2010 Prius 2ZR-FXE engine efficiency map

Discussion in 'Gen 3 Prius Technical Discussion' started by ken1784, Jun 1, 2009.

  1. sipnfuel

    sipnfuel New Member

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    It is very hard to say because the only figures that I have is that MG2 peak power is 80 hp (60 kW) and peak torque is 153 lb-ft or 207.4 N-m, max RPM is 13500

    I have no idea if 153 lb-ft is an overtorque condition. I assume 153 lb-ft is the direct output of the motor at the output shaft.

    Most motors are constant torque, which means that the same torque is available at all RPMs (even if it is not used). However, you can overtorque a motor, that is run it out of spec at lower RPMs, for a while without damaging it. I believe MG2 is liquid cooled, so it is likely it can be overtorqued at low RPMs. I'm not sure how this applies.

    Also MG2 is a hybrid Permanent Magnet Induction motor. The characteristics of a pure induction motor is easier to describe (it would be constant torque up to a certain RPM). For MG2, I don't know if available torque is different across RPM, it depends on how it is driven by the motor's drive (electronics).

    However, if you want to accept that 153 lb-ft is not an overtorque condition, and treat MG2 as an induction motor with 100% efficiency, then you can Toyota's figures to make some crude calculations. This will assume 153 lb-ft is available at 80 hp.

    The formula is:
    P (kW) = Torque (N-m) * 2 * Pi * RPM / 60000

    Solution is:
    RPM = 60 kW * 60,000 / 207.4 / 2 / 3.1415 = 2762.6 RPM

    Below this RPM, the same torque is available, but voltage & power is lower. Above this, torque goes down because Voltage is limited to 650 V, power is limited to 60 kW (in reality it is the current that is limited).

    Torque (N-m) = 60000 * P / (2 * Pi * RPM)

    So at 4,000 RPM
    Torque = 60000 * 60 / (2 * 3.1415 * 4000) = 143.2 N-m = 105.7 lb-ft

    At 13,500 RPM
    Torque = 60000 * 60 / (2 * 3.1415 * 13500) = 42.4 N-m = 31.3 lb-ft

    However, the above calculations use a lot of assumptions, and don't factor in other losses.

    Perhaps someone else can chime in with better info.
     
  2. pakitt

    pakitt Senior Member

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    sipnfuel - thanks for the useful info - with the assumptions one could theoretically draw a torque vs. rpm curve - the problem though is that there is a reduction gear from MG2 to the wheels and there is a conversion factor of the ICE rpms in the PSD, which I don't know - that is, if the ICE is spinning at 4000 rpm, what is the actual speed of the wheels? And does the torque vs rpm have to do with wheels speed (no!).
    But if you want to combine the torque vs rpm chart of the MG2 and the ICE, can you use the same rpm axis? - if that is the case, this is what I got, reconstructing the ICE curve by looking at the torque charts I have seen here posted - it looks a bit weird....
    In my chart I get 133kW at 5200 which is clearly wrong...it means that the kW generated by the MG2 at higher rpms should be going down and not be still at 60kW (which is what I needed to use in your formula though to get the torque - which seems reasonable).
    The kW values in the spreadsheet are calculated using the formula you mentioned.
     

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  3. sipnfuel

    sipnfuel New Member

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    The gear reduction ratio is 2.63 : 1
     
  4. sipnfuel

    sipnfuel New Member

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    To answer your other questions, the wheels are connected to the PSD by the ring gear. MG2 is also connected to the ring gear.

    So the wheel speed and MG2 RPM are directly related by a fixed ratio. This makes it easier to describe pure EV mode.

    The ICE is connected via the Planetary carrier. The ICE gives 72% of its torque to the wheels, and the other 28% to MG1. MG1 converts this torque to electricity, which after conversion is fed to the batteries, or MG2. However, this 72/28 split seems to be the maximum. It can be that the ICE gives 100% to the wheels and 0 to MG1. It depends on whether MG1 needs to generate electricity.

    MG1 is the sun gear. It is the element that balances the other two. It can spin forwards, or not at all, or backwards to keep the wheel speed (Ring Gear / MG2) compatible with the ICE's RPM.

    Keep in mind that even if MG1 is not spinning, it can provide a torque, although it is not providing any power (HP = 0 because RPM = 0). This is not as odd as it seems, remember electric motors can provide torque from 0 RPM to its max RPM.

    Don't forget that the ICE can not provide any torque at about below 1000 RPM. It can spin there, but it won't burn any fuel.
     
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  5. Tideland Prius

    Tideland Prius Moderator of the North
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    Now I'm curious sipnfuel, whether what you've describe is one reason Toyota is able to offer a traction control similar to the one found in their regular vehicles? A higher max rpm and the overtorque function means that the wheel can be allowed to spin before the traction control kicks in compared to the older Prius where the electric motor is more susceptible to damage if the wheels spin.
     
  6. sipnfuel

    sipnfuel New Member

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    I'm not sure.

    When the wheels are spinning without traction, it is high RPM, low torque. This means in the motor applies a high voltage, low current. Then when it suddenly gains traction, since the car is not moving, the wheels suddenly come to a stop (it has gripped the road finally). This generates a torque on the wheels opposite in direction to which they were spinning, which is what slows them down. This torque is transmitted to the PSD, where it is absorbed by its components.

    In a traditional ICE / transmission, there is a mechanical connection from the wheels to the engine. The inertia of the engine probably absorbs most of this. In an automatic, probably the torque converter absorbs most of it.

    In an electric motor, basically the rotor in the motor is spinning, and then all of a sudden it is not spinning. The rotor is not mechanically connected to the stator. It is only linked electromagnetically. So actually this instantaneous torque is not transmitted mechanically, but electromagnetically, in the form of a high current spike. This is because rapidly changing magnetic flux generates an EMF. This spike goes through all the windings in the motor and back to the electronics. Most likely it doesn't reach the electronics because of fuses and diodes. The motor probably heats up for a split second, then the rest of the motor acts like a heat sink and absorbs it.

    If TC is disabled, you can probably do this once nothing bad would happen. Do it 5 - 10 times in 1 minute and you can burn the motor. Actually, you do this as few as 10 times an hour and you can destroy the motor's insulation.

    The current spike produced is actually proportional to the torque generated. So I think if you produce like 1500 lb-ft of torque backwards on the tires, you sent something like 1000% of the current rating into the motor.

    The electronics are super fast, so it can detect this and power off before. Basically by killing the circuit, the current blip can not flow. The reason this can occur is the electronics can shut off in a microsecond, but the current blip will take longer (on the order of a fraction of a second) to be generated due to inductance, capacitance, magnetic reluctance, etc.

    Anyways, this is what I think the TC is doing. It detects slip and powers off before the blip can occur. When the tires finally grip, the electronics are off, hence the reduced power everyone experiences. The shock gets transmitted to the only available component that is coupled, the ICE.

    ------

    Overtorque in an electric motor is where you run a higher than rated amount of current in the electric motor. You can do this at lower RPMs because the voltage is not high. In other words, you haven't maxed out the power rating of the motor. So you can run a higher current at lower voltage. The only thing is you can not do this for very long because higher current = higher resistive heating. It can destroy the insulation, cause shorts, or decrease its lifespan.
     
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  7. Tideland Prius

    Tideland Prius Moderator of the North
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    Thanks for the explanation!! It wasn't too hard to understand (I hate circuitry).

    So if that's the case, what's different in the new electric motor on the Gen 3 that allows Toyota to do this that they couldn't on the Gen 2 (the early models basically killed all power, leaving the driver SOL instead of slowing the wheel spin down enough to get grip and move the car)?? Is it the way the motor is designed? Is it because it can handle a higher voltage spike before becoming damaged?
     
  8. telmo744

    telmo744 HSD fanatic

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    Thanks for your post.
    Pakitt, speedometer errors are of much importance, as you said.
    If you see the first measurements, 130kph (143 in speedo) is 6,5l/100 for Prius, and your measurement at 150 is 7 litres/100km for the Polo. Still not bad for the 1.4TDI ;)
     
  9. sipnfuel

    sipnfuel New Member

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    Pakitt, I found a 2nd source that shows my calculations and assumptions are actually spot on. There is no overtorque at all. So you can use that formula.

    However, power drops off after 4000 RPM. How much I do not know. Just factor in that after 4000 RPM, Power is less than 60 kW, and thus torque drops off even faster beyond 4,000. This is probably caused by bearing friction, torsion, air drag, etc. inside the motor.
     
  10. sipnfuel

    sipnfuel New Member

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    Hi Tideland. I want to be able to answer your question but I need a better understanding of the differences between how you perceive Gen II TC, Gen III TC, Conventional TC to be. More detail, the better.

    I don't want to threadjack to keep talking about MG2 and Traction Control, but I might be close to an answer.
     
  11. usbseawolf2000

    usbseawolf2000 HSD PhD

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    Gen3 can spike to 650V but Gen2 is limited at 500V. IGBT inverter is also direct (better) cooled in Gen3. That would be my guess.
     
  12. pakitt

    pakitt Senior Member

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    Guys, thanks for all your help here, but I am getting a bit confused as I try to make a model of the torque and power curves for the HSD of the Gen 3.
    A recap here, correct me if I am wrong.

    The wheels (let's assume 15" rims, without tires, the worst case - i.e. the highest rpms at max speed) are connected to MG2 via a reduction gear. This reduction gear multiplies the rpm at the wheel 2.36 times to the MG2. Right?

    So at 180km/h, a 15" rim that covers 1.2m per revolution, will need to spin 2508 rpms, which means the MG2 is spinning at 6595 rpms.
    If this is all correct (and worst case), then the ICE clearly is running slower (limited electronically at 5200 rpm, right?).
    Max HP from the ICE is at the max rpm (73kW/99HP @ 5200rpm). Whereas max torque is 142Nm @ 4200 rpm.
    Now, what are the rpms of the ICE at max speed???

    Second point. I have read somewhere that one of the electric motors, wrt Prius 2nd gen, has a much higher rpms limit of 13500. Which one, MG2 or MG1? Guess what, max MG2 rpms*2 = 13190rpms....

    Third point - max voltage is 650V, what is the max current considering that the torque is reduced from 400Nm to 207Nm and power increased from 50 to 60kW?

    Forth point: here and here I am reading completely different things...
    MG2 max rev speed is 13500 up from 6400rpm. Moreover:

    So...there are in the Prius Gen 3 *two* planetary gearsets - one is the PSD and the other one is the "speed reduction" gearset as per description above. The connection from the wheels to the MG2 is therefore not 2.63 rather 3.267.

    If this is true, and it appears it is, then the MG2 speed at max speed is, at least, 8192rpms. But since MG2 is the sun of another planetary gearset, we don't know the ratio from sun to ring (connected to the wheels with a ratio of 3.267:1) - does anybody know what it is?

    I can only assume that if the MG2 is rated for max wheel speed, then MG2 must be spinning at least at 13000rpm (like per calculation above) and the ratio to the ring gear in the speed reduction gearset is something like 1.59:1. Does anybody know this? If this is all true a plot for the overall HSD power/torque vs rpm gets quite complicated...

    If all above is correct, PSD is in principle the same, but all the PSD models out there are not correct for the Prius 3 when showing MG2 speeds and vehicle speed - like this (btw very good) one.
     
  13. pakitt

    pakitt Senior Member

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    PS: found a post here that might help.
     
  14. sipnfuel

    sipnfuel New Member

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    I think you forgot the final reduction at the differential. It is 3.905 or something very close to that figure.

    Edit: This number seems to be for Gen II Prius. According to sources it is 3.267:1 for Gen III, but yes, you have to factor this in.

    Pakitt, to correct you a bit
    MG2 is connected to the PSD using 2.63 ratio. The PSD is connected to the Wheels by 3.267 ratio. I think you need to multiply the ratios to get MG2 to the wheels.

    Max MG2 RPM = 13500
    13500 RPM / (2.63 * 3.267) = 1571.19 Max Wheel RPM

    Wheel = 24 in. diameter
    Circumference = 75.4 in = 6.283 feet
    Max Speed = Max Wheel RPM * Circumference
    Max Speed = 1571.19 RPM * 6.283 feet per rev = 9871.79 feet per minute = 112.2 miles per hour
     
  15. sipnfuel

    sipnfuel New Member

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    Tideland -

    While winter is almost over, there are still many puzzled by the TC.

    The Gen II and Gen III basically have the same configuration. The two biggest differences are Gen III MG2 that spins at 13500 RPM vs Gen II MG2 6700 RPM (but limited to 6000 RPM), and a bigger ICE producing more torque across all RPMs.

    During loss of traction/slippage/regain of traction, it should cause the AC Synchronous motor to desynchronize. AC Motors can only provide torque when they are synchronized. When it is desynchronized, you can run all the amps through the stator and no torque can be transferred. Analogy would be like breaking a driveshaft. But you can resynch to the rotor's speed in order to provide torque again.

    This is why loss of traction is bad, in addition to causing high currents to flow through wires, destroying insulation.

    The Prius has to know position & speed of the rotor at any given time to maintain synchronization. The prediction can not be 100% correct. It has sensors to detect the rotor's speed and position. and then it corrects for the error to maintain the synchronization.

    The rotor speed is dictated by wheel speed, and vice versa. During loss of traction, basically any prediction of what the rotor will do in the next moment can be thrown out the window. It could suddenly grip the road, and the rotor RPMs would decrease, or it could slip even more, increasing RPMs. Beyond a certain difference in RPMs, the inverter can not compensate enough and the motor will descrynchronize. You can not instantly change from one frequency and phase to another because the way in which you can force the currents & magnetic fields to change is not instantaneous.

    All you have to do is exceed stall torque to have the rotor slip one pole and then it would desynhronize. If it just slips one pole, it would likely resyncrhonize all by itself. But a large enough event would basically require a power down, or reduced power state of MG2, in order to resynch.

    My best guess is the Gen III has a better method of maintaining or resynchronizing than the Gen II.

    It could be the Gen II slip sensors feed-back to a different ECU than the one that controls MG2. Then it would have to communicate to the other ECU. This would have a lag that would describe the lurch, stop, lurch stop of the Gen II that you describe. So perhaps in the Gen III, the slip sensors are more centrally located in one ECU. This is pure speculation, someone with more info would have to help me on this.

    Additional hardware differences that may make a difference is a VFD with much faster switching, higher resolution sensors, better data buses, faster processors, higher tolerances. Software differences may include better algorithms for error recovery.

    Also, roughly the Gen III MG2 has half the torque but twice the speed, and slightly higher voltage. If it has half the number of poles, it would also require half the number of permanent magnets. This would explain the 2x speeds, but not necessarily. It could be the same and just the VFD runs at 2x frequencies. In the latter case, if my thoughts are correct, the magnetic fields are weaker by 2x thus allowing them to be varied more rapidly to maintain synchronization. I need another engineer to chime in.

    Can you confirm that when TC kicks in for the Gen II or Gen III, the ICE is usually not running and it's only using battery power? I don't know if the Gen III uses ICE/MG1 combo to help out during TC.
     
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  16. Tideland Prius

    Tideland Prius Moderator of the North
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    Good point. I don't recall hearing the engine rev so it's possible that it's holding a constant and set max rpm (e.g. when you're in neutral and you press on the accelerator, it only revs up a little)
     
  17. lovingUcbog

    lovingUcbog New Member

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    Excuse my question: how do you guys check the rpm? is there any particular setting to do that or i have to buy a separate device?
     
  18. cwerdna

    cwerdna Senior Member

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  19. telmo744

    telmo744 HSD fanatic

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    I have a question, that could be answered very quickly by someone with a scangauge fitted to a 3Gen.

    How much is the ICE spinning drag with no load?

    First approach: difference between fake regen above and below 46MPH...
    Or am I wrong?

    [note: in a normal ICE, takes about 15Nm off the shaft...]

    edit: found out by a quick search that a normal 1.4 Otto ICE rated 60kw would have a total of 7kW friction loss, and a pumping loss of 5kw - without further reference (rpm, for instance)...but gave a good idea of the share.
    Assuming pumping losses to be close to zero in the 2ZR-FXE, total losses will be close to the friction losses alone, then be about 60% of a similar ICE engine.
    So it can be like...9Nm...at 1200rpm (thank you, dearest E-CVT), gives roughly 1200W.
    Can anyone confirm? Seems a bit low to me...
     
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  20. telmo744

    telmo744 HSD fanatic

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    Well, I've got one clue at
    http://www.techno-fandom.org/~hobbit/cars/warpstealth.html
    (Again thank you, Hobbit)

    quote:
    "Fuel-cut is maintained, and the retarded intake
    cam timing reduces the amount of air sucked in around the throttle flap and
    through the engine to almost zero. This is a very low-resistance state for
    the engine to be in, and it only takes a kilowatt or two to keep all that
    merrily turning."
     
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