RESEARCHES REGARDING THE MATHEMATICAL SIMULATION OF KINETOSTATICS OF THE THREE-POINT HITCH COUPLERS USED TO AGRICULTURAL TRACTORS

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1 The 4th International Conference Computational echanics and Virtual ngineering COC - OCTOB, Brasov, omania SACHS GAING TH ATHATICAL SIULATION O INTOSTATICS O TH TH-POINT HITCH COUPLS US TO AGICULTUAL TACTOS V Pădureanu, Năstăsoiu Translvania Universit, Brasov, omania, padu@unitbvro Translvania Universit, Brasov, omania, mnastasoiu@unitbvro Abstract: The paper presents an analtical method of the development and of analsis of three-point hitch couplers used to agricultural tractors As we know, the object of kinetostatics is the stud of all forces which acts upon the mechanism elements during their motion This stud is made starting from the following initial data: the kinematic scheme of the mechanism, the geometrical sizes of mechanism elements and the coordinates of kinematic couples Within the calculations are not taken into account the inertia and the friction forces from the kinematic couples The mechanism is dived in three kinematic groups The stud and the simulation of kinetostatics mechanism are made for each group depending on the piston position in the lift clinder of the mechanism Thus we determine the forces of the kinematic couples in all the mechanism elements, including the force from the piston rod, for each mechanism position, starting with the working position and finishing with the one of transport We present the results of the researches made upon wheeled tractors U 6 and U 6 T ewords: kinetostatics, three-point hitch couplers, agricultural tractor INTOUCTION The dnamic analsis of the three-point hitch couplers is to determine all the forces from its elements arising from the eternal drive tasks Analsis is done b groups, starting from the group that we know as eternal forces Initial data for calculation are: the kinematical scheme of the three-point hitch couplers for which we know the dimensions and the coordinates of all the points, for the analses position the weight of the three-point hitch couplers farming machine (the elements mass of the mechanism, is usuall neglected) the resultant of the eterior forces (of working resistances) which acts upon the mechanism In calculations, the result of the eterior forces is represented b and components, applied to the point S In the calculations that follow there are not taken into account the frictional forces of the mechanism and also the inertial forces The kinematics scheme of the mechanism is presented in figure TH OCS AN ACTION CALCULUS The calculus of ground reaction The traction force from a plough is given b the relation: t, () where: the horizontal element of the useful resistances of the plough: khb k the specific resistance of the ground h the working depth of the plough b the plough width plough (the frictions of the operating parts with the ground) The resultant of the vertical forces (fig ) is given b the relation:, sum where is the plough weight 6 the unwanted resistances of the () 6

2 igure : The scheme of the three-point hitch couplers[] The forces and reactions calculus for the 6 7 groups The reaction 7, is equal with the force from the central couplin bar 7, and it is determined from the moments equation in ratio with se point (fig ): t S S 7 cos 7 sin sin t S S 7 cos from where t S S 7 cos sin And the reaction elements are: 7 7 cos 7 7 sin (3) (4) igure : The scheme of the forces calculus of the group 6 7 The elements of the reaction 6 from the fie hinge are determinde from the forces projections from the two aes: t t 7 () (6) The reaction resulted in this joint will be: The inclination angle α is determined b the relation: (7) 7

3 8 (8) or (8 ) The forces and reactions calculus for the 4 groups In order to determine the forces (reactions) from this group we use figure 3 irst, we determine, the elements of the reaction, equal with the hanger 4: sin ) cos(9 cos ) sin(9 (9) igure 3: Scheme for the forces calculus of group 4 [] The reaction is determined from the equation moments of all the forces in proportion with all the forces with point:, sin cos rom where, sin cos 4 () Net, we determine the reaction from the joint : Y X () The inclination angle α is determined b the relation: () or (3) The forces and reactions calculus for 3 groups The reaction, is equal with the force from the core of the lift clinder, it is also determined, in this case, from the equation moments in proportion with C point (fig 4):

4 igure 4: Scheme for the forces calculus of group 3[6] sin 34 C 34 C A c cos 3 C A 3 from where 34 C 34 C A c cos3 C A sin3 The elements of this reaction are: cos 3 sin 3 The reaction in C joint is determined from the equation of forces projections: X Y The inclination angle α 3 of the lift clinder is determined b the relations: AB 3 AB AB AB or 3 B A B A (8) B A B A, (4) () (6) (7) 3 APPLICATIONS O TH THOTICAL SACS PO In this section of the paper is presented a part of the theoretical researches performed on U 6 T tractor, tractor which is representative for the omanian fleet tractors There have been used the following entrance data, according to the second categor (v S ISO 73-): the coordinates of the fi points (in mm): A(-, ), C(3, ), (3, 49), (4,89) the dimensions elements (in mm): AB = 6, CB = 94,8, C = 6, = 76, = 9, = 8, = 637, = (49), S = 8 the angles values: α = (the inclination of the lift clinder besides the horizontal plane), β = 4 (the angle between the levers CB and C) the plough weight = 4, kn, the plug width b = m, the working depth h =,3 m, the specific resistance of the ground k = 3 kn kn The researches results are graphicall presented: the forces variation in the elements of the three-point hitch couplers depending on the specific resistance of the ground (fig ) the force variation of the piston rod during the lifting up of the agricultural machine in the transport postion (fig 6) 9

5 igure : The forces variation of the three-point hitch couplers elements depending on the specific resistance of the ground igure 6: The force variation of the piston rod during the lift-up of the agricultural machine in transport position ( min = 87 mm): = 99 mm, = 49 mm, 3 = 9 mm 3

6 igure 7: The force variation of the piston rod during the lift-up of the agricultural machine in transport position ( ma = 964 mm): = 99 mm, = 49 mm, 3 = 9 mm 4 CONCLUSION The calculus algorithm developed allows the determination of the forces in all the elements and the joints of each threepoint hitch couplers nowing the value of the piston rod we can correctl calculate the parameters of the acting lift clinder The value of the rod piston force is insignificantl influenced b the position of the superior coupling bar, but, the position of the point on the inferior couplin bar (the distance ) has a great influence upon the value of this force (over two times) NCS [] Năstăsoiu, S, şa Tractors, idactic and Pedagogic Publishing House, Bucharest, 983 [] Guskov, V V Traktorî, ciasti III, onstruirovanie i rasciot, Vîşeişaia şkola, insk, 98 [3] * * * S ISO 73- Three-point hitch couplers [4] * * * echanical ngineer's Handbook ditura tehnică, Bucureşti, 976 [] Năstăsoiu,, şa esearch on the dimensional snthesis of the three-point hitch couplers used at agricultural tractors, The th International Congress on Automotive and Transport ngineering CONAT, Volume VI- Heav and Special Vehicles, Brasov, 7-9 October, pg 47 [6] Năstăsoiu,, şa esearches on the mathematical modeling of the kinematics of three-point hitch couplers used at agricultural tractors, The th International Congress on Automotive and Transport ngineering CONAT, Volume VI-Heav and Special Vehicles, Brasov, 7-9 October, pg 3