ICE to wheel transmission efficiency value at 60 mph

I dug this up for 'ya... http://serieshybrid.com/FreedomFormula/images/Drivetrain_Comparison.pdf

Hope it helps... Would love to learn as much as possible about all your research!

 

I know there were efficiency graphs created by I think bob wilson on various speeds.

The mechanical path is very efficient from the ice to the wheels with no belts for parasitic losses. IIRC there are just four universal gears. At your steady 60mph on a flat road the psd will generate power in mg1 which gets transmitted to mg2 and must go through another universal gear. I would guess this portion of energy would get around an extra 10%-15% loss. If you tell us the ICE rpm we can calculate what percentage of this power takes the electrical path, but to change this the only way is to change the gear ratio in the psd. That would make a different speed less efficient.

Why Prius can get 50 mpg even at constant highway speed? | PriusChat

Bob calculated 87% efficiency, but we need the speed of mg1 to calculate what it is at 60 mph, as efficiency varies with speed.

 

Bob thinks its fairly constant, and I think transmission efficiency changes with load. Bob is going to experiment on Saturday, so lets wait till he gets back, to see how the experiment goes. The rest is just IMHO.

The transmission efficiency should get better as mg1 revs fall, hitting a maximum at
MG1/MG2 RPM's (Scangauge) | PriusChat

MG1 = ( 18 / 5 ) * Engine - ( 143 / 145 ) * MG2



MG2 has a fixed ratio to speed, I think its
MG2 = 121 *speed
At 60 this would be
MG2 = 121 * 60 = 7260

. Lets say it works out to around
MG1 = 3.6 * ICE - 7160, that would mean the transmission is most @60mph efficient around 2000 rpm on the engine. Bellow that some power is generated in mg2 and sent to mg1 (over drive), above that some is generated in mg1 and sent to mg2 (lower gear). The software is likely to choose the point where the engine is most efficient though, as this has a bigger impact than transmission efficiency.

The transmission efficiency should be lowest at very low speeds, where power mostly goes - ice ->mg1 electricity->mg2.

Looking at transmission efficiency, you want to power from the battery at low speeds, then recharge the battery later. This would definitely be true <5mph, I'm not sure what the cutoff speed would be. The most the transmission efficiency can be is 92%, going through 4 gears, from bob's description. The worst case is going through 5 gears and electrical pathway, which can only take place when you start moving, that might be (.98)^5x.85 = 77%, but as soon as you get above a few miles an hour it should head towards that 92%.

It appears from bob's description, there are 3 gears after the psd, since the ratio is fixed, this could be replaced with one. That would make the transmission 4% more efficient, but there may be difficulty manufacturing it.

 

At home I have a SAE paper by a Georgia Tech engineer comparing the Toyota and two-mode transmission efficiency. He claimed the Toyota transmission was nonlinear with significant losses that the two-mode 'cured.' I could not fathom his analysis so I can't say it is accurate. But I agree it is an interesting area of study.

If there is a non-linear, efficiency change, I would expect to see it as an increase in transmission temperatures during times of inefficiency. So far, I haven't looked for this pattern because it is so difficult to quantify. My attempt to measure transmission oil temperature showed it takes about 20 minutes to reach a steady state condition. I made a drain plug with a thermistor to measure the oil temperature.

Bob Wilson

 

Bob, the heat will be in the electrical path, not the mechanical one, when it is less efficient, not in the transmission oil. GM's 2 mode transmission does appear more efficient, but couple that with a less efficient ice, and you get lower efficiency. The most efficient transmission is a single speed single gear, but that is rarely the most efficient system as the ice needs to operate outside its efficient range. The gen 3 ice, because it makes power at lower rpm, actually makes the tranmission more efficient than a higher revving lower toque engine.

Out of curiosity, what did he claim was the range of efficiencies of the prius transmission.

 

I will have to go back to the source paper. But thanks to Google, I found my posting about this paper:

But while looking for the paper at SAE, I found:

Going back to your question, what I found were claims in the first paper that are factually wrong. For example claiming a 15.6 kW loss at 80 mph in a 24 kW maximum, MG1-MG2 flow:

• (24-15.6 )/ 24 ~= 35% efficiency :: nonsense!

I am a great believer in having a good math model but sometimes you have to "look through the telescope" and this just buggers the imagination. We're talking a substantial heat loss with significant cooling issues.

Now the reason I measured the oil temperature is because it has always played a role in cooling the stators. In addition to conduction through the case, the oil is 'sprayed' on the stators and drips down to the pan. What I was looking for was the thermal change, how long it took to reach a steady state condition.

The ~20 minutes means a proper experiment will have to record the ambient temperature during the test to measure the dT. Then we can use both radiant and conductive loss formula to estimate the heat loss. However, there may be short-cut.

MG1 is sandwiched between the water cooled, thermostat controlled ICE and MG2, the fixed, convective cooled end. The ratio of MG1-to-MG2 temperatures would be a good indicator of heat flow by treating MG1 as connected to the constant temperature heat-sink of the engine (the thermostat opens more has heat load increases). Then run a series of 30 minute benchmarks at different speeds recording and plotting the MG1-MG2 temperatures. IF there is a non-linear, efficiency problem, we would expect to see MG2 temperatures climb higher than MG1 rather than hold at a fairly constant ratio.

Transaxle 'telescope'

There is another approach ... measure the electrical loads directly. Before I got my first Graham miniscanner, I had started testing use of clamped coils to measure electrical flow through MG1 and MG2. A soft core that passes through a coil makes a transformer with the AC flow of a conductor that passes through the coil. MG1 and MG2 are variable frequency, AC loads but two identical coils would be needed:

• high resistance load resistor - this measures the voltage
• low resistance load resistor - the ratio of this voltage to the high resistance should be proportional to current

Calibrate them on the bench and then install them in the car using 'glue' circuit, we should be able to read out power passing through a leg of MG1 and MG2. Direction would be solved by comparing the voltages . . . source will always be greater than sink. In effect, a clamp-on, power meter.

Motivation

Now I had the energy to do these early clamp-on experiments because I did not have a credible source of recordable engineering data (aka., Graham miniscanner.) But it will take a while for me to see value in measuring the electrical losses between MG1 and MG2. I don't see the payoff unless there is some 'knee' in the values that identifies an optimum solution. But my existing mph vs MPG charts would show that if it existed but since the NHW20, I have only found one knee and it is very minor.

Other than curiosity, I need to see some insight that this metric might provide that mph vs MPG charts don't. I'm not trying to be lazy, just practical use of my time.

Bob Wilson

 

It is tempting to think the torque and relative motion of MG1 to the transmission case means the amount of energy that flows over the bidirectional MG1<=>MG2 path varies relative to the mechanical path. Over time, I remember seeing proposals to drive the car to minimize MG1 rotation only to discover in reality this never happens.

In practice, MG1 will pass through 0 rpm with a momentary draw from the traction battery but in reality, MG1 'never sleeps' at 0 rpm. So I was looking forward to the paper "An Analytic Foundation for the Two-Mode Hybrid-Electric Powertrain with a Comparison to the Single-Mode Toyota Prius THS-II Powertrain" by Jerome Meisel, Georgia Institute of Technology, SAE 2009-01-1321, March 2009 in the hope it would provide a credible, math model to further understand these flows. It partially succeeded but also showed why it is so important to gather field observations to validate a math model.

Understand I have other criticisms with this paper and GM's recent announcement that they were dropping the two-mode transmission pretty well made half of this paper moot in the market place. But the graph that suggests variable power flow over the MG1<=>MG2 path and can be found in "Fig. 10 Power losses in the 2-MT and the THS-II transmissions power the Toyota Prius with (angular rotation) = 1500 rpm and 2500 rpm."

When you look at Figure 10, it looks like there are times when the MG1<=>MG2 power flow drops to zero but what is not shown is the role the traction battery plays by supplying the "missing power" while MG1 rotation reverses. In practice, MG1 flips between generator and motor modes, reversing the power flow and often rotation. For example:

This field data shows that normal and energy recirculate modes happen all the time across different ICE rpms and power. What you don't find are stable, MG1 running at zero power when the ICE is producing power (sampling errors not withstanding.) The reason for this is without power, either generated or sourced, there is no counter torque needed to pass mechanical energy through the power split device.

This efficiency chart shows the bi-modal operation:

The car flips between normal and "heretical" or what Toyota calls "energy recirculate mode" all the time. Note that there are "zero power" times on the MG1<=>MG2 path but they also correspond to no mechanical path power . . . there is no free lunch.

Now what is interesting is to see the mapping of energy recirculate mode:

In effect, energy recirculate mode is 'over drive' for the Prius, one side of the curves in figure 10 from the Meisel paper. It happens all of the time to put the ICE in a fuel efficient rpm and power mode. The increased ICE efficiency more than making up for any apparent loss in just the transmission.

Meisel's paper tried to model Prius transmission efficiency but sad to say, did not include field data. Worse, the narrow focus on just one part, the transmission electrical path, without accounting for the improved ICE performance left a big gap. As long as we never forget that ONLY 28% of the ICE torque and power passes through the electrical path and 72% via the mechanical path, the total transmission efficiency makes sense.

So using Graham miniscanner collected data, I generated the following ELECTRICAL ONLY PATH efficiency:

Using partial fractions and taking 80% as the measured electrical efficiency:

• (80% * 28%) + (98% * 72%) ~= 93% overall transmission efficiency

Note that I show a lower efficiency because I have also included the vehicle electrical overhead. A pure transmission efficiency analysis would omit vehicle overhead but real world Prius owners have to pay this 'tax' anytime the car is turned on.

The Meisel paper does a credible job of discussing one narrow aspect of Prius transmission performance relative to the two-mode. However, it fails to clearly show the total transmission efficiency and that is a shame. I agree that the discontinued two-mode transmission should be more efficient than the Toyota system. However, the paper does an excellent job of describing the discontinued two-mode.

GM in effect replaced the hydro-mechanical part of an automatic transmission with a 'power-split' device. Sad to say, they could not (or choose not) to figure out how to make it standard across all of their automatic transmissions. In pursuit of 'better efficiency,' it became too heavy and complex and as such, an opportunity was lost to improve their fleet, not just the heavy vehicles.

Bob Wilson

 

Remember the electrical path at low speeds is similar to selecting lower gears in a manual transmission. You would not try to start driving a manual transmission car in 4th gear. At higher speeds its locking out over drive, like deciding you don't want to use 5th gear on a manual. The key to the power ratio, is the ratio of speeds the electrical path should be
Power percent electrical = 28% x MG1/(0.28MG1 + 0.72ring) where MG1 and ring are the rpm at mg1 and at the ring gear shaft. When mg1 is acting like a motor an not a generator the sign is negative.

Since the prius is a fairly low torque application, the single gear ratio is fine. The gen III because of the choice of gear ratio and ice and motors, has a more efficient transmission at high loads, where the hsd has the highest transmission losses.

Yes, the two mode and toyota's multigear synergy drive are difficult to sell because of costs, not efficency. The Gen III implementation should reduce losses. Its interesting the bad part of the curve for hsd is high speed, low ice rpm, which means you are going fast either down hill or decelerating ;-), since we should not be in this situation a large percentage of the time, those losses will not result in large cumulative poor mileage.

 

I think the frontal area is 28 sq ft in the gen III. I would use 0.37 for engine efficiency, and 0.9 for drivetrain efficiency. I'm not sure, what are the experimental results at 60 mph and70 mph

 

Hi everyone

It is very interesting discussion. My numbers for the transmission efficiency are calculated using the method of this post Measuring GenIII Prius energy (power) flow with OBD | PriusChat

The power flow scheme that the OBD tells me for the point closer to 60mph (flat and stable speed) is next:



From my numbers, the transmission efficiency, comparable with other cars in which the 12Volt alternator is before the gearbox, is (7687 [PSD power to wheels] + 1040 [HybBattCharging] + 330 [12VoltSystem] ) / 11466 = 79%

Big hugs from Frank

 

Thanks Frank!

I need a little time to digest your numbers but one still stands out, the traction battery sink:

• 1040 W
• 659 W (other post)
• 777 W (other post)

These numbers seem a little high. I was used to seeing the sink and surge in normal driving and figured the heating was normal chemical and resistance effects.

Perhaps you might share over what time interval these data values were accumulated and typical sampling times?

Excellent work!

Bob Wilson

 

I read that as power going to the electrical system, I have no idea how much it is.

The battery can source 27kw, it should be able to sink much more than 1KW (charge) for a while. As it charges I would expect it to slow or stop It makes it hard to figure out how much of the electrical losses are in the eCVT versus going to the electrical loads of the car.

I would guestimate about 550 w would be the electrical losses going between the motors (eCVT losses), the rest would be for charging or other electrical systems. That would give 1863w losses in the ecvt according to the diagram, from 11466 ICE power. This should give a transmission efficiency of 84%. It is lower than I would expect but in the balpark.