|
|
|
Ari Holopainen / theory | |
| GEARBOX THEORIES Note equations:
Geometrical Gear Steps: Geometrical gear steps means that every gear step between two sequential gears is always the same, so for example in 10-speed transmission gear step 1-2 is equal to gear step 2-3, which is equal to gear step 3-4 and so on up to gear step 9-10. For more information check equations. That’s the theory, in practise gear steps are almost the same. Trucks need large overall gear ratio (15-20) which means great number of gears (9 or more) to prevent too large gear steps. With one main gearbox you can’t get enough gears so you need also splitter or range-change unit, or both. Splitter unit (small gear step) means that there are low (L) and high (H) version of each gear of main gearbox. Gears are in order 1L-1H-2L-2H-... so you have alternately easy splitter shifts without main shift lever movement and compound shifts with splitter and main gearbox. Range-change unit (large gear step) means that you go through gears of main gearbox twice in upshifting procedure, first in low range and again in high range. For example in 10-speed transmission first you shift through gears 1-5 in low range and then gears 6-10 in high range. In H shift pattern 1st and 6th gear are in same position, then again 2nd and 7th and so on. Both splitter and range-change unit require geometrical gear steps. If you drive constant mesh gearbox (not synchronized) you have to match speeds of gearbox parts manually by double clutching and engine rpm changes: First you press clutch pedal and disengage current gear. Next you release clutch and use engine speed to match speeds of gearbox parts. Then you press clutch again, shift to new gear and release clutch to complete the shift. You have to decrease engine rpm in upshifting and increase in downshifting. If gear step is for example 1,33, engine speed 1600 r/min and you upshift, desired engine speed is 1600 r/min / 1,33 = 1200 r/min (drop -400 r/min). Reversed with same gear step and engine speed 1200 r/min you get to needed engine speed in downshifting 1200 r/min x 1,33 = 1600 r/min (+400 r/min). This double clutching procedure is much easier when gear steps are all same so you know how much to decrease or increase engine rpm. Note that gear step is only a factor, absolute decrease or increase in engine speed depends on current engine speed. But geometrical gear step has a problem. Let’s assume that gear step is that same 1,33. When you drive 10 km/h and accelerate and upshift so that engine rpm is same as in previous gear, new speed is 1,33 x 10 km/h = 13,3 km/h, so speed increase is only +3,3 km/h. When you drive 70 km/h and do the same upshifting procedure, new speed is 1,33 x 70 km/h = 93,1 km/h (+23,1 km/h). This large difference in speed increases means that in low speeds when the acceleration is fastest you have to shift often, so often that you rather skip some gears. In middle gears transmission works fine but in high speeds when you need most power and acceleration is slowest you have only few gears. And this is not good. This means that gear steps in low speeds could be larger and gear steps in high speeds smaller. That is where progressive gear steps come in. Progressive Gear Steps: Progressive gear steps means that the higher gear the smaller gear step between gears. This is done by basic gear step (usually 1,1-1,7) and progression factor (1,0-1,2). Here is how it goes in 5-speed transmission: In gear step 4-5 there is only basic gear step. Gear step 3-4 is basic gear step x progression factor. Gear step 2-3 is basic gear step x (progression factor)^2. Finally gear step 1-2 is basic gear step x (progression factor)^3. For more information check equations. That’s the theory, in practice it’s not easy to get perfect progressive gear steps because number of teeth of gear wheels are integers. Other thing is that you change ratios a little when matching engine and gearbox. For example rapid increase in engine’s torque curve at the often used speed means difficulties to maintain constant speed. When speed decreases engine gives less torque and speed decreases even more and acceleration gives more torque so speed increases easily more than you want. Let’s go back to upshifting example. If gear step 1-2 is 1,80, you drive 10 km/h and do the same upshifting procedure, new speed is 1,8 x 10 km/h = 18 km/h (+8 km/h). If gear step 4-5 is only 1,20, you drive 70 km/h and upshift in the same manner, new speed is 1,2 x 70 km/h = 84 km/h (+14 km/h). Now speed increases are much closer to each other than in geometrical gear steps. This means that gears divide better through the speed range. But also gearbox with progressive gear steps has some problems. You can’t use either splitter or range-change unit with main gearbox that has progressive gear steps or at least progression must be very small. In splitter problem is that for example splitter’s gear step 1,18 splits equally only gear step about 1,40 but larger gear steps of lower gears will be splitted unequally. So in lower gears every other gear step will be small (splitter shifts) and every other gear step larger (compound shifts). In range-change unit problematical are middle gears: for example in 10-speed transmission gear step 4-5 will be as small as gear step 9-10 but in higher speed gear step 6-7 will be as large as gear step 1-2. You can make main gearbox with progressive gear steps but it works good in high range only: While gear step 6-7 can’t be too high, in low range gear step 1-2 will be a little bit too small. But problem won’t diminish during upshifting (like in geometrical gear steps) because gear steps get smaller and smaller due to progression so every gear step in low range is too small. So you’ll need gear skipping or low range will be just continuous shifting. In 8- and 9-speed transmissions (large gear steps) they often make a compromise so that gear step 7-8 (also 3-4 due to range-change unit) is smaller than the others. This helps to keep engine rpm in economic zone in different speed limits. These auxiliary adding problems means that maximum amount of gears is 7 plus reverse in manual transmission with progressive gear steps. There are 2 reasons for that. Firstly you can’t handle more gears with single shift lever and H shift pattern. Other thing is that main gearbox will become very large which means that some of the gear pairs will be very far from bearings and that is not good under high torque. This limited number of gears is not enough for trucks because gear steps in lower gears will become too large when you need large overall gear ratio. Automatic gearboxes (both conventional planetary gear sets and double clutch gearboxes with multiple countershafts) can have more than 7 gears with progressive gear steps. Comparison Between Geometrical And Progressive Gear Steps: Here is 2 diagrams which show difference between geometrical and progressive gear steps. Saw profile diagram shows engine speed and velocity in upshifting procedure when you accelerate to engine rpm of maximum power before upshifting. Traction diagram shows available traction for driven wheels in each gear. In table below links there are ratios that are used in diagrams.
Grey areas in traction diagram show the power you can’t get because engine rpm of maximum power doesn’t match to current speed in any gear. You need continuously variable transmission to get engine’s maximum power in all speeds or you need engine that can produce maximum power in larger area than in single engine rpm. Note that traction curve in 5th gear reaches to speed 250 km/h but the maximum speed is less because driving resistance (not shown in this picture) becomes larger than traction earlier. Conclusion: As long as number of gears is 7 or less best solution is progressive gear steps. When you need 8 gears or more solution is main gearbox with splitter or range-change unit and geometrical gear steps or small progression in gear steps. When you need 12 gears or more solution is main gearbox, splitter and range-change unit, with geometrical gear steps. Progressive-like Gear Steps In Truck Transmissions: There are also truck transmissions that try to imitate progressive gear steps. I call this progressive-like gear steps. First check 2 shift patterns of next link. 13-speed Eaton Fuller has 5-speed main gearbox (4+crawler) and 3-speed compound splitter/range-change unit. Reason why it’s progressive-like is splitter which is available in high range only. So in low range (gears 1-4) there is basic gear step and in high range (gears 5L-8H) number of gears is doubled and gear steps are halved. History of this transmission is in 3 gear pairs which create auxiliary. In early version they managed to get only 3 gears, so they had to abandon splitter in low range. Later they have rearranged gear wheels in auxiliary, so auxiliary has 4 gears and splitter is available in both ranges. New version has therefore 18 gears but Eaton hasn’t abandoned 13-speed transmission. More info about 13-speed transmission is in Eaton’s webpages. Scania’s 10-speed splitter-type transmission (GS771) is also progressive-like. Essential in that gearbox is swapped 8th and 9th gear. This arrangement brings halved gear steps in gear pairs 7-8, 8-9 and 9-10. Typical upshifting combination with this gearbox is (1)-3-5-6-7-9-10 so first you shift only with main gearbox (large gear steps), then in middle gears you use splitter and at least shifting 9-10 is done with halved gear steps. Under heavy load possible upshifting combination could be 1-3-4-5-6-7-8-9-10 so you start to use splitter earlier and use all halved gear steps. Halved gear steps are very handy compared to normal gear steps of 10-speed transmission. Problem in this transmission is too small overall gear ratio for heavy trucks. Also Scania’s 8-speed GR875 transmission for mid range trucks has progressive-like gear steps: 4 main gears has progressive gear steps together with large gear step range change. This arragement means that gear steps in low range are all too small without gear skipping but from range change and in high range there is nice progression in gear steps. For more info you can check Gear Step Diagram in Scania P250 brochure. [Back to main page] |
|
Primary content in this document is © Ari Holopainen. All other text, images, or trademarks in this document are the intellectual property of their respective owners. |
| |
©2005 LUGNET. All rights reserved. - hosted by steinbruch.info GbR |
