TRASCO Couplings IN L

Transcription

1 RCO Couplings RCO JUOFX COU O COU

2 RCO couplings escription RCO flexible couplings consist of two metal hubs and an elastic gear ring which is resistant to oils, chemical agents and heat. he construction allows safe power transmission between driver and driven shafts, absorbing impact loads, and torsional vibrations. n its class RCO coupling transmits more power in relation to the physical space occupied. t has a very compact design and allows safe power transmission by absorbing peak loads and torsional vibrations. oreover, the elastic deformation of the polyurethane gear ring compensates angular and radial misalignments and also absorbs small shaft length variation. he involute profile of the gear ring teeth prevents high stress concentration on reduced surfaces and the crowned profile avoids the transmission of axial stress. he high duty factor of RCO couplings is due to the fact that the elastic element works under compression and never under flexion. RCO couplings are suitable for working in both horizontal and in vertical positions and easily support any load variation or reversal. he two coupling halves are electrically insulated from each other. RCO RCO execution pider execution execution X 94/9/C compliance t is possibile to ask for specific certification for use in hazardous area according to C standard 94/9/C. RCO couplings are available with specific mounting/operating instruction manual and conformity. For information, please contact our technical office. ubs are available in cast iron 25, die cast aluminum alloy or forged aluminum. pecial request hubs are available in steel or cast iron 40. n the base execution, R RCO couplings are available in two different versions: precision or economy. n all other executions, only the precision type is manufactured. he difference between and type hubs is that in the precision execution the circular sections of the hubs are precision machined, while in the economy execution, they are simply deburred. he version allows lower axial displacement as indicated in the technical performance table. ach hub is available in two types and, which can accommodate maximum bore size in mm corresponding respectively to the first and second number of the coupling designation. esides the various executions shown in the catalogue, it is always possible to manufacture coupling hubs for special applications. 1

3 pider he gear ring is made of a particular polyurethane resin which shows great advantages in comparison to the standard polyurethans on the market. n fact it is very resistant to aging and hydrolysis (therefore, also suitable for tropical climates) as well as fatigue proof and abrasion proof. t is self-dampening and shows a great resistance to the main chemical agents, acids, oils, and ozone. pecial types of gear rings are available in order to provide the right solution for each specific application covering a large range of temperatures and resisting specific chemical agents. (hore) Colour Compound dmissible emperature [ C] on work tandard spiders peaks pplications 92 h Yellow olyurethane from - 40 to + 90 from - 50 to the most of industrial application (low-mid power) 98 h Red olyurethane from - 30 to + 90 from - 40 to high torque narrow angular misalignment torsion rigidity 64 h reen olyurethane from - 30 to from - 30 to dampened areas internal combustion engines (hore) Colour Compound piders for special applications dmissible emperature [ C] on work peaks pplications 94 h - Orange olyurethane from - 50 to from - 60 to h - reen ytrel from - 50 to from - 60 to White olyurethane from - 20 to from - 30 to internal combustion engines / high dynamic solicitations / highly dampened areas high solicitation applications / high torsion rigidity / high temperature areas high torsion rigidity / high temperature areas / high resistance 2

4 RCO coupling sizing as per 740/2 RCO coupling sizing is made according to 740/2. Couplings must be selected to ensure that the max feasible torque is never exceeded during operation. t is necessary to have correct sizing, so that all conditions hereunder are respected. 1) erify the nominal torque he nominal torque of the coupling must be higher or equal to the nominal torque of the drive multiplied by the temperature safety factor. ote that: K [ m] Where is the motor nominal power in kw. K max Z u m = 9550 K m [ [ m m] ] n [ m] [ m] = K 9550 n = K9550 [ m] n u Kmax K Z [ ] [ ] [ m] 2) erify the maximum torque he max torque of the coupling K must [ be mhigher ] Kmax or equal to the starting torque s multiplied by the safety factors, z, u where [ ] u m is the higher value between = Z u Kmax 9550 driver [ m] [ m] and n driven units. K max K K max KW W [ m ] [ m Z] u [ [ ] ] [ ] [ m] 3) erify torque with reversal KW Kmax W m K m m n case of torque with reversals a it must Kr be verified w that: a r w KW K a r Kmax w + W [ m + m] 1 a r w where kw = torque with reversal, which the coupling can bear, and w = torque variation of the drive. n case of drives with high torsional K KW a W [ r m] w + vibrations + (eg. 1piston compressors, combustion engine) it is recommended to make a torsional a r w vibration calculations in order to guarantee the correct functioning of the coupling. lease consult our technical office. RCO a a + r w hock + load safety 1 factor r w hock load type U ight 1,4 edium 1,5 ard 1,8 emperature safety factor ( C) 30 C / +30 C +40 C +60 C +80 C 1 1,2 1,4 1,8 afety factor for frequency of starting tarting/h Z 1 1,2 1,4 1,6 ub shaft connection check ub shaft connection must always be checked by the user. t is important to verify the maximum torque in the drive is lower than the torque which the hub shaft connection can bear. n case of keyway connection, it is important to verify the tensile strength of the hub material with the load which the keyway seat must transmit. color Coupling nominal torque m Kmax Coupling maximum torque m KW orque with reversal transmissible by the coupling m otor nominal torque m otor peak torque m W orque with reversal of the machine m emperature factor Z tart frequency factor u otor or driven-side shock factor otor nominal torque kw n rpm min -1 3

5 of stress eriodic armonic 2W W isalignment a a r w [ ] 19/24 1,2-0,20 1,30 24/32 1,4 1,1 0,22 1,30 28/38 1,5 1,2 0,25 1,30 38/45 1,8 1,4 0,28 1,30 42/55 2,0 1,6 0,32 1,30 K 48/60 2,1 1,7 0,36 1,30 55/70 2,2 1,8 0,38 1,30 65/75 2,6 2,0 0,42 1,30 = /90 3,0 2,4 0,48 1,30 90/100 3,4 2,8 0,50 1,30 125/145 4,6 3,4 0,60 1,30 n [ m] [ m] 100/110 3,8 3,0 0,52 1,30 Kmax Z u 110/125 4,2 3,2 0,55 1,30 n=1500 min -1 K [ m] [ m] he values shown in the table for radial and angular misalignment, must be corrected in case they are simultaneously acting on the coupling. he sum of the admissible value () and the respective values shown in the table must be lower or equal to 1. Kmax KW W [ m] [ m] w a a + r r + w w 1 100% a aximum axial misalignment - execution mm a aximum axial misalignment - execution mm r aximum radial misalignment mm w aximum angular misalignment 100% r ynamic torsional rigidity K ynamic torsional rigidity Cdin is the first derivate of the nominal torque of half coupling in respect to the torsion angle. ϕ is the torsion angle of half coupling in respect to the second half. s a general rule, Cdin is greater than C and depends on the stress acting on the coupling. dk dϕ ϕ 4

6 echnical performances he technical performances below refer to all types of RCO executions and are valid for the indicated spiders when couplings are correctly selected. For particular applications needed, such as very high chemical resistance, spiders made of special material are available. Contact our echnical epartment. RCO orque ax. speed ynamic torsional rigidity echnical features pider - 92 h - YOW 19/24 24/32 28/38 38/45 42/55 48/60 55/70 65/75 75/90 90/ * 110* 125* K [m] Kmax [m] KW [m] 2, n (v=30m/s) [min -1 ] n (v=40m/s) [min -1 ] Cdin (1 K) [m/rad] Cdin (0,75 K) [m/rad] Cdin (0,5 K) [m/rad] Cdin (0,25 K) [m/rad] orsion angle ϕ (K) ( ) 3,2 ϕ (Kmax) ( ) 5 ampening factor Ψ (-) 0,80 Resonance factor R (-) 7,90 *= 95 h orque ax. speed ynamic torsional rigidity echnical features pider - 98 h - R 19/24 24/32 28/38 38/45 42/55 48/60 55/70 65/75 75/90 90/100 K [m] Kmax [m] KW [m] 4, n (v=30m/s) [min -1 ] n (v=40m/s) [min -1 ] Cdin (1 K) [m/rad] Cdin (0,75 K) [m/rad] Cdin (0,5 K) [m/rad] Cdin (0,25 K) [m/rad] orsion angle ϕ (K) ( ) 3,2 ϕ (Kmax) ( ) 5 ampening factor Ψ (-) 0,80 Resonance factor R (-) 7,90 orque ax. speed ynamic torsional rigidity echnical features pider - 64 h - R 19/24 24/32 28/38 38/45 42/55 48/60 55/70 65/75 75/90 90/100 K [m] Kmax [m] KW [m] 5,5 19, n (v=30m/s) [min -1 ] n (v=40m/s) [min -1 ] Cdin (1 K) [m/rad] Cdin (0,75 K) [m/rad] Cdin (0,5 K) [m/rad] Cdin (0,25 K) [m/rad] orsion angle ϕ (K) ( ) 2,5 ϕ (Kmax) ( ) 3,6 ampening factor Ψ (-) 0,75 Resonance factor R (-) 8,50 5

7 RCO couplings for motors according to C standards (spider hardness 92 shore) [kw] [m] 3000 [1/min] K [kw] 1500 [1/min] [m] K [kw] 1000 [1/min] [m] K [kw] 750 [1/min] [m] K 2 poles d x l poles 0,75 2,5 9,2 0,55 3,7 6,2 0,37 3,9 5,8 0,18 2,5 9, x40 1,1 3,7 6,2 0,75 5,1 4,5 0,55 5,8 19/24 3,9 0,25 3,5 6,5 19/24 19/24 19/ ,5 5 4,6 1,1 7,5 3 0,75 8 2,8 0,37 5,3 4,3 24x ,2 7,4 3,1 1,5 10 2,3 1,1 12 6,6 0,55 7,9 2, ,8 2,2 15 5,3 0, ,2 8,1 1, /32 5,3 24/ /32 4 1, / x , ,9 2,2 22 3,6 1,5 21 3,8 5, , ,5 36 6, ,6 2,2 30 7,6 7,5 25 9,2 28/38 28/38 28/38 28/ , ,5 49 4, ,7 5,5 55 4,1 38x , , ,2 7, /45 9,1 38/45 38/45 5, / x ,5 60 7, , ,1 7, , ,7 18, ,1 48x , , ,2 42/55 42/55 42/ ,3 18, , / , ,1 55x , , , ,9 48/60 48/60 48/ , , , ,4 55x110 60x / /70 2, /70 2, ,6 60x140 65x , , , ,1 75/ /70 2, , , ,2 75x , , /90 3, ,5 75/90 75/90 65x , , , , , , , , /90 90/ , , , ,2 80x , , /100 3, ,7 90/ / , ,9 75x140 95x , ,3 90/ , , ,8 80x x , ,3 otor nominal torque kw otor nominal torque m K afety factor d x l otor shaft s end mm 6

8 R... R R base program R... RCO couplings are dimensionally manufactured to hub types and, the difference being the maximum shaft diameter which hubs can accept (corresponding respectively to the first and second code number). he long hub execution (allows full cover of the motor shaft) is t available in both and executions. aterials used for manufacture are: cast iron grade 25 (all sizes); aluminum, diecasting cast iron grade 40 and steel upon request. R... R R... RCO Fg ozzo "" ozzo "" Fg imensional specification hubs in / 1 / C Fg execution execution execution execution max max t 19/24* / / , / / / , / / , / ozzo ozzo 90/ "" "" , / / , / * intered steel imensional specification hubs in aluminum max max Fg execution Fg / 1 / C 19/ / / , / / / , Fg alid bore for execution Order form R 42/55 RCO R hub precise execution; standard execution ipo xecution ; xecution ong hub RU 38/45 RCO R aluminum hub xecution ; xecution R 19/24 R RCO R spider Yellow colour if not indicated, R red, green 7

9 tock range ubs with finished bore 7, keyway, stop screw aterial* ub execution tock range bore /24 *U = luminum - C = teel - = Cast iron 24/32 28/38 38/45 42/55 48/60 55/70 65/75 75/90 90/100 U C U U U U U etscew specifics per hub dimension ub dimension t / / / / / / / / / / / / t R... 8

10 R taper bush series RCO couplings type R are manufactured in cast iron 25. hey combine the typical high performances of standard couplings with the mounting and dismounting advantages offered by the R- taper bush: -they are ready to be mounted; -they are manufactured in two different executions: 1 Ø 1 and 2 (see picture); they solve the problem of fighting corrosion; hubs type 1 may be axially moved for spider replacement; they may be used in all types of machinery. 2 Ø RCO Ø / (6545) /100 * 3535 (9090) , * Only 1 execution aper bush 2 28/ (2820) , / (2820) / (4025) / (4040) , / (5030) / (5030) , Ø Ø 1 Order form R 42/55 1 R 19/24 R Ø RCO R hub for taper lock 1 xecution ; 2 xecution pider Yellow if not indicated, R red, green aper lock type ransmissible torque [m] 1108 (2820) (4025) (4040) (5030) (6545) (9090)

11 RC series for use with -OCK elements type 8 Ø his execution has been introduced to incorporate advantages offered by the -OCK locking elements in "RC" CUZO the shaft-hub 1 cal. esterno connection. he system allows for a quick, safe and backlash free mounting without the use of keyway and eliminating the need for lock washers, spacers and stop rings. any different solutions may be created 1 to solve all kinds of application needs. 2 We include hereunder a very useful example.n fact, the same hub bore allows the fitting of different shaft diameters. "RC" secuzione 2 Ø Ø Ø "RC" CUZO 1 cal. interno F 1 F 2 F 3 "RC" secuzione d 1 2 aterial* Fig. 38/ C 3 42/55 48/ C 3 Ø , C / C / , / / , *: C = steel / 25 = cast iron 25 / -400 = pheroidal cast-iron 400 Order form RC 48/60 R 38/45 R RCO RC hub for -OCK type 8 pider Yellow if not indicated, R red, green Fig. 1 xternal Cal Fig. 2 C 8 F20 / 55 -OCK element ore diameter xternal bore diameter Fig. 1 nternal Cal Fig. 3 10

12 R R series with intermediate shaft his series allows the joining of two shafts (even very distant) through two RCO couplings and an intermediate shaft (length w ) of customized dimension. he presence of two polyurethane rings allows high dampening zw w capability and large radial misalignments. ubs are classically made from cast-iron, while shafts are from steel; though, different materials can be used, according to different applications. RCO ozzo ozzo execution / 3/ C execution / / , / / / , / / , / / , / / , / valid bore for execution Order form R... R 42/55 RCO R hub recise execution; standard execution xecution ; xecution ong hub R... U R... R 38/45 R pider Yellow if not indicated, R red, green R haft length on request. zw w 11

13 R C3 series with intermediate shaft his series allows the joining of two shafts (even two spaced) through two RCO couplings and an intermediate shaft (length R2 ) of customized dimension, fixed with hubs through shrink-disc. he presence of two polyurethane elements allows high dampening capability and large radial misalignments. ubs are classically made of cast-iron, while shafts are made of steel; though different materials can be used according to different applications Ø R R2 ZR2 imensions R-C3 nternal hub xternal hub OCK 3 elements dmin dmax R2 ntermediate shaft s 2 ZR2 crew min. 1 3 in [m] dr C [m/rad m] ,5 61,5 109 R x2.0 68,36 10x16 4X10 4,9 19/ R x x18 4X10 4,9 24/ R x ,9 20x28 6X / ,5 117,5 177 R x x34 6X18 17 Ø 38/ R x x43 6X / R x x53 6X / ,5 178,5 261 R x x59 8X22 41 R / / CR x ZR2 55x71 8X / ,5 220,5 307 R x x77 8X22 41 R Order form R 48/60 per cal 3 R 38/45 R RCO R hub pider Yellow if not indicated, R red, green ntermediate shaft on request / 2/ C

14 RF flange series his series, with flanges, has been developed for applications on heavy machinery and to combine different shafts and flanges solutions. haft-shaft: using two hubs type F, allows the replacement of the elastic element without traversing of either motor-machine or driven-machine. haft-flange: using one hub type CF and one type R. Flange-Flange: using two hubs type CF. c c r b a RCO b F CF b a C a R... R F F CF c CF min max a C r C a r 19/ / , , c 24/ / , , / / , , , / , , / / , / / , / , b / 1/ C 90/ F , / / , / alid bore for execution. b a b c b c CF Order form haft side flange F execution F R... R F c C a c RFF 48 For hub R order form please see RCO R base program CF RFCF 48 r Ring side flange F and CF execution CF CF r umber of screws / 1/ C 13

15 b r F c RF C flange series he RF C series has the same characteristics as the F series, while being compact in dimension. F CF c b c C r F CF b F / 2/ C min max b c 24/ , / , , / , / / , / / , / , / , / / , / b c b r C r alid bore for execution. R... Order form haft side flange F execution F R CF F F RFF 48 For hub R order form please see RCO R base program RFCF 48 Ring side flange F and CF execution c CF CF CF r umber of screws C r c 14

16 R double cardanic series t allows compensation of high axial, radial and angular misalignment. oreover, the use of the double spider allows for double the torsion angle and provides very high dampening effect. Ø Ø Ø Ø Ø RCO C C r R... 24/ R ,89 28/ , R / ,15 42/ ,26 48/ , R ,36 55/ R... 1,52 65/ , ,75 75/ / , C ,5 Ø Ø Ø Ø Ø w [ ] 1 30 alid bore for execution R... R R Order form For hub R order form please see RCO R base program R R R... R 48/60 pacer element F a ore of hub mm F b ore of hub mm r aximum radial misalignment mm w aximum angular misalignment 15

17 R FR drum brake series his series has been developed to suit drum-brake (FR) transmissions. t is constituted as an elastic coupling screwed to the brake band. Components are either made of cast-iron (25), spheroidal cast-iron (400), or steel according to application. lso, assembling of different dimensioned brake bands to any kind of coupling is allowed. ee below tables. FR FR Ct j6 r b b R FR - drum brake b x b W FR [kg] J FR [kg m 2 ] min -1 with max 30 m/s 160x ,12 0, x Cd ,45 0,03 FR x ,87 0, x ,95 0, x ,00 8, x ,00 14, x ,00 27, ; max FR 400x ,20 0, x ,00 2, ; min (25) (400) (teel) a 28 FR ,5 20 2, FR , FR , FR ,5 28 3, FR , / 3/ C 65 FR ,5 35 4, FR , FR ,5 45 5, FR , FR ,5 55 6, FR , j6 r a r FR Order form For hub R order form please see RCO R base program RFR FR RFR 48 rake side hub Ct j6 r b and on request. WFR RFR weight kg JFR RFR moment of inertia kgm 2 r umber of screws 16 b

18 R FR brake disc series his series has been developed to suit disc-brake (FR) transmissions according to 15431/ t is constituted as an elastic coupling screwed to the brake band. Components are either made of cast-iron (25), spheroidal b cast-iron (400), or steel according to application. lso, assembling of different dimensioned brake bands to any kind of coupling is allowed. ee below tables. RCO Cd FR r a j6 FR a FR R FR - brake disc a x a / 3/ C 200x12,5 X X ,93 0, x12,5 X X X X ,66 0, x X X X X X ,62 0, x X X X X X X X - 15,23 0, x X X X X X X X 23,96 0, x X X X X X X 47,72 2, x X X X X X X 60,93 3, x X X X X 94,91 7, Ct j6 r 900x X X 118,95 12, b W FR [kg] FR J FR [kg m 2 ] min -1 with max 40 m/s ; min ; max (25) (400) (teel) 28 FR ,5 20 2, , FR , , FR , , FR ,5 28 3, ,5 8 b 55 FR , , FR ,5 35 4, , FR , , FR ,5 45 5, , FR , , FR ,5 55 6, , FR , ,5 20 r Cd Order form For hub R order form please see RCO R base program RFR RFR 48 isc on request. rake side hub Cd FR j6 r a WFR RFR disc weight kg JFR RFR moment of inertia kgm 2 r umber of screws 17

19 RCO couplings weight and moment of inertia fig.1 fig.2 fig.3 R aluminum fig.4 fig.5 fig.6 19/24 24/32 28/38 38/45 42/55 48/60 55/70 65/75 75/90 90/ / / /145 R ( esecuz.) fig. 1 R ( esecuz.) fig. 1 R ( esecuz.) fig. 1 RU (esecuz. ) fig. 1 RU ( esecuz.) fig. 1 RU ( esecuz.) fig. 1 R fig. 2 RF (CF) fig. 3 RF (CF) fig. 4 W [kg] - 0, , , J [kgm 2 ] - 0, , , W [kg] 0,56 0,78 0,67 0,22 0,31 0,26-0,3 0,18 0,42 0,14 RF (F) fig. 5 pacer element R fig. 6 J [kgm 2 ] 0,0002 0,0004 0,0003 0, , , ,0003 0, , ,00006 W [kg] 0,92 1,25 1,1 0,36 0,49 0,43 1 0,58 0,3 0,69 0,22 J [kgm 2 ] 0,0005 0,0009 0,0007 0,0002 0, , ,0007 0,0008 0, , ,00013 W [kg] 1,97 2,5 2,25 0,77 0,98 0,9 1,7 0,8 0,313 0,933 0,35 J [kgm 2 ] 0,0017 0,0027 0,002 0,0007 0,001 0, ,0026 0,001 0, , ,00035 W [kg] 3,1 3,85 3,46-1,5-2,8 1,41 0,76 1,81 0,51 J [kgm 2 ] 0,0035 0,006 0,0047-0,002-0,0036 0,004 0,0012 0,0023 0,0007 W [kg] 4,2 5,3 4, ,7 1,62 0,89 2,27 0,67 J [kgm 2 ] 0,006 0,01 0,008-0,004-0,0078 0,005 0,0017 0,0035 0,001 W [kg] 6,4 7,8 7, ,82 1,47 3,55 0,97 J [kgm 2 ] 0,012 0,02 0, ,012 0,012 0,0035 0,007 0,002 W [kg] 9,7 11,8 10, ,9 3,46 1,89 4,89 1,43 J [kgm 2 ] 0,024 0,035 0, ,014 0,017 0,0059 0,0123 0,004 W [kg] 15,2 20, ,8 5,03 3 7,86 2,2 J [kgm 2 ] 0,051 0,082 0, ,065 0,032 0,0125 0,0275 0,009 W [kg] 26,2 30,2 28, ,4 7,9 4,87 13,54 3,9 J [kgm 2 ] 0,13 0,17 0, ,162 0,073 0,033 0,108 0,025 W [kg] 32, ,5 7,55 20,15 - J [kgm 2 ] 0, ,139 0,063 0,14 - W [kg] 45, ,8 10,15 27,05 - J [kgm 2 ] 0, ,255 0,11 0,242 - W [kg] 68, ,4 14,9 40,9 - J [kgm 2 ] 0, ,463 0,21 0,48 - Weight and moments of inertia are calculated on hubs with max diameter bore. 18

20 ables for RCO couplings with taper or splined bores ø ø RCO aper 1:5 per: OC - UCR- UC - ÜRO Code ø d + 0,05 b J9 t2 + 0,1 k a1 9, ,5 a2 16,85 3 1,8 18,5 a3 19,85 4 2,2 21,5 a4 21,95 3 1,8 21,5 a5 24,85 5 2,9 26,5 a6 29,85 6 2,6 31,5 a7 34,85 6 2,6 36,5 a8 39,85 6 2,6 41,5 aper 1:8 per: O - C - R YR - JO & ROZZ RZOCC - - UR-FU Code ø d + 0,05 b + 0,05 t2 + 0,1 k b1 9,7 2, b2 11,6 3 7,1 16,5 b3 13 2,4 7,3 21 b ,5 17,5 b5 14,3 3,2 8,5 19,5 b6 17,287 3,2 9,6 24 b7 17, ,3 24 b8 17, ,7 24 b9 22,002 3,99 12,4 28 b10 25,463 4,78 15,1 36 b11 25, ,5 36 b ,78 15,3 32,5 b13 28, ,1 38,5 b14 33,176 6,38 18,8 44 b15 33, ,8 44 b16 43,057 7,95 3, b17 41,15 8 3,1 42,5 aper 1:10 per: RKR F F - Code ø d + 0,05 b J9 t2 + 0,1 k c1 19, ,1 32 c2 24, ,1 45 c3 29, splined profile Code ize ead itch. of teeth - 5/8 14,28 16/ l- 3/4 17,46 16/ /8 20,63 16/ ,81 16/ J 1 1/8 26,98 16/ C- 1 1/4 29,63 dic /8 33,33 16/ /2 36,51 16/ /4 42,86 16/ F 2 9/16 63,5 16/ Code ize ead itch. of teeth olerance x 14 14,4 1,6 9 0, x 25 26,25 1, , x , , x 31 31,5 1, , x ,9 20 0, x , x , ize ead itch. of teeth 20 x 1 x 18 x x 1,25 x 14 x 7 17,5 1, x 1,25 x 18 x 7 22,5 1, x 2 x 13 x x 2 x 14 x x 2 x 16 x x 2 x 18 x x 2 x 21 x x 2 x 22 x x 2 x 24 x