Tuesday, September 29, 2009

(Trans)Mission: Possible

In our second installment of automotive tutelage, you’re going to get the shaft. A couple of them, in fact. The drivetrain of a car is full of ‘em: crankshafts, camshafts, input shafts, output shafts, drive shafts, halfshafts, etc. We’re going to focus on the inner workings of a manual transmission (aka: tranny, gearbox, four-on-the-floor): the Input/Output shafts between the crankshaft and the driveshaft.

Before we dive in, let’s discuss purpose. The purpose of any transmission is to use the limited rpm range of your engine and power band to achieve higher speeds and better efficiency. If you’ve ridden a bicycle with gears, you know that lower gears are used for lower speeds, that higher gears are for higher speeds, and that you have to progressively shift through different gears to maximize your own power. You cannot start off in the highest gear and expect to get up to speed quickly nor can you stay in the lowest gear and expect to get anywhere quickly. Gearing makes use of your momentum and allows you to effectively use your power in a comfortable manner. Simplistically speaking, it takes the same power to go 0-5 as it does from 5-10, 10-15, etc. because you just keep adding to your momentum – just like pumping your legs on a swing. OK?

Okay. The difference between your bike gears and a car’s manual transmission is just how they’re laid out – a bike uses a chain and a derailer to go from gear to gear; a car’s gears mesh continuously and are engaged/disengaged to shift. Your front bike gear with the pedals is akin to the tranny’s Input shaft and the rear sprocket on your Schwinn is comparable to the Output shaft. The size in relation to one another is the gear ratio, expressed as output:input. So, if your front sprocket has 17 teeth (or cogs) on it and the rear has 34, the gear ratio is 34:17, or 2:1. (Figuratively equivalent to 1st gear on a mountain bike.) Here’s where it gets a little tricky: you have to interpret the numbers in the ratio as a gear reduction to come up with something meaningful – a 2:1 gear ratio means that every rotation of the output will require two rotations from the input or every rotation of the input results in 1/2 rotation of output. Think about riding your bike in first gear – your legs are rotating much faster than your tires are and, if you actually look at the gears, you’ll be on the smallest sprocket in the front and the largest in the rear – the lowest gear ratio. Progressing through your set of gears, the highest gear you have will relate to the largest front sprocket and the smallest in the rear. This difference in cog counts is exactly what’s going on in your car’s transmission. Replace your legs with an engine and the back tire with a driveshaft and the analogy is complete.

Lab Exercise: In a three gear situation, you have first at 3:1, second at 2:1, and third at 1:1. At 1000 rpm input, these numbers would relate to 333 rpm, 500 rpm, and 1000 rpm respectively. You can see that at the same input, your output is getting faster and faster as the gear ratios are getting larger and larger. Now, if third gear was 0.99:1 (or anything less than 1), your output will be spinning faster than your input and you are now in ‘overdrive’. Overdrive just means that the diveshaft is spinning faster than your engine – a 0.85:1 overdrive would result in 1176 rpm in the example above.

Advanced Lab: Since the differential has an internal gear ratio associated with it, your transmission’s output does not directly relate to your tires' speed. You may have heard of 411 gears, this just means that there’s an additional gear reduction of 4.11:1 in your differential, so at 1:1 in your transmission, it would still require 4.11 rotations of your engine (and transmission) to move your tires one revolution. Since the tires come in many different sizes, another calculation would be required to translate tire rotation to actual MPH (one of which is 2πr, or the circumference of a circle).

Real-World Lab: (The math portion of the lesson is almost over). What would your speed be in 1st, 2nd, 3rd, and 4th at 2500 engine rpm on a stock 1967 TR4A/IRS? Doing some research, you find out that the gear ratios of the TR4’s gearbox are:
First: 3.14:1
Second: 2.01:1
Third: 1.32:1
Fourth: 1.00:1

This would relate to the following output rmps at 2500 engine rpm:
First: 796 rpm
Second: 1244 rpm
Third: 1894 rpm
Fourth: 2500 rpm

Assuming a 3.70:1 rear (differential), the following would be the corresponding tire rpm:
First: 215 rpm
Second: 336 rpm
Third: 512 rpm
Fourth: 676 rpm

Now, given the original tire size of 5.95-15, this relates to an overall radius of approximately 12.75 inches, or a circumference of 80.11 inches. This means that for every rotation of the tires, they will move a distance of 80.11 inches. Since we have the distance per rotation and the rotations per minute, we can come up with total inches per minute and, with some additional math, miles per minute and, finally, miles per hour. As useless as it seems, the answers to the question are:
First: 16.3 MPH
Second: 25.5 MPH
Third: 38.8 MPH
Fourth: 51.3 MPH

What does it all mean? In theory, using the same amount of work from your engine, you can travel over 50 miles in an hour rather than just 16. Correlating this to when you start in the highest gear on a bicycle, the car would have to work very hard to get up to 50 MPH if it only had 4th gear.

I think the horse is dead so I will stop beating it. What you’re really interested in is how that gearbox works. You know that moving the gearshift around changes the gears but the rest is shrouded in mystery. Well, Sir, knowledge is about to be dropped.

Forgetting about Reverse gear for a moment, and remembering that the gears in a manual transmission have a constant mesh, it’s not a tough jump to imagine four sets of gears with varied sizes, approximately being of size that would allow for the ratios described above.

Now, looking at the same gears on their side (so we can arrange them inline), you see that you can have the gears described above rotating in pairs along two common axi (is that even a word?).

Taking it a step further and replacing each axis with a shaft will give you four geared pairs and constant mesh. Keep in mind that the gears are not fixed to the shaft yet so each pair is free to rotate independently.

We now move the pairs close together and assign labels to the shafts – ‘Input’ for the side connected to the motor and ‘Output’ for the side connected to the rest of the drivetrain. The pairs are still free to rotate on the shafts.

Making it a little more useful, we now affix the upper gears to the Input shaft. This is typically accomplished by having a splined shaft. We haven’t done anything to the Output shaft yet, so if, let’s say, the engine is running at 2500 rpm, the Input shaft will be rotating at the same speed, the Output gears will be rotating at various speeds (see below), but the Output shaft will stay dead.

Adding something to the Ouput shaft, specifically synchros, will give us a way to ‘engage’ the gears one at a time. Shown here, the transmission is figuratively in Neutral. The synchros can slide back and forth and there is a mechanism there on each surface to engage a gear when they meet. So, with no gears engaged, everything is still spinning with the exception of the Output shaft, as shown.

Finally, we shift into first. Neglecting clutching for our example, only the first gear is coupled to the Output shaft through the synchro and it’s spinning at almost 800 rpm.

So, we have the engine at 2500 rpm, the power is going through the Input shaft, meshing with the Output gears, first gear is engaged, thereby powering the Output shaft at 796 rpm, going through the differential to do more math and the car is cruising at 16 or so miles per hour. Let’s switch to second.

Now we’re at 25+ MPH. Third.

Approaching 40 MPH, the tranny’s output shaft is humming at almost 2000 rpm and we switch to fourth.

I think you get it. Wrapping up the lesson, the clutch is a mechanical link between the engine’s crankshaft and the transmission’s Input shaft. Along with mechanisms in the synchros and the gears themselves, the clutch’s job is to disengage power to the Input shaft so that switching from gear to gear doesn’t result in grinding. (By the way, since the gears are in constant mesh, grinding is not actually your gears but is rather from synchro to gear malignment.)

Oh, and as for Reverse, there’s an additional ‘idler’ gear that slides into place, reversing the direction of the Output shaft, seen here:

One last diagram of the actual TR4's gearbox. Looking from the top, the Output shaft is above the Input shaft (so the Input shaft is hidden), the clutch/engine would be to the right and the driveshaft/rear would be to the left. The 'mechanisms' that interact between synchros and gears are also seen here - they're called 'Dog Teeth' of all things.

May I squeeze in a final tidbit of information? If you notice, the Reverse Gear and Idler are straight-geared and the rest are angled. The angled gears reduce noise and mesh better than the straight ones. You've all heard the whine when you go in reverse - that's from the straight gears! Why not use angled for Reverse? That Idler would have a hell of a time sliding in and out if it were angled.

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