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A young researcher at the Dynamic Simulation Laboratory of University of Illinois at Chicago, along with a team of flexible multibody system (MBS) modelling experts from Finland and China, is working on non-linear finite element methods to simulate tyres that have a composite material description. Mohil Patel, whose research work has appeared in several peer-reviewed journals, is focussing on the finite element modelling of tyres using large deformation Absolute Nodal Coordinate Formulation (ANCF) framework, tyre-soil interaction and general vehicle dynamics. In this interview to Tyre Asia he and his research colleagues explain their current work. Excerpts

TA News Bureau

Can you detail the new computational multibody system framework for developing accurate tyre models using finite element Absolute Nodal Coordinate Formulation (ANCF) framework?

The computational multibody system framework detailed in our 2016 research paper for the analysis of tyres utilizes the absolute nodal coordinate formulation (ANCF) which is a large deformation and large rotation non-incremental finite element framework. There is no need for co-simulation approach when using ANCF finite elements in general multibody dynamics algorithms. The tyre modelling approach uses the concept of the ANCF reference node in order to model a rigid rim and uses linear constraints to connect the flexible tyre body (ANCF finite element mesh) to the rigid rim (ANCF reference node) at a pre-processing stage. Furthermore, the modelling approach uses a penalty based contact formulation and a distributed pressure force formulation that accounts for change in the tyre inner surface area. The composite and nonlinear nature of the tyre material can also be accounted for in this modelling approach through constitutive equations.

What have been the procedures that you have followed to create thegeometry for the multibody system analysis of the tyre?

The finite element tyre cross-section geometry was created by using a reference tyre cross-section image. Once a spline was mapped on the reference cross-section, ANCF shell elements can be fitted to the spline shape in order to mesh the tyre cross section. The cross-section can be then simply revolved in order to acquire the entire tyre mesh. In order to capture the tread details on the tyre outer surface, the Non-Uniform Rational B-Spline (NURBS) and numerical integration procedures can be utilized as well, without having to refine the tyre mesh to the level of the intricate tread details.

Please explain the modelling of composite tyres and the computationalprocedures that you have followed using continuum-based air pressure andcontact tyre force models?

The composite material properties are accounted for at a constitutive level by changing these properties at every integration point in the shell element thickness. Layer orientation can be captured through appropriate stress and strain transformation matrices. The composite ANCF shell element has been assessed and used. Furthermore, nonlinear hyperelastic material models like Mooney-Rivlin that can be used to model the tyre tread, have been successfully modelled and analysed in the published research literature with ANCF elements as well.

In order to capture the tread details on the tyre outer surface, the Non-Uniform Rational B-Spline (NURBS) and numerical integration procedures can be utilized as well, without having to refine the tyre mesh to the level of the intricate tread details

The continuum-based air pressure model uses a surface area integral to distribute the pressure forces on the tyre inner surface. Nanson’s formula which relates the current tyre deformed surface area to its reference configuration surface area is used to correctly account for the changes in the surface area brought upon by deformation. The contact model is based on a discrete penalty force and Coulomb friction approach in the normal and tangential directions respectively. The discrete nature of the contact means that the contact forces are applied as point forces in the contact patch of the tire.

You say that researchers were able to significantly reduce the number ofdifferential and algebraic equations that are otherwise needed to besolved. Please explain this.

The reduction in the number of differential-algebraic equations (DAEs) refers to the use of linear connectivity constraints between the tyre and the rim at a pre-processing stage. Due to the linear nature of these constraints, they can be eliminated at the pre-processing stage through an appropriate velocity transformation matrix. If these constraints were nonlinear in nature then they would have to be modelled as algebraic equations during the dynamic simulations thus increasing the number of DAEs to be solved for.

In what way can tyre engineers use your procedures to design tyres thatdeliver better wet grip and low rolling resistance?

Modelling tyres using the ANCF approach has two important benefits. First, a full finite element description of the tyre is achieved, which results in distributed inertia and elasticity description of the structure. Second, such finite element tyres can be easily incorporated into multibody dynamics simulations due to the non-incremental solution procedures used in ANCF. Important tyre performance indicators such as wet grip and rolling resistance can be extracted from the ANCF finite element simulations. Wet grip would of course involve modelling of the fluid-structure interaction. However, this can be achieved by correctly modelling the tyre tread details and the fluid itself. In case of ANCF tyres, the tyre tread details can be incorporated in the shell element surface through a combination of non-uniform rational B-splines (NURBS) and numerical integration, whereas the fluid can be modelled using the smoothed particle hydrodynamics (SPH) approach. Some work has already been done on such fluid-structure interaction that uses ANCF elements and the SPH approach.

Important tyre performance indicators such as wet grip and rolling resistance can be extracted from the Absolute Nodal Coordinate Formulation (ANCF) finite element simulations. Wet grip would of course involve modelling of the fluid-structure interaction

With regards to analysing rolling resistance which needs steady-state tyre rolling, ANCF elements are capable of correctly capturing large rigid body rotation along with local deformation near the tyre contact patch. Improvement of rolling resistance has to do with improvements in the tyre geometry and material, both of which can be modelled to the user’s required accuracy using the ANCF framework. Furthermore, in case of tyre geometry improvements, optimization algorithms can be utilized along with the ANCF approach in order to acquire a variety of new tyre shapes through which rolling resistance changes can be studied.


The research team


Mohil Patel has recently completed PhD from the University of Illinois at Chicago. His research was on new tyre modelling methods and their integration with multibody system (MBS) dynamics algorithms. His research interests include flexible MBS modelling, absolute nodal coordinate formulation (ANCF) finite elements and numerical methods. He is currently working at Navistar Inc. as a product development engineer and team lead.

Dr Grzegorz Orzechowski has been conducting research in automation, robotics and flexible MBS analysis. His current research interests include flexible MBS modelling, numerical methods for solution of equations of motion, ANCF finite elements, real time applications and control algorithms. He is currently a post-doctoral researcher at the Lapeenranta University of Technology in Finland.

Dr Qiang Tian has been focusing on flexible MBS dynamics over the past decade. His research interests are in modelling and simulations of lubricated clearance joints, efficient surrogate modelling of flexible MBS models and ANCF finite elements. Dr Qiang has published over 40 international journal papers including two highly cited papers of ESI. He is currently an Associate Professor at the Beijing Institute of Technology.

Dr Ahmed A Shabana is a university distinguished professor and Richard and Loan Hill Professor of Engineering at the University of Illinois, Chicago. His work for over 30 years has been on developing computational algorithms for the dynamics and computer simulation of constrained flexible MBS that include vehicles, machines, mechanisms and robotics. He is author of six books and over 200 refereed journal articles.

(Appeared in February-March 2018 issue of Tyre Asia)

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