DYNAMIC MODEL OF A LOGISTIC TRAIN WITH DIFFERENT STEERING SYSTEMS AND TIRE MODELS

Abstract

LOGISTIC TRAIN IS ONE OF THE RECENT SOLUTIONS APPLIED IN THE INTRALOGISTICS. IT BASES ON THE CONCEPT OF THE “MILK-RUN” DELIVERY METHOD THAT IS USED TO TRANSPORT MIXED LOADS FROM VARIOUS SUPPLIERS TO ONE CUSTOMER. THE MAIN PROBLEM IN THE IMPLEMENTATION OF INTRALOGISTICS TRAINS IS THE POSSIBILITY TO DETERMINE WHETHER THE TRAIN IS ABLE TO PASS THE GIVEN PATH WITHOUT A COLLIDING WITH SURROUNDING OBJECTS. CHOOSING ADEQUATE KINEMATIC PARAMETERS IS ALSO DIFFICULT WITHOUT SIMULATIONS. DYNAMIC MODEL PRESENTED IN THIS PAPER WAS PERFORMED FOR THE THREE MOST COMMON STEERING SYSTEMS FOR THE TROLLEYS: DOUBLE ACKERMANN STEERING SYSTEM AND TWO DRAWBAR SYSTEMS: CONVENTIONAL AND VIRTUAL CLUTCH. IN THE MODELS, A THREE-WHEELED TOWING TRACTOR IS CONSIDERED, WHICH IS EQUIPPED WITH AN ACTUATED STEERING WHEEL AT FRONT AND A TWO PASSIVE REAR WHEELS USED FOR STABLE MOTION. TWO TYPES OF TRAILERS ARE INCLUDED. FIRST ONE IS FITTED WITH THE DRAWBAR SYSTEM AND IT IS CONNECTED TO THE TRACTOR VIA A PASSIVE JOINT. IT HAS TWO REAR FIXED WHEELS AND TWO CASTER WHEELS IN FRONT. THE SECOND TYPE INVOLVES DOUBLE ACKERMANN STEERING SYSTEM AND IT HAS FRONT WHEELS THAT FOLLOW ACKERMANN STEERING PRINCIPLE. IN THAT CASE, A ROTATION OF DRAWBAR CAUSE THE TURN OF FRONT WHEELS. THE REAR WHEELS ARE SYNCHRONIZED WITH FRONT ONES BUT THEY ROTATE IN THE OPPOSITE DIRECTION. THE DYNAMIC MODEL WAS DEVELOPED FOLLOWING LAGRANGE’S THEOREM INCLUDING THE POSSIBILITY OF LATERAL SLIP. THE SYSTEM OF DIFFERENTIAL EQUATIONS WAS NUMERICALLY SOLVED. IN ORDER TO CALCULATE THE LATERAL FRICTION FORCES WE USED THREE DIFFERENT TIRE MODELS: LINEAR, SIGMOIDAL AND PACEJKA MAGIC FORMULA. THE RESULTS OBTAINED FOR DIFFERENT TIRE MODELS AND STEERING SYSTEMS ARE PRESENTED IN THE FORM OF ANIMATIONS PRESENTING TRAIN RUN IN VARIOUS CONDITIONS. THE ANALYSES HAVE SHOWN THAT THE USE OF SIMPLIFIED TIRE MODELS IS JUSTIFIED UNDER CERTAIN CONDITIONS.