Correcting Last Week's Errors
After discussing with Nick and Alex, I came to realise last week's calculations were based on completely flawed logic. I was for some reason under the impression that the thrust of the EDF needed to out-weigh the overall weight of the carriage, which is not true when moving horizontally (no force of gravity to overcome).
This means that the EDFs I ordered are definitely overkill for what I need them for, but they have already arrived (several days earlier than expected) and returning them and waiting for less powerful fans would just be a waste of time at this point.
To make everything work, I need to calculate the force required to move the entire carriage using Newton's second law of motion, F=ma.
- m is the mass of the carriage, which will be static once it's built
- a is the acceleration which will be variable depending on the position the carriage needs to reach
- F is the thrust required (in Newtons) to make the carriage move at the specified acceleration
The forces involved with EDFs can be very high, high enough to damage or break the motor in some cases. It is important to make sure the acceleration does jump from 0 to 100% too quickly. This means I need to be looking at the next differential up from acceleration, jerk.
Jerk is the rate of change of acceleration, in a similar way to how acceleration is the rate of change of velocity. By making small adjustments to jerk, even just between discrete values of 1, 0 and -1, it's possible to finely and smoothly adjust acceleration in a way which ensures the forces applied to the motor shaft aren't going to do any damage.
This graph shows a simulated change in jerk, acceleration, velocity and absolute position over a span of 200 discrete time steps:
Note that velocity and distance have been scaled to 1/10 and 1/100 of their true values respectively, in order to make the other elements of the graph properly visible.
Over the next couple of days, I will work on creating a dynamic visual simulation. This will help me visualise the equations I need to implement for the real hardware.
My updated Gantt chart for this week:
