Design and Performance Analysis of a Coal Bed Gas Drainage Machine Based on Incomplete Non-Circular Gears

Transcription

1 energies Article Design and Performance Analysis a Coal Bed Gas Drainage Machine Based on Incomplete Non-Circular Gears Guiyun Xu, Dezheng Hua *, Weijun Dai and Xiaoguang Zhang School Mechanical and Electrical Engineering, China University Mining & Technology, Xuzhou 226, China; xgyzxgl@63.com (G.X.); @63.com (W.D.); doctorzxg@63.com (X.Z.) * Correspondence: cumthdz@63.com; Tel.: Received: 6 October 207; Accepted: 7 November 207; Published: 23 November 207 Abstract: In order to solve problem reciprocating motion in no beam supported mining machines, putting energy saving as a starting point in Coal Bed Methane (CBM) exploitation, this paper designs a completely automatic reversing vertical drainage machine based on ory transmission. In field CBM exploitation, use s is an attempt at an innovation. First all, according to working conditions pump and use requirements, a scheme is established whereby one-way rotary motion motor is changed into reciprocating motion so that it could drive oil pumping rod to achieve upper and lower mining. Secondly, this paper has designed a new type reversing box as core component to replace traditional four beam linkage mechanism and also provides elaborate calculations. Finally, movement simulation reversing system is completed. Comparing motion simulation results with oretical ones, correctness our oretical analysis can be verified. Compared with traditional devices, new coal seam gas drainage machine model design has nearly % higher efficiency, which has obvious energy saving effects and reduces cost mining coal seam gas. Keywords: coal bed gas; non-beam supported mining machine; energy efficient; incomplete ; automatic reversing. Introduction Chinese coal bed methane resources are relatively rich and concentrated which makes ir exploitation a relatively new clean coal industry in world []. The exploitation technology coal bed methane is largely based on oil field experience, so traditional beam pumping unit is still used in most equipment, as shown in. Feng [2] analyzed main defects beam pumping unit according to its working conditions. The main one is that beam pumping units use crank rocker mechanisms, which leads to ir poor adaptability. When encountering some special coal seam gas, overall size pumping unit needs to be adjusted to change stroke, which seriously affects efficiency CBM exploitation. The low efficiency beam pumping unit is anor reason and energy waste pumping unit is very serious. Li and Fan [3], and Fu [4] have made some adjustments and improvements on basis conventional beam drainage machine appeared specific. However, Liu [5] and Fan [6] argue that this cannot solve fundamental drawbacks crank rocker mechanism improving performance in a relatively small range and poor adaptability and low working efficiency shortcomings beam pumping will still exist. Based on this series drawbacks, all kinds new non-walking beam drainage machine have emerged. At present, Li [7], Liu [8] and Qi [9] have all done a lot research on se machines which can be roughly divided into two types according to switching mode, namely mechanical Energies 207, 0, 933; doi:0.3390/en

2 Energies 207, 0, Energies 207, 0, Energies 207, 0, reversing and motor and reversing. motor reversing. Niu [0] Niu and [0] Shao and [] Shao have [] studied have studied typical typical chain drainage chain drainage machine machine as an and as anmotor example reversing. a non-beam Niu [0] mechanical and Shao [] reversing have studied device, as typical shown chain drainage 2. Themachine utility model as an example non-beam mechanical reversing device, as shown in 2. The utility model has example has advantages a non-beam good mechanical balancereversing performance, device, convenient as shown adjustment in 2. The advantages good balance performance, convenient adjustment balance, balance, utility small side small model force side has when force when advantages reversing reversing good and working and working balance performance, and light and light weight. weight. convenient The disadvantage The disadvantage adjustment that isbalance, that it has it has small more more side moving moving force when parts, parts, an reversing an unsealed unsealed and gas gasworking balance balance and system system light and andweight. it can it can lose lose The load load disadvantage protection protectionis leading leading that it to tohas higher a higher more failure failure moving rate. rate. parts, an unsealed gas balance system and it can lose load protection leading to a higher failure rate.. Conventional beam-pumping unit.. Conventional beam-pumping unit. 2. Chain-type pumping unit. 2. Chain-type pumping unit. Correspondingly, compound permanent magnet motor and linear motor reciprocating Correspondingly, compound permanent magnet motor and linear motor reciprocating machines, Correspondingly, shown s compound and 4, are permanent all drainage magnet machines motor and motor linear reversing motor type. reciprocating Compared machines, shown in s and 4, are all drainage machines motor reversing type. Compared machines, with conventional shown in s form, 3by and omitting 4, are all drainage reducer and machines complex motor reversing reversing system type. compound Compared with conventional form, by omitting reducer and complex reversing system compound with permanent conventional magnet motor form, drainage by omitting machine reducer has simpler and structure complex reversing and smaller system footprint. compound With permanent magnet motor drainage machine has simpler structure and smaller footprint. With permanent combination magnet frequency motor drainage conversion machine control has technology a simplerand structure compound and smaller permanent footprint. magnet With motor, combination frequency conversion control technology and compound permanent magnet motor, combination end balance frequency weight method conversion is adopted, control which technology makes andpumping compound unit permanent have good magnet energy saving motor, end balance weight method is adopted, which makes pumping unit have good energy saving effect. endby balance using weight control method knob control is adopted, starting which makes and stopping pumping state and unit have running good energy speed saving effect. By using control knob control starting and stopping state and running speed effect. motor, By we using can adjust control knob stroke control and frequency. starting Cui and [2] stopping and Zhang state [3] and have stated running that this speed type has motor, we can adjust stroke and frequency. Cui [2] and Zhang [3] have stated that this type has motor, relatively wehigh can adjust cost, poor strokeresistance and frequency. to earthquakes Cui [2] and performance Zhang [3] and have stated torque that is this constrainted type has relatively high cost, poor resistance to earthquakes performance and torque is constrainted relatively by strength high cost, permanent poor resistance magnet, toetc. earthquakes Zhao [4] performance and Ma [5] also andthink torque that is constrainted linear motor by strength permanent magnet, etc. Zhao [4] and Ma [5] also think that linear motor by reciprocating strengthdrainage permanent machine has magnet, problem etc. Zhao high [4] and cost Ma and [5] difficult also think maintenance. that linear motor reciprocating drainage machine has problem high cost and difficult maintenance. reciprocating drainage machine has problem high cost and difficult maintenance.

3 Energies 207, 0, Energies 207, 0, Energies 207, 0, Compound permanent magnet synchronous motor pumping unit. 3. Compound permanent magnet synchronous motor pumping unit. 4. Linear motor reciprocating pumping unit. 4. Linear motor reciprocating pumping unit. In order to obtain variable transmission ratio movement, concept arose In order to obtain variable transmission ratio movement, concept arose at historic In ordermoment. to obtain Dunkerley variablehas transmission provided ratio basic movement, exposition design and application concept arose at historic moment. Dunkerley has provided basic exposition design and application at elliptical a historic s moment. in his book Dunkerley [6]. In has provided 940s, group a basic exposition scholars in Japan design represented and application by Yamazaki elliptical s in his book [6]. In 940s, a group scholars in Japan represented by Yamazaki elliptical and Ota set s f in his new book upsurge [6]. In in 940s, study a group scholars s in [7], Japanwhich represented has formed by Yamazaki relatively and and Ota set f a new upsurge in study s [7], which has formed a relatively Ota perfect set f oretical a new upsurge system inabout study non-circlar s. Marius s [7], [8] which and Bair has[9] formed and aors relatively have perfect used perfect oretical system about non-circlar s. Marius [8] and Bair [9] and ors have used oretical computer stware system about simulation non-circlar and numerical s. Marius control [8] machine and Bair tool [9] technology and orsto have process usedany-curve computer computer stware simulation and numerical control machine tool technology to process any-curve stware simulation s. When and numerical Bijlsma [20] control studied machine gravity tool technology balance to device process putting any-curve forward s. When Bijlsma [20] studied gravity balance device putting forward s. train design Whenand Bijlsma parameter [20] studied calculation gravity method balance device putting s, forward se were used train to change design and train design and parameter calculation method s, se were used to change parameter reciprocating calculation motion method into continuous pendulum s, se motion. were Hebbale used to[2] change used reciprocating motion set reciprocating motion into a continuous pendulum motion. Hebbale [2] used a set into realize a continuous stepless pendulum speed regulation, motion. Hebbale thus improving [2] used a efficiency automobile set realize fuel stepless pumps. speed Doric to realize stepless speed regulation, thus improving efficiency automobile fuel pumps. Doric regulation, [22] introduced thus improving efficiency s in automobile variable fuel movement pumps. Doric internal [22] introduced combustion engines, [22] introduced s in variable movement internal combustion engines, s providing in variablecompression movement ratio, internal variable combustion displacement engines, and providing combustion variable at compression constant volume, ratio, providing variable compression ratio, variable displacement and combustion at constant volume, variable greatly improving displacement and advantages combustion piston at constant mechanisms. volume, Okada greatly[23] improving in study advantages jumping robots, piston in greatly improving advantages piston mechanisms. Okada [23] in a study jumping robots, in mechanisms. order to change Okada speed [23] in ratio, a study designed jumping robots, s in order to change to change ratio, speedresulting ratio, designed in high order to change speed ratio, designed s to change ratio, resulting in high torque and high speed characteristics. Putting energy saving as starting point in CBM exploitation, torque and high speed characteristics. Putting energy saving as a starting point in CBM exploitation, to solve problem reciprocating motion for no-beam machines, according to an incomplete nonto solve problem reciprocating motion for no-beam machines, according to an incomplete non-

4 Energies 207, 0, s to change ratio, resulting in high torque and high speed characteristics. Putting Energies 207, energy 0, 933 saving as a starting point in CBM exploitation, to solve problem reciprocating 4 9 motion for no-beam machines, according to an incomplete as core mechanism circular non-switching as core type mechanism reversing device non-switching proposed by type Marius reversing [8], this device paper proposed designs by a kind Marius incomplete [8], this paper designs a kind automatic incomplete reversing vertical drainage automatic machine. reversing Owing vertical to drainage higher work machine. efficiency Owing to higher mechanism work efficiency than crank rocker, mechanism stable work, than robustness crank to rocker, damage stable and low work, cost, robustness utility to model damage has and practical low cost, design utility value. model has practical design value. The The rest rest paper paper is organized is organized as follows: as follows: in in 2, new 2, structural new structural design and design working and working principle principle automatic automatic reversing reversing machine machine for for s s are are summarized. summarized. Through Through consulting consulting and and using using relevant relevant data, data, 3 introduces introduces design design pair. pair. 4 gives gives a brief brief analysis analysis performance performance row row mining mining machine. machine. The The kinematic kinematic simulation simulation analysis analysis incomplete incomplete train based train on based Automatic on Automatic Dynamic Analysis Dynamic Analysis Mechanical Systems Mechanical (ADAMS) Systems is (ADAMS) demonstrated is demonstrated in in provides 6 provides an actual an application actual application our product. our product. Our conclusions Our conclusions are summarized are summarized in in Structure Design and Working Principle Drainage Machines 2.. Overall Structure Design Drainage Machines As shown in 5, working mechanism drainage machine is as follows. The motor is connected with cycloid pinwheel reducer reducer by a belt by a drive belt linked drive to linked to reversing box reversing box core through core athrough coupling. a coupling. The two speed The two transmission speed transmission for extracting for extracting machine s machine s stroke is connected stroke is connected between between periodic rotation periodic output rotation shaft output andshaft cylinder, and cylinder, which is fixed which with is fixed twowith winding two belts, winding hanging belts, on hanging vertical on frame vertical roundframe crownround sheave, crown withsheave, a belt connected with a belt withconnected counterweight with box counterweight and a belt-connected box and a sucker belt-connected rod. After sucker motor rod. is After started and motor is power started is transmitted and power to is transmitted to reversing box, reversing output shaft box, drives output cylinder shaft drives to complete cylinder a cycle to complete positive a and cycle reverse positive rotation and through reverse which rotation each through inputwhich shaft rotates each input for one shaft circle, rotates andfor one drainage circle, machine and realizes drainage amachine stroke. When realizes a cylinder stroke. When is used for cylinder winding is used belt for winding sucker belt rod, belt sucker which rod, is connected belt which withis connected counterweight with is released, counterweight sucker is released, rod runs upwards, sucker rod andruns drainage upwards, machine and is drainage upper machine stroke. is in When upper cylinder stroke. releases When cylinder belt connecting releases sucker belt connecting rod, oil pumping sucker rod, runs downward, oil pumping androd runs drainage downward, machineand is in drainage lower stroke. machine By changing is lower size stroke. motor end By changing small pulley size and motor input end speed small pulley and input speed reversing box, a regulation reversing is made changing box, a regulation cycleis time made output. changing By adjusting cycle time two output. speedby transmission adjusting between two speed cylinder transmission and between cylinder box, and number turns box, cylinder number is changed turns as well cylinder as stroke is changed discharge as well as machine. stroke discharge machine. 5. General structure an automatic reversing vertical drainage machine for s. permanent magnet synchronous motor, 2 small belt pulley, 3 big belt pulley, 4 cycloid pinwheel reducer, 5 reversing reversing box, 6 counterweight, box, 7 cylinder, 7 cylinder, 8 stroke 8 stroke reducer, 9 pumping reducer, 9 pumping rod, 0 transmission rod, 0 transmission belt, vertical belt, vertical frame, 2 crown frame, 2 crown sheave. sheave.

5 Energies 207, 0, Energies 207, 0, Transmission Scheme and Working Principle Incomplete Non-Circle Gear Gear Reversing Box Box Under premise constant rotation direction design reversing box aims to realize up and down movement sucker rod through outputting an automatic reversing circular motion and n driving cylinder. The Themovement suspension point point in ina acirculation circulationcycle cycleis isgenerally as asfollows: starting downward from upper limit, suspension point accelerates to to a certain extent, and n maintains a rapid uniform motion. When near limit position suspension point begins to to decrease. When box changes output rotation direction, starting to accelerate rapidly from lower limit position, point reaches and maintains a certain position and begins to slow down close to limit position, so drainage is is completed by cycle. 6 is is a structural sketch reversing box, and its its specific working process is is as as follows: power is transmitted to input shaft by cycloidal reducer, where input shaft is is designed to to rotate clockwise, and 5 is is rotated clockwise. At this time, 5 is is engaged with part 6, 6, and is is disengaged from The power is transmitted from 6 to 4 by cylindrical spur 7 and 8, 8, outputting from cylindrical spur 8 through cylindrical straight 9 counterclockwise to output shaft The input shaft and 5 clockwise rotate rotate degrees, degrees, causing causing 6 and 6 and cylinder cylinder 7 counterclockwise 7 counterclockwise one time, one time, 4 and4 spur and spur 8 clockwise 8 clockwise one time one and time and output output shaft 0 shaft and0 spur and spur 9 counterclockwise 9 counterclockwise one time. one time Sketch a reversing box. box. input shaft, 2, 3 transmission shaft, 4, 4, 6 driven, 5 driving, 7, 8, 9 spur, 0 output shaft, box. As shows, when input shaft rotates 80 degrees and continues, As 7 shows, when input shaft rotates 80 degrees and continues, engages with part and is disengaged from part 5 engages with part 4 and is disengaged from part 6. The power is transmitted from to by coaxial spur and spur 6. The power is transmitted from 4 to 6 by coaxial spur 8 and spur 7, outputting from cylindrical spur 8 through cylindrical straight 9 clockwise 7, outputting from cylindrical spur 8 through cylindrical straight 9 clockwise to to output shaft 0. The input shaft and 5 rotate clockwise from 80 degrees to output shaft 0. The input shaft and 5 rotate clockwise from 80 degrees to 360, 360, causing 6 and cylinder 7 to rotate clockwise one time, 4 and spur causing 6 and cylinder 7 to rotate clockwise one time, 4 and spur 8 8 counterclockwise one time and output shaft 0 and spur 9 clockwise one time. In this counterclockwise one time and output shaft 0 and spur 9 clockwise one time. In this process, process, in addition to input shaft and 5, motion direction, time and in addition to input shaft and 5, motion direction, time and angle angle or components are just opposite first 80 degrees. or components are just opposite first 80 degrees. In cycle input shaft to rotate 360 degrees input shaft and In a cycle input shaft to rotate 360 degrees input shaft and a 5 clockwise rotate at fixed speed. The output shaft 0 and in first half cycle are in nonclockwise rotate at a fixed speed. The output shaft 0 and 9 in first half cycle are in a nonuniform motion counterclockwise rotation and second half by clockwise. The output movement uniform motion counterclockwise rotation and second half by clockwise. The output movement embodied on cylinder drainage machine is basically that in stroke cylinder rotates embodied on cylinder drainage machine is basically that in a stroke cylinder rotates counterclockwise first and n clockwise. counterclockwise first and n clockwise.

6 Energies 207, 0, Energies 207, 0, Engagement condition s when input shaft rotates 80 degrees. input shaft, 2, 2, 3 transmission shaft, shaft, 4, 4, 6-driven 6-driven,, 5 driving 5 driving,, 7, 8, 9 spur 7, 8, 9 spur,, 0 output 0 output shaft. shaft The Design Non-Circular Gear Pair Pair 3.. Transmission Principle Non-Circular Gear Pair 8 is a diagram pitch curve a pair with variable transmission ratio and outer engagement, taking as driving wheel and 2 as driven wheel. We set center distance two s to a, a, setting angle as ϕφ and instantaneous angular velocity as ω, setting 2 angle as ϕφ2 2 and corresponding to instantaneous angular velocity ωω2. 2. At initial moment, φ ϕ = = 0, 0, φ2 ϕ= 2 0, = 0, angular velocity ω ωis is described by by ω ω= dφ/dt = dϕ and /dt and angular angular velocity velocity ω2 = dφ2/dt. ω 2 = dϕ When 2 /dt. When is engaged is engaged with with 2, re is 2, a re certain is arotation certain function rotation function relation: relation: ϕ 2 = 2 FF(ϕ ( ) ) () () In variable transmission ratio and external meshing drive, transmission In variable transmission ratio and external meshing drive, transmission ratio function i ratio function 2 is described by: i 2 is described by: i 2 = ω = dϕ d/dt / dt d i ω 2 dϕ 2 /dt = dϕ = f (ϕ dϕ 2 f( ) ) (2) (2) 2 2 d2 / dt d2 f (ϕ ) = f ( ) F (3) (ϕ ) (3) In range ϕ F ( ), this is a finite and positive smooth function. According to Equations () (3), angle In function range ϕφ, 2 this is a 2 finite can beand obtained positive by: smooth function. According to Equations () (3), angle function φ2 2 can be obtained ϕ by: ϕ ϕ 2 = F(ϕ ) = dϕ F 0 i = 2 ( ) d 2 0 f (ϕ 0 0 i 2 f( ) d ) dϕ (4) (4) From 8, when two s transmit at any moment, re is a point P relative velocity From equal to zero, 8, when which two is a node s transmission transmit at and any also moment, instantaneous re is velocity a point P center. relative velocity When equal to point zero, Pwhich is at is line a node centers, transmission relative speed and also two instantaneous s is zero, velocity ω r center. ω 2 r 2 = ω When O P = ω 2 point O 2 P is = at 0, andline instantaneous centers, relative transmission speed ratio two is s available is zero, from: = = =0, and instantaneous transmission ratio is available from: i 2 = ω = r 2 = a r (5) ω 2 a r i2 2 r r (5) 2 r r When two center distance a is constant, transmission ratio is variable making corresponding When rtwo, r 2 to becenter variable, distance that a is instantaneous constant, center transmission P position ratio is is not variable fixed. At making this time, corresponding trajectory r, instantaneous r2 to be variable, center that P is a instantaneous curve, center which P position is instantaneous is not fixed. At line this time, two s, trajectory called instantaneous pitch center curve. P is a curve, which is instantaneous line two s, called pitch curve.

7 Energies 207, 0, Energies 207, 0, O 2 2 r 2 2 r O 8. The pitch curves a pair s. In combination with above analysis, equations pitch curves pairs are summarized in form polar coordinates. According to Equation (5), polar equation pitch curve can be obtained by: a r (ϕ r( ) = ) a a = (6) (6) + i 2 + f( f (ϕ ) ) According to Equations (2) and (5), curve equation 2 can be obtained by: { ai2 r2 = a r ((ϕ )) = 2 +i i 2 2 ϕ 2 = ϕ 0 i dϕ 2 = ϕ (7) 0 f (ϕ ) dϕ (7) 2 d d 0 i 0 2 f ( ) With respect to and 2 described above, measuring direction ϕ and ϕ 2 is opposite With torespect corresponding to rotation and angle 2 described ω and ωabove, 2. Therefore, measuring when direction center distance φ and a pair φ2 is opposite to corresponding pairs is determined, rotation angle pitch ω and curve ω2. Therefore, driving when wheel center can bedistance obtained bya only pair knowing transmission pairs is ratio determined, function, and pitch n curve pitch curve driving wheel driven wheel can be is by only Equation knowing (7) [24,25]. transmission ratio function, and n pitch curve driven wheel is obtained by Equation (7) [24,25] Design Non-Circular Gear Pair 3.2. Design The purpose Non-Circular designing Gear a Pair drive is that suspension around at dead center has slower movement speed and stable commutation, running rapidly in middle section The purpose designing a drive is that suspension around at dead stroke to improve working efficiency. Because changing speed stroke, each section center has slower movement speed and stable commutation, running rapidly in middle section pair can be allocated as follows. For driving non circular 5, as shown stroke to improve working efficiency. Because changing speed stroke, each section in 9, taking center O pair can as origin polar coordinates curvature radius pitch be allocated as follows. For driving non circular 5, as shown in curve varies counterclockwise increasing gradually in 60 degrees before transmission, 9, taking center O as origin polar coordinates curvature radius pitch curve unchanged in 2 60~20 degrees, decreased in 20~80 degrees, and it is varies counterclockwise increasing gradually in 60 degrees before transmission, unnecessary to calculate it in 3 80~360 degrees. unchanged in 2 60~20 degrees, decreased in 20~80 degrees, and it is unnecessary to calculate it in 3 80~360 degrees.

8 Energies 207, 0, 933 Energies 207, 0, Energies 207, 0, Energies 207, 0, Distribution pitch curve driving 5. Distribution curve driving driving 9. Distribution pitch pitch curve Distribution pitch curve driving 5. Due to toconstant distance centers 4,4,like like it varies Due constant distance centers pitch pitch curve curve 6 it6varies withwith Due Due to constant distance centers pitch curve 4, like6 6 itwith varies with to constant distance centers pitch curve 4, like it varies distribution driving s. From 0, taking center O 2 as origin distribution driving s. From 0, taking center O2 as origin polarpolar distribution driving s. From 0, taking center O as origin polar distribution s. From 0, taking center O 2 as 2 polar coordinates, driving radius curvature varies counterclockwise increased inin 4, in does not needneed coordinates, radius curvature varies counterclockwise increased 4,origin in does not coordinates, radius curvature varies counterclockwise increased in 4, in does not need to coordinates, radius curvature varies counterclockwise increased in 4, in does not to be calculated in no-tooth no-tooth area decreasedagain again in in in 6.need to be calculated in area 5, 5, decreased 4,4,and andunchanged unchanged in 6. be calculated in in no-tooth area area 5, decreased again in in in 6.6. to be calculated no-tooth 5, decreased again 4,4,and andunchanged unchanged in 0. Distribution pitch curve driven s 4, 6. Distribution pitch pitch curve s 4, 6.4, Distribution curvedriven driven s, 0.according Distribution distribution pitch curve above driven s 4, 6.curve and motion As shown in to pitch shown according distribution be above pitch curve andchanging motion state As inpair,, regulation to transmission ratiocan formulated as angle As shown in, according totransmission distribution above as pitch curvechanging and motion state in pair,, regulation ratio can formulated curve angle shown driving 5 [26]. to As according distribution beabove pitch and motion state pair, regulation transmission ratio can be formulated as angle changing driving 5 [26]. state pair, regulation transmission ratio can be formulated as angle changing i 2 driving 5 [26]. driving i 5 [26]. 2 i 2 i 2 i 2 Tm i 2 Tm 2Tm Tm 2Tm 2Tm T3 3T m T 3 T m T3 T23T m T 3 3 T m 4T 3 2T m T3 4T m T3 T3 3T m T 3 2T m T3 4T m T3 i 2 i 2 i 2. Curve drive ratio function.. Curve drive ratio function...curve Curve drive driveratio ratiunction. function.

9 Energies 207, 0, Energies 207, 0, In, A is maximum ratio, and B is minimum. In angle allocation driving, Tm = π/6, T3 = 2Tm, K = (A B)/2Tm and J = (A B)/Tm 2. By In using, Aintegral is maximum relation, function ratio, relation andb i2 is with minimum. angle In angle allocation driving, T m = π/6, T 3 = 2T m, K = (A B)/2T m and J = (A B)/T 2 φ change driving can be deduced as: m. By using integral relation, function relation i 2 with angle ϕ change driving can be deduced as: k 0 Tm J ( 2 Tm ) Tm 2Tm i k 0 ϕ T m 2 0 2Tm 2Tm T3 (8) J(ϕ 2T m ) T m ϕ 2T m i J[ (2 Tm T3 )] 2Tm T3 3T m T3 2 = 0 2T m ϕ 2T m + 3 (8) J[ϕ k 3T m T3 4Tm T3 (2T m + T 3 )] 2T m + ϕ 3T m + T 3 With rotation angle k change driving 3T m function + T 3 can ϕ be 4T obtained m + T 3 by integrating as: With rotation k angle A change driving function can0be obtained Tm by integrating as: 2 2 ( B JTm 2 JTm J ) A B Tm 2Tm kϕ + A 2 0 ϕ T m (Bi JT 2 m + 2JT m ϕ 2 Jϕ 2 2 B ) + A + B 2 T m ϕ 2 T2T m m T3 (9) i 2 = B 2T m ϕ 2T m + T 3 (9) [B JT m JT (4T m + T 3 ϕ ) 2 J(4T m + T 3 ϕ ) 2 2 [ B JTm 2 JTm (4 Tm T3 ) J (4 Tm T3 ) ] A B 2Tm T3 3Tm T3 2 ] + A + B 2T + T 3 ϕ 3T m + T 3 k(ϕ 4T m k ( T 3 ) + A 3T m + T 3 ϕ 4T m + T 4 Tm T3 ) A 3Tm T3 4Tm T3 3 Combined with actual conditions reversing box, we should try to get angle φ2 ϕ 2 driven 4, 6 tood part large in order to increase s meshing area and andreduce error, error, generally taking taking φ2 as ϕ as degrees degrees (300 degrees (300 degrees in this article). in this article). The design Theparameters design parameters are as follows: are as center follows: distance center distance pair a = 360 pair mm, a = maximum 360 mm, maximum transmission transmission ratio i2max ratio= i 2max 2.8, = minimum 2.8, minimum transmission transmission ratio i2min ratio = i 2min /3, angle = /3, angle driven driven 4, 6 = 300 4, 6 = degrees, 300 degrees, so so pitch pitch curve curve driving driving non- 5 ( 5 ( 2a) 2a) and and curve curve section section s s 4, 64, ( 6 2b) 2b) are are calculated by by a MATLAB a program [27,28] (a) (b) The pitch curve s. s. (a) (a) The The pitch pitch curve curve 5; 5; (b) (b) pitch curve s 4 and Establishment Non-Circular Gear Pitch Curve 3.3. Establishment Non-Circular Gear Pitch Curve In order to machine s, it is necessary to fit incomplete pitch curves to complete In order to machine s, it is necessary to fit incomplete pitch curves to a complete closed curve. Using imported pitch curve obtained by closed curve. Using imported pitch curve obtained by programming programming calculations in MATLAB (R20b, MathWorks, Natick, MA, USA), Computer Aided X calculations in MATLAB (R20b, MathWorks, Natick, MA, USA), Computer Aided X Alliance (CAXA) Alliance (CAXA) put two rotation centers as center a circle, taking put two rotation centers as center a circle, taking a circle 90 mm a circle 90 mm radius to fit driving toothless and a circle 270 mm radius radius to fit driving toothless and a circle 270 mm radius for driven one. for driven one. For transition region an active, we take tangent circle 90 mm For transition region an active, we take tangent circle 90 radius at end point effective section curve. For transition region driven mm radius at end point effective section curve. For transition region driven non-

10 Energies 207, 0, Energies 207, 0, circular, middle section intersection tangent line at end point effective, curve circular and, middle circle for section middle 270 mm section radius intersection are intersection taken. The tangent final fit tangent figure line atis line shown end at point end point 3. effective effective curve and curve circle and for circle 270for mm270 radius mm radius are taken. are taken. The final The fitfinal figure fit is figure shown is shown in in Fitting curve s. (a) Fitting curve driving ; (b) fitting 3. Fitting curve s. (a) Fitting curve driving ; (b) fitting curve driven. curve driven. In design this paper, modulus m is 2, tooth width b is 250 mm, In In design this paper, modulus m is 2, largest outer diameter R is 270 mm, addendum coefficient tooth is, and width b isclearance 250 mm, coefficient largest largest outer c* outer is diameter diameter In this R is paper, R 270 is mm, 270 mm, addendum prile addendum coefficient coefficient h is, and clearance a is, and is designed clearance by means coefficient a c* generating coefficient is Inc* this paper, (pinion In this cutter), paper, prile which is a method prile meshing is designed between by means is involute designed acylindrical generating by means spur a (pinion s generating and cutter), which (pinion iss. a cutter), method Finally, which meshing we is use a method between CAXA to involute create meshing cylindrical between spur involute sprile, and cylindrical as shown spur s. in and Finally, 4. we use CAXA s. tofinally, create we use CAXA to create prile, as shown in prile, 4. as shown in 4. (a) (b) (a) (b) 4. Non-circular prile created created by by CAXA. CAXA. (a) Driving (a) Driving ; ; (b) driven (b) driven non- 4. Non-circular prile created by CAXA. (a) Driving ; (b) driven non-.. circular Design Non-Circular Gear Reversing Box 3.4. Design Non-Circular Gear Reversing Box With every turn input shaft reversing box, drainage machine With every turn input shaft reversing box, drainage machine completes a row extraction action, and that means it s done a run. Regardless magnitude completes a row extraction action, and that means it s done a run. Regardless magnitude reverse stroke, reversing box box always has has this this characteristic. The The stroke stroke size size reverse stroke, reversing box always has this characteristic. The stroke size drainage drainage machine directly directly reflects reflects rotation number roller, and it it is is related to effective drainage machine directly reflects rotation number roller, and it is related to effective working radius roller. The number turns roller is determined by working radius and roller. second The number turns between roller is determined roller and by reversing box and second transmission between roller and reversing reversing reversing box. box In and order to second simplify transmission structure between second roller transmission and and reduce box. In order to simplify structure second transmission and reduce energy losses energy reversing losses box. during In order transmission, to simplify output structure shaft second transmission reversing and box reduce can be energy losses during transmission, output shaft reversing box can be

11 Energies 207, 0, during transmission, output shaft reversing box can be directly connected with roller by using one s in transmission, and transmission ratio between reversing box output shaft and roller is one. In case where reversing box output shaft is directly connected to roller, this paper designs structure reversing box. In processing deduction, unit angular velocity is defined as revolutions per second. When stroke value drainage machine polished rod is maximum, it satisfies S max = 2.5 m, and roller diameter satisfies d = 300 mm. In a stroke, speed output shaft 0 is same as that cylindrical spur s 9 which is on output shaft 0 (see 6): n output = n 9 = n roller = S max πd stroke 60 = S max stroke 9π (0) The speed cylindrical 8 in engagement with standard cylindrical spur 9 is same as that driven s 4 and 6. In a stroke, driven s 4 and 6 rotate 300 degrees, average speed n 8 standard cylindrical spur 8 is: n 8 = n 4 = stroke 60 = stroke 36 () When stroke value is maximum, it satisfies S max = 2.5 m, actual transmission ratio i 89 between standard cylindrical spur s 8 and 9 will satisfy: i 89 = n 8 n 9 = 0.3 (2) When number teeth pinion 9 satisfies Z 9 = 8, and large s 8 and 7 satisfy Z 8 = Z 8 = 60, actual transmission ratio will satisfy: i 89 = n 8 n 9 = 0.3 (3) When modulus satisfies m = 2, We can get S max = 2.6 m, diameter large cylindrical spur s 8 and 7 are 720 mm, and diameter small cylindrical spur 9 is 26 mm. 4. Efficiency Analysis New Drainage Machine and Old The automatic reversing vertical drainage machine designed in this paper abandons four-bar linkage beam pumping units, so re will be some improvement in work efficiency, and we will discuss problem efficiency. Generally, we regard polished rod eye drainage machine as dividing line, efficiency above it is called ground efficiency, and efficiency under it is called downhole efficiency. This paper studies use automatic reversing vertical drainage machine instead beam pumping unit, so only ground efficiency is simply analyzed. Because continuous change polished rod load when drainage machine is working, its instantaneous input and output power also changes in real time, so average working efficiency each cycle is analyzed in order to facilitate calculations.

12 Energies 207, 0, () The ground efficiency beam pumping unit The ground efficiency traditional three pumping equipment is mainly affected by efficiency transmission parts, like motor, belt drive, reducer and four-link linkage, so ground efficiency formula is calculated as: η ground = η η 2 η 3 η 4 (4) In formula above, η motor working efficiency; η 2 belt pulley working efficiency; η 3 reducer transmission efficiency; η 4 four-bar linkage transmission efficiency. Motor working efficiency: efficiency motor nameplate is generally data at a load rate greater than 60%, and its maximum value is not more than 0.95, but when beam pumping unit is working, load is always changing and power factor motor is low, so efficiency η motor is only 0.8 at most. Belt pulley working efficiency: referring to mechanical design manual, belt transmission efficiency is 0.96, which is efficiency independent load. Considering actual working condition, belt pulley transmission efficiency drainage machine is between 0.85 and 0.90, and highest efficiency is Reducer transmission efficiency: refer to mechanical design manual, transmission efficiency is 0.98, with a total three pairs; bearing transmission efficiency 0.99, with a total three pairs; calculated η 3 is 0.9. Four-bar linkage transmission efficiency: energy four-bar linkage pumping unit is mainly lost at bearing and wire rope and burner, bearing transmission efficiency is 0.99, with a total three pairs. The transmission efficiency η 4 four-bar linkage is 0.95 when efficiency wire rope is Based on above analysis, ground efficiency beam pumping unit can reach maximum: η ground = η η 2 η 3 η 4 = = 0.62 (5) (2) Ground efficiency analysis automatic reversing vertical drainage machine The electric efficiency η : Non-circular automatic reversing vertical drainage machine designed in this paper cancels switching mode type four-bar linkage, it uses reversing box for reversing, and adopts a balance system similar to a seesaw. In course work, load on roller varies little and motor roller can still work when its load rate is greater than 60%, polished rod is in rapid motion in most strokes, and it can remain uniform, too. Therefore, this motor is relatively stable at work and has high efficiency, which can reach η = The transmission efficiency η 2 : The automatic reversing vertical drainage machine is mainly powered by s and pulleys, similarly, pulley efficiency η 2 is 0.9. The transmission efficiency η 3 : Referring to mechanical design manual, efficiency cycloid pin reducer is 0.96, and transmission efficiency transmission in two shift is 0.98, with a total two pairs. The transmission efficiency bearing is 0.99, with a total three pairs, and efficiency η 3 is The transmission efficiency η 4 : The four link mechanism was cancelled, two pulley groups were added, efficiency was 0.99, belt efficiency was 0.98, and total efficiency η 4 was Through above analysis we can see that ground efficiency automatic reversing vertical drainage machine is up to: η ground = η η 2 η 3 η 4 = = 0.73 (6)

13 Energies 207, 0, It can be seen that when calculating two kinds row production equipment with maximum target value, efficiency new type drainage machine is % higher than that conventional beam pumping unit and positive effect is obvious. Energies 207, 0, Kinematics Analysis Based on ADAMS 5. Kinematics Analysis Based on ADAMS 5.. Kinematics Simulation Analysis Gear System at Incomplete Non-Circular Gear Reversing Box 5.. Kinematics Simulation Analysis Gear System at Incomplete Non-Circular Gear Reversing Box The inside box is mainly composed a driving, two driven The inside s, two large cylindrical box is mainly straight composed s which a are driving coaxial with two driven, two driven s and a small s, cylindrical two large spur cylindrical. The straight mains parameters which are each coaxial with at two driven box are shown s and in Table a small : cylindrical spur. The main parameters each at box are shown in Table : Table. Main parameters each in box. Table. Main parameters each in box. Number Angle Breadth Gear Name Modulus Number Angle Breadth Number Gear Name Modulus Teeth Pressure Tooth (mm) Number Teeth Pressure Tooth (mm) driving driving driven driven Standard cylindrical spur (big) Standard cylindrical spur (big) Standard cylindrical spur (small) Standard cylindrical spur (small) Importing system at at reversing box into ADAMS, according to to kinematic relationship, this this paper paper adds adds necessary necessary kinematic kinematic pairs onpairs on system at incomplete system at incomplete reversing box. reversing In orderbox. to verify In order correctness to verify correctness design, contact design, force is defined contact in force is defined mesh, in and 0. r/s is mesh, usedand as 0. input r/s shaft is used speed. as After input parameters shaft speed. are After set up, parameters simulation are isset performed, up, simulation input is shaft performed, input shaft reversing box rotates a circle, reversing and box output rotates shaft a circle, rotates and in reverse output direction, shaft rotates thisin isreverse a movement direction, cycle, this is time a movement is 0 seconds. cycle, Therefore, time is in0 seconds. simulation Therefore, interface, simulation interface, time is set tosimulation 20 s, and time step is size set to is20 sets, toand 0.0, step video size screenshot is set to 0.0, is shown video in screenshot 5. is shown in Simulation video screenshot reversing box box system s system s movement. In post-processing, rotational speed output shaft is is obtained. We remove unsteady state reversing box when it it is is just started, take simulation curve output shaft speed reversing box when it it is is working smoothly at at 0 0 s~20 s (as shown in in 6).

14 Energies 207, 0, Energies 207, 0, Simulation curve output shaft speed reversing box. 6. Simulation curve output shaft speed reversing box. The simulation curve ten seconds shows output shaft speed reversing The simulation box drainage curve machine ten seconds in one shows stroke, It output can be seen shaft that speed driven reversing accelerates box very at rapidly drainage machine first sixth in one stroke, time, It maintains can be seen a that fast and driven constant motion in accelerates middle sixth very rapidly time, in and decelerates first sixth very time, rapidly maintains last a fast sixth and constant time. motion It can be in concluded middle sixth that in terms time, and movement decelerates characteristics, very rapidly in simulation last sixth results time. are completely It can be concluded in accordance that in with terms design movement requirements. characteristics, Although simulation output shaft results speed are changes completely are consistent in accordance with with motion design requirements requirements. Although polished rod, output some burrs shaft speed are changes are consistent with motion present in simulation curve. requirements polished rod, some burrs are present in simulation curve. Visibly, re is a certain deviation between prile designed by Visibly, re is a certain deviation between prile designed by means generating (pinion cutter) which is a method meshing between involute cylindrical means generating (pinion cutter) which is a method meshing between involute cylindrical spur s and s and ideal value, especially place where spur s and s and ideal value, especially place where pair is just beginning to engage. That means when largest teeth active pair is just beginning to engage. That means when largest teeth active are meshed with driven, burr simulation curve is more are meshed with driven, burr simulation curve is more prominent. prominent. Considering that ordinate itself is very small, burr jump is actually not large, after using ADAMS digital filter Butterworth to filter out high frequency signal dash jump, it is shown in Filtered simulation curve output shaft speed reversing box. As shown in 8, filtered curve is basically same as oretical value As shown in 8, filtered curve is basically same as oretical value output shaft speed reversing box. 8 is oretical calculation taking output shaft speed reversing box. 8 is a oretical calculation taking into account output shaft speed in one stroke. As reversing box has an into account output shaft speed in one stroke. As reversing box has an impact impact during commutation, re will be a relatively large jump in speed variation at fifteenth seconds. As low speed commutation, jump value is not large.

15 Energies 207, 0, Energies 207, 0, during.5 commutation, re will be a relatively large jump in speed variation at fifteenth seconds. As low Energies speed 207, 0, 933 commutation, jump value is not large. 5 9 Speed output shaft (r/s) Speed output shaft (r/s) Time (s) Time (s) 8. Theoretical calculation value output shaft speed reversing box Theoretical calculation value output shaft speed reversing reversing box. box Movement Analysis Drainage Machine Polished Rod Displacement 5.2. Movement 5.2. Movement Analysis Analysis Drainage Machine Polished Rod Rod Displacement The kinematic simulation results reversing box output shaft are compared with oretical calculation values, and correctness design is verified. The output shaft speed simulation curve is processed by scaling and integral commands curve editing in ADAMS postprocessor to validate wher stroke this whole drainage machine meets design requirements. Equaling to effective line speed roller outer diameter, polished rod speed drainage machine is: The kinematic simulation results reversing box output shaft are The kinematic simulation results reversing box output shaft are compared compared with oretical calculation values, and correctness design is verified. with oretical calculation values, and correctness design is verified. The output shaft The output shaft speed simulation curve is processed by scaling and integral commands curve speed editing simulation in ADAMS curve ispostprocessor processed by to validate scaling wher and integral stroke commands this whole drainage curve editing machine in ADAMS meets postprocessor design requirements. to validate wher Equaling to stroke effective thisline whole speed drainage roller machine outer diameter, meets design requirements. polished rod Equaling speed to drainage effective machine line speed is: roller outer diameter, polished rod speed drainage machine is: V πd n 03π. n polishedrod roller roller roller (7) V πd n 03π. n polishedrod roller roller roller (7) Consequently, simulation V polishedrod curve = πd roller output n roller shaft = speed 0.3π n roller reversing (7) box is enlarged by 0.3π times by scaling command, and effective output line speed roller, Consequently, namely polished simulation rod speed, curve is obtained. output Then shaft integral speed scaled curve is processed, reversing box and is enlarged curve by drainage 0.3π times machine by polished scalingrod command, displacement andover time effective will be output obtained, lineas speed shown roller, in namely 9. polished rod speed, is obtained. Then integral scaled curve is processed, and curve drainage machine polished rod displacement over time will be obtained, as shown in 9. Consequently, simulation curve output shaft speed reversing box is enlarged by 0.3π times by scaling command, and effective output line speed roller, namely polished rod speed, is obtained. Then integral scaled curve is processed, and curve drainage machine polished rod displacement over time will be obtained, as shown in Polished rod displacement curve that varied with time Polished rod rod displacement curve that varied with time.

16 Energies 207, 0, Energies 207, 0, Energies 207, 0, It can be seen that polished rod rodtakes takes0 0 sas as aperiodic motion, motion, and and maximum maximumstroke stroke is It can be seen that polished rod takes 0 s as a motion, and maximum stroke is about is about m, m, that that is to issay, to say, drainage drainage machine machine is is times 6 times /min, /min, and andstroke stroke is 2.6 is m, 2.6 which m, which fully about 2.6 m, that is to say, drainage machine is 6 times /min, and stroke is 2.6 m, which fully meets fully meets design design requirements. requirements. In addition, In addition, re is re quite is asmall quite sharp small sharp point at point crest at crest curve meets design requirements. In addition, re is a quite small sharp point at crest curve so curve that so that curve does curvenot does change not change smoothly. smoothly. The cause The cause this phenomenon this phenomenon is that is that polished polished rod so that curve does not change smoothly. The cause this phenomenon is that polished rod not rod is accelerating not accelerating from from rest when rest when it's moving it's moving up and up and down, down, but but it has it has asmall smallreverse velocity. not accelerating from rest when it's moving up and down, but it has a reverse velocity. Therefore, in in stroke curve, slope slope wave wave peak peak and and trough trough attachment is is not not 0, 0, and and re re Therefore, in stroke curve, slope wave peak and trough attachment is not 0, and re is is a small small cusp. cusp. is a small cusp. 6. Industrial Application 6. Industrial Application The new pump in inthis this paper paper compared with with beam beam pumping pumping oil machine oil machine has hasfollowing following main The new pump in this paper compared with beam pumping oil machine has following main system main system differences: differences: new a new type type transmission mechanism, converting rotational motion into system differences: a new type transmission mechanism, converting rotational motion into reciprocating, is is designed to to replace replace four four link mechanism link mechanism a beam pumping beam pumping unit. Thenunit. according Then reciprocating, is designed to replace four link mechanism a beam pumping unit. Then according to change to change adaptability adaptability core institutions, core institutions, adjustable adjustable stroke mechanism stroke mechanism and balancing and according to change adaptability core institutions, adjustable stroke mechanism and balancing device aredevice designed are and designed new and pump new system pump diagram system isdiagram shown inis shown 20. in This pump 20. This changed pump balancing device are designed and new pump system diagram is shown in 20. This pump is tochanged drum type to pump drum type with pump vertical with frame vertical from frame conventional from conventional by designby reversing design transmission reversing is changed to drum type pump with vertical frame from conventional by design reversing transmission device, mainly device, composed mainly composed a motor, adjusting motor, adjusting stroke mechanism, stroke mechanism, speed reducer, speed reversing reducer, transmission device, mainly composed a motor, adjusting stroke mechanism, speed reducer, reversing device, roller, device, androller, counterweight and counterweight parts. parts. 2 is a 2 is reversin boxreversing device photo, box reversing device, roller, and counterweight parts. 2 is a reversing box device and photo, 22and is a field test 22 is photo field test a coal photo seam gas coal extraction seam gas machine extraction based machine on incomplete based on device photo, and 22 is a field test photo a coal seam gas extraction machine based on incomplete s. s. incomplete s. 20. Model pump system composition diagram. 20. Model pump system composition diagram. 2. Non-circular reversing box device. 2. Non-circular reversing box device.

17 Energies 207, 0, Energies 207, 0, Conclusions 22. Field test photo proposed CBM exploitation machine. Based on characteristics polished polished rod movement rod movement at at coalbed coalbed methane methane drainage drainage machine, machine, this paperthis designed paper adesigned a reversing box reversing which conformed box which toconformed its movement to its requirements, movement requirements, simulated it bysimulated dynamic stware it by dynamic ADAMS, stware and compared ADAMS, and simulation compared value simulation with value oretical with calculation oretical value. calculation The design value. method The design this method machine isthis not machine only suitable is not for only coalbed suitable methane for coalbed wells, methane but also for wells, oil field but also pumping for oil units, field as pumping units, as automatic reversing automatic verticalreversing drainage vertical machinedrainage can alsomachine be used for can oil also production. be used for This oil production. article mainly This draws article mainly following draws conclusions: following conclusions: () According to characteristics inconvenient adjustment and low efficiency () According working parameters to characteristics beam pumping inconvenient unit, a new type adjustment drainage and machine low efficiency is proposed to working replace parameters conventional girder beam with pumping unit, a new type as drainage core for machine coalbedis methane proposed well to replace pumping devices. conventional girder with as core for coalbed methane well (2) pumping Through devices. transmission principle incomplete reversing box, a detailed (2) Through design calculation transmission incomplete principle incomplete is carried out, reversing non-uniform box, a detailed motion design calculation pair incomplete is adopted to realize variable is carried speedout, movement non-uniform in stroke motion drainage machine, pair andis adopted automatic realize reversing isvariable realizedspeed by cooperating movement with in or stroke cylindrical drainage s machine, box, and n automatic model reversing incomplete is realized by cooperating with andor reversing cylindrical s systemin is established. box, n model incomplete and reversing (3) system The paper is established. analyzed working performance drainage machine, and completed (3) The oretical paper calculation analyzed working polished performance rod speed and acceleration; drainage machine, efficiency and completed new type oretical drainagecalculation machine and polished conventional rod speed beam pumping and acceleration; unit is compared efficiency and analyzed new simply, type andrainage results machine show that and efficiency conventional new beam type pumping drainage unit machine is compared is about and % analyzed higher simply, than that and traditional results show walking that beam efficiency type pumping new unit. type drainage machine is about (4) % Wher higher than meshing that process traditional onewalking pair beam type pumping pairs unit. reaches oretical (4) Wher calculation value meshing is verified process by ADAMS; one pair n whole pairs reaches reversing oretical train is calculation simulated by value ADAMS, is verified and by ADAMS; output shaft n speed whole and simulation curve reversing polished train rod is simulated displacement by ADAMS, are obtained. and Based output on shaft comparison speed and with simulation oretical curve values, polished accuracyrod displacement design verified. are obtained. Based on comparison with oretical values, accuracy design is verified. Acknowledgments: The authors are grateful to anonymous referees for ir valuable comments and Acknowledgments: suggestions for improving The authors presentation are grateful to this paper. anonymous Project funded referees by for ir Priority valuable Academic comments Program and suggestions Development for improving Jiangsu Higher Education presentation Institutions this paper. (PAPD). Project Production, funded Prospective by Priority Joint Academic Research Projects Program in Development Jiangsu Province Jiangsu (BY ). Higher Education Institutions (PAPD). Production, Prospective Joint Research Projects in Jiangsu Province (BY ).

18 Energies 207, 0, Author Contributions: Guiyun Xu and Weijun Dai contributed new design and simulation; Guiyun Xu and Xiaoguang Zhang designed test device; Guiyun Xu, Weijun Dai and Dezheng Hua completed process model machine; Dezheng Hua wrote paper. Conflicts Interest: The authors declare no conflict interest. References. Tang, Y. Coalbed Methane Resources and Prospects in China; Academic Year Chinese Geological Society: Beijing, China, Feng, C.B. Syntic description status and energy-saving method on oil-abstracting engines in oilfield. Inn. Mong. Petrochem. Ind. 2008, 34, Li, D.; Fan, J.; Wang, L.; Kou, C. Curved beam pumping unit. Oil Forum 203, 32, Fu, H.; Zou, L.; Wang, Y.; Feng, Z.; Song, Z. Study on design and simulation analysis double horse-head pumping unit based on compound balance structure. Proc. Inst. Mech. Eng. Part C 205, 229, [CrossRef] 5. Liu, C. Energy-saving improvement for convention oil pumping unit oilfield. Energy Conserv. Petroleum Petrochem. Ind. 20,, Fan, W.M.; Song, J.C. Design a new energy-saving driving system for oil pumping unit. Mach. Des. Manuf. 204, 7, Li, Q.; Deng, Z.; Chen, H.; Peng, X. No beam pumping unit s dynamic analysis. J. Liaoning Shihua Univ. 204, 34, Liu, J.; Cui, J.; Xiao, W.; Fu, D.; Yang, L.; Li, L. Design mechanical reversing device without switching for pumping unit. Oil Field Equip. 205, 44, Qi, Y.-G.; Chen, J. Dynamics analysis electrical machinery commutation for intelligent pumping unit. Oil Field Equip. 2008, 37, Niu, S.G.; Zhao, Y.H. The research chain type hydraulic pumping unit long stroke. Mach. Tool Hydraul. 2005, 8, Shao, Z.M.; Niu, S.G. The study long stroke pumping unit with hydraulic-chain drive. Oil Field Equip. 2005, 4, Cui, J.; Xiao, W.; Feng, H.; Dong, W.; Zhang, Y.; Wang, Z. Long stroke pumping unit driven by low-speed permanent magnet synchronous motor. Soc. Petroleum Eng [CrossRef] 3. Zhang, Z.; He, L. PMSM control simulation based on pumping unit. TELKOMNIKA Indones. J. Electr. Eng. 204, 36, 08. [CrossRef] 4. Zhao, Y.; Yan, H.; Wang, S.; Zhao, D.; Liu, D.; Xu, H.; Yang, X. Research on multi-section effective linear motor pumping unit. In Proceedings IEEE International Conference on Mechatronics and Automation, Harbin, China, 7 0 August 206; pp Ma, W.Z.; Zhang, H.M.; Sun, J.Y.; Tian, D.B.; Pang, H.F. Research on design linear drive motor new pumping unit. Adv. Mater. Res. 202, , [CrossRef] 6. Dunkerley, K.J. Mechanism; Longmans Green and Co Publisher: London, UK, Ma, Y. Gear Design Variable Drive Ratio Limited Slip Differential. Ph.D. Thesis, Wuhan University Technology, Wuhan, China, Marius, V.; Laurentia, A.; Ana, C. A brief synsis noncircular s. Constanta Marit. Univ. Ann. 20, 6, Bair, B.W. Computerized tooth prile generation elliptical s manufactured by shaper cutters. J. Mater. Process. Technol. 2002, 22, [CrossRef] 20. Bijlsma, B.G.; Radaelli, G.; Herder, J.L. Design a compact gravity equilibrator with an unlimited range motion. In Proceedings ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE), Charlotte, NC, USA, 2 24 August Hebbale, K.; Li, D.; Zhou, J. Study a infinitely variable transmission. In Proceedings ASME 7th Annual Dynamic Systems and Control Conference Research Workshop Israel Science Foundation on Infinite Products Operators and ir Applications, San Antonio, TX, USA, October Doric, J.Z.; Klinar, I.J. Efficiency a new internal combustion engine concept with variable piston motion. Therm. Sci. 204, 8, [CrossRef]

19 Energies 207, 0, Okada, M.; Takeda, Y. Synsis and evaluation that realizes optimal ratio for jumping robot. In Proceedings IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Tokyo, Japan, 3 8 November 203; pp Litvin, F.L. Noncircular Gears: Design and Generation; Cambridge University Press: Cambridge, UK, Litvin, F.L.; Gonzalez-Perez, I.; Fuentes, A.; Kenichi, H. Design and investigation drives with s applied for speed variation and generation functions. Comput. Methods Appl. Mech. Eng. 2008, 97, [CrossRef] 26. Sun, K.; Zheng, F.; Chen, D.; Tong, T. The design method and analysis based on variable ratio function. J. Mech. Transm. 203, 37, Zhang, J.; Bin, Y.U.; Shui, J.; Qi, X. Design pitch curves s based on MATLAB. Mach. Electron. 206, 34, Lei, L.I.; Chang-Long, D.U.; Yang, S.G. Solving planetary pitch curve based on MATLAB. Coal Mine Mach. 2008, 29, by authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under terms and conditions Creative Commons Attribution (CC BY) license (