More weight lifting

I have had a couple of extruder jams recently when doing the first layer infill. I do that at 195°C to avoid it sticking to the raft. It seemed that ABS was much harder to extrude at that temperature, so I did a range of tests to find out how flow rate and force vary with temperature.

I used my lead kebab test rig with this extruder, which has a 0.5mm nozzle: -



Most measurements are averaged over 8 tests of extruding 40mm of filament, so it took a long time to get these results.

These are the basic measurements: -

Flow rate for a given force seems to increase fairly linearly with temperature. The single points are the weight that I found gave about my normal extrusion rate of π mm³/s. Below are the same points plotted against weight: -



So force does increase rapidly below 220°C.

Glossy

I downloaded this clever object from Thingiverse. It was created by wizard23 using a parametric CSG evaluator plugin for ArtOfIllusion that he and the other the guys at MetaLab are developing.



The two halves screw together and fit perfectly.



I gave it a glossy finish by painting it with acetone. It looks like it is still wet but it actually dries almost instantly.

All torque and no traction?

As promised, I have tested two more drive methods. The first was a 13mm knurled wheel that I had lying around. Handily it was on the end of an 8mm shaft, so I just pushed it through a skate bearing and pressed that into a bearing block.



The results were: -

	PCL	5Kg
	HDPE	10Kg
	ABS	12Kg
	PLA	>12.5Kg

Surprisingly, a bit better than the same diameter timing pulley that I tested previously. I did have to set the gap quite small for the softer plastics, so the filament comes out quite squashed, which may cause problems downstream. The torque is much more even than with a timing pulley.

The final test was a threaded pulley made by the method aka47 blogged here. Following Andy's instructions, I milled a 6mm slot into a block of steel mounted in my lathe's tool post.



I removed the lathe's chuck and backplate and mounted a collet directly in the spindle taper for best centering and stiffness.

I used the shank of an M4 cap head bolt as an axle and some oiled steel washers for spacers, rather than PTFE as Andy's recommendation.



The next bit is magic. You put a tap bit in the lathe's chuck and advance the pulley towards it by 0.05mm each time the pulley revolves. This is viewed from above: -



You would imagine that the inner diameter would have to be exactly an integral multiple of the thread pitch, and the same for a knurling tool. Oddly it doesn't seem to matter, and I can't explain why, even having observed it.

My first attempt was with a M3 x 0.6 tap. I got the height a bit wrong but is was still usable.



The inner diameter of the thread is only 2.4mm, so the filament did not sit in it easily. I made another with an M4 x 0.7 tap, which has an inner diameter of 3.3mm. Perhaps the best fit would be M3.5 x 0.6 but I don't have one of those.



I mounted the pulley on the splined shaft that I had tested before and reprapped yet another bearing block.



I picked the pulley inner diameter as 13mm to get comparable results with my previous tests. Ideally it should be smaller to reduce the torque required. For all but the 4mm splined shaft test I had to use a socket wrench to wind the shaft.



This gave the best result of all the pinch wheel tests, but not as good as screw drive on PCL.

	PCL	6Kg
	HDPE	>12.5Kg
	ABS	>12.5Kg
	PLA	>12.5Kg

I tried the M3 pulley and that was better still, raising PCL to 8Kg. Here is a summary of all the tests: -

	PCL	HDPE	ABS	PLA
4mm splined shaft	2.5 Kg	3.0 Kg	5.0 Kg	7.5 Kg
13mm timing pulley	4.0 Kg	10.0 Kg	8.5 Kg	>8 Kg
13mm knurled wheel	5.0 Kg	10.0 Kg	12.0 Kg	>12.5 Kg
13mm M4 worm pulley	6.0 Kg	>12.5 Kg	>12.5 Kg	>12.5 Kg
13mm M3 worm pulley	8.0 Kg	>12.5 Kg	>12.5 Kg	>12.5 Kg
M5 thread	9.0 Kg	>12.5 Kg	>12.5 Kg	>12.5 Kg

The red figures are lower or marginal compared to the force required to extrude 0.5mm filament at 16mm/s.

My conclusion is that the worm pulley is the best pinch wheel drive method. It also does the least damage to the filament. It does require a lathe though. On the other hand, using an M5 hex head bolt, a couple of ball bearings and some RP parts requires no lathe and should have better grip. That is the direction I am going to go.

Pulling power

There are a lot of extruder drive methods kicking about at the moment, so I decided to evaluate a few by measuring the amount of force they can apply to the plastic before it slips. Rather than build complete extruders, I just made mock ups of the final drive and measured the force they could apply to a spring balance.

My first test was using a splined shaft as a minimalist pinch wheel. This was inspired by Adrian Bowyer's knurled design. I wanted to try it because you can get steppers with splined shafts, so it would be a ready made solution rather than needing a knurling tool and a lathe. I used a 4mm splined shaft that I had lying around. Being that small means the torque required to turn it is quite modest.



I mounted it between ball bearings, which were a press fit into a plastic housing: -



The Meccano gear is just acting as a knob at the moment. I pressed the filament onto it using a skate bearing acting as a roller.



This is my sophisticated test set-up: -



I wind the knob by hand until the filament slips and observe the maximum force for each type of plastic. I noted that tightening the screws past the point where the splines are fully sunk into the filament does not increase grip, it just flattens the plastic more and needs more torque.

The results were: -

PCL	2.5Kg
HDPE	3Kg
ABS	5Kg
PLA	7.5Kg

Not surprisingly the grip gets better with the harder plastics. Unfortunately PCL and HDPE need quite a lot of force to extrude, so this drive method is not really good enough for them. A larger diameter shaft should give more grip due to a larger contact area and possibly deeper splines.

The next method I tried was Zach's pinch wheel drive using a square tooth timing pulley.


This needs much higher torque, but gives a much better grip, particularly with the softer plastics. As you might expect the torque is very uneven as the pulley moves from tooth to gap to tooth.

With HDPE, it pulled out of the chuck before slipping, so I switched to an alternative connection to the spring balance.



The results were: -

PCL	4Kg
HDPE	10Kg
ABS	8.5Kg
PLA	>8Kg

PLA slipped from the chuck and snapped when using the alternative coupling, so the true figure is probably higher, but it far exceeds the force needed to extrude PLA anyway.

HDPE has shot up the ranking because although it is quite soft and very slippery, if you can get a grip on it, then it is very tough.

Only PCL is marginal compared to the force needed to extrude it.

Zach uses a bigger opposing wheel, so maybe that would give a bit more contact area.

The next thing I tried was the original screw feed design, to get a benchmark, as that is what I have been using so far. It can feed all four plastics reliably, the only problems I have had with it are that the bearings wear out after 100's of hours of use, easy to fix by using ball bearings.

The implementation I used for the test has phosphor bronze bearings and a stainless steel screw. Rather than use threaded rod and try to fasten a nut on the end, I used a hex head bolt. Long ones don't come with enough thread, but you have to run a die over it anyway to sharpen the thread.


It is very hard work tapping stainless steel. For my first attempt I made the mistake of turning the top bearing land before tapping, so that I didn't mar the thread in the lathe chuck. Even though I made the land 3.5mm diameter rather than 3mm, the torque required to tap it actually twisted the shaft where it was turned down. My nice polished bearing surface became a dull and wrinkly spiral!

The other half of the drive is made from HDPE. I think this is a big factor in making it work well as the HDPE is very slippery and doesn't seem to wear much.



A self tapping screw secures the PTFE insulator in the clamp.

The other crucial modification is to angle the screw so it bites gradually at the bottom by spacing the top with two M3 washers and only having two very strong springs at the bottom. Here it is under test: -



The grip was too high for my chuck, and the coupling shown above kept snapping PLA, so I made a brass coupling.



This has a 5mm bore that narrows to a 3mm hole in the bottom. I melt the end of the filament to a blob and feed it through the top.

The results were: -

PCL	9Kg
HDPE	>12Kg
ABS	>12Kg
PLA	>12Kg

My spring balance has a maximum reading of 12Kg.

So the screw drive has dramatically more pulling power. It is however, very mechanically inefficient. A lot of torque is wasted by the friction cutting the thread. This can be reduced by shortening the amount of thread engaged. I plan to try it with an opposing roller instead of the HDPE filament guide.

The threaded drive does do more damage to the filament, but the only downside of that seems to be that some dust is produced. The lower filament has been chewed by the timing pulley.



Two other drive methods I plan to try are a knurled shaft and Andy Kirby's worm wheel. That looks like it might have similar grip to a thread, but without as much friction. A lot harder to make though.

Constipated Extruder

My "New Year" extruder, which is the one on HydraRaptor that I use to build things, stopped working while building the first layer of an object. That is the lowest temperature layer, so the plastic is at its most viscous.



I couldn't get it to work again, so I removed the drive and tried pushing the filament by hand. I couldn't shift it. I measured the temperature of the molten plastic with a thermocouple and it was correct, so I deduced that the nozzle must be blocked. I removed the nozzle and when I pushed the filament this came out: -



It is dark and glassy looking. No idea what caused it, but it seemed to have blocked the nozzle. I cleared it out with a drill and reassembled it. I took the opportunity to measure its performance with my "lead kebab" test jig.

Even though this extruder has a 0.3mm nozzle and no taper in the PEEK insulator, it works better than the tapered PEEK extruder with a 0.5mm nozzle.



The most notable difference is that this one has a much bigger heater chamber, so perhaps a smaller heater bore melts the plastic quicker.

I got this interesting graph of flow against force, averaging over five runs of 20mm : -


I think the steep part of the curve is where the flow through the nozzle dominates the force required and the first part is where the plug friction dominates. The point where I operate it is right on the knee of the curve. I suspect adding a taper would straighten it out, but I don't want to strip down my only working extruder to prove that.

So I don't know what caused the blockage, but it is the second time I have had an extruder block, so it goes to show that a detachable nozzle is advisable.

Taper relief

As tapering the stainless steel insulator made so much difference I went back to my PEEK extruder to try the same thing.



I used the tapered reamer to open it up to 5mm at the bottom end.



I had to remove and replace this with the heater hot. You can see where ABS has run up the thread and then burnt when it met the air. This seems to seal the thread as long as the initial leak is slow enough. I don't think HDPE would seal in the same way, so I run ABS first when I assemble an extruder.

The taper made a big difference. HDPE pushed with 4.6Kg went from 1.1 mm³ to 5.3 mm³ and the times got more consistent. I think it is beneficial in four ways: -

• It removes the friction of sliding the plug along the wall.
• It increases the bore where the very viscous, just-melted plastic is, reducing the viscous drag by a fourth power.
• It thins the hot end of the insulator making the thermal gradient steeper.
• The wall being thinner and having a bigger surface area will allow more heat flow into the melting plastic.

Foolishly I didn't measure any ABS flow rates before I made this mod. ABS extrudes at 4.5 mm³ when pushed with 4.6Kg and only 1.3 mm³ when pushed with 2.3 Kg. This is odd in that the differential between ABS and HDPE is less with this variant.

The performance with HDPE is a bit better than the stainless steel extruder when it was fitted with the same nozzle, but the ABS performance is considerably worse. I can't explain why that would be.

A third variant would be to use a longer PEEK tube with a taper to dispense with the heatsink and hopefully be strong enough without the washer and bolts. I think I will have a look at drive mechanisms for some light relief before coming back to that.

It looks like about 5 Kg force should cover the plastics I have tried so far. I don't think anybody has tried pinch wheel with the slippery plastics (HDPE and PCL) so I will have a go at that.

Simply better

I find it very satisfying when making something simpler also makes it better. I tested the simplified heater / nozzle design using the same stainless steel insulator and heatsink arrangement, so I could get a direct comparison of the results.



The heater warms up a lot faster than the one made with two AL clad resistors. It also extrudes faster and the times are more consistent. ABS pushed with 2.32Kg went from 3.7 mm³ to 4.6 mm³, an increase of 24%. HDPE pushed with 4.6Kg went from 3.8 mm³ to 9.3 mm³!

The nozzle is 0.6mm rather than 0.5mm, which reduces its contribution to the pressure by a factor of 2, but all my other tests have shown that what happens at the other end of the heater dominates the force requirement. As I improve things though, the nozzle hole becomes more significant.

Here are the drawings :-



Although it looks complex it isn't difficult to make with a drill press, drill vice, and some taps and dies.

I glued the thermistor in with Cerastil, but I expect it could just be wrapped in tin foil and jammed in like the ceramic resistor, taking care to insulate the wires of course. I use PTFE sleeving.

I didn't need to seal the threads with PTFE tape. I just screwed them up tight and there was no sign of any leakage.

The next thing to try is putting a taper in my PEEK version to see if that can be made to perform as well as this one.

Of course I haven't built anything yet with any of these designs, so caveat emptor.

Rheology

Rheology is the study of the flow of matter and that is what I have mainly been doing for the past few weeks. When I made my experimental set-up to measure flow rate versus extrusion force I expected to be able to produce some nice graphs for different plastics and different temperatures. I found this excellent page which derives the formula for flow rate I in a pipe in terms of pressure P, radius a, viscosity η and length L.

I = πΔPa⁴ / 8ηL

A cylindrical section of flow is considered. Since it flows at a constant speed the force pushing it forwards, which is the pressure plus the viscous drag from the faster inner cylinder, must equal the force retarding it, which is the viscous drag from the slower outer cylinder. Integrating twice yields the formula.

Until recently I had assumed that the large amount of force required to extrude was due to pushing viscous plastic through a tiny hole. The equation shows that for a given flow rate and viscosity, the force is proportional to the length and inversely to the fourth power of the bore.

The RepRap V1.1 extruder has a heater barrel that is 45mm long with a 3mm bore and a nozzle with a 0.5mm hole that is about 3mm long, so that would mean that it is about (3/0.5)⁴×3/45 = 86.4 times harder to push the plastic through the nozzle than the heater. However, that assumes the viscosity is constant. At the point where the plastic melts the viscosity tends towards infinity, so the actual force required to push the filament through the heater is much higher. I have had some extruder configurations where it was hard to push the filament even without the nozzle attached. This simple experiment showed that cutting off 5mm of the heater barrel from the cold end made a significant difference.

Despite these observations I expected the flow rate to be directly proportional to pressure and, with a constant pressure provided by gravity, I expected the flow rate to be constant. In fact the flow rate varies wildly from one run to the next and often increases towards the bottom of the fall. Flow is not directly proportional to pressure, it increases faster than pressure does, and lower pressures seem to give more erratic results.

I tried improving my test equipment to see if I could get more consistency. I reduced the size of the opto tab to record just the last 20mm of the fall, so things had plenty of time to reach equilibrium. I also made a piece to guide the tab into the slot as the weights have a tendency to rotate and make it catch.



I also tried force cooling the heatsink with a small fan. I made a cowling to stop the fan cooling the heater.



This is probably the most complicated shape I have modelled so far. The only mistake I made was not leaving enough room for two of the nuts to hold the fan. I used self tapping screws instead. If I were designing it again I would put tubular bosses behind the screw holes and use four self tappers. It takes some time to get used to designing in plastic. I tend to use a lot of nuts and bolts, and so do RepRap designs, but they are rarely used in commercial plastic products.



The fan didn't seem to make much difference when extruding ABS, either in the variability or the flow rate. If it did affect the flow rate its effect was lost in the variability.

So after some thought about where the variability was coming from I came to realise that it is an inherently unstable experiment. A lot of the force required is pushing the solid plastic plug through the entrance to the extruder.

For ABS and PLA, which both have glass transitions, the situation in the thermal transition zone looks like this.



When the filament meets the point in the thermal barrier where the temperature is above Tg (the glass transition temperature) the filament transitions from its glassy brittle state to a soft rubbery state. In this state it will change shape as force is applied, but it will not flow. Further down it gets to the point where it melts and becomes a very viscous fluid until it warms up to extrusion temperature, where the viscosity is much less. The soft plug gets compressed length-wise by the extrusion pressure, which makes it expand outwards and grip the wall of the insulator. This greatly increases the force required to push the filament, which in turn causes even more outwards force. If the plug is long enough, relative to the coefficient of friction with the wall, it can become impossible to slide it along. Applying more force simply exerts more force against the tube wall, increasing the friction to match the extra push. This is the condition that causes the extruder to jam.

A plug is formed even in plastics without a glass transition, like HDPE and PCL. Molten plastic simply flows backwards until it freezes.

The plug acts like a piston pushing the molten plastic out of the nozzle. Its front face is continually consumed by melting, but the back is replaced by new plastic that is softening.

To prevent the jam, either the coefficient of friction has to be low, or the thermal transition, and hence the plug, has to be short. An outward taper seems to help a lot.

I was asked for a drawing of my tapered stainless steel transition zone, so I drew one from measurements and extrapolation of the taper. The result was scary: -

I hadn't realised I got so close to rupturing the pipe, although it may not actually be as close as the drawing implies. It does work well though.

The reason the plug leads to an unstable result is that the slower the filament travels, the longer the plug is and so the resistance increases and the flow slows further. I.e. a positive feedback effect. It is also why increasing the force gives a disproportionate increase in flow rate. The faster flow reduces the plug length (because the plastic has less time to absorb heat) reducing the resistance, so more pressure gets to the nozzle, increasing the flow rate.

One implication of this effect is that an open loop DC motor is never going to work well. Another is that measuring the force applied to the filament is not a good guide to the nozzle pressure.

I think a more consistent experiment would be to extrude at the desired rate and measure the force applied. The plug would then have a fairly constant length and hence the force should be fairly constant.

Although I cannot get any accurate measurements from the experiment, I did get a rough idea of the force required to extrude various plastics at the extrusion speed I use. I.e. I added weights to get the flow rate around π mm³.

Material	Diameter	Temperature	Nozzle	Weight	Flow rate
HDPE	3.1 mm	240 C	0.5mm	4.60 Kg	3.81 mm3
HDPE	3.1 mm	200 C	0.5mm	4.60 Kg	2.39 mm3
PCL	2.8 mm	150 C	0.5mm	4.60 Kg	3.44 mm3
ABS	2.7 mm	240 C	0.5mm	2.32 Kg	3.67 mm3
PLA	2.9 mm	200 C	0.5mm	3.32 Kg	6.95 mm3

The viscosity of PCL and PLA drops rapidly with temperature, for example PLA would not extrude at all at 180°C but was very fast at 200°C.

The next thing to try is putting a taper in my PEEK extruder and evaluating the copper welding nozzles.

Three times better

I made a plastic mounting plate to allow me to test the new stainless steel extruder in my test rig.



Here it is under test: -



I felt that this design was working well. Now I have the figures to back it up. It is three times better! I.e. with the same weight the extrusion rate is three times faster through the same nozzle and at the same temperature. With 8.27Kg I am now extruding HDPE at 9.43 mm³/s.

This is a dramatic improvement, especially considering it did not work at all until I added the taper to the end of the transition zone. It shows that the design of the entrance to the extruder is critical and at least as important as the exit.

It is really good news because using stainless steel as the insulator really simplifies the extruder and at the same time extends its temperature range and makes it strong and reliable.

By replacing the heater block with one made with a vitreous enamel resistor and a screw-in welding nozzle, I should have a design that can be made with a drill press, a couple of taps and a die.



I haven't tried the welding tip yet, but now I have a means of comparing it against the standard nozzle.

If at first you don't succeed ...

Remember this?



It was my last attempt to get a high temperature extruder idea working. ABS jammed in it, so I put it to one side. This morning I made a slight modification and got it to work extremely well.

The filament was getting stuck in the end of the stainless steel tube where it enters the heater block. I removed the PTFE tape from the threaded joint as I thought that may have been insulating it. That made a small improvement. I could push ABS through it by hand, but only just.

I then flared the hole with this tapered reamer so that it has a 5mm inside diameter at the end, tapering back to 3.6mm, which is the internal diameter of the stainless steel tube.



That made all the difference, I can now extrude my oversized ABS very easily and even HDPE only requires moderate force.

I am not sure why it made so much difference. It makes the wall thinner, so the heat from the heater can get to the plastic easier. It also reduces the friction of the plastic against the inside pipe wall because any downwards motion causes the plastic to come away from the wall.

The next step is to connect it to my test rig to get some comparative pressure figures. My feeling is this extrudes more easily than my PEEK version. That may well benefit from a taper as well.

Lead kebabs

I am aware that I have often stated things like "HDPE needs more force than ABS to extrude" and a "short thermal transition is easier to push plastic through than a long one" but I have never produced any figures to back up these statements. In fact I don't think anybody on the RepRap project has published any extruder pressure figures. Odd because it is the key piece of information needed to design an extruder and it isn't too hard to measure.

I have put together a test rig to measure the rate of extrusion for a given pressure, which I can vary. That will allow me to evaluate different extruder barrel and nozzle designs quantitatively.

I designed most of the parts in CoCreate and printed them with HydraRaptor.



The boss on the far right has mounting holes which match the extruder pump and holds a PTFE cylinder over the filament entrance of the thermal break. I chose PTFE for its low friction. I place a 55mm sample of filament into the cylinder and then push it down with a piston laden with weights. The piston is just the end of a 6mm aluminium rod turned down to 3mm.



An M6 nut stops the green cylindrical saddle, which carries the weights, from sliding down the rod.

The top of the rod is held in line by a guide that it clips into and slides through. A flag 40mm long slides through an opto switch to allow me to measure how long it takes to extrude 40mm of the sample.



The 2mm thick green ABS allows a little IR through, not surprising as it lets some visible light through as well. It was not enough to give a bad logic level but I painted it with black paint to be on the safe side. I should have used black ABS!

The opto connects to the unused filament empty input of HydraRaptor's extruder controller and the heater and thermistor connect to their usual places. A simple Python script tells me how long it takes the flag to pass.

My first idea for weights was to use reels of solder and that is what I designed the rig to accommodate. I managed to muster this little lot, which weigh about 2.2 Kg.



That weight only managed to extrude HDPE at a rate about 1.1 mm³, which is only about 1/3 of the rate I normally extrude at, so I figured I needed about 6Kg to get realistic results.

I needed long thin weights with a hole in the middle, so I ordered some stackable lead sash window weights. I got 10lb, 5lb, 3lb and two 1lb. That allows me to add any weight between 1 and 20lbs in 1lbs increments. A shame they are not in kilograms but sash windows are rather traditional. They cost £50 including shipping so not a cheap solution but they should be handy for measuring motor torque, etc.



They were supposed to be next day delivery but I ordered on Sunday and got them Thursday. The two one pound weights were not the painted stackable ones I ordered and paid for. When I complained I was told they don't stock them any more. Why they let me order them and invoiced me for them I don't know. I shall not be using that company again!

I made a new saddle for the weights to ride on, a centralising collar for the top and two containers for the unpainted weights.



I also insulated the heater with ceramic wool. That reduced the heatsink temperature from 67°C to 57°C by stopping convected heat from the heater warming it. Unfortunately the boss that holds the PTFE cylinder covers a large area of the heatsink. When I make a new pump I will try to leave more of the aluminium exposed.



With this heater, which is a 20 x 20 x 12 mm block with the thermistor mounted halfway between the heater and the melt chamber, the simple bang-bang temperature control works extremely well. The temperature measured at the thermistor varies by less than 1°C. I have an LED which shows when the heater is on. With previous heater arrangements I see it go on and off at about 0.5 Hz. It does not switch cleanly on and off but fades in and out because of noise in the thermistor reading, i.e. I get PWM for free. With this heater the LED simply gets brighter and dimmer, so I have proportional control with just a single if statement! Who needs PID?

Here is the experimental set-up: -



So far the results are a bit disappointingly inconsistent. Six runs loading it with 55mm of 3.1mm HDPE filament and measuring the time to extrude 40mm of it at 240°C through a 0.5mm nozzle with a weight of 8.27Kg gives the following times: -

90, 95, 100, 114, 163 and 98 seconds.

I have no idea why there is such a big variation. 96s would correspond to 3.14 mm³/s, which is the normal rate I extrude at. So we are looking at a force of 81N. With a 5mm shaft that Adrian's pinch wheel design uses that would require a 0.2 Nm motor, I think. You need some margin so it would be the top end of what a Nema 17 can provide.

I don' think I counter bored my 0.5mm nozzle like I did my 0.3mm one, so I may be able to reduce the force somewhat. A lot more experimenting required I think.