How to measure the speed of a 3D printer - its hotand. And not only speed


    Pic.0 KDPV - my head testing facility

    When I started developing hot-spots for printers, the first of the difficulties was to systematize and organize data and measurements. Also an important problem is that the descriptions most often provide parameters that are very difficult to even compare with something. This article is written in order to understand the various ways of describing the speed of a printer and to show a measurement technique that gives, in my opinion, fairly consistently reproduced results.

    If it is interesting to you - I ask under kat.

    How to measure the speed of the printer head? This parameter is one of the determining the speed of manufacture of a given part, therefore it is very important. Often, a linear extrusion rate of mm / s is used. It seems logical - the faster the melt is squeezed out, the faster the head can move.


    Fig.1 This is a head, a nozzle and a smoothing penny. Depicted conditionally.

    Figure 1 shows the head with a nozzle and a flat surface around the nozzle - a smoothing penny. This surface serves to level the extruded hot plastic. Usually its diameter is taken twice the diameter of the nozzle. Often it is, but it is not a prerequisite. Now let's see how molten plastic can be squeezed out.


    Fig.2 Squeezing plastic with a string

    The simplest case is 1) squeezing the fishing line straight into the air . Thus, it can be conveniently measured by length. Often, data are given on the speed of the head in this way: in millimeters per second - mm / s. Unfortunately, this method does not give an accurate idea of ​​performance. First, the thread under a number of conditions inflates when exiting the nozzle due to the high melt viscosity. This greatly distorts the actual diameter of the thread. In some of my designs, at very high speeds, the diameter of the thread was three times the diameter of the nozzle from which it was extruded. Why this happens, it is better to consider in another article. Also, the thread can stretch under the action of its weight - if it was squeezed hot enough. It can also stick together, bend.

    Option 2) - the thread is squeezed out onto the desktop with some smudging, as is usually done when the printer is in operation - to the width of the smoothing pen . This is necessary for the qualitative connection of plastic threads into a monolithic product. In this case, the performance can be calculated approximately by multiplying the speed of movement of the head by the width of the extruded thread and the height of the layer (the height of the head above the table). V = W * A * H With a height equal to half the diameter of the nozzle and a width of the thread equal to two diameters of the nozzle, the value will be close to 1). More precisely - about 0.78 of the speed of the thread extruded into the air, since the area of ​​a circle is less than the area of ​​a square, and this case is more like a square in cross section than a circle. The exact calculation is difficult because the edges of the wall have a curved shape.


    Fig.3 Squeezing the thread to the width of the smoothing knob

    However, in Slicer we can set the width of the thread equal (but not less) to the diameter of the nozzle!

    The actual data for the nozzle was 0.5 mm, the thread width was 0.58 mm (measured) and the layer height was 0.15 mm. Details printed very well.


    Fig.4. Bottom view - narrow thread. It can be seen that the smoothing penny is not occupied by the entire width.

    In this case, the speed of movement of the head, with the previous volume performance, will greatly increase. Approximately 2.61 times compared with the case in 1).

    Yes, when drawing, for example, a circle, some plastic smearing on the sides of the leveling surface may occur (the penny is stained). In Figure 5, you can see how plastic smearing will occur on the sides of the leveling pen when drawing a circle. The head describes the circle itself without turning, therefore, when the head moves, the direction of movement of the melt from the nozzle describes the circle.


    Fig.5 Changing the direction of smearing of the polymer melt along the surface of the smoothing pen when drawing a circle (in 10º steps) The

    question of the pros and cons of applying a thread width equal to the nozzle diameter is not considered here. In my opinion it is quite good, but it depends on the specific requirements and even the beliefs of the person who writes.

    So, we see that with equal performance of the nozzle by weight and volume of extruded molten plastic, we can get the values ​​of linear velocity and 0.8 and 1 and 2.6, depending on the conditions of extrusion and spreading. In fact, more - what prevents to make a layer height of 0.1 mm?

    It turns out that the most accurate and unambiguous indication of the speed of extrusion in mm ³ / s or mg / s. There is still a subtlety in the fact that plastic is of different specific weight. For example, the specific weight of polyamide is 1140 kg / m³, and ABS is only 1050. Therefore, I usually use mm³ / s to estimate the performance of the head. However, it is still worth pointing out with which nozzle this result is achieved. So more precisely, because the resistance to outflow through the nozzle, even with a diameter of 0.5 mm, has a significant impact on the performance of the head. As an example, let me give you experience with the nozzle µR Ø1.1mm (small resistance) - the maximum performance Vv = 49.3mm³ / s, against a normal nozzle with Ø0.5, the maximum performance of which was only 25.1mm³ / s.

    From this example, it is clear how important a constructive reduction in resistance in the nozzle. This is possible.

    So what value of this parameter will be large and how small? Let's count.

    For example 25 mm³ / s. When flowing out of a nozzle with a diameter of 0.5 mm, the linear velocity at the nozzle exit will be W = V / S. S = π * d² / 4 = 3.14 * 0.25 / 4 = 0.1963 W = 25 / 0.1963 = 127 mm / s.

    This is the performance of extrusion fishing line into the air. If, however, it is applied with a layer of 0.15 mm thick and 0.5 mm wide, the linear velocity of the head may be about 330 mm / s. It turns out already very high speed - compare with 40 - 60 - 80 mm / s recommended by manufacturers.

    A few pictures - the results of extrusion at high speeds.


    Fig.6. Very well pressed plastic.

    In Figure 6, transparent ABS plastic is a well-known supplier. It turned out to be surprisingly uniform at very high extrusion speeds. These samples were extruded from Ø3mm filament at a feed rate of 420-720 mm / min (a similar flow rate for Ø1.75mm would be 1260-2160mm / min). The cool was Ø1.1 and µR - with particularly low resistance (this is a sample for experiments essentially defective, but low resistance.) Volumetric extrusion speed Vv = 51-68mm³ / s. Pay attention to thin tails. From this place began the sample. Due to the short break in extrusion, which was necessary to break the thread and press the Start button, the plastic managed to warm up more than the next part. The more heated plastic has a lower viscosity, the blow-up due to interlayer friction is smaller, therefore the thickness of the fishing line is smaller here. At such speeds, the heat loss of the filament is very large. On faster samples, when breaking, it even broke off more like a clay column, did not stretch at all. Underheating, although 300ºС is set. Bulging from nozzle diameter 1.1mm to 3mm at the exit. In fact, when printing this bloat practically does not interfere. For high-precision printing of pretty statues, the smallest speeds are used anyway, and the details are printed as accurately, except with bubbles.


    Fig.7 But white plastic, not so uniform

    White ABS of the same manufacturer, Fig.7, but apparently with a filler for imparting white color, turned out to be not so uniform. Here the same nozzle, the feed rate of 420-570. Smashed to pieces for weighing - otherwise it would not fit on the scales. Mixed different samples, because everything is similar. Such heterogeneity probably also does not promise anything particularly bad for printing. You will be surprised, but if the melt appears on the nozzle section with a constant flow, albeit slightly changing viscosity, as in this figure, if the slicer is set correctly, normal results will be obtained. In theory. So far, with such speeds, the head does not move very well.

    Here are significantly more unpleasant symptoms:


    Fig.8 Pork tails on the fishing line

    Not very clearly visible, but if you look closely, you can see strange twists on the fishing line. It seems to me that it looks like pig tails, like in the fairy tale about three piglets. This is a sign that the filament does not have time to melt to the center and the elastic center remains in the middle. This specifically prevents typing. Parts simply do not stick to the substrate. They are torn off by an elastic thread.

    But the resistance of the head plays not only a negative role. A nozzle with a rather long spout (the narrowest part of the nozzle - how to say - the depth of the nozzle?) Has a stabilizing effect on the fishing line. It turns out more even and without bloating.

    Is it always necessary? At the price of low speed ...


    Fig.9 Smooth fishing line from the slow nozzle


    Fig.10 Uneven fishing line, blown up from a quick nozzle.

    Nozzles are different. The speed of the experiments shown in the pictures - for a slow nozzle Vv = 18 to 28 mm ³ / s - Well, it didn’t work anymore ... For a fast one, from 31 to 38 mm ³ / s.

    Here are test tubes printed with a single-layer wall, with a 0.5mm nozzle. The wall thickness is 0.58mm


    Fig.11 Test tubes

    The speed was not exorbitant - 130mm / s, linear heads. As you can see, the thread fits exactly in a row in a row. This is made of trimmer fishing line - nylon, so the products are quite flexible. Sidebreaking is not a defect of the retract, it is not for nothing that 7 test samples. These growths promise the ability to significantly increase the speed of movement of the head. But this is a matter of the future.
    This is just a beautiful picture - a piece of transparent fishing line from Figure 6, but under a
    large magnification.


    Fig.12

    It is clearly seen that the bubbles are located closer to the axis. There is still to find out - why they appear. It is clear that they were formed by water vapor. This is not destruction - with the destruction of the bubbles would be located near the walls. The center is warming worse. So there are two options - either when the head is exhausted along the axis, a zone of frostbite is created, or water vapor from the walls has time to evaporate, but not from the internal areas.

    Now let's discuss a little performance measurement. How to make experiments.

    As we have already decided above, it is best to use scales to evaluate performance. This is a convenient, affordable and accurate tool. With it, you can get quite a lot of information about the processes in the head.

    The technique of the experiment on extrusion to determine the performance.

    To control the extruder motor using the program Pronterface. Heat control and temperature control are different, depending on the conditions of the experiment, either through Pronterface, or through a control and monitoring card that I made for the stand on which I test the heads. The board is made using Arduino - nano, supports work with a thermocouple and PID control of the heater temperature. This is much more convenient, since the response time of the thermocouple is much less than the response time of the thermistor, because I make thermocouples from Constantan and Ø0.1mm nichrome wire. Stand in Figure 0 KDPV

    I plan a series of experiments in advance. Set the length of the filament E, mm, I usually use 100 or 150mm. Possible and more accuracy will be higher, but it is ruinous in terms of filament consumption. The extrusion rate S is also set in mm / min. Pay attention to the dimension, here - exactly in a minute! The step values ​​of the experiments is set based on the fact that the maximum performance fell on a range of values.

    An important criterion for assessing whether the head and the extruder cope or not is the slip coefficient. What it is? At a low feed rate, for example 30-60 mm / min, the hobbol teeth are pressed into the filament and propel it when the hobbolt is rotated forward. There is no slipping at all. At some point, the teeth of the hobbol begin to tear through the plastic. To a certain degree of slippage, the pushing process continues normally, but not 100%. Above, instability begins and the extruder locks, because a hobbol can gnaw a hole in the filament, whereupon the pushing ends. Well, I have such a reality and such a hobbolt.

    Here is what the experiment will look like to determine the performance of the head at filament feed rates of 90; 150; 210 with a feed length of 150mm.

    Heat the head. We install a small feed, for example 50mm and the feed rate is also small, for example 30-60 mm / min. Started. This is a cleaning. When a simple heated plastic tends to flow from the head, a void is formed. It will affect the following result. You should have enough time to set E = 150 and S = 90. As soon as the extruder's motor stops, cut off the thread to be extruded to the root and immediately press the start for the entered parameters. While the thread of the first experiment chokes enter the following values. When the extrusion ends, instantly break the thread and start with the new values. You put the thread out for weighing. So with the whole series. The shortest interruptions reduce the effects of post-extrusion and leakage. After weighing the obtained samples, We look how much the sample weight differs from the reference one. You can calculate it based on the weight of the calculated filament length - 150 mm or from experience with a very small feed, when the extrusion can be confidently considered complete.

    So, squeezing at least 80% of the expected volume is the limit of stable operation of the extruder and the head, in my opinion. In fact, this area is very narrow and the experiments are well repeated. Typically, a deviation of 1-2%.

    Another important point in the experiments is a laboratory journal. This refers to the recording and ordering of their experiences, assumptions and calculations.


    Fig.13 My working journals on 3D printer from 2013

    By the way, based on the physics of extruder slippage, it is obvious that with equal slippage the force of the filament by the hobbol will be equal. With good accuracy. Thus, we can obtain indirect data on the pressure in the head.
    Here is an example from experiences:


    Fig.14 Fragment of the Excel file (Libre Office) for the calculation of experiments. Extra cleaned
    The head is the same. The nozzles are replaceable uR and N. For the first, the actual output is 46.67 mm³ / s, with a feed ratio of 79% supplied from the maximum expected.

    For the second 25.14 mm³ / s and 80%. Based on the same pressure coefficients are almost equal. We use a simplified formula for calculating fluid resistance.

    ΔP = K * W * L / D²

    Where ΔP is the pressure drop caused by the resistance, K is a certain coefficient that includes the melt viscosity (for polymers the composition and structure of which is quite variable is not the hope to know it, and not really wanted), W is the velocity of the fluid, L is the length of the resistance portion , D - diameter of the hole in which events occur. This formula can be derived from the Poiseuille equation for the Newtonian laminar motion:

    Q = πd4ΔP / (128µL)

    Where Q is the flow through the cross section, although in mm³ / s, d is the hole diameter, ΔP is the pressure drop across the hole, that is, the resistance is pressure required for flow. µ is the viscosity and L is the length of this hole. If we apply the simplest formula for the flow rate flow rate to this:

    Q = w * πd² / 4

    where w is the flow rate, we get

    ΔP = 32 * µ * W * L / D².

    Since the viscosity for polymers is highly variable and depends both on viscosity and on molecular weight (on manufacturing technology), 32 * µ for simplicity designated K. Why do we use the formula for laminar flow? There is such a Reynolds criterion that determines the conditions for the transition from laminar to turbulent flow. More than 10,000 - "advanced turbulent flow." More than 2300 - undeveloped. So, the Reynolds criterion back depends on viscosity. The greater the viscosity, the lower the Reynolds criterion. In the case of polymer melts, viscosity is always very high. About Newton / non-Newtonian fluid, it is certainly interesting, but for non-Newtonian fluids we can only notice a slight deviation of the dependence of the flow rate on pressure in one direction or another. Melt back will not flow. In one embodiment, non-Newtonian fluids - a visco-elastic flow can manifest itself in the form of a blowing up of a filament at the exit from the nozzle. But this is obviously not the main reason and we will not consider it here.

    So, we have two experiments with close resistance:

    46.67 mm³ / s for a nozzle with obviously low resistance and

    25.14 mm³ / s for a conventional nozzle with a diameter of 0.5 mm.

    The resistance to bursting will be approximately equal.

    If we had only liquid plastic in the wide part of the head, we would get the equality:

    K * W1 * L1 / D1² + K * w1 * l1 / d1² = K * W2 * L2 / D2² + K * w2 * l2 / d2²

    Here we compare two experiments with a nozzle with low resistance and with a normal one.
    The flow rate in the first case will be: 46.7 / (3.14 * 1.1² / 4) = 49mm / s.
    Speed ​​in the widest part of the head: 46.7 / (3.14 * 3² / 4) = 6.6 mm / s.
    For a conventional nozzle, respectively: 128.0 mm / s and 3.55 mm / s.

    Let's substitute: K * 6.6 * 39 / 3² + K * 49 * 0.2 / 1.1² = K * 3.55 * 39 / 3² + K * 128 * 0.6 / 0.5² =>

    28.6K + 8.1K = 15.4K + 307K => 36.7K = 322.4K

    Here we assume that a nozzle with a small resistance has a nonzero length, for example, 0.2 mm. Yes, the equation failed. But you can see how many times the resistance of the nozzle increased with decreasing its diameter, from 8.1 to 322.4. Why then does inequality arise? Because we have because the filament enters the head in a solid form.


    Fig.15 Melting of the filament.
    Melting goes approximately like this: - first a very thin layer of the melt, then it thickens. The filament moves relative to the head wall at a speed w, and the liquid changes its speed from 0 to w. Friction in a thin layer is much higher, hence the unfolded inequality.

    Everything. Thanks for attention.

    PS This article was preceded by articles: https://geektimes.ru/post/285136/

    And there are three parts, though there is a bit long and something slightly out of date:

    https://geektimes.ru/post/259832/
    https: / /geektimes.ru/post/259738/
    https://geektimes.ru/post/259730/
    And the one with which he started - https://geektimes.ru/post/258580/

    PPSAs I understood, many commentators see a stand and consider that this is a necessary and difficult part of measuring the speed of a printer head. No - the stand is just a replacement for the printer itself. Lift the head of the printer higher - and you will be the same. It is inconvenient to change the head every time and reconfigure the printer if you need to print. Yes, and all parts of the fray. The bottom line is that with the simplest methods you can get some pretty tricky data. For me, always in this regard, the model was Michael Faraday with his Candle Story. The simplest methods are serious conclusions. By the way, look what installationpeople do instead of banal weighing. And another conclusion: advertising data on the speed of printing should be treated with the understanding I have set out - the difference with reality can easily be several times even without deception, but simply because of a different measurement technique.

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