{"id":3936,"date":"2016-11-14T12:00:34","date_gmt":"2016-11-14T17:00:34","guid":{"rendered":"https:\/\/dyzedesign.com\/?p=3936"},"modified":"2024-05-30T08:30:01","modified_gmt":"2024-05-30T12:30:01","slug":"printing-300-mm-s-part-2-calculations","status":"publish","type":"post","link":"https:\/\/dyzedesign.com\/fr\/2016\/11\/printing-300-mm-s-part-2-calculations\/","title":{"rendered":"Printing at 300 mm \/ s – Part 2 – Calculations"},"content":{"rendered":"

This second part will discuss the measurable and calculable limits of the parts explained in Part I. It will be very useful if you want to find the theoretical limits of your machine.<\/p>\n

Next part will show firmware and slicer configuration, real experiments, and prints.<\/p>\n

Make sure you read\u00a0the first part<\/a> which explores the components involved in both speed and acceleration performance.<\/p>\n

\n

Motion<\/h1>\n
<\/div>\"Printing<\/a>

Speed and position graph<\/p><\/div>\n\n

As we have previously seen the relation between speed, acceleration, and jerk, we will now explore these parameters in our goal to achieve 300 mm\/s. Let’s consider our printer have an acceleration setting at 3000 mm\/s^2. Remember that most printers have lower settings.<\/p>\n

\"TimeToAccelerate=\frac{Speed}{acceleration}=\frac{300mm/s}{3000mm/s^2}=0.1s\"<\/p>\n

Knowing that our printer takes 0.1 second to reach its full speed isn’t very useful. However, we can find the minimum distance for maximum\u00a0speed easily.<\/p>\n

\"MinimumDistance=\frac{1}{2}*Acceleration*Time^2\"<\/p>\n

\"=\frac{1}{2}*3000*0.1^2=15mm\"<\/p>\n

15mm is quite long for a single edge. Remember that this distance is for accelerating only<\/strong>. The worst case, like a square edge, will require decelerating too, so the same length will be required. In short, we need to print a 30mm square<\/strong> if we want to reach 300 mm\/s during a fraction of a second. In this case, the average speed will be about half of the max speed, so 150mm\/s .<\/p>\n

Hotend<\/h1>\n

As you’ve seen in\u00a0part 1, we have determined that the maximum output flow using a 0.40mm nozzle is about 15 mm^3\/s at 250\u00b0C. The optimal line width is between 1.1 and 1.5 times the nozzle diameter, so between 0.44mm and 0.60mm. Let’s consider a line width of 0.50mm for this example. We can now determine the maximum layer height:<\/p>\n

\"LayerHeight=\frac{Flow}{LineWidth*Speed}=\frac{15mm^3/s}{0.50mm*300mm/s}=0.10mm\"<\/p>\n

0.1mm layer is a good setting for printing great quality prints. We will see later if we can obtain a quality print with these settings!<\/p>\n

\n\n
\n

Extruder<\/h1>\n

Based on the hotend maximum flow, you can determine the filament speed and your motor rotation speed.<\/p>\n

\"FilamentSpeed=\frac{4*Flow}{\pi*FilamentDiameter^2}\"<\/p>\n

\"=\frac{4 * 15 mm^3/s}{ \pi * (1.75mm^2)^2 }=6.23 mm/s\"<\/p>\n

To measure the rotation speed, it is better to use the firmware steps\/mm than measuring the outer diameter of the driving wheel. The teeth penetration in the filament is important to consider. We will consider the values for the DyzeXtruder GT, and we will compare the result with the motor specs later.<\/p>\n

\"RPM = FilamentSpeed*StepsPermm*TurnPerSteps*60\"<\/p>\n

\"6.23mm/s * 742 steps/mm * 1 turn / (200*16 steps) * 60 s/min =86.5RPM\"<\/p>\n

Stepper motors are rated from 800 up to 5000 RPM, depending on the motor, voltage, and driver. 35 RPM is nothing to worry about.<\/p>\n

\n

Motors<\/h1>\n
<\/div>\"Printing<\/a>

Stepper curve from Applied Motion<\/p><\/div>\n\n

Steppers have a unique torque-RPM curve due to the way they work. They start\u00a0with a high torque which slowly decreases\u00a0with speed. Depending on the parameters, some motors will be able to maintain their maximum torque for a wide range of speeds.<\/p>\n

If we take the 0.9\u00b0 stepper motor from the previous example, we can easily find the maximum RPM for maximum torque using the following formula:<\/p>\n

\"MaxRPM=\frac{Voltage}{Inductance*2*Current*Steps}*60\"<\/p>\n

\"=\frac{12V}{0.004H*2*1.68A*400steps/rev}*60=133.9RPM\"<\/p>\n

133.9 RPM may sound\u00a0low, but remember that it is the maximum speed at maximum torque. The maximum speed with lower torque is determined by experimentation and torque curves should be consulted.The torque is lower because the voltage applied is reduced by the back electromotive force (back EMF), thus each coil can’t reach the full magnetic force. Back EMF increases with motor rotation speed.<\/p>\n

\n

Extruder Motor<\/h2>\n

As you can see, the previous motor has no problem driving a 5.65:1 geared extruder for a 300 mm\/s print. The actual motor inside the DyzeXtruder GT is much smaller and requires a lower current thus increasing the maximum RPM at maximum torque to 310 RPM. The specs are 1A, 200 steps and 0.0058mH. This motor can still run faster while maintaining its output torque.<\/p>\n

\n

Axis motor<\/h2>\n

Accelerating at 3000 mm\/s^2 requires strong axis steppers. Depending on the driving mechanism, higher speed or higher torque will be required. The methodology is very simple:<\/p>\n