Opti­miz­ing Tire Tread Patterns for Reduced Splashing

A case study with Par­ti­cle­works® and CAESES®

The devel­op­ment of advanced auto­mo­tive systems in recent years such as elec­tri­fi­ca­tion, self-driving systems, and enhanced safety systems among others has led to a drastic increase in the number of elec­tri­cal com­po­nents such as sensors, radars, and cameras. Avoiding wetness of these com­po­nents to avoid damage and cor­ro­sion, so that they function effec­tively and reliably, is of great interest. One useful approach is to mitigate splash­ing of the vehicle’s body and under­body, which is one of the main causes of water damage. This study describes a sim­u­la­tion-driven opti­miza­tion process to inves­ti­gate the influ­ence of tire tread patterns on water splashing.

CFD Sim­u­la­tion Model

The model domain used in the sim­u­la­tion was a symmetry model of half the front section of the vehicle, or essen­tially a quarter model with a focus on the left front wheel and nearby surfaces. This was deemed to be a rea­son­able trade-off in terms of sim­u­la­tion speed and accuracy. Nat­u­rally, the sim­u­la­tion included the forward motion of the vehicle (set to 80 km/​h), as well as the rotation of the wheel (65.4 rad/​s), which then would scatter and splash the water dis­trib­uted on the road surface.

Splash­ing caused by the movement of a vehicle along a wet road is a chal­leng­ing sim­u­la­tion problem. A meshless particle method based on MPS (Moving Particle Sim­u­la­tion) was used, which has the advan­tage that it can directly handle the dynamic motion of water droplets modeled as par­ti­cles inter­act­ing with the sur­round­ing envi­ron­ment. Also, being meshless, the method is well suited for detailed geome­tries with motions and multi-phase fluids, being typ­i­cally faster and more effi­cient than con­ven­tional CFD solvers. The com­mer­cial CFD code Par­ti­cle­works®, devel­oped by Prom­e­tech, was used for the sim­u­la­tions. For more tech­ni­cal details about Par­ti­cle­works® and the MPS method, you can visit their website or take a look at the paper upon which this study is based. 

Para­met­ric Tire Model

CAESES® was used to auto­mat­i­cally generate the various designs of the tire and its tread patterns, based on changing the values of the para­me­ters over a given range. Geometry vari­a­tions of the various treads, grooves, dimples, sipes, etc. were made by adjust­ing the spacing, width, depth, and arrange­ments of the features. Even topo­log­i­cal changes are possible, whereby the number of these features can change, which can be very powerful in an opti­miza­tion study when coupled to a meshless CFD solver like Par­ti­cle­works®. The images below show an example of a tire model built in CAESES® inspired by airless or non-pneu­matic tires with their inter­est­ing spoke struc­tures designed to support the weight of the vehicle and elim­i­nat­ing the pos­si­bil­ity of ever having a flat tire.

The present case study is a demon­stra­tor project to show the method, tool­chain, and workflow, and thus, a less complex con­ven­tional tire was studied in order to have faster com­pu­ta­tions. The tire tread model was described with 12 para­me­ters related to the geometry of the treads and lon­gi­tu­di­nal grooves (inner and outer), includ­ing width, depth, tread length and cur­va­ture, number of treads, etc.

The fol­low­ing ani­ma­tion illus­trates how design can­di­dates can easily be gen­er­ated by changing the values of select design vari­ables. This image shows only the 4 vari­ables that were changed in the 2nd stage of the opti­miza­tion (see below).

Automa­tion Workflow and Opti­miza­tion Strategy

In addition to CAD capa­bil­i­ties, CAESES® is also a process inte­gra­tion and design opti­miza­tion (PIDO) platform. It gen­er­ates the design variants by changing the para­me­ters within the set range of upper and lower bounds, while respect­ing any defined geo­met­ric con­straints. Then, the model is exported and passed to Par­ti­cle­works® to conduct the simulations.

The objec­tive function was spec­i­fied as the area subject to water splash­ing, which was to be min­i­mized. These result values from the sim­u­la­tion were passed back to CAESES® and the opti­miza­tion algo­rithms used them to rank each design and to further adjust the geo­met­ric para­me­ters to create new designs with the aim of con­verg­ing on the one with the best per­for­mance. The fol­low­ing figure shows an example of the under­body surfaces that became wet due to splash­ing, shown in red.

In the first opti­miza­tion step, a DoE (design of exper­i­ments) study was run on 50 cases using the built-in Sobol algo­rithm, which is a quasi-random sampling method of the design space. The result of this initial sweep indi­cated that 4 of the 12 para­me­ters had a larger influ­ence on the objec­tive function. There­fore, only these 4 para­me­ters were further varied in the second opti­miza­tion step. The specific para­me­ters were related to the width and depth of the outer groove, as well as the cur­va­ture of the treads.

In the second step, a Response Surface opti­miza­tion approach was applied to create a sur­ro­gate model. A Radial Basis Function network was adopted to approx­i­mate the response surface. First, the initial response surface was gen­er­ated using 20 sampling points (4 design vari­ables x 5). A Latin Hyper­cube Sampling was applied to generate addi­tional sampling points. After that, the response surface was iter­a­tively updated by adding sampling points based on selected variants along the Pareto frontier. Finally, a total of 50 com­pu­ta­tions were per­formed. On this sur­ro­gate model, the Multi-Objec­tive Genetic Algo­rithm (MOGA) was used to search for the optimal solution in each iter­a­tion. The history of the objec­tive function is shown in the graph below. This figure shows a large vari­a­tion of the objec­tive function for each iter­a­tion, and thus it appears that the design space had many local optima. Based on this study, the 28th iter­a­tion showed the best results, which was thus con­sid­ered to rep­re­sent the ​“optimum” tire tread arrangement.

Results and Conclusions

The result of the opti­miza­tion study was that the total wetted area from the tire splash­ing was reduced by 14.1%, relative to the baseline case (130,953 mm² vs. 112,469 mm²). This was achieved since the opti­mized tire tread pattern managed to deflect some of the water towards the side and the rear of the tire. The com­par­i­son of tread geome­tries between baseline and best case are shown below, along with the figures showing the CFD results of the splash­ing patterns.

This demon­stra­tor study has illus­trated how CAESES®, coupled to Par­ti­cle­works® in an auto­mated workflow, was very effec­tive at explor­ing a large number of design can­di­dates and for con­duct­ing an opti­miza­tion in order to sig­nif­i­cantly improve the tire tread design in terms of reducing water splash­ing char­ac­ter­is­tics on the under­side of the vehicle. The MPS method employed by Par­ti­cle­works® was ideally suited for sim­u­lat­ing the chal­leng­ing physics of splash­ing caused by the motion of a vehicle trav­el­ing along a wet road.

We would like to acknowl­edge and thank Dr. Sunao Tokura from Prom­e­tech Software Inc., Japan, the devel­op­ers of Par­ti­cle­works®. This case study is based on a pre­sen­ta­tion given at the NAFEMS World Congress 2021 entitled ​“Shape Opti­miza­tion of Tire Tread Pattern to Minimize Water Splash­ing on Vehicle Body Using Particle Method CFD Simulation”.