Black and blue

I got some of the 3M blue masking tape that Vik Olliver recommended as a bed material for PLA. It seems to be available up to 50mm wide, so four strips covers the bed of my machine.



Whereas I could not get PLA to stick reliably to MDF, it sticks easily to the tape.



Why is it black? Well my feed of PLA from the overhead hanging basket snapped. It must have got kinked and bent through too sharp a radius. When I pushed the new end into the top of the extruder to restart it, I must have caught some of the grease from the top bearing. The grease is yellow, but as soon as the stainless steel bearings have run for a while it turns black. That small amount of material was enough to turn the first few layers of my object dark grey.

The object was a complicated shape and came out very hairy: -



It took a lot of cleaning up and has some defects and weak spots where there is a lack of material due to the oozing that occurs on the way there. I have some compensation for this effect, which works well for ABS. Basically I estimate the amount of ooze from the time the extruder is off and then run the extruder for a while to replace it before starting a new thread. I think the constants need to be completely different for PLA.

The object was relatively large, but showed no sign of warping, even when removed from the bed. The base of it is completely flat.



I had successfully removed several small objects but I damaged the tape removing this one. It was easy to replace one strip and reducing the temperature of the first layer from 210°C to 180°C seems to allow large objects to be removed easily.



Another problem I had was the PLA started revolving fairly quickly in the extruder, making the hanging basket spin. Each time it revolves it reduces the amount fed by one thread pitch. If it happens too much the object has material missing. I fixed it by applying some oil to a felt washer that the filament passes through. A good reason for moving to a pinch wheel feed though.

I made a 65mm cube shaped box and it showed no sign of lifting from the bed.



It was easy to remove though and this time did not damage the tape. Even after it was removed the base stayed fairly flat.



Much better than my attempt to make the same box in ABS some time ago.



Not only did it curl after it was removed from the base, it also ripped itself open at the corners while it was being built. There is also a wavy distortion on the left face which I had not encountered before.

I think what happened is that when the cracks opened the edges lifted, causing the nozzle to bear down on the wall it had already built. That meant there was excess plastic for the gap between the surface and the nozzle. Normally when that happens blobs are left on the surface. When the next layer is done the nozzle just plows through the blobs. Because the walls are only 1.5mm thick in this case, and tall, they flexed sideways instead. That caused a ripple and the effect seems to build up layer on layer. I could see the wall flexing as the nozzle passed over it.

So PLA allows bigger objects to be made before a heated bed or chamber becomes necessary.

Even relatively large PLA objects can be made without a raft. That saves a lot of time and material, but you do have to get the z-calibration spot on and the bed perfectly level.

The masking tape makes a good, cheap, reusable bed material and it is quick and easy to replace if you do damage it.

Mixed decay, mixed blessing

Having set the correct off time to suit my motor I can now micro step it with equal spaced steps, but only if I disable the mixed decay mode.


When the chopper switches off it can do it two ways. It can turn on both low side transistors. That short circuits the motor and lets the current recirculate. If the coil was a perfect inductor and the transistors perfect switches, the current would circulate forever and you would have a superconducting magnet. Real coils and transistors have some resistance, which causes the current to decay, but as these are relatively small the mode is called slow decay.

This is fine and efficient until you take the motor's back emf into account. During the rising part of the sine wave the magnet is moving towards the pole piece, so it generates a voltage that causes the current to fall faster. The on time gets longer to compensate and all is well.

On the trailing edge of the sine curve the magnet has gone past the pole piece and generates a voltage that increases the current in the coil. If it is going fast enough it can mean that the current doesn't fall at all during the slow decay period. As I showed previously that can cause a severely distorted waveform which makes the motor noisy.



The Allegro chips offer a mixed decay mode, where they switch to fast decay for part of the chopping cycle on the downward half of the sine curve. In fast decay mode one low side and one high side transistor turn on and reverse the voltage across the motor. That overcomes the BEMF and causes the current to fall much faster. It also returns current to the supply rail, which can upset some power supplies if there isn't some other load to absorb it.

Mixed decay gives a current waveform like this: -



The off time is fixed, so the current falls further making the ripple greater. If you set the percentage fast decay to give a clean waveform at your top speed, then the ripple increases at slower speeds. It is maximum when stationary, when there is no BEMF and fast decay is not required at all.

The problem is that the target current is the trip point of the comparator, so it is the peak of the chopping waveform. That means the average current is less by half the ripple current giving a positional error.

With the low inductance motor I am using, the ripple current has a large amplitude, so the error introduced when the motor is stationary is about the same as a micro step. That means the first step with fast decay is about twice as big as it should be and the last step is virtually zero.

With the A3977 I can disable fast decay and the steps are fairly even, but fast running is then distorted. The PFD setting needs to change with speed.

With the A3983 that I have used on my new extruder controller the PFD setting is fixed at 31.25%. That means I can't get evenly spaced microsteps with the NEMA17's that I have, when running slowly. Not a big problem with the extruder because I plan to gear it down 40:1, which means one micro step is only about 0.02mm. I am only using microstepping to give smooth motion rather than extra resolution.

The problem is exaggerated because not only am I using a low inductance motor, but I am also trying to run it at 1A, whereas it is rated for 2.5A. At 2.5A the off time would be about 2.5 times smaller, so the ripple would be 2.5 times less. The steps in the current waveform would be 2.5 times bigger, so the distortion would be reduced by 6.25 times. As it is about one microstep now, it would reduce to 1/6th of a microstep, so would be acceptable. The temperature rise would then be 6.25 times greater of course.

I was planning to use A3977s for my axis control though, where positional accuracy is important. I am beginning to think I will be better off just using dual H-bridges and doing the rest in software using a powerful micro with a fast ADC.

To be able to cope with a wide variety of motors you need to change the current, the off time setting and the percentage of fast decay. You also need to take the ripple current amplitude into account to control the average current, rather than the peak. All these things could be automated with a software solution.

Motor Maths

In a previous post I showed the pitfalls of constant off time choppers like the A3977. Basically you have to set the off time long enough to be able to deliver the lowest current step of the microstepping, otherwise the steps are not equally spaced.

Forrest raised the point of how do you do that without a scope. It is fairly easy to calculate from the target current, supply voltage and motor resistance using nothing more complex than Ohm's law. It did take me a few days to come up with a formula that matched my measurements, but that was because I was accidentally running the chip without synchronous rectification enabled.

The motor current is equal to the reference voltage divided by 8 times the sense resistor. The maximum sense voltage is 0.5V, so a sensible value for the sense resistors is 0.2Ω, giving 2.5A maximum with 4V at the reference pin. My lash up uses two 0.5Ω resistors in parallel giving a 2A maximum.

The minimum current required on the first step of the microstep will be I × sin(π/2n), where n is the number of microsteps. In this case n is 8 so the smallest current step is 19.5% of the full current. To calculate the minimum off time needed we need to be able to work out what the duty cycle will be to get a given current.

Here is what the sense resistor waveform looks like when the current is set to 1A and the motor is stationary. The on period is 3μS and the off period is 20μS. The supply voltage is 12V.



The sloping top of the waveform is actually an exponential curve, but at this scale it is very close to linear and to simplify the calculations I have just used the average value.

So we know that 1A flows from the supply for every 3 out of 23μS. That gives an average current from the supply of 1A × 3 /23 = 130mA. Indeed the supply current measures 260mA as there are two coils energised (I set it to full step mode to make this measurement).

When the chopper is on energy flows into the inductance of the motor, increasing its magnetic field slightly. During the off time the current flows in a loop consisting of the motor and the two low side transistors. Power is dissipated by the motor's resistance, so it loses energy by its magnetic field decreasing slightly. We can calculate the duty cycle by reasoning that the energy going in during the on state must equal the energy coming out in the off state.

The motor is a Lin 4118S-62-07 NEMA17 motor I got from Makerbot. It has a coil resistance of only 0.8Ω. That means the resistance of the sense resistor and the on resistance of the FETs in the chip are significant in the calculation.

During the on state current flows through one top transistor, the coil, one bottom transistor and the sense resistor. All the resistances convert electricity to heat so the power going into the magnetic field is the power drawn from the supply minus the resistive losses in the circuit.

Power = VI or I²R, Energy = PT.

So we have (V_supply × I - I² × (R_motor + R_sense + R_{DS(on) source} +R_{DS(on) sink})) × T_on.

In this example (12 - (0.8 + 0.25 + 0.36 + 0.45)) * 3 = 30.4 μJ.

During the off state the current flows through the motor resistance and two low side transistors, so the energy lost is: I² × (R_motor + 2 × R_{DS(on) sink}) × T_off.

In this example (0.8 + 2 × 0.36) × 20 = 30.4 μJ, so theory matches practice (using typical values from the datasheet for R_DS(on)), always very satisfying.

So if we call the total resistance in the circuit with the switch on R_on and the total when it is off R_off we have: -

R_on = R_motor + R_sense + R_{DS(on) source} +R_{DS(on) sink} = 1.86Ω
R_off = R_motor + 2 × R_{DS(on) sink} = 1.52Ω

Then T_off = T_on (V/I - R_on) / R_off

For our example if we set the minimum T_on (T_blank) to be 1μS, I = 0.195A, so T_off is 39μS.

At 1A T_on will then be ~6μS. So the minimum chopping frequency will be ~22kHz and the maximum will be 25kHz.

C_T = T_blank / 1400 = 714pF, so use 680pF.
R_T= T_off / C_T =58K, so use 62K.

So in conclusion using the simple formulas above it is easy to calculate the correct values for a given motor, supply voltage and minimum current. I wish the datasheet and apps note had included this formula.