Universal Mechanism software Simulation of dynamics of road vehicles in Universal Mechanism software www.umlab.ru um@umlab.ru

Road vehicle as a mechanical system Creating models Contents Background Road vehicle as a mechanical system Creating models Simulation of vehicle dynamics Verification

Road vehicle components Background Road vehicle components Kinematics of cars

Engine

Off-road vehicle

Transmission components Differential Cardan shaft

Author: Vlad Govorov, BSTU, Bryansk, Russia Grader Grader GS 18-05 by Bryansk factory of road machines. Velocity: 40 km/h Pavement: asphalt in satisfactory condition Author: Vlad Govorov, BSTU, Bryansk, Russia

Dynamic test: vertical load VAZ 2109 Dynamic test: vertical load Here you can see a quasi-static test. Slow force of high amplitude acts on the car body that causes large displacements of the car body and gives us a possibility to determine summary stiffness of the suspension including changing geometry of the suspension.

UM Caterpillar Simulation results Tracked vehicle in the test range with irregularities in staggered order Simulation results

UM Caterpillar Simulation results Tracked vehicle on a vertical obstacle Simulation results

Truck/trailer SAE lane change, V=88 km/h SAE lane change (Society of Automotive Engineers, 1993) maneuver, V=88 km/h. It is used for estimating rearward amplification and several other safety related performance measures. When the test is conducted in the field, several variables are recorded during the manoeuvre for later processing; the main ones being the lateral acceleration of the centre of the steer axle and the lateral acceleration of the center of gravity of the sprung mass of the rearmost trailer.

Low-speed 90º turn, V=10 km/h, R=11.25 m B-double Low-speed turn (closed-loop path following simulation) for estimating low-speed offtracking Low-speed 90º turn, V=10 km/h, R=11.25 m

Pulse steer Pulse steer, V=100 km/h Моделирование динамики грузовика с прицепом при совершении маневра «рывок руля». Pulse steer, V=100 km/h

Step steer Step steer, V=100 km/h

Three-wheeled light vehicle (1) Double lane change, V=14 km/h

Three-wheeled light vehicle (2) Double lane change, V=14 km/h

Single-cylinder engine Student work Single-cylinder engine

Student work: cart Police turn

Student work: police turn

Student work: drifting

Road vehicle as a mechanical system Creating models Contents Background Road vehicle as a mechanical system Creating models Simulation of vehicle dynamics Verification

Simulation workflow Real mechanical system or its prototype 1 Preparing input data and conception of a model 2 Describing kinematical model 3 Describing dynamical model 4 5 Automatic generation of equations of motion Researches starts from problem statement and obtaining the source data (steps 1, 2). After that the model of the mechanical system is prepared (steps 3, 4) and its equations of motion are automatically generated. Numerical simulation of these equations gives us dynamical behavior of the model. Analyzing model’s dynamical performances 6

Technical objects as multibody systems Bodies + Joints Force elements All mechanical systems are represented in the program as a set of rigid or flexible bodies interconnected by means of joints and force elements.

Rigid body: Image Inertial parameters Rigid bodies Once again: any model is a set of bodies, joint and force elements. Rigid bodies has its inertia parameters and graphical image. Inertia parameters are mass, moments of inertia and position of the center of mass.

Joints Joints Translational Rotational 2 - 6 d.o.f. joints Quaternion “Universal Mechanism” software supports using joints of various types that allow to describe all practically feasible kinematical pairs. 2 - 6 d.o.f. joints Quaternion Rod

For Hendrickson Pacific Ltd. Force elements Bushing Air spring Bushing Different heavy vehicle suspension in this slide demonstrate variety of built-in types of force elements in “Universal Mechanism”. Bushings, air springs, dampers – all these elements can be successfully modeled in UM. Damper For Hendrickson Pacific Ltd.

Force elements Airspring Damper Shown here an airspring and a damper are modeled its non-linear force diagram.

Heavy vehicle suspension Cobblestone pavement, V=100 km/h.

UM FEM: Flexible bodies For Hendrickson Pacific Ltd. Finite-element model of the leaf spring

UM FEM: principle of operation Simulation of hybrid system (system of rigid and flexible bodies) Import of dynamic and static modes from FEM software (ANSYS, MSC.NASTRAN) FEM-model from ANSYS, MSC.NASTRAN Rigid body model from Universal Mechanism Hybrid model in Universal Mechanism + = To include a flexible body into your hybrid model in UM you need first to develop its model in external FEM software

Durability analysis Workflow Workflow of the durability analysis module

Kompass 3D –> Universal Mechanism interface

SolidWorks –> Universal Mechanism interface Here you can see an example of data import from SolidWorks. In the top figure you can see the model in SolidWorks, in the bottom one – the same model in Universal Mechanism.

Autodesk Inventor –> Universal Mechanism interface Import from Autodesk Inventor

Matlab/Simulink interface Example 1. Stabilization of the inverted pendulum The UM Control module allows to import Matlab/Simulink models to UM models. Here you can see the classical model of the control of an inverted pendulum. UM model includes a cart and the inverted pendulum on it. Control system is modeled in Matlab/Simulink. The control system takes an angle of declination of pendulum as an input and calculates a force F, that should be applied to a cart to stabilize a pendulum in upper unstable position, as an output.

Matlab/Simulink interface Example 1. Stabilization of the inverted pendulum Slide shows the examples of moving the inverted pendulum with turned on and off control system. Free motion Controlled motion

Matlab/Simulink interface: ABS simulation ABS model in Matlab/Simulink

Braking coefficient / Slip diagram Kienhöfer, F.W., Cebon, D. Improving ABS on Heavy Vehicles Using Slip Control 38

Simulation results: vehicle speed with ABS without ABS Vehicle speed

Simulation results: with ABS Angular r velocity of wheels Longitudinal slip

Simulation results: without ABS Angular velocity Longitudinal slip

Simulation in Matlab

Road vehicle as a mechanical system Creating models Contents Background Road vehicle as a mechanical system Creating models Simulation of vehicle dynamics Verification

Creating models (UM Input) Tree of elements Program package Universal Mechanism consists of two programs: UM Input for model description and UM Simulation for analysis of its dynamics. Please have a look at the main window of UM Input program that is shown in this slide. Identifiers Inspector Screen shot of UM Input program

Automatic generation of equations of motion Deriving equations in symbolic form using a built-in computer algebra system (C, Pascal codes) Numeric-iterational generation …………………………………………………………. _Frc_Vctr[1] := _._ap[3]*_.ix+_._ap[3]*_.mass*_._c2* _._c3*_.length*_.length+_._ap[3]*_.mass*_._c3*_.length*_.length-_._ap[3]*_.mass*_.length*_.length* _._s2*_._s3+ _._ap[3]*_.mass*_.length*_.length-0.1634* _._ap[3]*_.mass*_._c2*_._c3*_.length-0.1634*_._ap[3]*_.mass*_._c3*_.length+0.1634* _._ap[3]*_.mass*_.length*_._s2*_._s3-0.3268* _._ap[3]*_.mass*_.length+0.02669956*_._ap[3]*_.mass +2*_._ap[2]*_.ix+_._ap[2]*_.mass*_._c2* _._c3* _.length*_.length+2*_._ap[2]*_.mass*_._c3*_.length* _.length +2*_._ap[2]*_.mass*_._c2*_.length *_.length-_._ap[2]*_.mass*_.length*_.length*_._s2*_._s3 Elements of equations are computed on each step of numeric integration After describing the model the step of the generation of equations of motions. Universal Mechanism supports two such methods: symbolic and numeric-iterative. Let us consider them more detailed. Symbolic method assumes generation equations of motion as source files in C or Pascal with posterior their compilation by one of the supported external compilers. As a result of compilation the UMTask.dll appears. This *.dll is used by UM Simulation program for numerical integration of equations of motion. Numeric-iterative method assumes generation of equations of motion on each step of numerical integration directly in UM Simulation program. Let us consider advantages and disadvantages of both methods. In terms of CPU efforts the symbolic method is faster. It provides decreasing CPU efforts up to 10-30% for complex (more than 10-20 degrees of freedom) models. For rather simple models CPU efforts for both methods are roughly the same. The symbolic method during generation of source code fulfils its optimization from the point of view of CPU-efforts. On the other hand the symbolic method of generation of equations of motion expects any external compiler to be installed on the same computer. Universal Mechanism supports Borland Delphi, Borland C++ Builder, Microsoft Visual C++ as external compilers. At the same time the numeric-iterative method does not suppose explicit steps of generation and compilation of equations of motion and seems to be simpler in usage. also implemented in UM (sometimes very useful) very fast! Generation of equation in symbolic form and the following compiling them as DLL is one of the reason why UM is faster that many other software

Road vehicle as a mechanical system Creating models Contents Background Road vehicle as a mechanical system Creating models Simulation of vehicle dynamics Verification

Analysis of Models (Simulation Module) Here you can see the main window of the UM Simulation program. There are animation and graphical windows. Screenshot: Simulation Module Any number of animation and plot window

Simulation: on-line visual representation of results 3D animation of motion 3D animation of vectors (forces, velocities, accelerations) 3D animation of trajectories plots (coordinates, velocities, accelerations, applied and reaction forces etc.) Animation of motion of mechanical system takes place simultaneously with plotting results. This is very useful at the stage of checkout a model when faults in the model are visible right after simulation starts. Expander: direct dynamic problem

Processing of Variables Simulation tools Processing of Variables Every computed variable from graphical window or from list of variables can be processed with Table processor Window of statistics Important role for effective analysis of dynamics of mechanical systems plays facility of postprocessor for analyzing obtained results. Built-in table processor and statistical tool let the user a possibility to carry out such analysis quickly and effectively.

Simulation tools Original Filtered There are possibilities to export any graph to Microsoft Excel as a diagram or to filter the process as it is shown in this slide. Original Filtered

Steering wheels Cobblestone pavement, V=100 km/h.

UM Automotive: tire models, library of suspensions Pacejka Magic Formula FIALA tire model Tabular and experimental tire models Road excitations Pointwise input (for measured data) Analytical expressions Synthesis of the road profile based on its spectral power density Superposed pointwise/analytical/generated by spectral power density road profile UM Automotive widens the functionality of UM Base configuration and includes program tools for description of a mathematical models of tires, road plan, road excitations, as well as … (see the next slide) Library of spectral power density of typical road surfaces

UM Automotive: maneuvers Maneuvers with closed-loop steer control Trajectory + Driver model (MacAdam’s model, Second order preview model) … and mathematical models of drivers and tools for maneuver description.

Eigenmodes 0,40 Hz 0,82 Hz 1,10 Hz 1,39 Hz

Road vehicle as a mechanical system Creating models Contents Background Road vehicle as a mechanical system Creating models Simulation of vehicle dynamics Verification

National road transport commission of Australia Heavy Vehicles National road transport commission of Australia Model 2: Truck-trailer Model 1: B-double ADAMS CAR UMTRI’s Yaw/Roll AUTOSIM Universal Mechanism To compare and determine if there is acceptable agreement between simulations from Universal Mechanism and other computer-based modeling packages special verification was done. Two test models of heavy vehicles were created in different modeling programs and results of simulation their dynamics were obtained. National road transport commission of Australia carried out numerical experiments in ADAMS/CAR, UMTRI’s constant velocity Yaw/Roll program and AUTOSIM and our laboratory did the same in Universal Mechanism. Computer models of a truck/trailer and a B-double are considered. In total four simulations were devised that would test and compare a range of features in the models. Pulse steer and step steer inputs were used in the two simulations that employed open-loop steer control, and closed-loop control was used in path following tasks of a high-speed lane change and a low-speed 90° turn. Results of comparison are presented in next slides. SAE Lane change, 88 km/h

Simulation results: pulse steer ADAMS Yaw/Roll AUTOSIM UM Comparison of reports shows very good agreement between Universal Mechanism and other modeling packages.

Simulation results: pulse steer ADAMS Yaw/Roll AUTOSIM UM

Thanks for your kind attention Simulation of dynamics of road vehicles in Universal Mechanism software www.umlab.ru um@umlab.ru