished only by the system parameters, that is to say the coefficients of mass, damping and rigidity matrices. The topology, i.e. the arrangement and the connection of the masses to each other, is identical. In this group, for example, the dual-mass flywheel and the clutch with torsion damper in the clutch disc are found. The second group includes systems which differ from the first group, i.e. from

DEVELOPMENT

Vibration and Damping

the system with two degrees of freedom, by their topology with either additional degrees of freedom being added or the connection between the masses modified. In this group, for example, absorber systems with parallel connection of masses are found. “Blank zones” can be identified here. It goes without saying that this solution tree is only one example of how known solutions can be analyzed with regard to their physical effect and be shown within a structure overview. Such a systematic arrangement provides a good overview independent of the construction and it provides clear clues to new approaches which have so far not been investigated and which therefore have a high innovative potential. The overall potential, i.e. the actual suitability of this solution for the task in hand, has to be determined during the potential assessment.

For the basic understanding of new systems, despite fast computers and highly developed simulation software available today, the setting up of the equations of motion, their solution and discussion is indispensable. The method used when setting up the system of differential equations is particularly important here. Often the approach according to Lagrange is chosen here because it allows non-linear behavior to be considered as well. The linearization following this step, for example using the perturbation method, allows the working of the system to be understood very rapidly. The influence of individual parameters on the basic system behavior can often efficiently be studied using the equations of motion.

2.2 Theoretical Preliminary Calculation

After identifying new approaches of fundamental interest, the next step is usually to search for ideas for producing design solutions and to provide a rough assessment of these ideas. The ideas are developed into design drafts and provide a basis for the theoretical preliminary calculation.

2.3 Simulation Calculation

In the context of the theoretical potential assessment of ideas, a frequent problem is not that the system parameters must be precisely optimized, but that initially suitable parameter combinations need to be found. The speed of the calculation can be more important for this than the precision. Limiting value considerations of the relevant system parameters are useful here for assessing and understanding the system behavior. These sensitivity studies are,

2.1 Categorizing Existing Solutions

Figure 1: Solution tree with "blank boxes"

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however, only possible with the help of fast simulation tools, which are either available on the market or must be developed inhouse. 2.4 Construction of Prototypes and Function Tests

If the theoretical preliminary calculation and the simulation calculation give a promising result, a functioning prototype is designed and built in order to verify the theoretical results found so far. During the design and dimensioning, it must be remembered that a large number of parameter variations and combinations can be included in the prototype, so that during the subsequent functional assessment in the vehicle, an optimized match can be found using only a single prototype. For this reason is it possible that the design of the prototype will deviate strongly from the later series design. During the functional testing in the vehicle, different driving conditions, such as wide open throttle, coast, idle and engine start are to be measured and subjectively assessed. The measured data provides valuable information about the matching of the

vibration simulation model to the actual system behavior in the vehicle. 3 System Synthesis in the Solution Tree

By filling in the fields left blank in the solution tree with known solutions as in Figure 1, the completed solutions tree as in Figure 2 is obtained. If the starting point is a system with two degrees of freedom, e.g. a dual-mass flywheel, the system topology can be modified by adding an additional mass. If this mass is only connected to one of the existing degrees of freedom, this can result in an absorber connected via a link of a certain stiffness to the primary or to the secondary side. With a connection via a friction link, however, an additional damping mass arises. During a closer examination of speedadaptive absorber systems, further variations could be identified. In particular the gyroscopic absorber deserves mentioning. With this absolutely novel system, the moment is not transmitted via the stiffness term as for the conventional absorber, but only via the terms proportional to speed.

However, it is also possible to integrate the additional masses into the moment flow between the primary side and the secondary side, which results in a three-mass flywheel. After the systematic generation of such novel solutions, their potential must be assessed in the next step. 4 Examples of the Potential Assessment of Novel Approaches

Using the example of the potential assessment of a speed adaptive absorber, it rapidly becomes apparent that the analytical calculation will provide valuable insights into the principle suitability of alternative systems. The design and function of the considered Salomon absorber is not explained here, instead we refer to [1]. With the help of the Lagrange equations, the non-linear differential equations are set up for a flywheel with integrated Salomon absorber, Figure 3. Already with the differential equations of motion, important insights about the system behavior can be gained which are

3 System Synthesis in the Solution Tree

Figure 2: Completed solution tree

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Titanium

then confirmed by practical testing of the functioning prototypes in the vehicle. The non-linear differential equations show that even with purely single-frequency excitation, higher vibration orders will be observed for the flywheel motion as a result of the quadratic and cubic terms for the absorber deflection. By means of a perturbation calculation [2], the differential equations can be linearized, Figure 4.

By means of these linear differential equations of motion, the system behavior becomes even more apparent. The first equation includes the balance of moments for the flywheel. If the vibration moment Mt sin(nΩt) of the engine is exactly the same size as the moment generated by the absorber mt R0 S1’’, the flywheel acceleration is zero, i.e. the flywheel rotates uniformly. In this case the damping D is also zero, and the absorber vibrates homogeneously. This can,

MATERIALS

of course, not be realized, because in the realized design there will always be damping. Therefore the absorber requires for the compensation of the damping losses an excitation mtR0’’ from the flywheel acceleration. Furthermore, it must be recognized that the vibration frequency of the absorber depends on the rolling factor q and the path parameter m. This means that the absorber becomes maladjusted and therefore less effective if the absorber slides in its track in-

4 Examples of the Potential Assessment of Novel Approaches

Figure 5: Vibrations of the flywheel in the time domain and the frequency domain as solutions of the non-linear differential equation system

Figure 3: Non-linear differential equations for the speed-adaptive absorber

Figure 4: Linear differential equations for the speed adaptive absorber

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Figure 6a: Clutch disc with dampening additional mass on the secondary side Figure 6b: Dual-mass flywheel (DMF) with additional dampening mass on the secondary side

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4 Examples of the Potential Assessment of Novel Approaches

Figure 7: Calculated angular acceleration of the gearbox input shaft when utilizing an additional dampening mass

Figure 8: Angular acceleration of the gearbox input shaft when utilizing a clutch disc with additional dampening mass with a four-cylinder diesel vehicle

stead of rolling (change q) or if a modification to the shape of the track occurs, for example due to wear (change m). For investigating the effect of the nonlinear terms in figure 3, it is necessary to transform the non-linear differential equations of motion into a numerical simulation model. Figure 5 indicates the angular acceleration of the flywheel for the un-dampened non-linear differential equation system for the time domain and the frequency domain.

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For an excitation with only a single frequency (here for example 400 rad/s), a small remaining peak appears in the frequency domain at this frequency which has not been totally absorbed, and a relatively large peak at 800 rad/s and a very small peak at 1200 rad/s. The result of the non-linear terms in the differential equation is a frequency transformation. The vibration simulation therefore quite clearly indicates early on that the exciter vibration it is dimensioned for will be absorbed but at the same time that an unde-

sired increase of higher order vibrations is to be expected from the use of the absorber. By means of the procedure explained as an example and the numerical vibration simulation, additional different new approaches in the solution tree were investigated with regard to their functional potential. It was found out that absorber systems of different types will not operate satisfactorily, because they will only absorb individual frequencies or excitation orders, and this narrow-banded effect is at least insufficient for the prevention of gear rattle, [1]. In the following, a further example of a vibration simulation calculation will be shown. Systems with two degrees of freedom were investigated (torsion dampened clutch disc or two mass flywheel), in which an additional third mass is connected to the masses on the primary side or on the secondary side. Figure 6a and Figure 6b show examples of two connection variants. Because for systems with several degrees, particularly if dry friction is used, the analytical calculations do not give a satisfactory result, different parameter combinations were investigated with a tool for numerical simulation. This in-house-developed simulation program calculates the amplitudes on the primary side, the secondary side and the additional mass and the relative angle between the individual nodes of the linear system. The characteristic frequencies and mode shapes are determined and displayed. Short simulation times allow the rapid carrying out of large parameter studies, so that valuable conclusions can be drawn about the system behavior. Figure 7 demonstrates that when utilizing an additional damping mass on the secondary side of the torsion damper on the clutch disc, compared to the conventional system, the angular acceleration of the gearbox input shaft can be considerably reduced. In order to reach optimum functioning, tuning of the system during the driving test is still essential despite the simulation, however the results of the simulation indicate the limits within which the system parameters can be varied, which means that the necessary experimental costs are significantly reduced. The positive results from the simulation are widely confirmed in the driving test, Figure 8.

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