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Ari Holopainen / epicyclic1 | |
| 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.
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