The P4014 printers have four fans. The combination of low-melt polyester toner and a large catridge suggests the printer innards have to be kept cool, however the high speed suggests a powerful heater in the fuser so the printer has to be able to counter that effect with sufficient air-flow. Used continually a P4014 series printer is close to being a 1 kilowatt heater, so it needs those fans.
57 Error is one of the fans. The printer has four fans in its base model and the duplexer adds a fifth as it partly blocks the fuser vent area. Although they are nicely engineered fans they are a bit noisy and there are suggestions that as the printers get older, the axles and bushings get a bit eccentric and foam cushioning ages the machines get prone to rattling noises.
Laser printers almost invariably use heat to fuse the toner into the page. It takes a considerable amount of energy to raise 60 pages per minute to about 150 centigrade for fusing to take place. In operation the P4014 series use just under a kilowatt of electricity on average - so it is acting as a small fan heater. The fuser is not totally efficient at transferring all that energy into the paper so the fans are needed to extract it from the printer.
The P4015 and P4515 machines have a rather large cartridge full of special low-melting point polyester toner that is intended to save about 15% of the electric cost of running the fuser. However this toner does need to be kept cool even though the developer end of the cartridge is innevitably next to the fuser.
The fans feed clock signals back to the DC controller so it can detect them not moving properly. However there are suggestions that this doesn't always work as it should because the fuser can go to 50.3 and 50.9 overheat errors.
It is worth making sure that users are not blocking fan vents with things like ledger files piled against the machine. Yes, the printer does make a handy bookend on a desk but it also needs about 150mm (6 inches) clearance on all sides for adequate ventilation.
Find the fan that has stalled. (Some versions of the service manual are wrong on the fan numbering).
It is usually easy to spot dead fans; with the printer off push a blade gently by hand and it turns reluctantly if at all. Fan failures are almost always related to the bearing although the resulting overload might conceivably fry the built-in drive circuit. One point to watch out for is the enjoyable sport of cleaning fans by blowing compressed air at it; as well as making a dust cloud the fast-spinning blades over-voltage the drive circuit and kill it. This could damage the DC controller as well. Use a brush instead.
We have tried to get the fan numbering above correct but HP getting it wrong is unhelpful. Furthermore they could correct the problem by updating the firmware - so the list above might become wrong (yuk). It means you can't trust a fan error on these printers; verify which specific fan has the problem (unplug them one at a time? ).
Fans can often be cleaned up and repaired. Take the label off and there is a circlip underneath holding the hub of the fan and it's bushing onto the shaft. Clean and re-lubricate the shaft and bushing. Exactly how the bearing is done varies hugely and is a significant factor in fan life.
Failed fans are normally replaced; repair takes too long and is too often followed by another failure.
I tried querying Google with
P4015 "57.01 ERROR" in quotes and got just
About 38 results; almost all the familiar sites. I'll just pick out a few:
I then tried Google with
P4015 "57.03 ERROR" in quotes and this time it said
About 151 results; again the familiar sites.
Queries for 57.04 etc gave very similar results so that topic doesn't seem worthwhile pursuing.