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Ari Holopainen / epicyclic2 | |
| C. Planetary Gear Ver III:
This planetary gear ver III looks like Planetary gear ver II with 2 sun gears but idlers in planet carrier makes it behave like Basic planetary gear with annulus. Sun gear B equals to annulus.
Planetary gear ver III has 3 parts: Sun gear A (SA), Planet carrier with idlers, planet wheels A (PA) and planet wheels B (PB) and finally Sun gear B (SB). You can get 6 different ratios plus direct drive as 7th ratio. Basic ratio of this planetary gear can be calculated with equation u=Z(PA)/Z(SA)xZ(SB)/Z(PB), Z means number of teeth in current gear wheel. In this Lego case you have Z(SA)=Z(SB)=16, Z(PA)=24 and Z(PB)=8 so you get basic ratio u=3,00. Ratios can be calculated with equation N(SA)+uN(SB)-(1+u)N(planet)=0 where N means part’s rotation speed. This is same equation as in basic planetary gear except that there is sun gear B instead of annulus.
Note that I have used bricks to get planet carrier, but it’s rotating part so don’t attach it to lego frame. Bearing bricks are not modeled in these pictures. If you prefer studless parts here is example how to build planet carrier.
There are also other basic ratio possibilities if you use other axle bases. In next table there are examples where this planetary gear ver III is used as a part of planetary gear set. Check named planetary gear sets to see how to build table’s planetary gears. Table contains also other available basic ratios that I haven’t used yet.
C.1. Lego version of Simpson planetary gear set
Simpson planetary gear set is an old automatic transmission which has 3 gears plus reverse. It contains 2 identical planetary gears which are connected together so that it has 4 parts: compound sun gears (S), single annulus (A), single planet carrier (P) and compound annulus & planet carrier (AP). There are also ratio calculations for all gears. Lego version is not automated and uses different kind of planetary gears so gear parts are a little bit different: compound sun gears A1 & A2 (AA), single sun gear B1 (B), compound planet carrier 1 & sun gear B2 (PB) and single planet carrier 2 (P). Sun gears AA equal to sun gears of real Simpson and sun gear B:s equal to annuluses.
Lego version has 2 clutches (C1 & C2) and 2 brakes (B1 & B2). Real Simpson has also a freewheel clutch which works in 1st gear and makes gear connecting simpler and driving behavior smoother while there is no engine braking in 1st gear. In lego version brakes are not shown in all pictures or original LDraw file so check Schematics or Gear set brakes. Essential in brake 2 is that rotation of planet carrier is limited but planet wheels can rotate free. Schematics also shows ratios and how to engage the gears. Simpson planetary gear set is quite simple compound planetary gear set. You get easily good ratios with progressive gear steps with large variety of basic ratios. Gear engaging is also quite simple (for a planetary gear set) while you need to activate 2 elements of brakes and clutches to get a gear. Simpson has also some problems: you need to add extra planetary gear to get more gears or larger overall gear ratio. One interesting thing is that you can recognise Simpson planetary gear set by looking ratios. Firstly Simpson is 3-speed transmission and secondly 3rd gear is direct. And third point is that ratio equations in 1st and 2nd gear are i(1)=2+1/u and i(2)=1+1/u so ratio of 1st gear is always two point some decimals and ratio of 2nd gear one point same decimals. Fourth point is that reverse ratio i(R)=-u so in reverse ratio is -1 / same decimals. So if you see for example ratios 2,40, 1,40, 1,00 and -2,50 you check -1/0,40=-2,50 and you are sure that it’s Simpson planetary gear set with basic ratio u=2,50. C.2. Lego version of 6-speed ZF Ecomat
ZF Ecomat is a 6-speed plus reverse automatic transmission for trucks and buses. It has 3 identical planetary gears which are connected so that there are 5 parts (check Real ZF Ecomat in picture links). There is also a ratio calculation example for 3rd gear.
Lego version uses different kind of planetary gears so parts and their names are different. 5 parts are: single sun gear A1 (named as A), compound sun gears A2 & A3 (AA), compound planet carrier 1 & sun gear B2 (PB), monster part sun gear B1 & planet carrier 2 & sun gear B3 (BPB) and finally single planet carrier 3 (P) as output. Planetary gear set has 3 clutches (C1-C3) which choose input between A, AA and BPB and 3 brakes (B1-B3) which lock parts A, PB and BPB in turn. You have to activate 2 elements of clutches and brakes to get a gear. Brakes are not included in all pictures or original LDraw file so check Gear set brakes to see where to put them. Also Schematics or Gear set parts show which parts need brakes. While this is lego version of real planetary gear set you have to disengage and engage only 1 clutch or brake during shifting, so shifting procedure is easier and faster compared to situation with disengaging and engaging 2 elements each. Identical planetary gears cause also 1 problem: gear step 5-6 is too large but there is no easy way to fix it. Problem occurs in both real version and lego version, but in lego version gear step problem is even larger. 3 planetary gears mean also that ratio equations are quite complicated especially in gears 3rd and 5th when torque goes through all planetary gears. ZF Ecomat is available also in 5-speed version which means abandoned 6th gear and by adding extra planetary gear there is also a 7-speed version. C.3. Planetary driving direction changer
This one is a planetary driving direction changer for tractors. In lego world driving direction changer is useless item but this example shows how to do it with planetary gear. Important point in this planetary gear is that basic ratio is 1,00. Sun gear A is input, sun gear B is output and planet carrier is connected to sun gear A (forward drive) or locked to ground (reverse drive). Locking is done by clutch gear that meshes with locked gear.
Building tip: move input axle little bit forward so it won’t collide with planet wheels (check Top view). This driving direction changer and B.1. Planetary range-change unit have same parts as input, output and locked part. But range-change unit doesn’t have idlers on planet carrier and basic ratios are different, that’s why these auxiliaries behave so different ways. Other notable thing is that I have already used this structure earlier in B. Centre Differential Ver II, check differentials. In differential use basic ratio 1,00 is used to get 50%-50% torque allocation. C.4. Lego version of Hydra-Matic
4-speed Hydra-Matic is a very old automatic transmission and it contains 3 planetary gears. Front planetary gear handles shifts 1-2 and 3-4, middle planetary gear is for shift 2-3 and rear planetary gear helps to get a reverse gear. Lego version uses different type of planetary gears so parts have different names than original Hydra-Matic. Check picture Real Hydra-Matic for original Hydra-Matic and Schematics for lego version.
Original Hydra-Matic had couple of interesting features. Firstly Hydra-Matic didn’t have torque converter but fluid coupling which was (in power flow) located after front planetary gear. This meant that in 1st and 3rd gear fluid coupling rotated slower than engine which made it to behave “softer”. It allowed very nice and smooth move off while fluid coupling had a lot of slip but slip decreased soon when engine rpm increased. In shifting 1-2 fluid coupling started to rotate at engine rpm so it “tightened” which made gearbox to respond better to acceleration. Another interesting feature was how middle planetary gear was locked direct in 3rd and 4th gear. Middle planetary gear’s sun gear got torque from fluid coupling as earlier but annulus was connected direct to planet carrier of the front planetary gear. This arrangement divided power flow to mechanical and hydraulic route so that only about 38 % of torque went through fluid coupling. It reduced significantly slipping of fluid coupling which meant better efficiency and less fuel consumption in high speed driving even though fluid coupling didn’t have a lock-up clutch. But shifting was Hydra-Matic’s weak point. In shift 1-2 rapid speed increase of fluid coupling made car easily to jump forward during shifting especially when throttle was full open. And shift 2-3 had timing problems while gearbox operated 4 elements of clutches and brakes at the same time. Other problems were that Hydra-Matic was too complicated, heavy and expensive for personal car use. For more information check Wikipedia’s article about Hydra-Matic. C.5. Lego version of Allison 1000
Allison 1000 is an automatic transmission, that contains 3 planetary gears and has 6 gears plus reverse. Each planetary gear has different ratio which means that ratio equations look horrible. Planetary gears are connected together so that transmission has 6 parts: check picture Real Allison 1000 for original transmission and Schematics for lego version. These pics also show ratios and how to get the gears. Allison 1000 has 2 clutches (C1-C2) and 3 brakes (C3-C5) and you have to engage 2 elements to get a gear. Lego version is modeled so that brakes are included.
Allison 1000 is pretty similar as ZF Ecomat. Middle and rear planetary gears are arranged same way in both transmissions, differences are in front planetary gear. In ZF Ecomat front annulus is connected to compound middle planet carrier and rear annulus while in Allison 1000 it is individual part. Front sun gear can be chosen both input and locked part in ZF Ecomat but in Allison 1000 this part is constant input. These differences mean that ZF Ecomat has 3 clutches when Allison 1000 needs only 2. It also means that ZF Ecomat has pretty good ratios and gear steps with identical basic ratios in all planetary gears but Allison 1000 needs different ratio at least in front planetary gear. After I had finished pictures I found that I had forgotten something in LDraw file: 16 teeth clutch gear in locked axle needs a bush or it will slide away. Error is now corrected in LDraw file but you can see it in pictures. C.6. 3-speed powershift for tractor 2 motors & planetary gear ver III
This 3-speed powershift is 3rd motor-gearbox unit that uses 2 motors and a planetary gear. It has planetary gear version III that has basic ratio 6,00. Motor 1 is connected to sun gear A, motor 2 to sun gear B and planet carrier is output. High basic ratio gives small gear steps which makes it suitable for tractor’s powershift. It’s designed to replace 3-speed splitter unit in lego 45+45R-speed tractor transmission but you can add it in other tractor transmissions too. If transmission has already splitter unit you replace it with this powershift.
When you use extra forward-stop-reverse switch (pole reverser) you need only 1 battery box and this gearbox becomes very easy to use, check picture called Wiring. You choose driving direction with switches of battery box and powershift’s stage with that extra switch. In mechanical way this means that motor 2 orders driving direction and motor 1 orders speed. In powershift’s low motor 1 rotates in the opposite direction compared to motor 2. In medium motor 1 is stopped and in high both motors rotate in same direction. Check speeds and ratios from picture called Ratios. Building tip: Move planet carrier axle a little bit rearward to prevent possible collision problems between planet wheels and idler gear. C.7. 3-speed powershift for tractor version II 2 motors & planetary gear ver III
Here is upgraded version II of 3-speed powershift for tractor. It uses two motors and planetary gear ver III with basic ratio 5,00. This time planet carrier has studless frame. So this version II is a little bit simpler and gear steps are slightly larger compared to version I. This version is designed to use in 45+45R-speed tractor transmission version II. Here shown design has motors located parallel but for more narrow design you locate them vertical.
If you use low speed motors it’s possible that planet carrier can’t handle torque they give. So available is also alternative setup with enforced planet carrier. Motor 1 is connected to sun gear A, motor 2 to sun gear B and planet carrier works as output. For simple use you need forward-stop-reverse switch (pole reverser) which will be located between battery box and motor 1. Motor 2 is connected directly to battery box. Check picture Wiring or Battery box. So you choose driving direction with switches of battery box and powershift’s stage with that forward-stop-reverse switch. In powershift stage low motor 1 is running in the opposite direction compared to motor 2, in medium motor 1 is stopped and in high both motors run in same direction. Picture Ratios shows this version’s ratios and gear steps. As an option this powershift can be used as 2-speed version by using only stages medium and high. And you can use it without forward-stop-reverse switch, check next table for more info.
Building tip: To get planetary gear a little bit forward move planet carrier axle slightly out from its axle joiner. This is possible because 8 teeth sun gear A goes slightly inside planet carrier. Reason for this fine tuning is to prevent possible collision problems between planet wheels and idler gear. But if this fine tuning leads to situation where 16 teeth clutch gears don’t stay together you need to try this: put planet carrier axle full inside axle joiner to minimize gap, change location of support brick and use bushes to get planet carrier in right position. C.8. 5-speed powershift for tractor 3 motors & 2 planetary gear ver III:s
This 5-speed powershift contains 3 identical motors and 2 planetary gear version III:s. First planetary gear has basic ratio 1,25 and second 2,67. Motor 1 is connected to sun gear A1 and motor 2 to sun gear B1 (powershift motors). Planet carrier 1 is connected to sun gear A2. Motor 3 (drive motor) is connected to sun gear B2 while planet carrier 2 works as output.
This powershift is designed for 30+30R-speed tractor transmission that has 5-speed powershift and 6-speed range unit and is inspired by Valtra HiTech transmission. This powershift is remake with much more compact design so it’s usable in lego tractor without modifications. Original design is moved to page Junkyard if you want to check it. You need one battery box and two forward-stop-reverse switches (pole reversers) to operate this system. Left switch is connected to motor 1 (M1) and right switch to motor 2 (M2). Driving motor 3 (M3) is connected directly to battery box. Here is how you get the gears: In 1st gear both left and right switches are rearward so you are ready to move off with battery box’s switches forward or reverse. In upshift to 2nd gear you move left switch to middle position and further to forward for 3rd gear. Then 4th and 5th gear are connected by moving right switch to middle and forward positions. Downshifting is this operation reversed so first you move right switch to middle and rearward positions to get 4th and 3rd gear and then left switch to middle and rearward positions to get 2nd and 1st gear. So all in all this motor-gearbox unit gives 5 powershiftable gears with remote control shifting, no stopping for shifting, no shift lever with H shift pattern. Check pictures Data sheet and Control unit for more info. Building tip: move both planet carriers as forward as possible to prevent possible collision problems between idler gears and planet wheels. Note: I haven’t built or tested this design but there can be slipping in gears 2nd and 4th under high load. This slipping happens if driven motors start to rotate stopped motor. C.9. 9+9R-speed full powershift tractor transmission 3 motors & 2 planetary gear ver III:s Additional creeper unit (18+18R-speed version)
This transmission has incredible 9 remotely shiftable powershift gears in both driving directions and is now available with upgraded design. It contains 3 identical motors and 2 planetary gear ver III:s. First planetary gear has basic ratio 3,00 and second 1,33. Motor 1 is connected to sun gear A1 and motor 2 has ratio 0,93 before it’s connected to sun gear B1. Planet carrier 1 is together with sun gear A2. Motor 3 is connected to sun gear B2 and planet carrier 2 is output.
This version is remake with two improvements: design is more compact for easier use in lego tractor and possible slip in gears B1 and B3 under high load should be smaller. This slip happens if motor 1 starts to rotate stopped motor 2. If you want to check original design it’s moved to page Junkyard. To operate this powershift transmission you need one battery box and two forward-stop-reverse switches (pole reversers). Left switch is connected to motor 1 (M1) and it handles small step gears 1-3. Right switch is connected to motor 2 (M2) and it handles groups A-C. Motor 3 (M3) orders driving direction and is connected directly to battery box. Gear order is A1-A2-A3-B1-B2-B3-C1-C2-C3. For more info check pictures Data sheet and Control unit. Notable thing is that groups A-C are not real ranges, they are only because of two stick operation in lego design. Real full powershift transmission is operated with single sequential shift lever or +/- buttons. Other note is that real tractor transmissions has pure geometrical gear steps while high gears are only for transportation and main work is done in low or middle gears. Lego design has strong progression in gear steps so steps C1-C2 and C2-C3 are too small and step A1-A2 is too large. So there are only few gears in major working speeds and too much gears in high speeds. But this 3 motor and 2 planetary gear design makes gear steps automaticly progressive whatever you try to do. I have calculated ratios for this design with many lego planetary gear ratios but problem occurs. Overall gear ratio 8,53 is a little bit small for tractor but for example John Deere 9400 monster tractor has about the same overall gear ratio in its 12+3R-speed transmission. For lower speeds it’s easy to add optional creeper unit to lego design’s output axle. Creeper off has direct ratio 1,00 and on ratio 4,00 so creeper enlarges overall gear ratio to 34,13. Although you wouldn’t need lowest speeds creeper enables more small step gears in field working speeds so it’s not a bad idea to add it to your transmission. For shifting this creeper unit you have to stop and do manual shift from tractor.
Using tip: If you find two stick shifts too difficult you can skip some gears. First upshift through gears 1-3 with left switch and then groups A-C with right switch. This way you get 5 powershift gears and easy operating. D. Ravigneaux Planetary Gear:
This one is a compound planetary gear called Ravigneaux.
Ravigneaux planetary gear has 4 parts: Small sun gear (SS), Big sun gear (SB), Planet carrier (P) with small planet wheels (PS) and big planet wheels (PB), and finally Annulus (A). Small sun gear meshes with small planet wheels, which mesh with big planet wheels. Big planet wheels mesh also with big sun gear and annulus. Big planet wheels sound a little bit stupid, because they have same number of teeth as small planet wheels. Big means here double thickness: big planet wheels have gear wheels both sides of planet carrier. Input varies between 2 sun gears, locking parts are big sun gear and planet carrier, and output is always annulus. This lego version has 3 gears plus reverse. Normally ravigneaux planetary gear has 4 gears, and top gear is an overdrive. That will require planet carrier as third alternative input and that is not possible in this lego version. You need 2 equations to calculate ratios: N(SB)+u(1)N(A)-[1+u(1)]N(P)=0 and N(SS)+u(2)N(SB)-[1+u(2)]N(P)=0, N means part’s rotation speed. Basic ratios are u(1)=Z(A)/Z(SB) and u(2)=Z(SB)/Z(SS) in which Z means number of teeth in current gear wheel.
D.1. Ravigneaux-like planetary gear set
This Ravigneaux-like planetary gear set differs a little from genuine Ravigneaux. Small sun gear (SS), big sun gear (SB) and small planet wheels (PS) of planet carrier (P) are like in previous Ravigneaux planetary gear. But big planet wheels (PB) contain 3 different gear wheels (PB1, PB2 and PB3) and “annulus” (A) is actually sun gear with idlers. These modifications allow to use planet carrier as 3rd alternative input so this gear set has 4 gears plus reverse.
Equations N(SB)+u(1)N(A)-[1+u(1)]N(P)=0 and N(SS)+u(2)N(SB)-[1+u(2)]N(P)=0 work like in genuine Ravigneaux. But basic ratios are calculated different way: u(1)=Z(PB1)/Z(SB)xZ(A)/Z(PB3)=20/16x16/8=2,50 and u(2)=Z(PB2)/Z(SS)xZ(SB)/Z(PB1)=12/8x16/20=1,20. Check Schematics to see ratio equations and ratios. Like in real Ravigneaux this version has 3 clutches (C1-C3) and 2 brakes (C4-C5). This time also brakes are modeled in pictures and LDraw file, they are made from clutches that are on locked axle. Building tips: Planet carrier axle has extra bush outside of the bricks, use it to locate planet carrier as rear as possible. Move also output axle a little bit rearward while thin bush allows to do it. These modifications should prevent collision problems between big planet wheels and rigid gear wheels. D.2. Lego version of Lepelletier planetary gear set
This version of Lepelletier planetary gear set has 6 gears plus reverse. It’s based on Ravigneaux planetary gear but it has also front planetary gear. Ravigneaux has 3 alternative inputs, which are small sun gear (SS), big sun gear (SB) and planet carrier (P), while annulus (A) works as output. The idea of Lepelletier is that planet carrier of Ravigneaux gets torque direct but there is speed reduction with front planetary gear before small and big sun gear. In front planetary gear annulus (AF) is input, planet carrier (PF) output and sun gear (SF) is always locked. Like Ravigneaux Lepelletier has only 3 clutches (C1-C3) and 2 brakes (C4-C5). Although Lepelletier has 6 gears made by 2 planetary gears it still has progressive gear steps.
In this lego version front planetary gear is same type as planetary gear ver III and in the rear is Ravigneaux-like planetary gear set. If you need more info about Ravigneaux-like check previous chapter. From ratio calculation equations Ravigneaux-like’s equations work directly but you need also equation for front planetary gear: u(F)N(SBF)-[1+u(F)]N(P)=0. Basic ratio for front planetary gear is u(F)=Z(PAF)/Z(SAF)xZ(SBF)/Z(PBF)=24/20x16/12=1,60. Check picture Real Lepelletier or Schematics to see ratio equations and ratios of gears. This time ratio equations are quite complicated but if you put basic ratios in equations and calculate carefully you should get right results. But to get those equations, that’s a different story... check Ratio calculation example 2 for 4th gear. :-) Like in Ravigneaux-like also this planetary gear set has brakes modeled in pictures and LDraw file. One interesting fact is that Lepelletier planetary gear set has no direct ratio and that’s not typical to planetary gear sets. Reason for this oddity is that in Lepelletier Ravigneaux planetary gear has direct ratio only when speed is reduced with front planetary gear. All in all Lepelletier is very effective way to get 6-speed planetary gear set with progressive gear step: it has only 2 planetary gears, 3 clutches and 2 brakes.
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