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Ari Holopainen / epicyclic | |
| PLANETARY GEARS Table of Contents: Foreword A. Basic Planetary Gear - A.1. How to use it? - A.2. 3-speed Torsen-Matic - A.3. 2 motors & planetary gear B. Planetary Gear Ver II - B.1. Planetary range-change unit, gear step 4,00 - B.2. 4-speed planetary gear set - B.3. 5+R-speed planetary gear set - B.4. 4-speed planetary gear set ver II - B.5. 6+R-speed planetary gear set - B.6. 4+R-speed planetary gear set ver III - B.7. 15+6R-speed planetary gear set for tractor - B.8. 3-speed semiautomatic - B.9. 2-speed powershift for tractor [Shortcut to A.-B.] C. Planetary Gear Ver III - C.1. Lego version of Simpson planetary gear set - C.2. Lego version of ZF Ecomat - C.3. Planetary driving direction changer - C.4. Lego version of Hydra-Matic - C.5. Lego version of Allison 1000 - C.6. 3-speed powershift for tractor - C.7. 3-speed powershift for tractor version II - C.8. 5-speed powershift for tractor REMAKE - C.9. 9+9R-speed full powershift tractor transmission D. Ravigneaux Planetary Gear - D.1. Ravigneaux-like planetary gear set - D.2. Lego version of Lepelletier planetary gear set [Shortcut to C.-D.] E. 3-speed planetary gear set from 2 diffs - E.1. Version I, centre differentials - E.2. Version II, standard differentials - E.3. Version III, 44%-56% centre differentials F. Gearboxes from single differential - F.1. 5-speed - F.2. 6-speed - F.3. 8-speed G. High Ratio Planetary Gears - G.1. Version I, i=84,00 (with double i=7056,00) - G.2. Version II, i=64,00 - G.3. Version III, i=144,00 (with double i=20736,00) H. Freewheel Clutch [Shortcut to E.-H.] Foreword Here are located planetary gears and gear sets. Different type of planetary gears are located under different letters (mainly in A-D). First is introduced planetary gear and then how to use it in different kind of planetary gear sets. Some of those gear sets are my own design but there are also lego versions of real world’s planetary gear sets. Also equations for ratio calculations are introduced. If you check through planetary gears (no need for all gear sets) you can also learn how to calculate ratios of real world’s planetary gear sets not just ratios of lego gear sets. In chapters E-F are differentials as part of planetary gear sets. Note that basic differential is also planetary gear. You can also get high ratio from single planetary gears and they are introduced in chapter G. Last chapter H introduces lego freewheel clutch which is not actually a planetary gear. But in real world freewheel clutches are used in planetary gear sets so that why it’s here. Many planetary gear sets use two 16 teeth clutch gears connected together at their dog clutch side. If they don’t stay together in use you have two options: Minimize the gap that clutch gears make by moving axle with bushes, check this fine tuning. If this is not possible you can try non lego methods like Blu-Tack.
A. Basic Planetary Gear:
Here is a “weird” Lego version of the basic planetary gear.
Please note that “basic planetary gear” is actually quite complicated construction. “Basic” means that there is only one planetary gear, not compound planetary gears like Simpson, Ravigneaux etc. Basic planetary gear has 3 parts: Sun gear (S), Planet carrier (P) with 2-5 planet wheels and Annulus (A) with internal teeth. Every part can be chosen input (3 choices), locked (2 choices left) or output (the last part) so you can get 6 different ratios with one planetary gear. If you connect any two parts together you get the 7th ratio, direct drive. When you calculate the ratios of the planetary gear you need to know the “basic ratio” u=Z(annulus)/Z(sun) in which Z means number of teeth in current gear wheel. In this lego case you’ve got Z(annulus)=22 and Z(sun)=8 so you have basic ratio u=11/4=2,75. You can calculate ratios with equation N(sun)+uN(annulus)-(1+u)N(planet)=0 where N means part’s rotation speed. This is universal equation for basic planetary gears. While locked part doesn’t rotate (N=0) and ratio i=N(input)/N(output) you get the equations of the next table. If you need to calculate ratios of planetary gear set check first ratio calculation example 3 for all gears of Simpson planetary gear set. Simpson’s calculations are easy but calculations can become quite complicated, check ratio calculation example for 3rd gear of ZF Ecomat or ratio calculation example 2 for 4th gear of Lepelletier.
While planet wheels mesh both sun gear and annulus there is one requirement which must be satisfied: sum of number of teeth of sun gear and annulus divided with number of planet wheels must be even number. This reduces significantly available basic ratios. In this lego case you’ve got (8+22)/3=10 so it works fine but with 2 planet wheels this structure won’t work while (8+22)/2=15. One notable thing is that this lego construction doesn’t use a normal annulus with internal teeth gear wheel. This is the reason why equation Z(annulus)=Z(sun)+2xZ(planet) is not satisfied in this case. But anyway, this lego version of planetary gears works well and can handle higher torque than a single gear pair. A.1. How to use it? And how to use this planetary gear? Easiest way is truck’s planetary hubs, in which sun gear is input, planet output and annulus locked. It gives you speed reduction after the differential, so differential parts don’t need to handle so much torque. One example to lock annulus is use technic axle pin. Put 1 plate between 2 bricks to get axle pin high enough and then move 1 stud sideways (1 LU; 4 HU), that’s proper place for axle pin that locks annulus. Other possible location needs 1 brick over brick and 1,5 studs movement sideways (1,5 LU; 3 HU).
Other structure is 2-speed torque sensitive automatic gearbox. In this case sun gear is input, planet output but annulus has freewheel clutch. Under light load planetary gear rotates as a single block and ratio is (almost) direct. When load increases annulus tries to rotate in the opposite direction, but freewheel doesn’t allow it. Now planetary gear works with ratio 3,75. The more friction planetary gear has inside it the longer it stays in direct drive gear when load increases. On the other hand the more friction planetary gear has the worse efficiency you have in lower gear. If you forget wheel model team as planet carrier and use technic wedge belt wheel instead, planet wheels will tilt a little under load which means more friction. Placing planetary gear near to motor and speed reduction after it means high rotating speed and low torque, so planetary gear again prefers direct gear. When planetary gear is near to driven wheels and speed reduction is before it, it will shift easier to lower gear. There is no shortcut to get right shifting balance, you have to test different combinations every time you build a new transmission. Note that freewheel works only in forward, you have to lock annulus other way to enable reversing. For next options you need to modify planetary gear a little. Replace annulus’s inner parts with two 16 teeth gears with clutch. Leave one of the gears outside of the annulus. To make planetary gear work smoothly put the chain treads (internal teeth) only half over the tire and secure it with rubber belt. Now you can use annulus as input or lock 2 planetary gear parts together to get direct drive. Now, third option is to build planetary splitter unit with gear step 1,36. In splitter annulus is input, planet is output and sun gear is locked to ground (ratio 1,36) or connected to annulus (direct drive). Fourth option is planetary range-change unit with gear step 3,75. Like in 2-speed automatic gearbox sun gear is input and planet carrier output. Annulus can be connected to sun gear (high range) or locked to ground (low range). Fifth possibility would be centre differential of 4WD car with unequal torque allocation. In this case planet carrier would be input and annulus and sun gear outputs. The problem is that only 4/15 of the torque would go to sun gear’s output and 11/15 to annulus’s output and that is too unequal. With basic ratio 2,00 or less planetary centre differential will have proper torque allocation. A.2. 3-speed Torsen-Matic
I have named this 3-speed transmission as Torsen-Matic which comes from words torque sensitive automatic transmission. It contains a compound planetary gear which is made from 2 basic planetary gears. Planetary gears are connected so that there are 4 parts: compound sun gears (S) as input, single annulus (A), compound annulus & planet carrier (AP) and single planet carrier (P) as output. It was a little bit tricky to get compound annulus & planet carrier.
Torsen-Matic is torque sensitive so driving resistance tells what gear it chooses and how fast you drive. Here is how it works: When you move off inertia means high load so both annulus and annulus-planet try to rotate in the opposite direction but there are freewheel clutches which won’t allow that. Between freewheels is lever arm (freewheel chooser) which allows only 1 freewheel clutch to be active. Lever arm is balanced so that freewheel clutch of annulus-planet locks first so you are in 1st gear (ratio 3,75). When you get speed driving resistance decreases and annulus-planet starts to rotate in the same direction as input but single annulus still tries to rotate opposite direction. So freewheel of annulus-planet jumps up and lever arm allows freewheel of single annulus to lock. Now you are in 2nd gear and ratio is 2,16. When driving resistance still decreases also single annulus starts to rotate in input’s direction and you get 3rd gear. Note that there is no locking in 3rd gear so there is some slip and ratio is not 1,00 but almost. If driving resistance increases while you drive in 3rd gear single annulus wants to rotate in the opposite direction so freewheel clutch locks it and you are back in 2nd gear. If driving resistance still increases comes problem: freewheel of single annulus locks 2nd gear tighter and there is no shifting to 1st gear. But if you break torque shortly inertia keeps vehicle going and single annulus rotates temporarely in driving direction. This means that freewheel of annulus-planet is free to lock so you get 1st gear when torque comes back. Note that freewheels don’t work in reverse so you have to lock manually annulus-planet for 1st reverse gear or single annulus for 2nd reverse gear. These lockings work also in forward driving so you can drive in single gear (1st or 2nd). For locking there is a shift lever which positions from rear to front are 1_D_2. There is a lot of fine tuning before you can use Torsen-Matic. First you have to build annulus-planet carefully to make it rotate smoothly. Then you have to test how much speed reduction you put before and after planetary gears: near to motor it prefers high gears and near driven wheels low gears. In freewheel clutches there are adjustable parts resting against lever arm. You have to adjust them so that only 1 freewheel clutch works at a time. Note that there are 2 technic pin 1/2:s and plate 1 x 2 with handles in freewheel clutches. And finally you have to test how much weight you put on the annulus-planet’s side of the lever arm. It ensures that move off happens with 1st gear and balances shifting between 1st and 2nd gear. Although it’s difficult to make Torsen-Matic to work properly I managed to get next features: When you moved off on the floor (flat terrain) Torsen-Matic started with 1st gear, shifted to 2nd gear for a short time before shifting to 3rd gear. While driving on the floor it stayed on 3rd gear. On the other hand on the carpet (rough terrain) Torsen-Matic drove on 2nd gear so both shift 1-2 and shift 2-3 were right balanced. A.3. 2 motors & planetary gear, 4 speeds
This is quite interesting design. It contains 2 motors and a planetary gear: 1st motor is connected to sun gear and second to annulus while planet carrier works as output. While single motor has positions forward, stop and reverse with 2 motors you get 9 different combinations. Because planetary gear’s basic ratio differs from 1,00 (now 2,75), using only sun gear motor gives different speed than using only annulus motor. It also means that rotating motors in opposite directions doesn’t stop output. So altogether you get stop, 4 forward gears and 4 reverse gears. Problem is that you need 2 battery boxes or 2 forward-stop-reverse switches to operate this system.
You get 1st gear (or speed) by rotating sun gear motor forward while annulus motor is stopped. Shifting to 2nd gear is quite complicated while you have to turn sun gear motor into reverse and annulus motor into forward. Then it is simpler while shifting to 3rd gear is stopping sun gear motor (annulus motor stays in forward). 4th gear and full speed is done by rotating both motors forward. Check speeds and ratios from picture called Ratios. Reverse gears are done by reversing everything written before (first rotate sun gear motor in reverse and so on). So this construction is a little bit difficult to use but this way you get 4 speeds in both driving directions with fully remote controlled shifting system. No stopping or shift lever movement is needed to operate this motor-gearbox combination. And all this because of versatility of the basic planetary gear. You can also add normal gearbox after this structure so you get multi-speed motor and gearbox combination. Building tip: put tight rubber belt around annulus to keep its parts together. B. Planetary Gear Ver II:
Here is another basic planetary gear, this time there is no annulus.
This planetary gear has 3 parts: Sun gear A (SA), Planet carrier with planet wheels A (PA) and planet wheels B (PB) and finally Sun gear B (SB). Like in basic planetary gear every part can be chosen input (3 choices), locked (2 choices left) or output (the last part) so you can get 6 different ratios with one planetary gear. If you connect any two parts together you get the 7th ratio, direct drive. When you build this make sure that sun gear axle A and planet carrier axle are perfectly coaxial, it’s easy to build misaligned. Basic ratio of this planetary gear can be calculated this way: u=Z(PA)/Z(SA)xZ(SB)/Z(PB), Z means number of teeth in current gear wheel. In this Lego case you’ve got Z(PA)=Z(SB)=16 and Z(SA)=Z(PB)=8 so you have basic ratio u=4,00. This time ratio calculations use equation N(SA)-uN(SB)+(u-1)N(planet)=0 where N means part’s rotation speed. It comes from basic planetary gear’s equation when you put negative basic ratio and use sun gear B as annulus.
There are three other basic ratios available in this planetary gear with this axle base. Check differentials and there F. Interaxle Differential and its 3 torque allocations. Back output is now Sun gear A and two 16 teeth gears with clutch are Sun gear B. With different distances between gear wheels there are many other basic ratios available. All possibilities are shown in next table.
1) Studless planet carrier, 1,5 studs sideways, 1 stud up 2) 2 studs sideways, 1 stud up (in brick planet carrier vice versa) B.1. Planetary range-change unit, gear step 4,00
Here is an example how to use previous planetary gear. This is a planetary gear range-change unit with gear step 4,00. Sun gear A is input, sun gear B is connected to output and planet carrier has 2 options: locked to ground (low range) or connected to sun gear B (high range). Note that there is normal gear pair after the planetary gear. It means that planetary gear has ratios 1,00 and 4,00 but total ratios of this range-change unit are 1,50 and 6,00. This arrangement is to prevent collision problems between planet wheels and output axle.
B.2. 4-speed planetary gear set
Planetary gear sets are used in automatic transmissions. Gears are activated with clutches and brakes, and every gear has different locking combination. Both locking combinations and ratio calculations are quite complex “science” so it’s not easy to design a new planetary gear set. Check ratio calculation example for 3rd gear of ZF Ecomat or ratio calculation example 2 for 4th gear of Lepelletier to see what I mean. For easier ratio calculations check ratio calculation example 3 for all gears of Simpson planetary gear set. N is part’s rotating speed and u is basic ratio. This lego version is a 4-speed compound planetary gear set, which has 4 parts: single sun gear A1 (named as A), compound planet carrier 1 & sun gear A2 (PA), compound sun gear B1 & B2 (BB) and finally single planet carrier P2 (P) as output. Both planetary gears has the same basic ratio 2,33. Gear set has 2 clutches (C1 & C2) which choose between inputs A and BB. It also has 3 brakes (B1-B3) which lock A, BB or PA. 2 parts of clutches and brakes must be activated to get a gear. Brakes are not modelled in pictures nor LDraw file so check Schematics picture link to get the idea where to put them. Schematics includes also ratios and how to get different gears. In pictures large pulleys are used as planet carriers but if you replace them with 40 teeth gears locking may be easier. If you need ideas how to make brakes check Gear set brakes from B.4. 4-speed planetary gear set ver II or Gear set brakes from E. 3-speed Planetary Gear Set From Two Differentials.
One notable thing is that you have to switch gears manually by engaging and disengaging clucthes and brakes, automatic gear shifting or simple shift lever manual shifting are too difficult tasks for me. Other thing is that this transmission has (almost) geometrical gear steps. It was too difficult to get progressive gear steps with available basic ratios of this axle base. Third note is that normally planetary gear sets are purely coaxial constructions but this lego version has a side axle. Coaxial structures require hollow axles and gears which are rare in lego world: 2 16 teeth gears with clutch connected together is one example. In theory it is possibly to build non lego coaxial version of this planetary gear set with help of hollow parts and part rearrangement, but it is a little bit tricky to get power flow from input to BB through PA. The trick is that in this planetary gear ver II same size in sun gears A and B makes ratio between them always 1,00 but planet carrier can rotate free although power goes through it. But anyway this is not a good example of real world planetary gear sets because they use planetary gears with annulus and need a reverse gear. B.3. 5+R-speed planetary gear set
This 5-speed plus reverse planetary gear set is based on previous 4-speed version so check it first before you go further. This version has same parts A, PA, BB and P. First planetary gear has basic ratio u1=2,33 but second one has basic ratio u2=4,00. With this arrangement I managed to get better ratios and gear steps. Now there are 4 clucthes (C1-C4) from which first 2 choose input between A and BB, and last 2 choose output between P and BB. There are also 4 brakes (B1-B4) which lock all parts A, PA, BB and P in turn. 3 parts of clutches and brakes must be activated to get a gear. 5th gear is an exception: it uses only side axle so you need only 2 clutches but no brakes to get the gear.
There is some progression in gear steps in lower gears but higher gears have geometrical gear steps. It would be possible to get 6th gear (overdrive) but some parts would rotate much faster than input so 6th gear would have bad efficiency in lego version. That’s why I abandoned 6th gear and was satisfied with 5-speed version. In planetary gear sets normally only 1 part works as an output. It reduces number of gears but makes structure simpler with less clutches and brakes. This lego version has 2 output possibilities so number of gears is more than in normal 2 planetary gear set. It also means too much clutches and brakes. With part rearrangement it is possible to build non lego coaxial version from this planetary gear set, but it needs 1 modification: it’s not possible to lock BB so you have to forget 1st gear and use the abandoned overdrive gear as 5th gear instead. B.4. 4-speed planetary gear set ver II
This version II has different distance between sun gears and planet wheels so it has new basic ratio u=3,00. Everything else in this planetary gear set is identical to previous 4-speed version, it has same gear parts, clutches and brakes. So check previous 4-speed planetary gear set before you go further.
There is an example how to make brakes for this gear set, check picture Gear set brakes. Essential is that rotation of brake coupling part (gear set part A) and planet carrier (PA) is limited but planet wheels can rotate free when brake is activated. In that picture brake B2 is active so part PA can rotate less than half a circle, other brakes and clutches are free. New basic ratio gives 1 advantage to previous version: this planetary gear set has progressive gear steps instead of geometrical ones. It gives better ratios, gear steps and overall gear ratio. One possible problem is that gear step 1-2 may be too large but it doesn’t matter in lego use. It is difficult to figure out this planetary gear set from first 2 picture links so remember to check Gear set parts picture link. In that picture all lego parts in 1 gear set part are colored with the same color and different gear set parts have different colors, it helps a lot to understand how to build this gear set. I have used 2 blade rotor parts as planet carriers and brake coupling parts but you can use also 3 blade rotor, it works as well. B.5. 6+R-speed planetary gear set
This 6-speed plus reverse transmission contains 2 planetary gears but parts are different than in previous planetary gear sets. 4 parts are: single planet carrier 1 (named as P), compound sun gears A1 & A2 (AA), compound sun gear B1 & planet carrier 2 (BP) and finally sun gear B2 (B) as output. First planetary gear has basic ratio u1=1,56 and second u2=2,50. Gear set has 3 clutches (C1-C3) which choose input between P, AA and BP. It has also 3 brakes (B1-B3) which lock P, AA and BP in turn. 2 elements of clutches and brakes must be activated to get a gear. Brakes are not shown in pictures or LDraw file so check Schematics to see where they are. If you need ideas how to make brakes check picture link Gear set brakes in previous chapter.
I have searched through all basic ratio combinations (same axle base on both planetary gears) and this version gave the best results. Although it has 6 gears gear steps are still progressive which is very difficult task in planetary gear sets. Ratios, gear steps and overall gear ratio (5,67) are good for 6-speed transmission. Also ratio of reverse gear is good. With part rearrangement it is possible to build non lego coaxial version from this planetary gear set, but it needs tricks to get power flow from input to AA through P. Only problem is that in many shifts you need to disengage and engage 2 elements each. For smooth and quick operation gear set should need only 1 disengagement and engagement each in every shift. B.6. 4+R-speed planetary gear set ver III
I could say this 4+R-speed version is final product in my planetary gear set developing. It contains all important features of planetary gear set: It has a reverse gear and progressive gear steps and only 1 part works as output. All clutches and brakes are included in this design and only 1 element of clutches and brakes has to be engaged and 1 disengaged during shifting.
This version contains same parts as previous 6+R-speed version and these parts are: compound sun gears A1 & A2 (named as AA), single planet carrier 1 (P), compound sun gear B1 & planet carrier 2 (BP) and finally sun gear B2 (B) as output. Basic ratio in first planetary gear is u1=2,25 and in second u2=3,00. Gear set has 3 clutches (C1-C3) and 2 brakes (B1-B2), but you need only 3 shift levers to operate this gear set while brakes are located with clutches. This combining is possible because you never connect gear set part to another and lock it to ground at the same time. Brakes are done by clutches and locked gears. Gear steps are good and progressive, and overall gear ratio 4,25 is also good. While axle base of the first planetary gear is 2,5 studs this gear set needs lots of idler gears to locate side axles far enough. This makes construction quite complicated but it was difficult to find proper ratios and gear steps so that you need only 1 engagement and disengagement each during shifting. This requirement of simple shifting is also the reason why this gear set has only 4 gears plus reverse. In theory it is possibly to build non lego coaxial version of this planetary gear set but it once again needs tricks to get power flow from input to BP through AA. Later I found out that there is more compact design available when you use studless planet carrier in first planetary gear. With basic ratios u1=1,875 and u2=2,50 overall gear ratio is smaller but ratios are good and gear steps are progressive. I haven’t modeled this design yet. But you can use this version III as model and check from earlier table which gear wheels new planetary gears need so you can build new more compact version before me. B.7. 15+6R-speed planetary gear set for tractor
Here is one more concept in my planetary gear set designing. This time I tried to get more complicated design with more gears than before. So this one is planetary gear set for tractor and has no less than 15 forward and 6 reverse gears. Idea is taken from full powershift tractor transmissions made by planetary gear sets like John Deere’s old 15+4R-speed. Lego version is not powershift but very complicated planetary gear set due to large amount of gears.
First is front planetary gear in which sun gear A (named as AF) is input, planet carrier (PF) locking part and sun gear B (BF) leads to clutches of next gear set. Next is 3 planetary gears combined together so that there are 5 parts: single sun gear A1 (named as A), compound planet carrier 1 & sun gear A2 (PA1), compound planet carrier 2 & sun gear A3 (PA2), 3 combined sun gear B:s (B) and finally single planet carrier 3 (P) as output. Transmission has 5 clutches and 5 brakes, and brakes are done by clutches together with locked gear wheels. You need to activate 3 elements to get a gear: one in front planetary gear and two in compound planetary gear. In theory you can get 20 forward and 6 reverse gears from this construction but all gears are not used while unused ratios will be too close to used ones. In this 15+6R-speed version ratios and gear steps in both driving directions are close to real world’s powershift transmissions, also overall gear ratio is good. While high gears have significant overdrive ratios they can have bad efficiency in lego world. 11th gear is direct so it has best efficiency. Some of the ratio equations look terrible due to complicated structure of compound planetary gear, check picture Data sheet. But if you put basic ratios into equations and calculate carefully you should get right ratios. And if you used this you’d have to print gear connecting table (picture Gear connections) that you could check how to get the gears. Real powershift tractor transmissions have sequential shift lever or up and down buttons so they are semi-automatic and very easy to use. So, all in all this lego structure is too large for lego tractor and too complex to use because it’s manual so it’s not worth to build. But it shows that it’s possible to build very complex lego planetary gear sets when you have patience to calculate ratio equations and test them to lego planetary gears with different basic ratios. One interesting detail is that you can build coaxial real world’s version of this planetary gear set (Non lego coaxial 15-speed) although it’s tricky to get both clutch and brake for sun gear B:s. B.8. 3-speed semiautomatic 2 motors & planetary gear ver II
Here is another motor-gearbox unit that uses 2 motors and a planetary gear. This gearbox uses planetary gear version II with basic ratio 1,43. Motor 1 is connected to sun gear A and motor 2 to planet carrier while sun gear B works as output.
This version has only 3 speeds but it’s easier to use than 4-speed version. Motor 1 orders rotating direction of output and motor 2 orders driving gear. In 1st gear motor 2 is rotated to different direction than motor 1. In 2nd gear motor 2 is stopped and in 3rd gear both motors rotate same direction. Check speeds and ratios from picture called Ratios. If you have extra forward-stop-reverse switch you need only 1 battery box and using this transmission is very easy. You choose driving direction with battery box and gear with that extra switch, check picture called Wiring. So this is 3-speed remote control shifted powershift motor-gearbox unit that doesn’t need stopping or shift lever movements during shifting. So this lego design is semiautomatic and it’s quite close to real world’s 3-speed conventional automatic transmissions. Building tip: Move planet carrier axle a little bit rearward by taking axle joiner slightly out from motor output. This is to prevent possible collision problems between planet wheels and idler gear. Small bush in the sun gear B axle allows to move it rearward too. B.9. 2-speed powershift for tractor 2 motors & planetary gear ver II
Here is simple 2-speed powershift for tractor. It contains two motors and planetary gear ver II with basic ratio 4,00. Design is quite compact while it uses large pulley as planet carrier. This is designed for my tractor transmissions that need 2-speed powershift with gear step about 1,33.
Motor 1 is connected to planet carrier, motor 2 to sun gear A and sun gear B is output. While this is only 2-speed design using is quite simple: For powershift stage low run only motor 1 and keep motor 2 stopped, this gives ratio 1,33. For powershift stage high run both motors in same direction, this gives direct ratio 1,00. Motors can be run in both directions but transmissions this powershift is designed for contain also reverse gears. My idea is to operate this powershift with two stick IR remote control unit. On the other hand you can use forward-stop-reverse switch (pole reverser) with battery box. These options are shown in picture Control unit. As an extra feature there is also creeping mode in both control methods: In remote control design you run only motor 2 and keep motor 1 stopped. This gives ratio 4,00 but there will be slipping under high load because motor 2 starts to rotate stopped motor 1. In battery box design you can use position reverse which gives ratio 2,00. Building tips: Put both planet wheel axles in same angle (not in mirrored angle) when assembling planetary gear, this ensures that planet carrier is completely aligned with sun gear A. To ensure that sun gear B’s two 16 teeth clutch gears stay together minimize gap in planet carrier axle by moving 16 teeth gear forward. Move also output axle a little bit rearward to prevent possible collision problems between it and planet wheels.
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 REMAKE 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.
E. 3-speed Planetary Gear Set From Two Differentials: E.1. Version I, centre differentials
Here is 3-speed planetary gear set which is made from 2 centre differentials. You can think differential (50%-50% torque allocation) as basic planetary gear with basic ratio u=1,00. I have named parts as they are used in differential use so they sound a little bit odd for planetary gear set. 4 parts are: compound front outputs 1 & 2 (named as F) as input of gear set, single rear output 1 (R), compound differential housing 1 & rear output 2 (DR) and single differential housing 2 (D) as output of gear set. This equals to planetary gear set made from 2 basic planetary gears with compound sun gears and compound annulus & planet carrier, while sun gears are input and single planet carrier output.
This planetary gear set has clutch C1 and brakes B1 & B2. Brakes are not modelled in all pictures or so check Gear set brakes for an example of two kind of brakes. Gear set parts or Schematics shows alternative positions for brakes. While F is always input you need to activate only 1 element of brakes or clutch to get a gear. When you lock one output of differential, use other output as input and take power out from differential housing you get ratio 2,00. It’s opposite situation of stuck car with only 1 spinning wheel, in that case stopped wheel causes other wheel to spin double speed. Using compound differentials gives perfect ratio (1,33) to 2nd gear so gear steps are progressive. Overall gear ratio (2,00) is too small but it’s near to 3-speed Simpson planetary gear set’s one. E.2. Version II, standard differentials
This version uses standard differentials. While basic ratio is same 1,00 also ratios and gear steps are same. Only names of gear set parts are different. This time 4 parts are: compound left axles 1 & 2 (named as L) as input, single right axle 1 (R), compound diff housing 1 & right axle 2 (DR) and finally single diff housing 2 (D) as output.
Also this version has clutch C1 and brakes B1 & B2. Brakes are not modelled in all pictures so check Gear set brakes to see one example about brakes and where to put them. Picture only shows locations so if you build this gear set brakes will need more support. Gear set parts or Schematics also shows where to put brakes, although brake 2 is in different location. E.3. Version III, 44%-56% centre differentials
This version III has same centre differential parts as version I so check version I if you need more information. Basic ratio is now u=1,29 which gives larger overall gear ratio (2,29) but reduces gear step progression. Brakes are shown in all pictures and LDraw file. Power flow is not included because it’s same as in version I.
F. Gearboxes From Single Differential: F.1. 5-speed
Here is an idea how to get 5 gears from single differential. Differential’s left and right axle are alternately connected to input axle or diff housing or locked to ground. Diff housing works as output. There is an underdrive ratio u from input axle to right axle and counter ratio 1/u from input axle to left axle. You need 3 clutches (C1-C3) and 2 brakes (B1-B2) to operate this system and you have to connect 2 of them to get a gear. Check picture Schematics to see available ratios and how you get the gears.
One interesting thing is that when you connect underdrive ratio u and overdrive ratio 1/u to right and left axle at the same time you could think you get a direct ratio. But it’s not direct, actually it’s most difficult ratio equation in this gearbox. F.2. 6-speed
I found an easy way how to expand previous 5-speed gearbox to 6-speed version. You need 2 modifications: Put 16 teeth gears for idlers in gear pairs that are from input axle to left and right axle. Then put new 2 stage ratio v from input axle to right axle. It needs gear pairs S’(16C)-Mu(20) and Su(12)-Mu(20) to get ratio 2,08. This ratio v is used for new 1st gear, other gears are straight from 5-speed version. Now there are 2 clutches in input axle (C3 & C4) so gearbox has altogether 4 clutches and 2 brakes. Check Schematics to see how to get the gears.
Overall gear ratio 5,21 is normal for 6-speed gearbox and gear steps are mainly progressive. So you can replace normal 6-speed gearbox with this differential gearbox although this version is more difficult to use. F.3. 8-speed
When you use 3 different ratios from input axle to left axle (ratio u2) and right axle (ratios u1 & u3) maximum number of gears is 8 for single differential gearbox. But I had to test different ratio combinations to get suitable ratios and gear steps. Gear steps and overall gear ratio (5,00) in this version are quite small so this is pure close ratio gearbox. Gear steps are also progressive except gear step 7-8.
Like other planetary gear sets this gearbox is more difficult to use than normal manual gearbox with H shift pattern. If you manage to develop simple sequential shifting system for this gearbox, let me now about it. :-) G. High Ratio Planetary Gears: G.1. Version I, i=84,00, (with double i=7056,00)
This is a single speed planetary gear which has as high ratio as 84,00. It’s done by old differential, but differentials are special purpose planetary gears. While there are normal gear pairs in this transmission, input and output axles should rotate in different directions. But they rotate in same direction so ratio is actually -84,00.
High ratio means also that gearbox’s efficiency is very bad, so this gearbox is not useful for vehicle use. With 4 XS(8)-M(24) gear pairs you get ratio 81,00 and it works much better than this planetary gear. And how do you calculate the ratio? With differential works equation N(diff)=[N(left)+N(right)]/2 in which N means part’s rotating speed. So output speed N(right)=2xN(diff)-N(left). Differential housing has speed reduction to N(diff)=8/28=2/7 and left axle N(left)=14/24=7/12. So we get N(right)=2x2/7-7/12=-1/84. If rotation speed of left axle is double compared to speed of differential housing, right axle doesn’t rotate at all. Now the ratios are close to this situation, so right axle barely rotates. But like in backgammon, “Let’s double, shall we?” So here is also double version in which high ratio planetary gear is used twice giving extremely high ratio 7056,00. This means that even fast 4500 r/min lego motor needs over minute to rotate output 1 round.
Note that this double version is coaxial structure so there are three separate axles in input/output line. Second 24 teeth crown gear is not in input axle but in left axle of second differential. Check picture Top view parts. G.2. Version II, i=64,00
This high ratio planetary gear has same principle as my planetary gear version II although this planetary gear has more gear pairs in power flow. Essential is that number of stages is even number (2 in planetary gear ver II and now 4). To get high ratio you need two things: basic ratio u is near to 1 and planet carrier is input while sun gears A and B are locked and output parts. Now basic ratio u=8/12x16/12x16/14=64/63=1,016 and planet carrier is input, sun gear B output and sun gear A locked. So ratio i=u/(u-1)=(64/63)/(64/63-1)=64 in sun gear B. Note that output axle’s direction is reversed (i=-64) due to normal gear pair.
You have to remember that efficiency is not good in high ratio planetary gears so this planetary gear doesn’t suit to lego vehicles. For example 3 stage spur gear gearbox that uses gear pairs XS(8)-M(24) and two times XS(8)-L(40) gives better efficiency and higher ratio (75,00). If you want reverse ratio from this planetary gear you can simply swap sun gear A to output and sun gear B to locked part. Then ratio i=1/(1-u)=1/(1-64/63)=-63. Building tip: Planet wheels have possible collision problems with frame and output axle so you need some fine tuning. Use bushes to move planet carrier a little bit to output axle’s direction, sun gear B (16 teeth clutch gears together) allows that. Then move also output axle away from planet carrier, output axle has half bush is for that. G.3. Version III, i=144,00, (with double i=20736,00)
Here is another high ratio planetary gear that uses differential. This time ratio is as high as 144,00. Again ratio calculations need equation N(diff)=[N(left)+N(right)]/2 in which N is part’s rotating speed. So we get for output speed N(right)=2xN(diff)-N(left). Input speed to differential housing is N(diff)=16/24x8/24=2/9 and to left axle N(left)=14/16x8/16=7/16. This gives output speed N(right)=2x2/9-7/16=1/144. Although this version III is more complicated than version I you can still put two of these version III:s together. This double structure gives extreme ratio 20736,00 which means that fast 4500 r/min lego motor needs over four minutes to rotate output one round. H. Freewheel Clutch:
Actually freewheel clutch is not a planetary gear, but they use freewheel clutches in planetary gear sets, that’s why this is here. Freewheel clutches are used to disable engine braking in lower gears for smoother driving behavior and to simplify gear connecting. This one is from axle to axle freewheel clutch. Earlier in Torsen-Matic I have used from annulus to ground freewheel clutches.
Easiest way to understand how freewheel clutch works is to think multi-speed bicycle. While moving in forward pedalling locks the freewheel clutch and torque is transmitted. When you stop pedalling rear wheel keeps rotating free while freewheel clutch opens. So in locking direction torque is transmitted through freewheel clutch but only if output doesn’t rotate faster than input. Output can’t rotate input. When you try to reverse bicycle pedals rotate free and no torque goes through. But if you move bicycle rearward freewheel locks and rear wheel rotates pedals. So in freewheel direction no input’s torque goes through the freewheel clutch, but output rotates input if input doesn’t rotate faster than output. In this lego version key parts are technic connector toggle joints. In freewheel direction they hit to chain treads in such angle that they bound back but in locking direction at least one of them grabs hold of chain tread and starts to rotate output with input.
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