Heavy Vehicles Modeling with the Vehicle Dynamics Library

Heavy Vehicles Modeling with the Vehicle Dynamics Library

Niklas Philipson Johan AndreassonMagnus Gäfvert Andrew Woodruff

Modelon ABIdeon Sience Park, SE-22370 Lund, Sweden

Abstract

This paper presents and describes recent extensionsto the Vehicle Dynamics Library (VDL) for heavyand commercial road-vehicle modeling and simula-tion (VDL/Trucks). Until now, the VDL was targetedmainly at passenger cars applications (VDL/Cars).Users in this domain have been particularly enthusi-astic about the openness, flexibility, and extensibilitycompared to many competing solutions. These advan-tages which are inherent to Modelica technology areeven more important for heavy vehicles applications,where a much larger set of vehicle configurations andvariations must be supported. It has therefore been nat-ural to extend the scope of the library also into thisfield with the VDL/Trucks options presented in thispaper. New components and templates have been in-troduced to reflect many standard chassis layouts. Anumber of new experiment templates are also suppliedto make standard analysis tasks easy to perform.Keywords: heavy vehicles; trucks; vehicle dynamics;Vehicle Dynamics Library

1 Introduction

The Vehicle Dynamics Library (VDL) [1, 2] was orig-inally designed for studies on vehicle handling for pas-senger cars (VDL/Cars). It was early clear that anextension into the heavy vehicles domain would benatural. The inherent flexibility and extensibility ofthe Modelica-based solutions offers great benefits inthis domain where a vast set of vehicle configurationsand variants must be handled, such as combinationsof trucks, tractors, full trailers, semi-trailers, tankers,with various axle and powertrain configurations, andalso a wide range of payload conditions. This paperintroduces the VDL/Trucks option of VDL aimed atmodeling and simulation of heavy vehicles.Vehicle dynamics analysis of heavy vehicles and pas-

Figure 1: Truck-fulltrailer in a double lane-change

senger cars have many common inputs such as a hu-man driver model with similar driver-vehicle inter-face, road and environment properties, etc, and outputsof interest such as tire forces at the contact patches,chassis and suspension motion. Joints, links, springs,dampers, drivers, roads, and tires all produce simi-lar types of constraints on the model. A large set ofmodel components are therefore common for cars andtruck modeling. There are, however, some major dif-ferences between heavy commercial vehicles and pas-senger cars when it comes to chassis layout. The num-ber of axles, tires and trailers are some of the manyparameters that are combined to form a heavy vehi-cle configuration, while cars have a more static setup.This requires an even more flexible interface and tem-plate design for heavy vehicles than for cars.

The heavy vehicles option has been developed fromthe same library base as the car option. This meansthat the new heavy vehicle models can benefit from analready well tested and mature overall design.

Heavy Vehicle Modeling with VehicleDynamics Library

The Modelica Association 629 Modelica 2008, March 3rd − 4th, 2008

2 Heavy vehicle components

As mentioned above, there are many low levelcomponents that are shared between VDL/Cars andVDL/Trucks, but there are of course many examplesof new components and components that are used dif-ferently in the context of heavy vehicles [3]. Essen-tially, this is due to the difference in weight and di-mensions. The higher over-all weight requires differ-ent solutions and very large load variations means thatgood performance have to be achieved for a wide vari-ety of load cases. The higher center-of-gravity makesrollover rather than road adhesion the handling limit inmany situations. This section highlights some of theextensions made to VDL for heavy vehicle simulationto address these differences. Figure 2 shows a screenshot of parts of the library, indicating some importantnew additions.

Figure 2: Screen shot of parts of VDL as it appearsin Dymola. Some main extensions to VDL for heavyvehicles are indicated.

Suspension The suspension designs in heavy trucksare usually axle-based for the steerable and non-steerable wheels. Leaf springs are commonly usedfor both axle guidance and load support and are im-plemented as described in [4]. To meet the require-ment of high load variations the leaf springs are oftenmounted in such a way that the effective length of themdecreases when they are subjected to load. There arealso leaf spring versions that are equipped with helpersprings that becomes active when the vehicle is loaded.Air springs are often used in heavy vehicle suspen-sions in conjunction with trailing arms to easily ad-just for different load cases, see Figure 3. Air springscan be used to change the ride height of the vehicle byincreasing the air mass inside the spring, which alsoresults in a stiffer spring that can carry more load.

Figure 3: Typical heavy vehicle rear axles.

Frame The frame elasticity influences the load dis-tribution between the axles, and therefore the availablegrip from the tires. The elastic frame included in VDLtrucks has a torsional degree of freedom. It is easy toadd or change the degrees of freedom in the frame byextending the interface so the common template con-nectors are used.

Payloads The payloads can be static (e.g. a crane),dynamic (e.g. a tank for liquid load) or have vary-ing masses or mass distributions (e.g. cargo contain-ers). These different cases are supported with user-friendly configuration setup. The existing liquid pay-load model considers the dimensions of the tank and arotational damped degree of freedom for slosh.

Cabin The truck cabin is usually suspended fordriver comfort since the chassis suspension must be

N. Philipson, J. Andreasson, M. Gafvert, A. Woodruff


Figure 4: Sine-excitation of a tractor-trailer combina-tion with the liquid load in the tank modelled with witha one degree of freedom to capture dynamic load dis-tributions.

stiff to accommodate the high loads. The cabinsuspension is a linkage mechanism equipped withsprings, dampers and antiroll bars. The suspensionalso causes a relative motion between the steeringwheel and the steering gear since the steering wheelmoves with the suspended cabin. This is incorporatedin the vehicle templates and ensures that it is easy tochange the different subsystems such as the cabin sus-pension or the steerable axle linkage in an flexible way.

Couplings Heavy vehicle combinations often havetractor (driven) and trailer vehicle units. The attach-ment to guide and constrain the trailer can vary, but hasa significant effect on the handling and vehicle behav-ior. One of the most common couplings is a fifth wheelfor the tractor/semi-trailer combination. Full trailersand dollies usually have a draw bar and hook to attachto the tractor, driven truck, or preceding trailer (in thecase of road trains). The coupling must have a mass onboth sides of the joint or be locked to avoid a singularsetup when no unit is attached on one side. This isconveniently handled without much user interventionby the available components and templates.

3 Heavy vehicle templates

The variation and configuration space of heavy vehi-cle combinations are much larger then for normal pas-senger cars. Also, the components can be of vary-ing fidelity depending on the design and purpose ofthe model. A new set of templates for heavy vehiclecomponents has therefore been developed to sustainthe user-friendliness offered in VDL/Cars. These new

templates are based on the same usage principles as thecar templates, where templates for aggregate modelsare built by connecting replaceable components thatcan be parameterized depending on application. Anexample of a tractor template is given in Figure 5.

Figure 5: Tractor template with two rear axles.

The heavy vehicle interfaces for basic components arelargely the same as those for cars. Some changes in-clude extra connections to incorporate the frame andsuspended cabin. The axle-based suspension modelstypically have connectors for the axle and chassis, in-stead of using separate connectors for the left and rightsuspension linkage models. The templates still haveall connections and parameters predefined and propa-gated between models so they only require the replace-able components to be redeclared from the graphicalDymola user interface.The main chassis components include a number of sus-pension models that contain one or more axles, frame,coupling, wheels, and a body or payload. Trailers canalso include components for a dolly.The suspension templates are based on axle con-straints. The axle can be a steerable or non-steerableversion. The axle connects through the linkage to thechassis. The linkage has external or internal force el-ements such as coil/air springs or leaf springs, respec-tively, to support the chassis. An anti-roll bar is at-tached to the axle and chassis. The suspension compo-nents vary from the most basic bounce and roll degreesof freedom to detailed elasto-kinematic setups.

4 Experiments

Simulation experiments for passenger cars and heavyvehicles have many similarities and correspondinglyshare setup of e.g., drivers, roads and grounds, and en-vironments. Just as for cars, both the open and closedloop driver models are available. The double lane-



change road maneuver as seen in Figure 1 is useful foremergency handling evaluation since it excites the rollmotion which may cause roll-over [5]. The experimentis set up using a driver model that follows the road pathdefined by RoadBuilder [2]. The sine steering excita-tion experiment shown in Figure 4 is instead realizedusing an open loop steering robot while a drive robotis keeping the speed constant.For out-of-plane frequency response, the shaker tablecan be used [2]. It is implemented as a ground modelcontaining patches with time dependent altitudes, de-fined by inputs. Since a heavy vehicle can have morethan two axles, the shaker table has a configurablenumber of patches to suite any number of axles andwheel locations. Correspondingly, several suspensionrigs can be used together for detailed analysis of bogieaxles, see Figure 6.

Figure 6: Twin axle with load distribution linkage in asuspension rig.

5 Customization

Just as for passenger cars and light vehicles,VDL/Trucks is extended with a set of examples forheavy vehicles. This includes both truck with fulltrailer and tractor with semitrailer as seen in Figures 1and 4, respectively. Thanks to the flexibility inherentin the library, it is straightforward to re-configure theseand even build completely different equipages, as il-lustrated by the examples in this section.

5.1 Road Train

Equipages with combinations of a truck or tractor withtwo or more trailers forms a road train of the type com-

monly used in e.g. Australia. These vehicle combina-tions allow for one driver to freight a larger amountof cargo compared to a tractor pulling a single trailer.Unlike rail-carried trains that are self steered by therail-wheel interaction, road trains are more sensible todisturbances and may even exhibit instability if careis not taken. Additionally, road trains are heavy andthereby hard to stop which requires them to be able tosteer to avoid accidents. This puts high demands onthe design of trucks and trailers so that they safely canbe combined into road trains under a variety of loadconditions. In VDL, these configurations can be de-fined and tested conveniently. Figure 7 shows a set-upwith tree trailers pulled by a tractor.

Figure 7: Road train with three trailers, diagram view(top) and animation screen shot (bottom).

5.2 Moving tire test rig

Tire test rigs are can be subdivided into two main cat-egories depending on if the tested wheel or the groundsurface is moving. For the latter case, the ground istypically implemented as drum or a belt. The draw-back with these two concepts are on one hand that thebelt only makes it possible to use elastic surface ma-terial such as steel and on the other hand that a drumhas to have a curvature which impacts the tire-surfacecontact. To avoid this and to enable testing on real roadsurfaces such as gravel, asphalt, and ice under differ-ent conditions with respect to moisture, temperature,and so on, the tested wheel can be mounted on a mov-ing rig, typically attached to a heavy truck. However,



a moving rig is harder to control, especially since theforces generated from the tested wheel will affect thecourse of the truck. To investigate both the static anddynamic effects of the total system of truck, rig, andtire on resulting measurements, a moving tire test rigwas implemented by mounting a test rig with wheelonto a truck model as illustrated in Figure 8. The re-sults were then compared to standard test rig simula-tions and real mobile-rig mesurement results and pro-vided insight into the interpretation of sensor signals.

Figure 8: Mobile tire test rig mounted on a truck.

6 Simulink

Just as for passenger cars, heavy vehicles modeledwith VDL can be imported into the Simulink [7] en-vironment. Figure 9 shows an experiment layout inDymola [6] used for the yaw control application inSimulink shown in Figure 10. In applications like thisVDL/Trucks can provide models that are of great usein the design and validation of various chassis controlfunctions.

7 Future

Currently the VDL/Trucks option is focused on thechassis and covers well the most commonly used vehi-cle types. VDL/Cars have more complete support forfull vehicle modeling with templates for powertrains,drivelines, brakes, engines, etc. Future developmentwill move in the direction of complete vehicle model-ing also for heavy vehicles. Until then, many compo-nents are still available to build those subsystems frombase classes, but without extensive templates.

Figure 9: Experiment with in- and outputs forSimulink. Inputs: Steering wheel angle, enginetorque, gear, wheel brake clamp forces. Outputs: Ve-hicle states, tire forces and wheel spin velocities.

Figure 10: Yaw control application for the tractor-semitrailer combination shown in Figure 9.

8 Summary

This paper shows how the Vehicle Dynamics Libraryis extended with the VDL/Trucks option for heavyand commercial road-vehicle modeling and simula-tion. An overview of the recent additions is given andit is shown with several examples how the openness,flexibility, and extensibility from VDL/Cars is main-tained and extended.

References

[1] Modelon AB, Lund, Sweden. The VehicleDy-namics library, User’s Guide, Version 1.2, 2007.



[2] J. Andreasson and M. Gävert, The VehicleDy-namics Library - Overview and Applications.In: Proceedings of the 5th Modelica Confer-ence, Vienna, Austria, Modelica Association, 4-5September 2006.

[3] N. Philipson, Extension of a tool for vehicle dy-namics studies to handle heavy vehicle configu-rations. Master Thesis Report, KTH-AVE, 2007.

[4] N. Philipson, Leaf spring modeling. In: Proceed-ings of the 5th Modelica Conference, Vienna,Austria, Modelica Association, 4-5 September2006.

[5] E. Dahlberg and A. Stensson, The DynamicRollover Threshold of Commercial Vehicles - aSensitivity Study. International Journal of Vehi-cle Design, Vol. 40, No. 1-3, pp. 228-250, 2006.

[6] Dymola - Dynamic Modelica Laboratory,http://www.dynasim.se

[7] The MathWorks: Matlab and Simulinkhttp://www.mathworks.com



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Heavy Vehicles Modeling with the Vehicle Dynamics Library