## THE SPLIT TORQUE PRINCIPLE

General Motors used lockup clutches in some torque converter bus transmissions, but GM’s early passenger car automatics went a different path, obtaining some of the benefits of the lockup clutch through a novel application of a principle called “split torque.”

As some readers already know, in addition to providing direct drive, reduction and/or overdrive gearing, a planetary gearset can also be used as a differential, either splitting a single source of torque along two paths or combining two torque inputs into one. GM engineer Oliver K. (“O.K.”) Kelley applied the latter concept to the original Hydra-Matic as a way of reducing slippage in certain gears.

To understand the Hydra-Matic’s split torque arrangement, it’s important to first review a couple of basic points about the transmission’s unusual mechanical layout. In the early Hydra-Matic, all power flowed through the intermediate shaft, which was driven by the planet carrier of the front planetary gearset and drove both the fluid coupling impeller (the driving torus) and the hub of the rear multi-disc clutch.

This meant that **the impeller always rotated at intermediate shaft speed**, which was not necessarily the same as engine speed. The torus cover, which was bolted to the engine flywheel, drove the front oil pump and the annulus of the front planetary gearset at engine speed. However, if the front brake band was engaged, it locked the front unit sun gear so that the rotation of the annulus forced the planet carrier to orbit the now-stationary sun gear at reduced speed. This also multiplied engine torque; with the front brake engaged, intermediate shaft torque was equal to engine torque times the ratio of the front gearset.

In first, second, and reverse, there was no torque split. The intermediate shaft still drove the rear clutch hub, but with the rear clutch disengaged, the hub just spun idly. Therefore, all intermediate shaft torque was applied to the impeller and then hydraulically transmitted to the turbine, the main shaft, and the sun gear(s) of the rear planetary gearset.

In third and fourth, the rear clutch engaged, which locked the rear clutch hub to the rear brake drum, forcing them to turn with the intermediate shaft. Since the drum was affixed to the annulus of the rear planetary gearset, the annulus now also rotated at intermediate shaft speed.

However, the intermediate shaft was *also* still driving the fluid coupling impeller, which continued to transmit torque to the turbine and the main shaft to the rear sun gear(s). Therefore, **intermediate shaft torque was now split between the rear sun gear (through the coupling and the main shaft) and the rear annulus (through the rear clutch)**. The rear gearset’s planet carrier acted as a differential, combining those torque components and applying the result to the output shaft. O.K. Kelley likened this arrangement to a series parallel electrical circuit.

## CALCULATING THE TORQUE SPLIT

Since the intermediate shaft was simultaneously driving both the rear sun gear and the rear annulus any time the rear clutch was engaged, **intermediate shaft torque was divided between those gears**. The proportion of that split depended on the gears’ respective numbers of teeth and thus their gear ratio.

When torque was applied to the sun gear, the inertia of the output shaft (which was affixed to the planet carrier of the rear planetary gearset) exerted reaction torque on the annulus, attempting to turn it backward. However, with the rear clutch engaged, the annulus couldn’t turn backward because the intermediate shaft was driving it forward. The annulus therefore became a reaction member, multiplying the torque the sun gear applied to the planet carrier.

At the same time, the torque on the annulus and the inertia of the output shaft exerted reaction torque on the sun gear. Again, the sun gear wasn’t free to turn backward since it was being driven forward by the main shaft. Therefore, the sun gear also acted as a reaction member, multiplying the torque the annulus applied to the carrier.

In both cases, the torque applied to each gear had to be sufficient to overcome the reaction torque on that gear. Otherwise, the gear would resist and potentially stall the engine.

This may become a little easier to grasp if we apply some actual numbers. Let’s consider, for example, the earliest Model 180 Hydra-Matic, the version offered in 1940–1942 Oldsmobiles. That transmission’s rear planetary gearset had a single sun gear with 45 teeth and an annulus with 69 teeth. With the sun gear driving, the rear clutch disengaged, and the rear brake engaged, the rear gearset had a ratio of 2.53:1 (1 + 69/45).

With those gears, the rotation of the sun gear and the resistance of the planet carrier applied reaction torque to the annulus at a ratio of -1.53:1 (0 – 69/45) — that is, they attempted to turn the annulus backward at about 65% (100% / 1.53) of sun gear speed. To overcome that reaction torque, therefore, the annulus had to receive 1.53 times as much torque as the sun gear did.

Since the annulus and the sun gear were both driven by the intermediate shaft, the sum of the torque on the annulus (let’s call it T_{A}) and the torque on the sun gear (which we’ll call T_{S}) had to equal the torque on the intermediate shaft (T_{I}). So, in mathematical terms:

**T _{I} = T_{S} + T_{A}**

Since we also know that:

**T _{A} = T_{S} * 1.53**

Therefore:

**T _{I} = T_{S} + (T_{S} * 1.53)**

… which simplifies to:

**T _{I} = T_{S} * 2.53**

We can then solve for T_{S}:

**T _{S} = T_{I} / 2.53**

… and calculate the percentage of intermediate shaft torque applied to the sun gear:

**100% / 2.53 = 39.47%**

The percentage applied to the annulus is therefore:

**100% – 39.47% = 60.52%**

As we mentioned above, each gear acted as a reaction member, multiplying the torque the other gear applied to the planet carrier. However, **each gear was receiving only a portion of the input torque, so only that portion was multiplied**. In this case, torque applied to the sun gear was multiplied by 2.53:1 (1 + annulus teeth / sun gear teeth, or 1 + 69/45). With the annulus driving, the gear ratio was 1.65:1 (1 + sun gear teeth / annulus teeth, or 1 + 45/69), so torque on the annulus was multiplied by that amount.

Both the sun gear and annulus were acting on the same planet carrier, so the torque the sun gear applied to the rear planet carrier and output shaft (let’s call it T_{C}) had to be the same as the torque the annulus applied to the carrier. Or, in mathematical terms:

**T _{C} = T_{S} * 2.533 = T_{A} * 1.652**

As we determined above, the torque on the sun gear (T_{S}) was 39.47% of the total, and 39.47% times 2.533 (allowing for rounding) is 100%. The product of the torque on the annulus (T_{A}) was 60.52% of the total, and 60.52% times 1.652 is also 100%. Therefore, output shaft torque (T_{C}) equaled 100% of intermediate shaft torque. That meant that output shaft torque also equaled the sum of torque on the sun gear and torque on the annulus, or:

**T _{C} = T_{S} + T_{A}**

Again, in older Hydra-Matic transmissions, intermediate shaft torque was not necessarily the same as engine torque. In third gear, the front brake band was engaged, so intermediate shaft torque was equal to engine torque times the ratio of the front gearset. In an early Hydra-Matic, the front annulus had 54 teeth and the front sun gear had 24 teeth, so with the annulus driving, the gear ratio was 1.44:1 (1 + 24/54). In third, therefore, intermediate shaft torque (which again we can call T_{I}) was engine torque * 1.444. Torque on the rear annulus (T_{A}) was 60.52% of that, or about 87.4% of engine torque (1.444 * 60.52%). Torque on the rear sun gear (T_{S}) was 39.47% of intermediate shaft torque, or approximately 57% of engine torque (1.444 * 39.47%).

For example, if the engine were generating 150 lb-ft (203.4 N-m) of torque, third gear would divide and multiply that torque as follows:

**T _{I} = 150 lb-ft **[203.4 N-m]

*** 1.444 = 216.7 lb-ft**[293.8 N-m]

**T**[177.8 N-m]

_{A}= T_{I}* 60.52% = 131.1 lb-ft**T**[116 N-m]

_{S}= T_{I}* 39.47% = 85.5 lb-ftTorque on the rear carrier and output shaft (T_{C}) was therefore:

**T _{C} = 131.1 lb-ft **[177.8 N-m]

**+ 85.5 lb-ft**[116 N-m]

**= 216.7 lb-ft**[293.8 N-m]

The overall ratio in third, therefore, was 1.44:1 (216.7 / 150).

In fourth, the front band was off and the front clutch was engaged, so intermediate shaft torque equaled engine torque. If engine torque were 150 lb-ft (203.4 N-m), fourth gear would divide that torque as follows:

**T _{I} = 150 lb-ft **[203.4 N-m]

*** 1.00 = 150 lb-ft**[203.4 N-m]

**T**[123.1 N-m]

_{A}= T_{I}* 60.52% = 90.8 lb-ft**T**[80.3 N-m]

_{S}= T_{I}* 39.52% = 59.2 lb-ftTorque on the output shaft was therefore:

**T _{C} = 90.8 lb-ft **[123.1 N-m]

**+ 59.2 lb-ft**[80.3 N-m]

**= 150 lb-ft**[203.4 N-m]

… and the overall ratio in fourth was 1.00:1 (150/150).

## DEMULTIPLYING SLIP

Once you’ve finished recoiling from this unwelcome flashback to algebra class, you may be muttering, “What exactly is the point of all this? And what does it have to do with fluid coupling slippage?”

In the early Hydra-Matic, **the main shaft was hydraulically driven**: It was splined to the fluid coupling turbine. Therefore, the speed of the main shaft and rear sun gear were always reduced by slip within the coupling, causing them to turn slower than the impeller.

**The intermediate shaft was**, so while there were frictional losses, there was no slippage as long the rear clutch was functioning properly.

*mechanically*drivenThis meant that with the rear clutch engaged, the rear annulus was always rotating faster than the rear sun gear. In mathematical terms, the velocity of the annulus (let’s call it V_{A}) had to be greater than the velocity of the sun gear (V_{S}). The rear planet carrier “resolved” this speed difference — that is, rotation of the faster-moving annulus forced the carrier to orbit the slower-moving sun gear at some intermediate speed.

The velocity of the carrier and output shaft (let’s call it V_{C}) was proportional to the ratio of the planetary gears and the speed *difference* between the annulus and sun gear:

**V _{C} = V_{S} + ((V_{A} – V_{S}) / (1 + sun gear teeth / annulus teeth))**

For example, let’s suppose that a 1940 Oldsmobile equipped with Hydra-Matic is cruising in fourth gear at an engine speed of 2,500 rpm. Let’s assume for the sake of illustration that the fluid coupling is 96% efficient at coupling stage. Discounting mechanical losses, we can therefore assume that the turbine and main shaft rotate at 96% of impeller speed, or 2,400 rpm. The intermediate shaft rotates at impeller speed, which, since the front gearset is in direct drive in fourth gear, is 2,500 rpm.

With the gearing we described above (i.e., a rear sun gear with 45 teeth and a rear annulus with 69 teeth), we can calculate carrier speed as follows:

**V _{C} = 2,400 + ((2,500 – 2,400) / (1 + 45/69))**

… or:

**V _{C} = 2,400 + (100 / 1.65) = 2,460.5 rpm**

In other words, the annulus rotating at 2,500 rpm will force the carrier to orbit the sun gear at a speed of approximately 2,460.5 rpm. This reduces *effective* hydraulic slip from 100 rpm (4%) at the turbine to about 39.5 rpm (about 1.6%) at the output shaft.

To be clear, **this arrangement can’t and doesn’t prevent the coupling from slipping**. Think of it rather as a slippage rebate: Hydraulic slip still occurs, but you regain some of the lost rpm in the planetary gears. In this case, the split torque layout reduces the slippage-related speed difference between the engine and the output shaft by about 60.5% — which, not coincidentally, is the percentage of intermediate shaft torque that flows through the mechanical connection to the rear planetary gearset. Kelley’s patent disclosures described this effect as *demultiplication* of slippage.

This demultiplication effect was not limited to cruising speed. As long as this transmission remained in third or fourth, the partial lockup reduced slip by 60.5% even under acceleration, when the fluid coupling was significantly less efficient.

For instance, let’s suppose the Oldsmobile driver presses the accelerator to pass. Fluid clutches tend to lag a few beats behind the engine in situations like this, so if instantaneous engine speed rises to 3,000 rpm, instantaneous turbine speed might be only 2,600 rpm. In fourth gear, carrier and output shaft speed would therefore be:

**V _{C} = 2,600 + ((3,000 – 2,600) / 1.65) = 2,842.1 rpm**

This would reduce total slip (excluding mechanical losses) from 400 rpm (13.3%) at the turbine to about 157.9 rpm (5.3%) at the output shaft.

The split torque arrangement also improved engine braking — particularly in third gear, when the braking effect was further multiplied by the front gearset.

One drawback of this arrangement was that the rear planetary gearset was always planetating (that is, the planet gears were turning relative to their carrier) even in top-gear cruising, which incurred more mechanical (frictional) losses — and potentially more noise and vibration — than a conventional direct drive arrangement where the planetary gears all turn at exactly the same speed. The reduced hydraulic losses more than compensated, but a true direct drive top gear with a fully mechanical lockup clutch would have been even more efficient.

Still, you can see why GM’s corporate engineering team decided that wasn’t necessary. The split torque arrangement provided many of the benefits of a lockup clutch without sacrificing desirable fluid coupling advantages such as freedom from lugging and the ability to soak up powertrain vibration.

As Kelley explained in his patent disclosures, the split torque layout essentially allowed Hydra-Matic to have different fluid coupling characteristics in each gear. The coupling could be “loose” in the lower gears, allowing more slippage for smoother takeoffs and less creep at idle, because the split torque layout would effectively make the coupling “tighter” and more responsive in the higher ranges. Since the partial lockup was limited to third and fourth, there was no risk of stalling the engine at idle and therefore no need for the additional hydraulic controls a lockup clutch would have required. (Additional mechanical complexity was the last thing the early Hydra-Matic needed!)

GM’s Detroit Transmission Division, which built Hydra-Matic, used this layout for all single-coupling four-speed Hydra-Matic transmissions. The actual proportion of the torque split varied with the gearing of each application — for instance, Dual-Range Hydra-Matics, whose rear gearset had a single sun gear with 41 teeth and an annulus with 67 teeth, had a torque split of 62%/38% in third and fourth — but the effects and benefits remained substantially the same.

Well Aaron . . another masterpiece. This and the GM automatic history are probably the most definitive descriptions of these technologies on the Internet, excepting pure design and engineering treatises. Well done and thank you; this must have been an enormous amount of work.

I have yet to read this monumental work in depth. Whether it will add to my working knowledge is debatable, but my brain will benefit from the workout.

Aaron is probably now the best informed person in the world regarding the history of automatic transmission development

I appreciate the compliment, but I’m really not! This is a remarkably broad, convoluted, and idiosyncratic field and there’s a LOT I don’t know. For people who want a broader overview, I would recommend a book by Philip G. Gott entitled

Changing Gears: The Development of the Automotive Transmission, published by the SAE as part of their Historical Series in 1991. (At this point, an updated, expanded edition wouldn’t go amiss, given all the subsequent development in CVTs and automatics with five or more speeds.)