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Slip model

6 | SIMPACK News | March 2014

3RD PARTY PRODUCT | Antoine Schmeitz, TNO

TNO’s MF-Tyre / MF-Swift and the Delft-Tyre Toolchain

Fig. 1: Schematic view of the model structure

BRIEF HISTORY OF THE MODELAfter it was first published in 1987 and 1989, Pacejka’s Magic Formula model quickly gained broad acceptance as a highly accurate model for describing measured steady-state forces and moments occur-ring under various slip conditions. Later extensions to the basic Magic Formula have been made to include some of the transient behavior of the tire, e.g., by introducing relaxation lengths. Today, the latest version is capable of dealing with combinations of brake slip, sideslip, camber, turn slip, infla-tion pressure and transient responses up to

approximately 8 Hz. TNO’s first implementa-tion of the model (MF-Tyre) dates back to 1996.The need for more accurate vehicle dynamic simulations (also on uneven roads), includ-ing control systems like ABS and ESC, emerged in the 1990s. These applica-tions require the model to be valid for higher frequencies (> 30 Hz) and for short wavelengths (> 0.2 m), because many low frequency aspects of tire behavior are velocity-independent and can better be

expressed in terms of wavelength. This was the motivation for developing the Magic Formula-based Short Wavelength Interme-diate Frequency Tyre model (MF-Swift).In the first decade of this century, the em-

phasis of model develop-ment changed to impact harshness, ride comfort and road load (durability) applications. This resulted in the addition of a 3D

enveloping model and the inclusion and support of advanced road models for rough roads.

Tire models for vehicle dynamic analysis must accurately represent tire behavior, be computation-ally fast, reliable and robust. In addition, when applying tire models to virtual vehicle develop-ment, it is essential that the required model parameters are well and efficiently identified from common experiments. Consequently, not only a tire model is required, but also a full methodology. For this reason, TNO developed the Delft-Tyre Toolchain. Toolchain and the tire models MF-Tyre/MF-Swift consist of a portfolio of products and services to comply with all tire modeling needs.

“The automotive and tire industry were continuously

involved and supported the developments.”

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SIMPACK News | March 2014 | 7

Antoine Schmeitz, TNO | 3RD PARTY PRODUCT

Fig. 2: Typical cleat test validation result; 205/60 R15 passenger car tire

Fig. 3: Body input forces for vehicle driving over rough road; 19 inch run flat tires [2]

The development of MF-Swift has been carried out by TNO in close cooperation with Delft University, and later Eindhoven University. Throughout this time, the auto-motive and tire industries were continuously involved and supported the developments.

MODEL OVERVIEWA schematic view of the model is shown in Fig 1. The important elements of the MF-Swift tyre model are:

• Magic Formula• Contact patch slip model• Rigid ring• Obstacle enveloping model

• Magic FormulaThe well-known Magic Formula model of Pacejka can describe the steady-state tire slip forces and moments with high ac-curacy. Basically, this semi-empirical model consists of a set of equations that are pa-rameterized by fitting these to steady-state slip measurements.

• Contact patch slip modelA tire does not respond instantaneously to changes in slip; a certain distance must be traveled before the steady-state levels of forces and moments are reached. The tire relaxation behavior is caused mainly by the flexibility of the tire structure. This flex-ibility is included by elastically suspending the tire contact patch (via the rigid ring) to the wheel rim. For short wavelengths, the finite length of the contact patch must also be considered. This is accomplished by using the contact patch slip model that accounts for the contact patch transients.

• Rigid ringIt appears that when considering a maximum frequency of approximately 60–100 Hz, the deformations of the tire belt can be neglected. Consequently, the tire belt is modeled as a rigid body/ring which is elastically suspended with respect to the rim. Residual springs are introduced

between the ring and contact patch to en-sure that the overall stiffness of the tire (and relaxation lengths) is correct.

• Obstacle enveloping modelWhen rolling over short obstacles and rough roads, tire geometry and elasticity give rise to the nonlinear behavior of the tire forces and to changes in the effective rolling radius. To incorporate this enveloping behavior, the concept of the effective road surface is used. This effective road consists of plane height, slope, curvature and bank-ing. An obstacle-enveloping model, consist-ing of elliptical cams that touch the actual road surface, is used to generate it. Finally, the single point rigid ring model contacts this road surface and the slip forces from the Magic Formula act on it.

This model structure and the software implementation allow the user to select the level of complexity. For handling analyses, it is generally sufficient to use only the Magic Formula, whereas for road load simulations, the full complexity is required.

USAGE AND RANGE OF APPLICATION• All kinds of vehicle steering and han-

dling simulations, e.g., ISO tests such as

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8 | SIMPACK News | March 2014

3RD PARTY PRODUCT | Antoine Schmeitz, TNO

Fig. 5: TNO Tyre Test Trailer, winter testing

Fig. 4: MF-Tool parameter identification software

steady-state cornering, lane changes, J-turn, braking, sine with dwell, Fishhook, µ-split, low µ, rollover, parking effort, etc.

• Vehicle behavior on rough roads: impact harshness; ride comfort analyses; road load calculations for durability analyses

• Simulations in which control systems are involved that can excite or be influenced by tire dynamics, e.g., ABS, ESC, etc.

• Analysis of driveline vibrations• Analysis of shimmy vibrations; typically in

the range of 10–25 Hz

• Lap time and fuel consump-tion simulations

• Passenger car, truck, motor-cycle, raceing, and aircraft tires

• Delft-Tyre products are used by 70 % of the automotive OEM.

MODEL VALIDATIONDuring the development of MF-Tyre/MF-Swift, extensive effort has been spent on model validation. Dedicated tire test rigs have been developed to investigate tire behavior and check model capabilities. Some examples of the validation tests used are: force and moment tests, dynamic braking, dynamic steering, cleat tests, axle height oscillations, stiffness tests, etc. In addition, instrumented ve-hicle tests have been conducted in cooperation with vehicle OEM to demonstrate the ap-

plicability of the model for applications in vehicle development. An example of a typi-cal cleat test is shown in Fig. 2; an example of a road load simulation is shown in Fig. 3.

TOOLS AND SERVICESIn general, tire testing and parameter identification effort for tire models are very

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SIMPACK News | March 2014 | 9

Antoine Schmeitz, TNO | 3RD PARTY PRODUCT

Fig. 6: TNO Tyre Test Trailer, wet testing

important, as the quality of the process as a whole affects the final simulation accuracy, and the costs involved are relatively high. Consequently, it is required to have well-defined test procedures that can be carried out in common test facilities and to have tools available for identifying the tire model parameters. For this reason, TNO has developed the parameter identi-fication software MF-Tool (see Fig. 4), and offers services for parameter identification.The unique structure of MF-Swift has special advantages here, as the model consists of a number of relatively independent elements: the parameter identification process can be split up into a number of consecutive, small optimization problems in which a subset of parameters is uniquely determined. With MF-Tool, non-expert users can generate MF-Tyre and full MF-Swift tire property files within 10 and 60 minutes respectively.TNO is well experienced in conducting tire measurements. For the development of

MF-Tyre/MF-Swift, several unique tire test facilities were developed. In the most recent development, the TNO Tyre Test Trailer (Fig. 5 and 6) was adapted to perform winter testing under severe conditions.After the procedure and required tests to

obtain the model parameters, under-standing of the tire model is important for successful us-age. This is why

TNO has always been very open about its models and offers training and consulting services.

SUMMARY AND OUTLOOKTNO Delft-Tyre Toolchain is a portfolio of products and services that include the tire models MF-Tyre/MF-Swift, the parameter identification software MF-Tool and mea-surement, parameter identification, training and consulting services. MF-Tyre/MF-Swift is a versatile model that can be used for many applications. The complexity of the model can be selected for each simulation.

TNO is continuously developing its Tool-chain. Current research is focused on model-ing tire behavior under various operating conditions such as ice, snow, temperature, velocity, etc. In addition, more real-time ap-plications will be realized in the near future, e.g., for Hardware-in-the-Loop and driving simulator applications. Further improvement of the model for misuse applications is under investigation.

INFORMATION AND CONTACTFor an extensive description of the model, further references and many validation re-sults, please refer to reference [1].For information about tire model imple-mentation, please contact SIMPACK AG; for other questions, please find our contact information at www.delft-tyre.com.

REFERENCES[1] Pacejka, H.B., Tyre and Vehicle Dynamics, 3rdEdition, Butterworth-Heinemann, Oxford, 2011.[2] Schmeitz, A., Versteden, W., Eguchi, T., Road Load Simulation using the MF-Swift Tire and OpenCRGRoad Model, SAE Technical Paper 2011-01-0190, 2011.

“Current research is focused on modeling tire behavior under various

operating conditions such as ice, snow, temperature, velocity, etc..”

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