optimising driveline nvh performance at jaguar land...

© Altair Engineering 2011 1

Optimising Driveline NVH Performance at Jaguar Land Rover

Kevin Allin Principal Engineer, Driveline Systems, Jaguar Land Rover Banbury Road, Gaydon, Warwick, CV35 ORR, UK. [email protected]

and

Stephen Shaw Principal Engineer, Powertrain CAE, Jaguar Land Rover Banbury Road, Gaydon, Warwick, CV35 ORR, UK. [email protected]

Abstract

This paper details a technique for optimising driveline Computer Aided Engineering (CAE) system models, in order to minimise the response to known excitations, such as final drive unit transmission error and system out-of-balance forcing. The aim of the CAE analysis is to give the design team an understanding of how to desensitise the vehicle to these known excitations, and to enable informed decisions to be made, for example when trading attributes between Noise, Vibration and Harshness (NVH), and driveability, etc. The approach uses the forced response analysis capability within OptiStruct and the mesh morphing capabilities of HyperMorph to calculate the optimum settings for the various driveline parameters, such as centre bearing position, propshaft tube diameter, and mount stiffness rates. HyperStudy is then used to automatically submit a suite of OptiStruct runs, and subsequently perform a Design of Experiments analysis showing how the various parameters interact. The results are then combined in a multi-disciplinary optimisation run, to give an overall optimum position that also takes into account separate analysis runs, such as multi-body systems assessment of static displacements. Keywords: Optimisation, Driveline NVH, DOE, OptiStruct, HyperStudy

© Altair Engineering 2011 Optimising Driveline NVH Performance at Jaguar Landrover 2

1.0 Introduction

The driveline is normally defined as the propeller shaft, centre bearings, drive shafts, final drive units, and their associated joints; that is, the components that transmit torque from the gearbox to the driven wheels. As vehicles become increasingly refined, the noise and vibration contribution from the driveline can become more significant. The challenge is to minimise this effect by appropriate use of target setting and CAE modelling at the concept design stage, thereby reducing the requirement for costly palliative devices or energy-wasting torque-convertor slip. There are several well-known mechanisms by which the rotating parts within a vehicle driveline can cause noise and vibration which can be heard and felt inside the vehicle. These include:

(i) “Out-of-balance”, (where the driveline components are not perfectly balanced, and therefore impart a rotating force vector on the driveline as they rotate).

(ii) Axle whine, where imperfections in the gear mesh in the final drive unit ("transmission error") cause a torsional acceleration at the meshing frequency.

(iii) Engine firing order-driven torsional excitation. These excitations typically occur over a wide frequency range, and are transmitted to the inside of the vehicle via a complex system of interactions. The traditional approach has been to set both absolute modal targets and modal separation targets for the various components in the driveline. The modal separation targets enable obvious conflicts (such as coincident driveline bending and torsion modes) to be eliminated. The absolute modal targets present more difficulties, however, because it is rarely physically possible to lift the resonant modes above the excitation range. A further complication exists in the case of transmission error excitation, which is the main cause of audible axle whine in the vehicle. The excitation is a function of the dynamic transmission error, which is itself a function of the dynamic stiffness of the upstream and downstream driveline components. In other words, the modal behaviour of the driveline influences both the excitation and the response. For these reasons, the modal target approach has generally been superseded by a system modelling approach. The system model is subjected to a forced response analysis, where the appropriate excitation is applied to the model over the appropriate frequency range. The output is measured in terms of forces, displacements or accelerations at the various attachment points to the vehicle structure, for which there is a set of targets. This system modelling approach lends itself to the application of Altair's optimisation technology. Initial work applied the gradient-based optimisation within OptiStruct to improve individual attributes. For example, this technique was used to improve the axle whine response on the Jaguar S-Type in 2006. This was upgraded to a Design of Experiments (DOE) approach using HyperStudy in 2007, to enable the available design space to be fully explored. In 2010 a further enhancement to this technique was introduced, which uses multi-disciplinary optimisation to link the driveline system DOE described here with other related analyses, such as joint angle and driveability studies, that are conducted on entirely separate models


2.0 CAE Modelling Approach

2.1 Diagram and brief explanation of CAE driveline model

A finite element representation of the complete driveline was discretised from the CAD geometry using HyperMesh. The geometry had been de-featured so that a suitably large element size could be used while still representing the dynamic behaviour of the driveline system. RBE2's (Rigid Beam Elements), MPC's (Multi Point Constraints), and translational and rotational springs were used to define the joint articulations in the model. RBE2's and beam elements were used to represent the fixings in the model. The bulk and torsional behaviour of the power unit were represented separately in the model. Firstly, the engine and gearbox were represented torsionally in the form of a mass-elastic system. This consisted of a series of concentrated mass (CONM2) elements with torsional springs or MPC's connecting them. Each of these lumped masses were constrained to act only in one rotational DOF (Degree of Freedom). The MPC's were used to model the gearing ratios between the individual components of the transmission. The bulk of the power unit was represented by a lumped mass rigidly fixed to the engine and transmission mounts that were represented by translational springs. An example of the driveline system is shown in Figure 1a below. Typical resonant modes of this system model are shown in Figure 1b.

1D Engine 1D Gearbox Engine Mass on Mounts

Figure 1a: CAE Driveline model


Rear Drive Unit pitch in anti-phase with sub-frame pitch - 118Hz

Rear Drive Unit pitch/roll in anti-phase with sub-frame pitch - 135Hz

Driveline Torsion Mode 151Hz

Figure 1b: Typical Resonant Modes of the CAE Driveline model


A series of forced response analyses of the driveline system were completed to evaluate the performance of the system. Three separate excitation sources were used to evaluate the driveline model. These were excitation from the engine firing orders, excitation from propshaft OOB (out of balance), and excitation from final drive unit transmission error (axle whine). The engine excitation applied was the major firing order torque against frequency (for the running range of the engine) which was applied at the grid points representing each cylinder. The 2nd order (engine firing) torque from a typical four cylinder diesel engine is shown in Figure 2 below.

2nd Order Engine Excitation

0.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

800.00

50 60 70 80 90 100 110 120 130

Frequency (Hz)

To

rqu

e (N

m)

Figure 2: 2nd Order Engine Excitation

The propshaft OOB excitation was derived from a specified imbalance in the propshaft geometry. This is normally assumed to be a maximum of 25gcm, and a simple calculation can be used to generate the forcing function with respect to frequency, as shown in Figure 3 below. It should be noted the OOB forcing function was applied at the rotational axis of the propshaft at a point close to the final drive unit. To achieve a rotational out of balance excitation, two forcing functions were applied at 90º to each other geometrically and with a 90º phase lag between them.

Figure 3: Propshaft Out of Balance Forcing Function

The axle whine excitation is derived from a simple approximation of the transmission error in the geometry of the final drive unit gear teeth. The resultant forces from this are considered to follow the trend shown in Figure 4 below. This forcing function was applied at


the meshing point of the pinion and ring gear within the final drive unit, with two equal and opposite forces applied along the hypoid line of action. It should be noted that translational springs were used to represent the gear teeth as shown in Figure 5.

Axle Whine Forcing

0

200

400

600

800

1000

1200

200 250 300 350 400 450 500 550 600 650

Frequency (Hz)

Fo

rce (

N)

Figure 4: Axle Whine Forcing Function

Figure 5: Hypoid Gear Modelling to Allow Transmission Error Forcing

To evaluate the effect these excitation functions have on the refinement of the vehicle, the response at the major routes through to the vehicle cabin were considered. These routes included the final drive unit mounts and the centre bearing mount. This was done by extracting the forces in the springs representing the mounts for the three axial directions. The response force at the Rear Drive Unit (RDU) mounts is shown in Figures [6] below. The contributing modes (as shown in Figure 1b) have been highlighted.

Hypoid line of action

Ring Gear Tooth

Pinion Tooth

Pinion

Ring Gear

Forcing Nodes


RDU Pitch RDU Pitch/Roll Driveline Torsion

Figure 6: Response forces at the Rear Drive Unit (RDU) mounts

The peaks in these force traces have been found to correspond with NVH problems in the vehicle. The height of these peaks can therefore be used as an optimisation objective.


3.0 Optimisation of the System Model

The two basic processes for optimising the driveline system model within HyperWorks are shown in Figure 7 and Figure 8 below.

Figure 7: Gradient-based optimisation of Frequency Response Analysis in HyperWorks

Figure 8: DOE optimisation of Frequency Response Analysis in HyperWorks

TABLED1

CARD

DAREA

CARD

RLOAD1

CARD

DLOAD

CARD

TABDMP

CARD

FREQ1

CARD

EIGRL

CARD

SPC / MPC

CARDS

CASE

CONTROL

OPTIMISATION

FREQUENCY

RESPONSE

POST

PROCESSING

DESIGN

VARIABLES

DESIGN

OBJECTIVES

SHAPE

VARIABLES

Key:

HyperMesh

OptiStruct

HyperMorph

HyperGraph

Frequency Response Optimisation with Altair HyperWorks – Overall Process

Defines load direction and node id

Can combine multiple Rload cards

Defines frequency dependent load

Defines frequency range

for normal modes solve

Table of load vs frequency

Defines frequency range for frequency response

Defines geometrical changes

(e.g. length, diameter )

Defines damping vs frequency

characteristic

Defines property changes

(e.g. thickness, stiffness)

DESIGN

CONSTRAINTS

TABLED1

CARD

DAREA

CARD

RLOAD1

CARD

DLOAD

CARD

TABDMP

CARD

FREQ1

CARD

EIGRL

CARD

SPC / MPC

CARDS

CASE

CONTROL

OPTIMISATION

FREQUENCY

RESPONSE

POST

PROCESSING

DESIGN

VARIABLES

DESIGN

OBJECTIVES

SHAPE

VARIABLES

Key:

HyperMesh

OptiStruct

HyperMorph

HyperGraph

Frequency Response Optimisation with Altair HyperWorks – Overall Process

Defines load direction and node id

Can combine multiple Rload cards

Defines frequency dependent load

Defines frequency range

for normal modes solve

Table of load vs frequency

Defines frequency range for frequency response

Defines geometrical changes

(e.g. length, diameter )

Defines damping vs frequency

characteristic

Defines property changes

(e.g. thickness, stiffness)

DESIGN

CONSTRAINTS

TABLED1

CARD

DAREA

CARD

RLOAD1

CARD

DLOAD

CARD

TABDMP

CARD

FREQ1

CARD

EIGRL

CARD

SPC / MPC

CARDS

CASE

CONTROL

OPTIMISATION

FREQUENCY

RESPONSE

POST

PROCESSING

DESIGN

VARIABLES

DESIGN

OBJECTIVES

SHAPE

VARIABLES

Key:

HyperMesh

OptiStruct

HyperMorph

HyperGraph

HyperStudy

DESIGN

CONSTRAINTS

TEMPLEX

FILE

Hyperstudy

file (.xml)DOE

definitions

OptiStruct

batch solutionPOST

PROCESSING

OptiStruct deck with design variable definitions

Writing Multiple

OptiStruct decks

Gradient-based process

Additional DOE process


3.1 Manual Optimisation The first attempt at optimisation used statistical analysis software such as Minitab to define a suite of DOE runs. The CAE models were altered either in the pre-processing software for mesh changes, or by hand editing the Nastran decks for changes to card parameters. The separate Nastran decks were then solved in isolation, and individual forced response analyses are undertaken on each of the results files. Finally, the peaks of the forced response analysis were read from the graphs, and manually entered in Minitab to enable calculation of the main effects and interactions. This process was successful when correctly applied, but is time-consuming and also vulnerable to operator error, hence the requirement for automated optimisation. 3.2 Gradient – Based Optimisation with OptiStruct Changing the analysis method to OptiStruct enables simple gradient-based optimisation to be undertaken. The major attraction of this approach is that it allows simultaneous automatic optimisation of shape parameters (defined as HyperMorph shape variables), as well as numerical parameter such as thickness and stiffness values. An illustration of using a HyperMorph shape variable to control propshaft diameter is shown in Figure 9 below.

Figure 9: Propshaft Tube diameter change with HyperMorph The disadvantages of this gradient-based approach are:

(i) It is vulnerable to local minima (see Figure 10 below). (ii) It yields no data on how the various parameters interact, nor on their relative

importance.

Perturbations applied to the nodes in the centre section of

the rear prop tube, exported as a shape variable.

This shape variable can then be used to automatically

increase or decrease the diameter of this section of tube.


Figure 10: Vulnerability of Gradient-based optimisation to local minima 3.3 DOE Optimisation with HyperStudy, OptiStruct and HyperMorph To fully explore the design space, and avoid the drawbacks of a gradient based approach, a full Design of Experiments (DOE) study is required

To perform a DOE optimisation of the driveline model with HyperStudy, the following process was followed: 1) The basic model was exported as an OptiStruct deck, with no shape variables 2) The shape variables were set up in HyperMorph in the usual way, and exported as a shape file. (Optimization > shapes > export > Analysis code = Templex, Sub-code = Nastran) This creates two files called dline.node.tpl and dline.shp

3) The OptiStruct deck was then edited to remove all the grid cards and replace them with the GRIDS from the dline.node.tpl file created in section (2) above 4) The line DISPLACEMENT(SORT2,PUNCH,PHASE) = 100 was added to the case control section. This produces a punch file of the displacement of all the GRIDS in SET 100 5) Within HyperStudy, the model OptiStruct deck was converted to a Templex file (see example in Figure 11 below). 6) HyperStudy Responses were then set up to measure the peak force in the locations and directions of interest. 7) HyperStudy is the used to submit a batch of runs, varying the parameters that have been defined in the Templex file. (see example in Figure 12 below).

Response

Parameter value

Local Minimum

Optimium value

Start point

Response

Parameter value

Local Minimum

Optimium value

Local Minimum

Optimium value

Start point


Figure 11: Example Templex file for HyperStudy optimisation

Figure 12: Example DOE run matrix

{parameter(DVAR1,"Shape1", 0.0, -1.0, 1.0)} {parameter(cbrgY,"cbrgY", 42.8, 38.52, 47.08)} {parameter(cbrgZ,"cbrgZ", 42.8, 38.52, 47.08)} {parameter(dmprX,"dmprX", 4300.0, 3870.0, 4730.0)} {parameter(dmprZ,"dmprZ", 4300.0, 3870.0, 4730.0)} {parameter(thick,"thick", 1.65, 1.485, 1.815)} $$ $$ Optistruct Input Deck Generated by HyperMesh Version : 8.0 $$ Generated using HyperMesh-Optistruct Template Version : 8.0 $$ $$ Template: optistruct $$ $*$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $* $* CASE CONTROL $* $*$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $* TITLE = MSC NASTRAN FILE TRANSLATOR -- UNITS = MM ACCELERATION (OPTI,COMPLEX)=1 DISPLACEMENT (SORT2,PUNCH,PHASE)=1 FORMAT OPTI FORMAT H3D OUTPUT,HGFREQ,ALL SCREEN OUT $$------------------------------------------------------------------------------$ $$ Case Control Cards $ $$------------------------------------------------------------------------------$ $ $HMSET 1 1 "seta" SET 1 = 147234,158976,158983


4.0 Results

Typical DOE study results are shown in tabular format in Figure 13 below. This shows the peak force from each forced response run, in the specified direction and frequency range, for the three locations that were identified as being of most importance.

Figure 13: Typical DOE study results


4.1 Interpreting the Results

Figure 14: Main Effects Plot Figure 14 above shows the main effects at one of the measurement points. The most obvious conclusion from the Main Effects Plot is that two of the variables, Centre bearing X stiffness and Centre bearing Y stiffness, have a much lower effect on the final result than the other 4 variables. It is therefore possible to omit these two variables from any subsequent studies. Figure 15 below shows a comparison in acceleration at the RDU nose position for the nominal condition and optimised conditions.

Figure 15: Original (blue) and Optimised (purple) response at RDU nose position


5.0 Multi-Disciplinary Optimisation

The DOE approach described so far enables the powertrain CAE analyst to optimise and balance the driveline attributes within the system model. However, it should be noted that the same parameters also control other important aspects of the driveline's response. For example, the operating angles of the CV joints within the driveline are controlled by the mount rates and mount positions, as are the responses to transient conditions such as thump and judder. This attributes are normally simulated using separate multi-body systems models and spreadsheet-based calculations. Unfortunately, the requirements of these different attributes can often be in conflict with each other. For example, driveability requirements favour stiff mounting, whereas refinement requirements favour more compliant mounting. What is required is a way of simultaneously optimising the separate models. This is achieved by paramaterising the separate models in exactly the same way, and generating a single DOE matrix. The "Run Matrix" option within HyperStudy can then be used to generate a set of results for the driveline system model that can be combined with the results from all the other relevant models. The response can then be weighted, and an overall optimum position can be found, which takes into account all the modelling results.

6.0 Conclusions

The major advantage of using this approach is that there is now the ability to perform true optimisation at the system level. Once the model is initially set up, it is relatively simple to perform "what if?" studies exploring the whole design space. On a recent 4X4 driveline optimisation for example, in excess of 3,000 separate runs were undertaken in order to find a solution to an NVH problem. With a traditional analysis approach, this would not have been possible.

7.0 Future Work

The next enhancement to this work will be to introduce non-linear characteristics for all the bushes. This will extend the frequency range over which the forced response analysis is valid. A project is also under way to better define the plunge and articulation stiffness of the CV joints, which is currently seen as the weakest aspect of the modelling. Stochastic methods and robustness assessments will then be introduced to ensure that the recommendations remain valid for the expected production tolerances of the various parameters.

optimising driveline nvh performance at jaguar land...

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