By on July 8, 2014

T56_Magnum_1

In the automatic transmission racket, there have been new layouts and power flows galore lately. Your humble author has done a few articles detailing some of the more common designs in the North American market place, with the notable exception of the Aisin design. The design of a RWD manual transmission, on the other hand, is conceptually largely unchanged from the earliest 3 and 4 speed designs like the venerable M22 Rock crusher.This is not to say that RWD manual transmissions have not changed over the decades. The number of gears and torque capacities has increased, shift efforts have gone down, refinement has increased, which are all good things. This article provides some insights into the gear design and sizing for some of the more recent manual transmissions.

T56_Magnum_2

A RWD manual transmission consists of an input shaft, a counter shaft, and an output shaft (also referred to as the main shaft). The input shaft is connected to the engine through a friction clutch, while the output shaft is connected to the drive wheels through a final drive gear and a differential. The counter shaft is rigidly connected to the input shaft through the input gear set. It spins opposite to the input shaft in all gears, and counter to the output shaft in all forward gears. The input shaft and the output shaft are almost always coaxial. For heavier duty applications, there can be more than one counter shaft to increase load capacity. The basic components and operation of a RWD manual transmission are explained in great detail below.

For the uninitiated, this video explains manual transmission operation very well. It is 24 minutes long, and  many of the B&B  will need to pause this video a few times, but any time you spend understanding this video is time well spent. With that out of the way, let us get to the gear design, specifically the first gear.

The torque capacity of a gear set is determined by the following design parameters.

  1. Center distance between the main shaft and counter shaft (more is better for torque capacity)
  2. Face width of the gears (more is better for torque capacity)
  3. Helical angle of the gears (Does not make as much difference as 1 and 2, but generally speaking less angle is somewhat better)
  4. Gear ratio (Numerically lower is better for torque capacity, which is one of the reasons why the Corvette ZR1 has a 2.29 first gear ratio)
  5. The pressure angle of gear set (Complicated, it balances the contact life of the gear with the tooth root life)

The center distance of the TR6060 is 85 millimeters. Face width is 30 millimeters for the first gear (up from approximately 26 millimeters in the T56). The helix angle appears to be around 25 degrees, but as stated earlier it does not have a big impact on the torque capacity so the exact value is not as important. The TR6060 is offered in several first gear ratios, for the purpose of this article, we will focus on the Corvette Z51 first gear ratio, which is 2.97:1. The gear ratio is achieved in two steps. The first step is ratio between the input shaft gear and the counter shaft gear (38 teeth driven and 29 teeth driver), the second step is the first gear set (43 teeth driven, 19 teeth driver) for an overall gear ratio of (43*38)/(29*19) or 2.9655. One thing to note is that of the 4 gears, the number of teeth on 3 of them are prime numbers (43, 29, and 19) while the fourth one (38) is a multiple of a relatively large prime number. This is done to ensure that every teeth on a given gear meshes with every other teeth of mating gear the same number of times to maximize the operating life. With even-number-tooth gears, the same teeth tend to come into contact again and again, exacerbating potential issues.

Some of the essential gear nomenclature is shown in the figure below

There are two failure modes for a gear with no quality issues. The flank can exhibit surface scuffing and/or pitting if the contact pressure is too high or the lubrication is inadequate. Alternately, the tooth can break off at the root fillet due to excessive bending stress. Any given tooth root is essentially a cantilever under bending. There are several different methods to size gears: there are excellent AGMA standards, many different commercial software packages specifically meant to design gears, and Finite Element Analysis. Finite Element Analysis (or FEA) breaks down the geometry into several “elements” of a finite but small size. The underlying physics is solved for in each domain to assemble a stiffness matrix (and for dynamic problems a mass matrix as well), and the stiffness matrix is then solved for stresses in the part. We are going to use FEA to analyze these gears because in the humble opinion of the author, FEA is the most accurate of all design methods for gears provided it is done right.

For the rated 600 lb-ft torque capacity, the first gear set has to carry approximately 780 lb-ft. If the 43T/19T gear pair was a spur gear with “standard” gear design parameters with a 20 degree pressure angle, the stress contours for the gear design are shown below. The stress numbers are in MegaPascals or Newtons of force per square millimeter of area.

baseline_spur

The surface contact stress is well within the limits of what is generally accepted for gear steels, while the tooth root bending numbers are a tad high. You, the driver, would be limited to about 150 miles of driving at rated torque of 600 lb-ft in first gear, which is actually quite a bit of useful life. (Autocrossers beware! — JB) 700 MPa or 100 ksi is widely accepted as the cyclical endurance limit of good quality gear steels with proper heat treatment. The root fillet of the drive gear tooth is where we see the highest tensile stress of approximately 700 MPa or 100 ksi. But since the torque going through this gear set is mostly in 1 direction (except for engine braking or missed shifts into 1), the 100 ksi limit is a little conservative because for situations where tensile and compressive loads are not equal, there is approximately a 20% safety margin at the rated torque level. This correction in life is known as the Goodman correction, and it increases the life by a factor of 2 to 2.5. Therefore for this simplified spur gear set, the design life increases to approximately 400 miles at the rated torque of 600 lb-ft.

A simple way to improve the performance of this gear set is to make the 19T drive gear circular tooth thickness a little higher, at the expense of the thickness of the driven gear tooth, to “balance” the stresses in the two gears. This is also a good idea because the smaller drive gear sees more stress cycles per tooth than the larger drive gear anyway. The gear design shown above is also not practical because there is no lash between the gears, which is generally a bad idea for manufacturability of the parts among other things. The results for a modified gear are shown below

rackshifted_spur

It may be hard to tell from the stress contour, but the changes in the circular tooth thickness reduced the fillet root bending stresses by approximately 5 percent, increasing the margin in the design to approximately 25%, which gets the design life close to 500 miles in first gear at the rated engine torque of 600 lb-ft.

Now obviously the gears in a TR6060 are not spur gears, they are helical gears. If I had a large computer to run analyze the helical gear geometry, it would not be a big deal to analyze the gear geometry with the helical angle thrown in, but as it stands I have a laptop that does everything well except for number crunching. A helical gear obviously has higher loads acting on the gear teeth because of the additional axial thrust load. In other words, the gear isn’t just being turned, it is being shoved in a direction based on the angle of the helical gears. Think of it like a screw that doesn’t go anywhere. But a helical gear also has better contact ratio, i.e. more teeth in contact. In my experience, the difference in stresses between a well designed helical gear set and a spur gear set is less than 10%, unless the helix angle is very large (hence the caveat well designed).

Based on what I see in the TR6060 design, the first gear has a margin of approximately 20%, i.e. even though the rated torque is 600 lb-ft, it should be possible to run 700 lb-ft through the gears themselves. For the remaining forward gear sets (2 through 6), the diameter of the drive gear gets larger, which means that the stresses in the gear drop dramatically. For the second gear at maximum torque, for the spur gear geometry the stress contours are shown below. The fillet root stress is only about 550 MPa, or 80 ksi. A good quality gear steel with the correct heat treatment can deal with this level of stress for a long long time. With appropriate modifications, the 2nd gear has a margin of well over 50 percent, i.e. a life of at least 2000 miles at 600 lb-ft engine torque. (Autocrossers rejoice! — JB)

t56_2nd

 

For fifth and sixth gears, the design margin is usually well over 100 percent. The reason for this is the very high number of revolutions that these gear sets see under load. A 75,000 miles of durability in sixth gear with a 3.42 axle ratio and the usual range of tire sizes translates to 200 million stress cycles on the gear teeth. Therefore it is best to leave sufficient design margins for fifth gear and above.

Of course the TR6060 is often used in applications with only about 450 lb-ft of engine torque with this 2.97 first gear. In that case, the design life is much higher than the figures presented in this article. I would estimate that with a bone stock set up, the first gear will easily last 1200 miles or approximately 12000 WOT launches, the second gear is going to be good for at least 7000 miles, while other forward gears essentially have infinite life.

DISCLAIMER: I HAVE NOT looked at the bearings and the shafts, for these might very well be the weak link in the system, so if your transmission explodes @ 700 lb-ft of torque please do not hunt me down.

The purpose of this article is to provide the B&B with a glimpse of what goes into designing little parts that make up a whole car. Hopefully this article did meet the stated goals.

Acknowledgements: All the finite element analysis in this article has been carried out using a package called GGGears. This is a wonderful open source analysis package, though it is rough around the edges. The commercial equivalents cost a lot of money, GGGears does more than half of what the commercial packages do, and it costs nothing. More importantly, the source code is there for you to look at. Free as in freedom, and free as in beer.

helical

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39 Comments on “Saturation Dive: Manual Transmission Gear Design...”


  • avatar
    7402

    Awesome article. Best TTAC series ever. Keep up the good work.

  • avatar
    LeMansteve

    Very cool!

    I can tell you from experience, the bearings in the manual transmission for Honda’s D16Z6 engine will last approximately 100k miles. Probably more if you don’t do any cold launches.

  • avatar
    patman

    “The design of a RWD manual transmission, on the other hand, is conceptually largely unchanged from the earliest 3 and 4 speed designs like the venerable M22 Rock crusher.”

    Not only that, they practically are still M22 Rock Crushers, just with a fifth and sixth gear tacked on the end of the case – you can still plainly see the vestigial remnants of the old 4 speed boxes when you look at a five or six speed descended from the old classic musclecar 4 speeds.

  • avatar
    Da Coyote

    Great stuff. More, more!

  • avatar
    msmitka

    I’m not a gearhead (pardon) but as a judge for an auto supplier innovation competition (Automotive News PACE Awards) I’ve seen a few technologies, one aspect you don’t address is NVH. Here the prime number of teeth helps, whereas an even number begs for harmonics. I assume that harmonics also mean tooth wear and possibly amplified stresses and hence shorter life.

    One neat trick is to pseudo-randomize gear geometries so that the same point on each gear face doesn’t make the initial contact. This has to be at a very, very small “irregularity” but it then lessens the 19-times-a-rotation contact “click” with perfectly machined gears.

    My recollection is that such “phased” teeth (do I have the jargon right?) are easiest to do in-mold with powdered metal gears (Stackpole developed this).

    Anyway, a followup post would be nice! – I’m sure you have additional issues you could share.

    • 0 avatar
      Timur Apakidze

      I will be honest – NVH is not my area of expertise. Since all gears in a TR6060 (and most other transmission designs that I know of) are helical gears, by design the whole gear flank does not make (or leave) contact at the same time. There are profile and lead modifications dialed in, usually to account for system deflection and what not, but these modifications are very much deterministic and not at all random.

      For straight cut gears I can see pseudo-random gear geometries of being some value, but helical gears are several orders of magnitude quieter than spur gears in terms of absolute sound pressure level.

      Powder metal gears have applications in applications that don’t quite see the torque or the pitch line speeds these gears see.

  • avatar
    Felis Concolor

    That cutaway was too easy: my mind shouted “Tremec!” before I even registered the shifter location bracket.

    Back when I first started reading about power building and transmission mods, the practice of shot peening gear and case components was frequently mentioned as a means of removing stress risers along with smoothing machined surfaces to improve overall contact, reduce wear and improve the handling of shock loads. Are today’s steels or machining procedures obviating the need for such treatments?

    • 0 avatar
      Timur Apakidze

      Oh shot peening is still pretty much alive and well for helical gears. I bundled all of the heat treatment steps into the catch all “proper” heat treatment.

  • avatar
    brkriete

    Great article – very easy to read and interesting to see the analysis.

    I assume the limited life of lower gears (e.g., 600 miles) is acceptable because the car is generally only driven a few dozen feet in first gear at a time.

    • 0 avatar
      LeMansteve

      The gear life in the article assumes you are constantly applying the rated torque of the gearbox, which in this case is 600ft-lbs. Obviously we don’t always drive around giving max torque to the gearbox all day long, so the life of the gears are increased further.

      • 0 avatar
        Timur Apakidze

        Correct – all the quoted distances in this article are at full rated load.

        Besides even though the manufacturer rates this transmission to 600 lb-ft, the OEMS tend to use the 2.97 gears in less than 450 lb-ft applications. That increases the life of first and second gear substantially. I would take a gander and say in the Corvette Z51 application, there is at least 1200 miles at the full 450 lb-ft engine torque in first gear. That is a lot of driving around in first gear @ maximum engine torque.

  • avatar
    Instant_Karma

    This is the kind of article that interests me far more than stuff about infotainment systems and nitpicking the quality of interior plastic, such things aren’t completely trivial but I see them as secondary to the nuts and bolts of what makes a particular car motivate itself.

  • avatar
    epsilonkore

    Now THIS is a great article!

  • avatar
    carrya1911

    Fantastic article with a very cogent explanation of what could be a very complex topic. Well done.

    …although from now on I’ll be thinking of how long I leave my Accord in 1st and 2nd gear.

    • 0 avatar
      05lgt

      That short life isn’t just in 1st and 2nd gear, it’s in those gears at max torque. Unless all your starts are at full transmission rated torque you’ll get a lot more life. Even a rental doesn’t get to do all it’s starts like it was the drag strip, and even then; what are the odds that the engine can deliver the transmissions limits?

    • 0 avatar
      cronus

      Raw torque or fatigue are rarely the cause of gear failure. Usually the cause is impact loading, like if the suspension is bouncing under full throttle the tire will spin, then grab, then spin again. The inertia of the drivetrain will give a force that is several times the output of the engine.

  • avatar
    schmitt trigger

    Excellent in-depth analysis. Probably a little dense for the great unwashed masses, but if one has had some technical training, these articles are awesome. Keep them coming

  • avatar
    NeilM

    Great article. The video, on the other is is [cough, snork, hack] painful to watch in the extreme.

  • avatar
    Johnny Canada

    An, “unwashed mass” here, who really enjoyed this.

  • avatar
    Beerboy12

    I imagine an automatic gear box’s gears are designed much the same way.

  • avatar
    celebrity208

    The angular rotation of the input shaft is constant. However, as the contact-point/torque-transfer-point moves from the face to the flank doesn’t the angular rotation imparted onto the output shaft oscilate above and below the mean which occurs when the contact point is coincident with the interface between the face and the flank. If memory serves me correctly (likely not true) this was a significant area of research (by a limited few SMEs) in gear design at the turn of the century. True?
    If I’m right about the imparting of a high frequency oscilation into the trans parts because of the speeding up/slowing down/speeding up/… as teeth engage and disengage, to what level is this assessed during gear/transmission design?

    Regardless of whether what I just said has any merit, I must concur with the masses that I too love this series. May I suggest other components that I believe are likely up your alley: “Saturation Dive: Torque Converters” or “Saturation Dive: Differentials”.

    Thanks,
    -celeb.

    • 0 avatar
      Timur Apakidze

      Without going into too much detail – both gears have involute profiles, which means that if the gears are in an idealized mesh there will be no variation in the output speed for a given constant input speed. But the ability to manufacture gear forms with high dimensional accuracy means that the only significant sources of speed variation in the drive line are engine firing pulses and high angle universal joints.

      The small deviations from the idealized gear mesh lead to speed variations that are minuscule, but it shows up as noise.

  • avatar
    dal20402

    This makes me feel good about dishing out my car’s full 415 lb.-ft. of torque to its TR6060. But the weak link is certainly the clutch, not the transmission…

  • avatar
    JMII

    Any info on synchros and how they fit into the puzzle? My ’03 350Z Touring has already eaten one 6 speed manual box due to bad synchros and is slowly chewing away on box #2. The early Zs were know for this weakness as they only had 2 synchros “double cone” for 1st and 2nd. Thus 3rd gear grinding is a common problem. In newer models they finally starting putting triple cones in there which beefed them up (so I’m told).

    Also any advice on fluid? My transmission shifts much better (less notchy, smoother, less grinds) once its warmed up, so I should look at lighter weight blend? My research also indicates to only use GL-4 fluid which is safe for yellow-metal (brass) gears and avoid the newer GL-5 stuff for my particular tranny.

    For the record I track my car so I am pushing it way harder then “normal” use, but I’m dead stock so its not some built monster.

    • 0 avatar
      Timur Apakidze

      Sorry, don’t know anything about the Nissan transmission design philosophy. But if the synchronizers are getting chewed up, could it be that the clutch is not releasing all the way causing them to burn up? If you could post some pictures of the synchros it might be possible to make a judgement call. There is a possibility that Nissan undersized the synchros but that is not very likely in my opinion.

      You could also try the usual aftermarket fluids that the forum members have tried with success?

    • 0 avatar
      Lou Wambsganss

      I have had three Nissan 5-Speed manuals (FS5W71C) in trucks. They like a slightly thinner oil. I use Redline MT-85. It is a 75W85, instead of the more common 75W90.

      • 0 avatar
        JMII

        Some of the guys on the Z forums are mixing two different weights to come up with “hybrid” that the transmission seems to like. I was just looking for general information on why these synchros seems to sensitive.

  • avatar
    wmba

    Great primer article. I’d like to see more about the forces driving the gears apart, and their influence on the main and countershaft diameter, and subsequent case design. Deflections there can cause the teeth to not mesh the same every revolution and mash the bearings as well, if not held in check. You could easily have great gear design and a poor case trying to hold things in alignment, failing to do so and leading to failure. In the field, they’d blame it all on the gears when it is actually a case problem.

    Anyway, keep these articles coming. They’re really good.

    • 0 avatar
      Timur Apakidze

      There is a good 7000 lbs of force forcing the 1st gear set apart @ 600 lb-ft input torque. Therefore the first gear set is placed as close to the bearings as possible to minimize the bending moment on the shaft.

      To your point – the 7000+ lbs of force needs to be properly managed in the case. But with modern die casting technology, aluminum cases can both be lightweight and strong. Computer Aided Design is used extensively to design the transmission cases quite extensively.

  • avatar
    ravenchris

    Thanks again.

  • avatar
    gakoenig

    Nice meshing in the FEA. NX?

    • 0 avatar
      Timur Apakidze

      The FEA mesh is an automated mesh generated using gmsh. GGGears uses gmsh in the background to do the FEA mesh. Start to finish, the whole analysis takes 2 hours or so.

  • avatar
    Lou Wambsganss

    Thanks for this article! This kind of stuff is much more interesting to me than the minutiae of GM’s Chinese sales numbers.

  • avatar
    tp33

    Superbly written and highly informative article. Kudos to you, sir.

    Given the relatively low shelf life of the lower gears, it’s little wonder “city miles” tend to age a vehicle so much sooner. When I worked in Chi-town (but lived in NW Indiana) I’d regularly log dozens of “expressway” miles every week barely crawling above second gear. Minimal engine load to be sure, but it still makes me wonder just how much harder these bumper-to-bumper miles can be on a car. What would be the “highway miles” equivalent of 50,000 stop-and-go miles be, in terms of wear and tear on the tranny? 100K? 150K?

    • 0 avatar
      Timur Apakidze

      If you are running in first or second gear at less than half of the rated torque, the gears have essentially infinite life. Of course crawling on the highway is not easy on the clutch, the synchros, etc.

      So at minimal engine load, your gears are fine when you are crawling down I-94 in Chicagoland. Your brakes, your engine oil etc not so much.

    • 0 avatar
      jhefner

      You spend more operating hours in stop-and-go traffic in lower gears; but as Timur explained, unless your method of driving in traffic is to stomp on the throttle followed by stomping on the brake, the wear and tear at near idle conditions is minimal.

    • 0 avatar
      tp33

      Roger that. Thank you both. Glad to hear I wasn’t doing any real damage while building up my hulk sized left calf :)

  • avatar

    I still don’t understand why would not they just take a planetary set based transmission, then link the shift lever to oil valves. Put clutch instead of TQ, of course. Voila, torque capacity, no synchros.

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