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I understand that heater blocks act as kind of “low-pass-filter” on the temperature change of the hotend, but why do we need that?
Wouldn’t it be better to have as little metal as possible in order to be able to control temperature changes quickly and precisely (using PID, PWM plus maybe some predictions based on printed G-code)?
Let's look at the elements and what they do:
The Heater Cartridge (blue) is the device that converts electric to thermal energy to melt the plastic. 30 and 40 W are common.
The Thermosensor (red) is there to give feedback to the mainboard.
The Filament Path (gold) in this area is made up of the nozzle and the heatbreak, it contains the meltzone.
The Heater Block (transparent green) is the mounting for all parts. It also acts as the medium to transfer the thermal energy from the Heater Cartidge to the Thermo Sensor and the Filament Path. It also acts as a dampener for the control circuit.
Now, let's put things together and omit the wires and cold end (and internal geometry of the filament path, cause I am lazy):
Now, the construction gives us several reasons for the shape of the heater block:
You may easily notice that the temperature lines appear more straight as they come closer to the filament path and thermosensor. This helps to give the filament in the heatbreak and nozzle more even heating and better printing.
The mockup I made has a deliberate flaw though: a change in temperature first affects the filament and then shows up on the sensor, making the temperature in the filament path wobble to the extreme. The Heater Block acts pretty much as a transmitter just as much as a time dilation between the heating command and the pickup.
Because this arrangement is not very good, let's swap sensor and filament path around and look at the same lines.
Now we have a much shorter feedback loop, allowing our printer to react quicker to temperature changes and the filament path also gets heated more evenly. The temperature inside the filament path does change less around the target temperature. The whole block now acts mostly as a distribution medium but also as a storage for heat energy:
Up to this point, we did not take into account a very simple fact: the hotend drains thermal energy via two areas:
Factor 1 is simple and here a bigger heater block actually is positive: The thermal 'storage' capacity is dependant on the volume, so goes with $xyz \approx a^3$. The surface to emit heat from goes with $2\times(xy+xz+yz)\approx 6\times a^2$. Plotting a graph of that shows us the square-cube law: the capacity increase for one unit does increase the surface just by a fraction of that, so the storage gets better the larger the heater block is.
Factor 2 is why we need to have a storage of thermal energy in the first place: the flow of filament is not exactly the same all the time. Of course, we have moments of even flow, but we also have moments of low or no flow when the printer moves between parts of the print. This alteration of the drain of thermal energy from the heater block means that if we would go down to a bare minimum size, we'd heat up the block fast whenever we are on a move action and cool as the extrusion starts till equilibrium is achieved again. The more thermal capacity is there to store energy, the less the lack of extrusion will immediately affect the print and the more even the temperature will be in the filament path.
How is faster printing achieved with a special hotend? Well, 4 factors are used in hotends meant for very fast or very hot printing:
One of the prime examples would be an e3D-Volcano.
I think the idea is to not change the temperature fast. You want it to maintain a certain temperature so you have consistent flow. The extra mass at the hot end provides the mass which is needed to maintain the heat. If you don't maintain the heat while you print, you'll have inconsistent filament flow, which will screw up your print.
Heater blocks are used on hot ends because they are the current engineering compromise between the design factors of cost, reliability, lifetime, maintenance, and performance.
Ideally, there would be no heater block, the heater would have infinite wattage, the nozzle would heat and cool instantly while transferring heat to the filament, and the temperature of the molten plastic would be measured instantly.
But as this is engineering instead of magic, none of these conditions is the ideal. The engineering problem is to find the right compromise.
Each of these can be treated separately. How do we measure the temperature of the plastic? Assume we have a tiny thermocouple in the plastic flow. Why thermocouple? Because it is smaller, less prone to manufacturing tolerance, and is good for higher temperatures.
Imagine a heater where the heater wire forms the threads into which the nozzle screws and also where the nozzle has thinner walls to reduce the nozzle's thermal mass. Further, the nozzle is made of diamond which has almost ten times the thermal conductivity of brass. Yes, machining diamond is not easy, and the supply of large enough diamonds is limited, but we're trying not to compromise yet.
In this scheme, there is no heater block. We instantly know the temperature of the plastic, and we can dump large amounts of heat into the system to get a high enough temperature. We still must hold the nozzle in place and connect it with the filament source (typically the job of the "heat break"), so let's make that of thermally insulating ceramic so it stays out of the heat transfer process.
With this, we have a hot-end where we would have great control. We are directly measuring the parameter we care about -- the temperature of the plastic. We can deliver heat rapidly. When the extrusion rate increases, the temperature drops a little and we dump in more heat. The thermocouple is fragile (don't try a cold-pull), and is subject to wear. The nozzle is very expensive and difficult to make.
Ok, move the thermocouple to the outside of the nozzle's tip. Now we have a heater intimately wrapped with the threads of the nozzle. That is probably hard to make, so let's use a conventional heater cartridge that is very close to the nozzle threads. Let's put in as many heaters as we can pack together near the threads. If we angle the heaters they won't hit each other, so suppose we can put in four heaters spaced around the nozzle. More heat, less distance from the heat to the nozzle. Make this new heat block of silver, just like the nozzle. Silver has 80% higher thermal conductivity than aluminum. (Or we could use diamond, but really, who has diamonds that big?)
I was assuming a thermocouple to measure the nozzle temperature, and it is small enough that it could nestle into a small home in the nozzle. We could use a thermister pressed into a hole in the nozzle, but experience has shown that thermisters are fragile. We have found that the tiny glass beads are prone to either breaking of the glass, separating from the thin leads. The electronics to measure temperature with a thermistor is simpler and less expensive than a thermocouple and seems to have good enough resolution, accuracy, and temperature range. If we follow that experience, we will package the thermistor in a cartridge housing that is easier and more reliably placed and protects the thermistor from damage. But the cartridge is too large to connect directly with the nozzle, so we'll put it in the same block with the heaters. After all, they are silver and conduct heat very well.
This may be a better hot-end than the conventional system. It heats faster and more accurately measures the temperature of the plastic. But there are problems. Silver is heavier, and four heaters and their wiring have more mass than one. And, the holes for the heater cartridges are each in a different plane, so it is more expensive to machine. And the price for the silver may be a factor. Silver costs (today) \$215/lb, where aluminum is $0.80/lb.
In this answer, I have tried to show how heater blocks are useful for coupling the heat from the heaters to the nozzle and to show that there are alternatives with perhaps superior performance but problems with reliability or cost.
Edit: In a comment, the OP asks why we do not machine away extra material that is not required to couple heat to the nozzle, and correctly raised the issue of cost. There may also be a performance issue.
The conventional heater is only on one side of the nozzle. When the heater is cooled by the filament, it draws heat from all sides. The thermal mass on the non-heated side helps with stability by providing a source of heat from which the nozzle can draw.
On the heater side, a factor to consider is the coupling of heat from the heater cartridge to the heater block. Removing additional material should be evaluated to assure that it does not increase the thermal resistance from the heater to the rest of the block and the thermistor. This is important to help with thermal stability, and also to assure that the heaters do not overheat themselves.
For thermal conductivity values, I used this reference. For metals pricing, I used Google to find spot metal prices on 6/3/2019.
