IOP Conference Series: Materials Science and Engineering PAPER OPEN ACCESS Research concerning the evaluation of the connection forces in the oints of the sucker rod pumping units mechanism To cite this article: Bdoiu et al 08 IOP Conf. Ser.: Mater. Sci. Eng. 95 000 View the article online for updates and enhancements. This content was downloaded from IP address 48.5..8 on 4/0/09 at 04:5
9th International Conference on Tribolog (Balkantrib 7 IOP Conf. Series: Materials Science and Engineering 95 (08 000 doi:0.088/757-899x/95//000 Research concerning the evaluation of the connection forces in the oints of the sucker rod pumping units mechanism Bădoiu, Petrescu M G, Antonescu N N, Toma G 4 Petroleum-Gas Universit of Ploiesti, epartment of Mechanical Engineering, 00680, Ploiesti Romania Petroleum-Gas Universit of Ploiesti, epartment of Mechanical Engineering, 00680, Ploiesti Romania Petroleum-Gas Universit of Ploiesti, epartment of Mechanical Engineering, 00680, Ploiesti Romania 4 Petroleum-Gas Universit of Ploiesti, epartment of Mechanical Engineering, 00680, Ploiesti Romania dorin.badoiu@gmail.com, pmarius@upg-ploiesti.ro, nnantonescu@upg-ploiesti.ro, georgeta_tm@ahoo.com 4 Abstract: At present, the sucker rod pumping installations are the most used in the case of the wells in production, when an eruptive eploitation is not possible. The practice has demonstrated that an important role in increasing safet in the operation of the pumping units has the design of the various component bearings because of the etremel high values of the connection forces to which the are loaded. That is wh it is necessar to establish as accuratel as possible the values of these connecting forces. In the paper is analzed the dnamics of a conventional pumping unit mechanism. The dnamic stud which allows establishing the values of the connecting forces in the oints is performed within the Assur structural groups. The dnamic analsis was implemented into a computer program using Maple programming environment and finall it has been presented some simulation results in the case of a C-0-56-00 pumping unit. Kewords: pumping unit, connection forces, dnamics. Introduction At present, since most wells can not provide an eruptive eploitation, this is accomplished b pumping using the sucker rod pumping installations []. The functioning analsis of these installations must take into account man factors of which we can mention: the configuration of the pumping unit, the dimensions of the component elements, the pumping speed and the size of the sucker rod and of the tubing which contributes to the greatest etent to the load of the pumping unit. An important role in increasing safet in the operation of the pumping units has the design of the various component bearings because of the etremel high values of the connection forces to which the are loaded. In this regard the values of these connecting forces have to be established as accuratel as possible. In this paper it is analzed the dnamics of the mechanism of the conventional pumping units, thus establishing the variation on the cinematic ccle of the values of the connecting forces. The dnamic stud is performed within the Assur structural groups [-4]. A computer program using Maple programming environment [5] has been developed and some simulation results regarding the variation Content from this work ma be used under the terms of the Creative Commons Attribution.0 licence. An further distribution of this work must maintain attribution to the author(s and the title of the work, ournal citation and OI. Published under licence b Ltd
9th International Conference on Tribolog (Balkantrib 7 IOP Conf. Series: Materials Science and Engineering 95 (08 000 doi:0.088/757-899x/95//000 on a cinematic ccle of the values of the connection forces in the oints of a C-0-56-00 pumping unit are presented.. Pumping unit mechanism dnamics A conventional pumping unit which is part of a sucker rod pumping installation is shown in figure and in figure is presented the cinematic scheme of its mechanism. igure. Conventional pumping unit. With C,C and C were noted the mass centres of the cranks, connection rods and of the rocker, respectivel; m CGR is the total mass of the counterweights; m L is the mass of the two crank pin bearings; m L is the mass of the equalizer bearing; m tr is the mass of the equalizer considered to be concentrated in the point B; m CB is the mass of the horsehead considered to be concentrated in the point on the rocker. igure. Cinematic scheme of the mechanism of a conventional pumping unit. or establishing the position of the connection rods and of the rocker, the angles and are calculated b solving the following equations sstem obtained b proecting the vectorial equation corresponding to the closed contour O-A-B-C-O on the and aes:
9th International Conference on Tribolog (Balkantrib 7 IOP Conf. Series: Materials Science and Engineering 95 (08 000 doi:0.088/757-899x/95//000 l l cos l sin l cos sin l l cos sin where l OA ; l AB, l BC and C and C are the coordinates of the point C where is located the centre bearing. The angular velocities and the angular accelerations of the connection rods and of the rocker ma be calculated b deriving in relation to time the epressions of the angles ( and (, with the following relations: d d d ;, ( d dt d C C 0 0 d d ;, ( d d where and are the angular velocit and the angular acceleration, respectivel, of the cranks. Having established the values of the angles and it were determined the coordinates of the various points on the mechanism, including those of the mass centres of the component elements and of the point where acting the force (figure at the polished rod. The proections on the and aes of the speeds and of the accelerations of an point on the mechanism ma be calculated b deriving in relation to time the epressions of its coordinates, for eample in the case of the point, b using the following relations: ( ( v ( v d d d d d dt d dt d d d d (4 ( a ( a ( v ( v d d d d d d d d The mechanism comprises a single Assur structural group, namel a dad composed of the connection rods and the rocker. igure shows the loads corresponding to the elements of the dad, where G m g;,, are the weight forces of the connecting rods and of the rocker and m and m are their masses; g 9.8m/s is the gravitational acceleration that acts in the opposite direction of the ais; GL ml g is the weight force of the two crank pin bearings (it has been considered that onl half of the weight of these bearings is concentrated on the connecting rods, the rest remaining concentrated on the cranks; GL ml g is the weight force of the equalizer bearing; Gtr mtr g is the weight force of the equalizer; GCB mcb g is the weight force of the horsehead; m a ;,, are the inertia forces corresponding to the connecting rods and to the rocker i C and ac,, are the accelerations of their mass centres; M i JC ;,, are the inertia moments, where,,, are the mass moments of inertia corresponding to the connecting rods JC and to the rocker; il ml aa, il ml ab, itr mtr ab and icb mcb a' are the inertia forces corresponding to the two crank pin bearings, equalizer bearing, equalizer and to the horsehead, respectivel; is the force acting at the end of the polished rod. igure shows also the (5
9th International Conference on Tribolog (Balkantrib 7 IOP Conf. Series: Materials Science and Engineering 95 (08 000 doi:0.088/757-899x/95//000 proections on and aes of the connection forces from the two crank pin bearings ( and and of the connection force from the centre bearing ( 0 and 0. igure. The load scheme of the dad made up of the connecting rods and the rocker. The connection forces and ma be calculated b solving the equations sstem obtained from the following dnamic equilibrium equations in moments: M B 0 BA 0 BA GL il BC G i M i (6 M C 0 CA CA GL il CC G i CB G L il Gtr itr CC G i (7 C' G C M M 0 CB icb The proections on and aes of the connection force ( and from the equalizer bearing acting on the equalizer ma be established from the following dnamic equations in forces: 0 0 il i il itr (8 0 0 il i il itr GL G GL Gtr (9 In the previous equations it has been considered that the mass of the equalizer bearing is distributed evenl on the rocker and the equalizer. The proections on and aes of the connection force 0 from the centre bearing ma be calculated from the following dnamic equilibrium equations in forces: 0 0 0 il i icb (0 0 0 G G G 0 il i icb L CB ( where and. i i 4
9th International Conference on Tribolog (Balkantrib 7 IOP Conf. Series: Materials Science and Engineering 95 (08 000 doi:0.088/757-899x/95//000 igure 4 shows the loads corresponding to the cranks, where G m g is the weight force of the cranks ( m is their mass; i m ac is the inertia force corresponding to the cranks and a C is the acceleration of their mass centres; GCG mcg g and icg mcg aa' are the weight force and the inertia force, respectivel, corresponding to the counterweights; a A' is the acceleration of point A where the total mass of the counterweights is considered to be concentrated. Also, figure 4 shows the proections on and aes of the connection forces from the two oints connecting the two cranks and the output shaft of the reducer ( 0 and 0, the connection forces from the two crank pin bearings ( and and the motor moment M m at the cranks shaft. igure 4. The load scheme of the cranks. The proections on and aes of the connection force 0 ma be established from the following dnamic equilibrium equations in forces: 0 0 0 il i icg ( 0 0 il i icg GL G GCG 0 ( Net, the motor moment at the cranks shaft can be established from an equation in moments calculated relative to the point O: M O 0 M m OA OA GL il OC G OA' G 0. Simulation results The cinematic and dnamic analsis of the conventional pumping units mechanism has been transposed into a computer program using Maple programming environment. urther, are presented some simulation results in the case of a C-0-56-00 pumping unit. The dimensions of the component elements of a C-0-56-00 pumping unit (figure produced b Lufkin [6] are: OA = 4 in. (.0668 m; AB = in. (.58 m; BC =.07 in. (.8 m; C = 9 in. (.766 m. The coordinates of the point C are [6]: C in. (.894 m and C 6 in. (.4544 m. The total length of the cranks is: OA = 95 in. (.4 m. The functioning angular speed of the cranks epressed in rotations per minute is equal to 5 rot/min. The simulations have been accomplished b considering the following values of the other parameters involved in the calculation of the connection forces and of the motor moment: OA = 65 in. (.65 m; C = 0 in. (.794 m; m L = 55 kg; m L = 5 kg; m tr = 400 kg; m CB = 44 kg; q = 566 kg/m; q = 5.7 kg/m; q = 7.5 kg/m (q, q and q are the linear masses of the cranks, connecting rods and of the rocker, respectivel. In figure 5 is presented the variation on a cinematic ccle of the force acting at the end of the polished rod. i CG icg (4 5
9th International Conference on Tribolog (Balkantrib 7 IOP Conf. Series: Materials Science and Engineering 95 (08 000 doi:0.088/757-899x/95//000 igure 5. The variation on a cinematic ccle of the force acting at the end of the polished rod. In figure 6 it is presented the variation on a cinematic ccle of the motor moment M m and in figures 7 0 are presented the variations on a cinematic ccle of the connection forces 0,, and 0, respectivel. The curves correspond to the case when the angular speed of the cranks is equal to 5 rot/min and the curves and correspond to the cases when the angular speed of the cranks is equal to 7 rot/min and 0 rot/min, respectivel. In these two last cases we have considered an increase of the force values compared to the initial situation when the cranks speed is 5 rot/min, with 8% and 9.5%, respectivel. igure 6. The variation on a cinematic ccle of the motor moment M m when the angular speed of the cranks is equal to 5 rot/min (curve, 7 rot/min (curve and 0 rot/min (curve. igure 7. The variation on a cinematic ccle of the connection force 0 when the angular speed of the cranks is equal to 5 rot/min (curve, 7 rot/min (curve and 0 rot/min (curve. 6
9th International Conference on Tribolog (Balkantrib 7 IOP Conf. Series: Materials Science and Engineering 95 (08 000 doi:0.088/757-899x/95//000 igure 8. The variation on a cinematic ccle of the connection force when the angular speed of the cranks is equal to 5 rot/min (curve, 7 rot/min (curve and 0 rot/min (curve. igure 9. The variation on a cinematic ccle of the connection force when the angular speed of the cranks is equal to 5 rot/min (curve, 7 rot/min (curve and 0 rot/min (curve. igure 0. The variation on a cinematic ccle of the connection force 0 when the angular speed of the cranks is equal to 5 rot/min (curve, 7 rot/min (curve and 0 rot/min (curve. igure 6 shows that the motor moment variation curve retains the same allure in all three analzed cases and its etreme values are relativel close. igures 7 0 show that the connecting forces in the bearings of the analzed pumping unit mechanism have etremel high values, in this regard 7
9th International Conference on Tribolog (Balkantrib 7 IOP Conf. Series: Materials Science and Engineering 95 (08 000 doi:0.088/757-899x/95//000 highlighting the 0 connecting force in the central bearing. On the other hand it can be noticed that with the increase of the values of the force there is an important increase of the maimum values of all the connecting forces in the bearings of the pumping unit mechanism. 4. Conclusions In this paper it was analzed the dnamics of the mechanism of the conventional sucker rod pumping units. The dnamic stud was first performed within the component dad composed of the connecting rods and the rocker and then it was continued on its leader cranks. A computer program using Maple programming environment has been developed and so it was possible to establish the variation of the values of the connecting forces in the mechanism bearings and of the motor moment on the cinematic ccle, simulation results being presented in the case of a C-0-56-00 pumping unit. So, it have been highlighted the etremel high values of these connecting forces, in particular the values of the connection force acting in the centre bearing. Also it have been highlighted the increases in the maimum values of these connection forces with the increase of the values of the force at the polished rod. References. Popovici A., Equipment for the eploitation of oil wells (in Roumanian, Technical Publishing House; Bucuresti, 989.. Bădoiu., The namic Analsis of Mechanisms and Machines (in Romanian, idactical and Pedagogical Publishing House, Bucuresti, 00.. Bădoiu., Petrescu M.G., Toma G., On the analsis and snthesis of the quadrilateral mechanism, Journal of the Balkan Tribological Association, vol. 0, 6-68, 04. 4. Bădoiu., Toma G., On a dnamic optimization problem of the quadrilateral mechanism, Journal of the Balkan Tribological Association, vol., 50-60, 06. 5. Monagan M.B., Geddes K.O., Heal K.M., Labahn G., Vorkoetter S.M., McCarron J. and emarco P., Maple Introductor Programming Guide, Maplesoft, a division of Waterloo Maple Inc., 005. 6. 008/009 General Catalog Lufkin Oilfield Products Group website, 07, Available: http://infohost.nmt.edu/~petro/facult/kell/lufkin.pdf 8