Thermal gradients

Although my last extruder design seems to work, I am not very happy with it. I don't like the little fan because it is noisy, it isn't easy to make and it is not very thermally efficient. The main heat loss is via the stainless steel bolts and from the big flange. The only reason those parts are needed is because the PTFE insulator does not have the necessary mechanical strength and stability.

Some time ago I tried to use stainless steel as the insulator because it is strong, self supporting and withstands high temperatures. That attempt failed because my thermal gradient was too long; the hot to cold transition was about 50mm. The extruder would run for a while but would always jam before an object was completed. Once the stainless steel barrel was fully up to temperature the amount of filament that is soft but not fluid is sufficient to provide too much resistance to be pushed. This theory was confirmed when I tried a soldering iron heater, which also has a long thermal gradient along its length.

I also tried PEEK as the metalab guys had success with it but that seemed to suffer from the same problem.

I had always intended to revisit the stainless steel idea with a shorter transition zone but when I saw Larry Pfeffer's stainless steel extruder it provided an extra idea of thinning down the pipe at the transition. That allows a short transition without too much heat loss or loss of mechanical strength.

I did some experimentation with this test set-up.



I made a heater with an integral aluminium barrel by turning some aluminium bar in my four jaw chuck, the first time I have used it. I used two 12Ω resistors in parallel this time instead of one 6.8Ω. They give a bit more power and possibly lower internal temperature inside the resistors.

I measured the temperature along the tube at 5mm intervals. The thermocouple is slightly smaller than the internal diameter of the tube. The weight of its cable causes the tip to rest on the roof of the tube and the other end rests on the floor of the filament exit. The thermocouple is itself encased in stainless steel, so there will be some heat leaked along it. Hopefully its casing is thin enough to have little effect compared to the much thicker tube it is sampling.

The heater was powered from a bench power supply and the voltage adjusted manually to give around 240°C in the middle of the heater block. That needed 9.4V which is 14W. I can feel substantial heat rising from it so some insulation would make it a lot more efficient. I have got some ceramic fibre kiln insulation for that, another tip I picked up from Larry's blog.


The first test was with a threaded tube with no constriction. The gradient is not far from linear, it falls off faster when hotter due to more convection and radiation from the hot section. If we assume ABS would be soft but very viscous between say 75°C and 125°C we see that it covers 45 to 60 i.e. 15mm.

I then turned a 10mm section of the tube down from 6.4mm to 4.5mm. The internal diameter of the tube is about 3.6mm so that gives a wall thickness of 0.45mm. That made the gradient steeper between 35mm and 40mm but the length of the perceived problem zone gets bigger. I am not sure how Larry gets away without a heatsink. I think he is using thicker pipe so there is a much bigger difference between the conduction of the constricted section and the rest. Also it takes a long time for the problem to become apparent because heat travels slowly down the pipe.

The final test was done with a heatsink attached just above the constriction. The centre of the heatsink only reached about 28°C. The aluminium block I used to connect it got hotter but was still comfortable to touch so less than 50°C.



The gradient between 30mm and 40mm is now much steeper. Odd that it is not between 25mm and 35mm where the constriction is. Almost like there is a 5mm offset in the readings. Anyway the 125°C to 75°C transition is now only about 3mm.

If we assume the temperature difference across the constriction is 210°C - 80°C = 130°C, the conducted heat loss is temperature difference × thermal conductivity × cross sectional area / length. So 130 × 17 × π × ((2.25×10^-3)² - (1.8×10^-3)²) / 10×10^-3 = ~1.3W, about 1/3 of the loss through the bolts and PTFE in my previous design.

So it looks promising, I need to add a nozzle and some insulation and see if it will extrude.

Heater in a hurry hack

The heater in my last design has two layers of Cerastil that take 24 hours each to cure and the bobbin takes some time to machine. Attaching the wires and winding the coil is quite fiddly. Looking for a short cut I wondered if we could use power resistors. I had this one lying around to play with.



Unfortunately it is only rated for operation up to 200°C. In fact the datasheet says "It is essential that the maximum hot spot temperature of 220°C is not exceeded". Curious to see why, I put enough voltage across it to heat it up to 240°C. That turned out to be about 75W. It seemed quite happy at that temperature for several hours.

It is too big really for an extruder so I bought some smaller 10 Watt ones for £1.42 each.



These are only rated for 165°C but what the heck. I heated a 6.8Ω one to 300°C. At about 180°C it produces a little smoke but that soon goes. At 280°C it starts to smell bad, but at 240°C it seems happy. I left one powered up for a few days. The writing disappears and the connection tags oxidise, but its resistance is stable.

To make a heater I cut a 19mm x 19mm x 8mm block of aluminium from a bar, drilled a 5mm hole through it and tapped it to M6 to fit a heater barrel. The mounting holes of the resistor are big enough for M2.5 but there is not enough room for the head, or a nut. M2 is a bit weedy so instead I used 8BA bolts. These need a 2.8mm hole for tapping. A simpler solution would be to just file a flat on the head of an M2.5 bolt, drill a clearance hole and use a nut on the other side.



Here is the full assembly: -



I put heatsink compound on the M6 thread and under the resistor. I attached tinned copper wires with 300°C solder and insulated them with PTFE sleeving.

I have run the assembly for a couple of days and it held up. I am loath to recommend something which is unsound engineering, but it does seem a simple and robust solution as long it lasts a reasonable amount of time, say 1000 hours. Replacement is easy because the most time consuming thing is making the block which is reusable. I expect there might be some matching crimp connections to avoid the high temperature solder.

Quite a lot of heat is lost from the large surface area so some insulation would be a good idea.

New year, new extruder?

The RepRap design has always aimed to be cheap and easy to make from readily available materials. What I desire though is good performance and reliability, and put those priorities ahead of the others. To me they are absolute requirements and the others are things to be optimised afterwards. With that in mind I set about trying to design a reliable extruder that I can make with the tools and materials I have available.

As it is experimental I wanted it to be modular so I can swap out things that don't work. I started with the heater. It takes me two days to make one so I wanted it to be removable and reusable. I made an aluminium bobbin with an M6 thread through the middle of it so it can be fitted to different barrel designs. The outside diameter is 12mm and the inner diameter is 8mm. It is also 12mm long. The flanges are 2mm and 3mm with a 7mm gap for the nichrome and Cerastil.



The surface is roughed up to make the Cerastil adhere well. It has a hole to accept the thermistor to make it a self contained closed loop.

I put down a layer of Cerastil about 0.5mm thick using a plastic jig and left it to cure over night.





I used two strands of 0.1mm nichrome in parallel to make the heater. That only needs 90mm to make about 6Ω. I normally use 8Ω but I anticipated more heat loss in this design.

To make connections to the heater I used two strands of 0.2mm tinned copper wire and attached them with reef knots.


I then covered the knots in high melting point solder.

Using such fine copper wire may be a mistake as Bert pointed out on my previous post. Time will tell.

I made a jig to keep the wire taught while winding it on the bobbin.



At this diameter it is only about three turns of nichrome.

Finally I covered the windings in Cerastil H-115 and also used it to glue in the thermistor.



I made the barrel as short as possible. That turned out to be 25mm to have room for the heater and the nozzle and a mounting flange. The standard design uses a 45mm heater barrel.



The vaned section is a heatsink to keep the rest of the filament path cool. Sandwiched between the hot and cold sections is a 12mm length of 10mm diameter PTFE tube.



The idea is to keep the thermal transition as short and slippery as possible to make it easy to push the slightly molten plastic through. The PTFE extends 5mm into the heatsink to give a good contact area for cooling. It extends 2mm into the hot barrel and 5mm is in the air gap. It is an interference fit and is under compression. When it gets hot and expands the seal should only get tighter.

The metal parts were drilled to 3.3mm on the lathe and once assembled it was all drilled out to 3.5mm. As the PTFE was drilled in situ the hole is perfectly aligned and there are no gaps.

The thermal loss through PTFE, which has a conductivity of 0.25 W/m°C, will be: -

220 × 0.25 × π (0.005² - 0.00175²) / 0.005 =0.76W, assuming the heatsink is at 20°C and the barrel is at 240°C.

The barrel is held on by three M3×25 stainless steel bolts. The holes are counter bored so only the last 5mm of thread is in contact with the heatsink. Assuming the mean diameter of the thread is 2.75mm the heat loss through the bolts is: -

3 × 220 × 17 × π × 0.001375² / 0.02 = 3.3W

Longer bolts could reduce this by about half.

Here it is with the heater, nozzle and PTFE cover installed. There is heatsink compound between the heater and the barrel, and the nozzle thread is sealed with PTFE tape.



The wires are insulated with PTFE sleeving and terminated to a 0.1" header mounted on a scrap of Vero board. This mates with an old floppy drive power connector. I put the thermistor in the middle and the heater on the outer contacts so it doesn't matter which way round the connector goes.



The clamp seems to grip aluminium a lot better than it does PTFE but I also put an M3 bolt into a blind tapped hole to ensure it cannot slip. A good move as it turned out.

I powered it up without the pump and calibrated the thermistor. With the nozzle at 240°C the "cold" section reached 100°C and softened the ABS clamp. Obviously my home made heatsink is woefully inadequate.

To keep it cool I added a small fan. That keeps the cold section at 30°C, much better.



The black sheet is Teflon baking parchment that I used to stop the fan blowing on the hot section.

I haven't attached the motor yet but I have tested hand feeding white, green and black ABS as well as HDPE. The ABS feeds easily through the 0.3mm nozzle and the HDPE with moderate force. I think they will all work well with the motor drive.

When the filament is pulled back out only a few millimetres has expanded at the end. In contrast, without the fan the filament swelled most of the way to the top and jammed. You can see the difference here: -



Keeping the melted section short is the key to making the filament easy to feed. The other improvement is that the PTFE is no longer a structural element. It is held in compression and appears to make a good seal with simply a push fit.

I am sure I can both improve the thermal separation and make it easier to make with a couple of design iterations before redesigning the other half of the extruder.

Do we need nichrome?

While making a new heater I decided to try using stranded tinned copper tails rather than the solid tinned copper wire I used previously. The idea being to put less stress on the Cerastil covering.

I started with a standard piece of 7 x 0.2 stranded copper wire and removed the insulation. I found all seven strands too bulky so I decided to see how many strands I needed to carry 2A. I found that a single strand was cool to touch at 2A but very hot at 4A. I figured two strands would be sufficient for some margin.

The fact that a strand gets hot at 4A, and in fact red hot at about 5A, got me thinking that we could just use a single strand of copper for the heater. Nichrome is expensive, not that easy to obtain, and difficult to make connections to.

I measured the resistance of a strand 52cm long as about 0.3Ω (my meter only gives one digit). The strand measured 0.17mm diameter. Calculating its resistance from the resistivity of copper I get 1.72 x 10^-8 x 0.52 / (π (0.00017/2)²) = 0.39Ω.

At 4A the voltage drop was 2.6V giving a resistance of 0.65Ω and a power of 10W. The thermal coefficient of resistance is 0.0039 for copper so the calculated temperature of the wire is 20 + (0.65/0.39 - 1) / 0.0039 = 191°C. It was certainly hot enough to cut through ABS.

10W and 190°C are not far from the operating conditions of an extruder. I tried winding it on the bobbin I had made for my heater but it was about twice as long as I could accommodate. I am trying to make a very short heater at the moment so I went back to using nichrome. Also 2.6V @ 4A is too much for my current drive circuit but it would be easy to come up with a switch mode converter to drive it, or simply use the 3.3V rail of a PC PSU.

So it has definite possibilities. Making the connections would be trivial. Just start with a piece of 7 strand wire and cut it down to one apart from at the ends. Some high temperature solder would keep it neat but would not be essential. A standard heater barrel with some insulation would be about 7mm diameter so 24 turns would be required. If you keep it taught and wind it in a lathe or drill chuck you can get about 2 turns per mm with some concentration. That would easily fit the space currently allocated for the heater.

Simple experiment

Inspired by Demented Chihuahua's extruder work, I repeated his experiment using what was left of my old heater. I mounted it in a 30mm M6 stainless steel washer and clamped that in a vice. I used my 0.3mm aluminium nozzle, which I counter bored with a 0.7mm drill to reduce the depth of the 0.3mm hole to about 1.5mm.



I powered the heater from a bench power supply and adjusted it manually to about the right temperature. Green ABS is handy for this because it changes colour at 260°C so you can tell when it is too hot.

I can extrude filament by pushing it by hand with moderate pressure. It comes out at 0.4mm but I should be able to stretch it back down to 0.3mm without any problems. Even with a 0.5mm nozzle I can stretch it down to 0.3mm, but I lose positional accuracy because the orifice no longer defines exactly where the plastic goes.

Originally the heater was 5mm longer, with the excess protruding beyond the half nut. I found that cutting that piece off made it easier to extrude. It was probably a relatively cool section so the plastic remained very viscous there.

When a new piece of filament is inserted into the heater it extrudes very easily. After a while some plastic flows backwards and builds at the entrance to the heater. That causes considerable extra resistance. I plan to tackle that by having a short section of PTFE at the entrance with a heatsink the other side of it. The steep gradient across the PTFE should freeze the back flow over a short distance and, being super slippery, should allow it to slide back into the heater.

Another thing I tried was forcing out the plastic using the shank of a 1/8" drill bit as a piston. The further the drill got to the end of the heater the less force was needed to push it. That confirms what I had suspected. The force to push the plastic though the long 3.5mm section of the barrel is very significant compared to the force to squeeze it through the short small hole in the nozzle. So the heater needs to be kept as short as possible. Obviously there will be a point where the extrusion rate becomes limited by the rate the plastic melts if it is too short, but I expect that is much shorter than the current set-up.

New Materials

HydraRaptor's extruder suddenly stopped working in the middle of a build a few weeks ago. I tried upping the temperature and pushing the filament with pliers but it would not budge. All that happened was the heater barrel slipped a few threads in the PTFE insulator.

It was a bit difficult to find out what was wrong because it was full of solidified plastic when cold. I unscrewed the nozzle and placed it in some acetone to dissolve the ABS. It appears that the hole in the nozzle was blocked by burnt plastic. It probably formed when I had some high temperature accidents and experiments recently.

I should have realised the nozzle was blocked, but it has never happened before. If I had then I could have just unscrewed it, cleaned it out with acetone and put it back on again. In the event pushing the heater out of the PTFE pretty much wrote it off.

Not for the first time, I decided to rob parts from the extruder I was making for my Darwin. These are all made from different materials in order to see if small improvements could be made.

The barrel is made from aluminium. It is a better thermal conductor than brass, is easier to machine being a lot softer, and is cheaper.



To make the thermistor more easily removable I mounted it in ring of aluminium with a tapped hole.



The thermistor was glued in with Cerastil H-115 and the ring was screwed onto the barrel with some heatsink compound in the thread. By adjusting the beta I was able to get the reading to agree with a thermocouple inside the barrel to within a couple of degrees. I don't know if that means the ring was at the same temperature as the middle of the barrel or if it was lower and I compensated with a beta value that is not actually the beta of the thermistor. Either way it produces the desired result.

I also made an aluminium nozzle with a 0.3mm aperture. I broke the drill bit as it went through. I am not sure if that was due to the aluminium snatching more than brass does, or me being careless. I have broken loads of small drills recently and blunted some bigger ones by accidentally drilling with my lathe in reverse!



The picture also shows where the thermistor ring mounts.

Another modification I made was to put a PTFE cap over the nozzle.



This has two benefits: -

1. It is a good insulator so it helps to keep the nozzle warm.
2. Being non-stick, and also cooler than the nozzle surface, it stops filament from sticking to it. I use a brush to wipe the nozzle. This works well with HDPE but ABS tends to curl upwards and stick. Since I added this cap the nozzle wipe has worked 100%. It remains to be seen if it works with PCL and PLA.

It is a snug fit but when it gets hot PTFE expands a lot so it slips off. I held it in place with a tiny screw and an indentation in the nozzle made with a drill point.



Another new material I used was Polyetheretherketone (PEEK) instead of PTFE for the thermal break. This has similar insulating properties to PTFE and a slightly better working temperature range. It machines well but forms burs very readily.

I found it much sturdier at working temperature, I don't need a pipe clip to stop the barrel popping out now, but I think it may be a bit harder to push molten plastic through, being less slippery.



The other thing I changed was I used insulated nichrome. When using bare nichrome I have to put down a thin layer of Cerastil to insulate the barrel, leave it to set, then wind the heater and cover it with more Cerastil. That makes it a two day job. By using insulated nichrome I can just wind it straight on the barrel and then cover. But what I didn't think about was that I normally make the soldered connections under the Cerastil, which I could not do this way. All in all I think bare nichrome is best as it makes a much neater job. Here is the previous heater that I made way back in March :-



So after all these "improvements" how did the new extruder perform?



Not very well! I tried it with green ABS first but could not get it to extrude reliably. I swapped the nozzle for my previous 0.5mm brass one and that got it working.

I then switched to some plain ABS that I bought a while ago but have not been able to use because it is very oval. It was too wide for my previous extruder. This extruder has a 3.5mm bore so it should easily fit but I could not get it to work reliably. It takes an enormous force to push it into the extruder. I am not entirely sure why. If I pull it out and push some green in I can extrude the plain that is left in the barrel easily so it isn't any harder to push it through the nozzle but it is to push it into the heater.

Since I foolishly changed every material at the same time it is hard to evaluate which things are better and which are worse. I have recently formed the opinion that the extruder design is far from optimum. I think we need a much sharper thermal gradient and a shorter heater barrel. I think a lot of force is wasted pushing slightly softened plastic down the thermal break.

My next attempt will have a very short thermal break with a heatsink at the cold side. I will also make it easier to strip down and reassemble. A problem with the current design is that once the heater barrel is screwed in and full of plastic it is hard to remove it.

Sticking point

sid, who is a regular contributor to the RepRap forums, had an idea to get a soldering iron manufacturer to make a heater barrel assembly for RepRap. He approached a Chinese company with a specification and they sent him some prototypes. He forwarded one to me for testing. It appears that they ignored his specification and just sent a standard de-soldering iron element. Nevertheless it is a nice unit and looks eminently usable.



It has a tube running through the middle with an internal diameter a shade over 3mm. Ideally it needs to be about 3.5mm to cope with the worst filament I have encountered. My green ABS, being a little undersized, fits down it easily.

The heater has a cold resistance of 1.3Ω but, unlike nichrome, it has a big temperature coefficient, so its resistance increases significantly at it gets hot. It appears that it is a 12V 50W heater. We can drive this with PWM using a MOSFET provided the PSU can handle 9A peaks on the 12V rail in addition to what the steppers take, a tall ask. An inductor and diode could be used to reduce the peak current.

The other two wires are a type-E thermocouple. Unfortunately the thermocouple sensor board that Zach designed using the AD595 is for the more common type-K thermocouples. It can be recalibrated for type-E by adding extra resistors. However, the AD595 is an expensive chip because it is factory trimmed for accuracy. By the time you add external components the convenience and accuracy is lost so you might as well just use a cheap op-amp and a micro with an internal temperature sensor for the ice point compensation. E.g. the MSP430F2012 that I use for my extruder controller is a lot cheaper solution than the AD595 and can control the heater and motor as well.

To test the heater I clamped it by the mounting flange in a vice and hooked it up to a bench power supply. I measured the internal thermocouple's output with a millivoltmeter and also inserted a 3mm rod type-K thermcouple down the barrel. Here are the results: -

Voltage	Current	Power	Resistance	Temperature	Thermocouple	Calculated Temp
1 V	0.75 A	0.8 W	1.3 R	43 C	1.5 mV	42 C
2 V	1.20 A	2.4 W	1.7 R	106 C	5.6 mV	102 C
3 V	1.55 A	4.7 W	1.9 R	182 C	9.5 mV	160 C
4 V	1.80 A	7.2 W	2.2 R	275 C	14.5 mV	233 C
5 V	2.00 A	10.0 W	2.5 R	357 C	20.0 mV	314 C

The temperature column is as measured with my type-K thermocouple towards the nozzle end of the barrel. The calculated temp column is assuming 68μV/°C from the type-E thermocouple and a cold junction temperature of 20°C. There is a big temperature gradient along the barrel so the thermocouple reading depends on where it is placed.

As you can see we only need about 5V to drive the heater. The current would start at 3.8A and fall to 2A as it warmed up. This would be kinder to the PSU and safer than using 12V, but 12V would give a much faster warm up time. I expect something better than bang-bang control would then be needed to avoid massive overshoot.

When running horizontally the inlet tube stays cold and the mounting flange is just too hot to hold so it would be ideal for mounting to ABS or HDPE. This is because the barrel appears to be stainless steel, which is a very poor conductor of heat. The element must be towards the bottom so there is a continuous thermal gradient along the barrel.

The nozzle that came with it is made from copper with some type of plating. It had a hole to mate with the tube that sticks out of the end of the heater but it did not go all the way through. In fact it could not, as the tip comes to a fine point. I suspect this is a soldering iron bit that has been drilled out to fit.



I attempted to drill a 0.5mm hole through it but it just snapped the drill. Even drilling a 1mm hole snapped the drill. In the end I drilled a 2mm hole, but the drill bent and came out the side. I think it needed to be sharper for copper. Finally, I cut the point off and filled the 2mm hole with high temperature solder. That is soft enough to easily drill a 0.5mm hole through. It melts at 300°C so should hold up.



The heat damage is where I heated it up with a blow torch in an attempt to remove the broken drill bits. Copper expands a lot more than steel. That did not work so I tried to get it red hot to soften the drill bits so I could drill them away. I failed to get it red hot but I did melt the plating.

The shape is not ideal for making objects but it is good enough to see if I can extrude. In fact it extrudes well. I was able to push a piece of ABS through it easily by hand and it extruded at a very good rate.



The bit/nozzle is clamped on to the end of the barrel by an outer stainless steel sleeve tightened up by a threaded ring at the cold end. I was worried it would leak under extrusion pressure without some sealing. When I stripped it down I found it did leak a little but didn't get far. I suspect it freezes when it meets the outer sleeve.



So apart from the bore being a little too small this seems like a perfect solution: -

• It needs no construction apart from drilling the nozzle.
• It is mechanically sturdy.
• It should be very durable; soldering irons last a lifetime and they run at higher temperatures.
• It is cold enough to mount with plastic without any insulation. It does after all in a soldering iron although that is probably a thermoset plastic.
• The nozzle can be easily removed and replaced.

BUT, it has one fatal flaw, exactly the same flaw as my attempt to use stainless steel as a heat barrier in my experimental high temperature extruder. There is a slow thermal gradient along the length of the barrel. That means there will be a point about half way along where it is just hot enough to soften the plastic but not hot enough to make it flow. When you push a piece of virgin filament in it slides past that point easily because it does not have time to soften until it gets to a much hotter part of the tube. If however you stop extruding then the stationary filament has enough time to soften further up. When you push it again it expands to plug the tube but is not fluid enough to move. No matter how much force you apply you cannot move it. To get it going again you have to pull it out backwards, cut off the swollen bit and start again.

The reason the original extruder design does not have this problem is that the thermal gradient is in the PTFE. It is much shorter so the problem region that is soft but not molten is a lot shorter and the walls are very slippery so it can still be shifted.

I can't think of a solution to this problem. You could make the internal tube out of copper but then the top end would be hot so you would need a PTFE thermal break again. Also it would not be an off the shelf product, it would be custom to RepRap. Perhaps a taper at the problem region could stop it sticking.

The next extruder I am building has an aluminium barrel and nozzle and a PEEK thermal break. It won't suffer from this problem at least.

Suppression

Some time ago I blogged that the GM3 gearmotor generates a lot of RFI, which was interfering with TV reception in our house and corrupting I²C comms on HydraRaptor. I designed a simple suppressor that fixed the problem, details here.





Recently Zach Smith designed a nice little PCB version of it and produced a kit. He gave me a sample to test. Here it is installed on a GM3: -



To test it I wired a GM3 with no suppressor to a bench power supply with a pair of jumper cables about 30cm long. I viewed the noise on both motor terminals with a scope grounded at the PSU. This is what it looks like in the time domain.



It is massively noisy producing about 50V pk-pk. And here is the spectrum in the frequency domain: -



Although this is the 12V version of the motor it looks similar to the 6V version I tested before.

I repeated the same test with the suppressor fitted, measuring the voltage at the terminals of the suppressor.



The noise is vastly reduced, now only about 700mV pk-pk.



The spectrum is reduced drastically as well: -



Compared to my Vero board version, tested under the same conditions, it seems to work a bit better, but that could be down to variations between motors.

So the kit version works well and also gives convenient screw terminals or 0.1" header robustly anchored to the motor.

Dodecahedron

I fancied making a dodecahedron, an object with twelve pentagonal faces. It is an interesting shape and, as the sides slope at ~26°C, it can be made without support material. I searched the web for a 3D model for some time but could not find one. I also searched for how to model one in CoCreate, as it wasn't immediately obvious to me. That came up blank as well so I had to figure it out myself.

I started with a construction circle and divided it into 5 sectors with construction lines 72° apart. I joined the intersections to make the base pentagon.



I then extruded that to a height equal to the circle radius and with a draft angle of -26.56505°. This is the dihedral angle (2arctan((1+√5)/2)) minus 90°. That makes the base of the object and the first line of vertices above it.



I then made a new workplane on one of the partial faces. I projected the face onto the workplane and then added a construction circle through three of the points. A vertical line from the centre gives the missing fifth vertex where it meets the circle.



I then join the vertices to make the pentagon, extrude it inwards (negative) by the circle radius with the same negative draft angle.



That operation has generated two partial faces with all five vertices. I construct the pentagons from the vertices and extrude inwards by the circle radius until the shape is complete. A total of eight extrusions are required.



I then shelled the object to 2mm to make it hollow. That created a second part inside, revealing that the construction does not in fact make a complete solid. If that was important one could extrude one of the faces more than half way through, with no draft angle. I just deleted the second part.



The finished item is about 2.5 times initial circle radius across opposite flats. This one was based on a 10mm radius circle.



The file is available on Thingiverse.