## 2014-03-05

### Stepper Driver v1.1.3: tango: ready for manufacturing

So the next iteration of the stepper driver for the millathe has been laid out. It it fixes a few quirks on the waltz board such as some mussed up foot prints and lack of labelling on the dip switches. Also it takes up much less copper are and uses a different card edge connector, actually made to fit a 64 pin PCIe connector. Why? Because as it turns out PCIe connectors are
1. apparently way cheaper than other car edge connectors mostly likely because they're made in stupid quantities.
2. capable of carrying fairly high currents 1A+/pin*64 pins = more amps than a board this size should carry.
3. It's metric  and has a 1mm pin pitch, the 1mm pitch is nice and small shrinking the space the signals take up vs .1" pitch. Also I abhore standard units and .1" spacing is the bane of my existance.
4. A 2x32 pin connector is just about the right size for this board.

That being said lets take a look at this board, behold Tango:

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You might have noticed I did not skimp on the copper. all of the large current carrying traces (motor voltage, pwrgnd, all motor out/inputs) are straight up polygons. I figured there really was no harm in increasing the power sinking capabilities of the board. Actually there is some harm assembly will be slightly more painful, there are no thermals on this board, it is made to be soldered in an oven or with the aid of a hot air gun. The terminal connectors on the left hand side of the board just won't go on with out the soldering iron turned to the max other wise. However besides that one downside there isn't much of a case against using all of the power side copper that is is available in this scenario.  I would rather maximise dissipative capabilities and minimize dissipation.

As far as gate driving is concerned this circuit is still using the original A4989 output as the driver despite (in my opinion) it's relative low current output in the 10's to -barley 100's of mA range for maybe a 20Ohmish resistive values on the gate output. One this I might want to experiment with in this scenario is the ringing effects of an under damped gate vs. the losses from turning on slower due to the damped circuit. In order to minimize inductance ( and therefore overshoot/ringing) in the system each gate drive trace was routed in a pair with a trace going to the source of it's corresponding mosfet, similar to a parallel port matching each signal is matched with a return ground for lower inductance. With the smaller loop it will also lower noise from inductive coupling from the currents on the power side of the board.

In comparison with the last stepper board this one boasts a larger volume pair of decoupling caps for the motors, they could probably be smaller and they take up an ass load of room where assload is like 1cm^2 each... maybe not huge but for this board that is a big component. If you put a rectangle arround the board there is around 35cm^2 of area on this board making them take up around roughly 5.7% of all possible physical space.
But  on the plus side with the increased size of the capacitors allows me to use ones with higher voltage ratings/ capacitance ratings. That was a major limiting factor of the driver last time. Now the main voltage limitation is the power mostfets.

mosfets. this time around going with the DPAK FDD8778 again same fet as last time. One of the main reasons I'm going with it again is it's relatively low gate charge and reasonable on resistance (14mOhm@25C/10vgs). When operating at higher voltages my calculations say that according to the equation:

\\[ Psw = I_{ds} V_{ds} /2(Q/ I_{hl} +Q) \\
but apparent the latex add in I have isnt working... I'll edit this bit later.

Either way the important take away is this equation:

Psw = Ids*Vds/2*Qg*(1/ihl+1/ilh)

It represents the switching power losses occuring in the system.
As far as numbers go for me.

Vds=25V
Ids = 10A
Qg(that I care about) ~ 9nC
ihl/ilh~100mA with a complete short on the driver (I'm going to look at how low a value of gate resistors this circuit can get away with)
f=some weird poop

Now the stepper frequency, it has a linear correlation with your switching losses and is therefore important highly dependent on your control method. In the tango driver, the A4989 controller provides a hysteretic-constant off time current control method. A hysteretic controllers are also called bang-bang controllers, they are not constant frequency and the dependent on the system load. Often thermostats contol temperature using a bang-bang controller. Generally with a hysteretic controller you have a high limit and a low limit, when the output sense is below the lower limit the controller turns on the power full blast, then once the out put sense reaches the higher limit it turns off the power.

Example:
Your thermostat is set to 70 with +/-5 degree limits on the temperature, the temperature is dropping in your house because it's winter and cold outside. The temperature in your house drops to 65. The thermostat senses this and cranks on the heater; depending how large your house is and how powerful the heater affects how quickly your house heats up. Regardless of how long it takes, your heater is going to try it's damnedest to heat up that house as fast as it possibly can. Once your house is 75 degree the thermostat shuts off the the heater and your house begins to cool again. This cycle then repeats.

In the control of the stepper motor the controller is similar, but rather than having a lower limit it just turns the controller off for a fixed time. With this controller, the controller clock is 4MHz (set through a resistor) and the fixed off time is 87 clock cycles. This sets an upper limit pwm frequency of ~46kHz, giving us a decay time of 21.75microseconds. The load dynamics decide how long the on-period will be. The load: a big ass stepper motor, motors are commonly modeled as a voltage source, inductor and resistor. What matters most in this case is this motor inductance.

For a decay time of 21.75us assuming we are dominated by the motor inductance... the time constant is 2.8mH/.73Ohm = millisecond range = way longer than we care about (go on wikipedia and read about RC and L/R time constants if you are curious). Assuming steady state operation with the stepper motor which is ironically is a pretty bad case for this controller in terms of power dissipation, but that is another interesting discussion that is highly related but I don't want to get into right now.

If the motor is drawing 5A RMS on a phase

dIon=dIoff
Von*dton/L=Voff*dtoff/L
dton=Voff*dtoff/Von

You know what, maximum pwm frequency in the steady state is 35ish kHz and I'm tired of writing about this right now this post really went on a tangent. More about controls pwm frequency and losses later and how it relates to this controller.

Either way the drivers should have pretty much the same amperage rating as the last ones at (+10A) but with more voltage up to 25V till the fets poop them selves giving it 200W/ driver minimum for a bit of margin on the driving voltage, I'll be on the look out to better suited fets to increase the power density of the system since that is a real limiting factor at the moment.

I'm gonna go order the boards now.

## 2013-11-11

### Waltz Stepper Drivers: Functional Yet Noisy

After assembling one of the Waltz boards and only screwing up the the tiny driver once the board works!
There were only a few quirks in getting the board to run. A grounding issue between my laptop and the Arduino and the scope which made things flip out whenever the scope connected. Which means something isn't as well grounded as it should be, since half the outlets where I live don't have a ground that might have been the issue... connecting all grounds explicitly in the circuit fixed the grounding issue. From that point out operating the motor was pretty smooth. The board was hooked up to an arduino with modified 'blink' code to step the motor continuously in a given direction. Here's a video of the waltz board driving a stepper:

It worked well up to several kHz of step frequency if the step frequency got too fast the motor would just sit there and make a very annoying whining sound. The controllers were tested up to around 10A with no heat sinking or additional cooling. Using the 'will this burn my finger?' test methodology the main power fets remained cool enough up to around 6A that you could continuously keep you finger on them. At 10A they had a temperature of  'owfuckshitthathurts' after around 5s of keeping your finger on a fet, but it wasn't that 'burn on contact' kind of hot. In conclusion I should get some thermocouples/ temp sensors also the boards seem quite capable of being pumped over 10A. Once they are upgraded to D2pak FETs rather than the jankily soldered on Dpak FETs this might improved heat sinking and current capacity.

On the next rev of the stepper driver the caps are going to be swapped out so the motors can run at higher voltage. Hopefully this will push the motor PWM frequency out of the audible range. The way the A4898 does current control is a fixed off time system, this makes the output PWM of the system variable with various operating conditions such as  the voltage supply inductance of the motor and the decay rate settings on the controller. The noise and vibration also seems to vary greatly with the step frequency of the motor and the microstep settings. Motor operation seems much smoother and less noisy at increased speeds, this might be partially due to rotor inertia/velocity matching up with the commutation of the motor. There will have to be some characterization to find optimal operating points.
The motors being used are 27.4kgf*cm (381oz*in), 3.5Arms/phase, NEMA 23 hybrid steppers: data sheet. When stepping the motors vibrate enough on any hard surface to be really obnoxious, that's why the motor is sitting on a cushion in the video.

Next steps for the millathe project will include measuring up the millathe itself sizing it for a new set of ballscrews and mounting hardware. The next set of boards needs to be designed as well as the motherboard to hold all of the smaller stepper boards.

## 2013-11-06

### Stepper Boards have Arrived: Waltz v0.2

Woooooo the boards arrived like several weeks ago they arrived, but what ever they're getting posted about now so ...woooo stepper boards. They're all pretty n'purple n'stuff.
So far I've only assembled one and there seem to be no fatal errors on the board that will prevent it from functioning. Couple minor package errors and what not but whatever.

here's a pic of the board:
 I went with purple because why the hell not?
I've been slightly distracted from the project by work. However there will be more posts soon since there needs to be board testing.

In the mean time pretty boards are pretty, but pretty useless boards are pretty useless until they are tested otherwise.

## 2013-10-10

### Millathe Stepper Driver v0.2: waltz

In order to power the millathe's axes I decided to create a stepper driver with a higher current capacity than most hobby stepper controllers out there. Driving a mill seems to be above the capabilities of standard hobby stepper motors. Below is a picture of the board. I named this version 'waltz'.

 Waltz v0.2

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The waltz boards are currently being manufactured overseas in China at Myro PCB. Unfortunately as it turns out the first week of October is 'National Day' in China and the the factory closed down for the week a few days after the order was put in. On the flipside this gave me time to finalize/order components before the boards arrived.

waltz v0.2
Overview:

The waltz board is designed to fit in a 20 position 0.1" spacing card edge connector, this makes the board 53x62.5mm. Each board has two full bridges made to power a single bipolar stepper motor. The control of the motor is handled by an Allegro A4989. The FETs to be used in the half bridge are FDD8778 in a TO-263 package, each has 14mOhm of on resistance. These were chosen because of their relatively low gate capacitance/charge to reduce switching losses, however the majority of losses in this system will be ohmic. The Allegro A4989 was chosen because it  seemed like a good all in one solution for various  features such as current control, fast current decay and, up to 16th microstepping all while still supporting external FETs. The only two control inputs to the chip required are step and direction.

This brings us to how this system is going to be controlled. The plan is that several waltz boards will be plugged into a single motherboard carrying an arduino nano. Card edge connectors seemed like a modular way to stack multiple stepper drivers on a single board while having large amounts of connector contact area for the power paths and conveniently allowing for data to come in the same connector. The Arduino nano will partly be the brains of the operation. A computer will stream the control information (step and direction) for all of the waltz boards to the Arduino which will act as a buffer/ demultiplexer and timer making sure all of the outputs are  switched synchonously and with proper timing. This type of setup will take heavy calculation off of the arduino however the tool paths/ step patterns will have to be preprocessed on a computer before being sent to the arduino.

Concerns /Issues/Thoughts/Modifications:
-The current ripple for this system could be quite large depending what motor is chosen. That being said each capacitor is rated to pretty high ripple >4A ripple. However I would like to raise the input voltage to the motors, which would make this more of a concern.
-I would  like to increase the voltage of the system allowing for faster stepping and more awesomeness, this requires new bus caps as they are the limiting factor for the motor voltage, currently they are only rated to 16V.
-Screw these capacitors.
-I Screwed up the zener gate clamp pinout on using a 3-pin package...derp. In the mean time the diodes will have be added in a weird orientation. can be fixed on next rev.

That is all on the waltz board for now more updates when they come in and the mother board is ready to go.

## 2013-07-22

### Millathe: Initial State Pictures

The Millathe with tool post and homemade tool post holder, the spindel speed is adjusted through the pair of little leve : For some reason the door does not like to shut, it pushes against the lid of the gear box despite not looking bent, seems to close fine without the gear box lid though.

All the gears on this side are for the autofeed. Notice the small cracked plastic gear on the upper right. There is also a gear hidng be hind the 76 tooth gear which appears to be detached from its  shaft. On the left is the main drive belt, it goes down to the motor which is single phase 500W asynchronous:

The gear box/ shifter. While there is no back gear on this device it can go pretty slow (speeds are printed on the front of the lather below here it says Maximat7). Theres a little bit of rust on the steel gears and some wear from shifting visible on the phenolic gears but over all it doesn't seem to be in bad shape:

One day perhaps the traction system in the millathe will be redone or incorporated into the control system, but that is a project for the future.

## 2013-07-19

### The Millathe: A CNC story

So a long while back I managed to acquire an Emco maximat 7 machining center. It has been my goal to make it a CNC machine, however it has been sadly sitting in my living room waiting for me to finish busscooter, but now that that is done (besides a few safety features which need to be added). I've turned my sites to making this CNC dream a reality and things are finally starting to happen.

So hear's the deal: this machining center, or the millathe as it is has been nicknamed, is like 75% lathe 25% mill and 100% heavy, seriously the millathe isn't that big but weighs well over 100lbs.  Unfortunately I don't have pictures right now and am other wise not at home so those will get posted later. It also happens to be Austrian and metric which is wonderful because if you know me I tend to shun 'standard' units (really? Who calls 'units standard' when only a small fraction of the planet uses them?). The lathe portion of the millathe seems fully operable except for the lead screw; which is linked through a mess of gearing to what appears to be a cracked plastic press fit gear, so  cant be turned automatically by the spindle motor. The lead screw does have a knob so you can turn it by hand, but this project is about avoiding that. Unfortunately most of the gears in the lathe system seem to be of phenolic materials but they're functional for now, perhaps some time in the future I will rebuild the power part of the spindle drive but that's another project and another thing to add to the list of fixes.

Currently the plan is to make lathe portion CNC before turning to what ever may be wrong with the mill section of the machine. The list of key action items for modifying the millathe in no particular order  looks like this:

•  Replace lead screws (I might not replace them but they look a bit wonky).
• Add Backlash compensation, because no one loves backlash in automated systems.
• Acquire steppers for driving the Z and R axis screws giving control of the lathe port.
• Create method of supplying power to said steppers in order to control the system.
• Create control system for the steppers.
At the moment I've started looking at the control side of things.  The plan is to stream through USB to an arduino nano which can act as a buffer and send the signal out separately to each stepper driver synchronously. I plan on using the Allegro A4989 stepper motor driver to control all of these shenanigans. It will require that each motor needs 2 outputs from the arduino, one for step and, one for direction.
The outputs from the A4989 generally go straight to the gates of transistors but, it's tempting to instead direct them to some gate drives to allow them to drive larger fets for larger stepper motors. I haven't really done any calculations to justify this but it seems like it would be nice thing to have a one size fits all solution to driving steppers even if it is over kill. A pair of LM5109A gate drivers per stepper driver seem perfect for this task since they have inputs that can be driven separately allowing for whatever sort of control method the stepper controller feels like.

However last night I began to experiment with methods of sending arduino data over usb and had moderate success in getting LED's to count synchronously according to their appropriate digital out ports rather than by using the normal digitalWrite commands. This was kind of  interesting since apparently pyserial only sends data as strings and chars. Which to me this seems weird and inefficient but I'm not that experienced with data streaming techniques. Hopefully it will be able to send data at a pace appreciable enough to make it work other wise. I'll talk more about messing around with this in the next post.

I don't have any pictures of the millathe to post at the moment but I always feel bad not posting a picture so here have a repost of the  tool post holder I made for the millathe a while back. It is currently mounted on the millathe and works just dandily. yaaay reposts.

## 2013-07-15

### Math n Stuff (Specifically Geometric Algebra)

So one thing, I've been doing lately instead of building things is studying geometric algebra.

Now you might as why on earth would someone devote them self to some obscure type of math when vector calculus, differential equations and linear algebra satisfy most engineers. Geometric Algebra while not that widely known as far as I can tell (at least I know no mechanical engineers that know of it, but that really isn't saying much), has some pretty snazzy properties. I will babble about it for for a variety of reasons:
1. Its pretty cool (for debatable definitions of cool).
2. It has applications to a robotics engineering problem I have encountered and would like to solve.
3. Geometric algebra is like a general enough form of math that it encompasses several other forms of math used in various areas of engineering in a single construct and could be useful in a wide variety of engineering applications.
4. Writing down the important bits will help me remember it.

Honestly as a mechanical engineer it's been a bit of a 'mindfuck' learning mathematics from papers on maths. After reading several papers, maths from a mathematician's perspective seems very different from how I've thought about math up to this point and how I think more applications oriented think about math. As a meche I was looking at maths in what I think was a practical yet backwards thought process that dictated math functions the way it does because that's the way the world works; but I think mathematicians would say math functions the way it does because of the way that people decided to define it is as a logical construct, regardless of how reality works. Which I would say is much more accurate and leaves the door open to interesting ways types of constructs. Math only functions how it does because of how we define it, it just so happens the world was nice enough to allow its self to match up with some of out logical patterns that we like to call 'math'.

Either way, back to geometric algebra.
Some of its useful characteristics:
Geometric Algebra naturally models geometric things we tend to care about in a concise fashion,  it can be extended to n dimensions, and structures that represent imaginary numbers are naturally formed by the algebra without actually having imaginary numbers. Remember those weird things where $i^2 = -1$? That is an 'imaginary' number. In geometric algebra (what I consider one of the most useful properties) you can represent more than just $i$, the algebra can be used for quaternion representations where the imaginary numbers are extended to $ijk$ or extended even further to represent arbitrary set of 'imaginary' constants which would all have the property $n^2 = -1$ while remaining orthogonal to each other in an whatever dimensional space.
If you're an engineer you might realize the utility of that last bit, it allows you to perform rotations of abitrary dimension using rotors which are kind of like generalized versors.

While I don't know of any applications where you would want to use >6 dimensions but I think it's kind of nice that geometric algebra gives you the option.

For a bit of history on Geometric Algebra http://catdir.loc.gov/catdir/samples/cam033/2002035182.pdf

Otherwise I'm going to talk about some of the technical details of geometric algebra. This are defined in terms of the geometric product, which is the fundamental  operation of geometric algebra, it is denoted by a lack of symbol ,similar to what we do with multiplication. It has the properties of multiplicative associativity, and distributivity over addition. In the following example $a,b$ and $c$ are multivectors but you can think of them as normal vectors right now. The geometric algebra rules that:

1.Associative: $a(bc) = (ab)c$
2.Distributive: $a(b+c) = ab + ac$

Note the geometric product is non commutative, I think that this property is best thought of as a feature because it ends up giving the outer product of the geometric some important characteristics. The inner and outer products of the geometric algebra are defined in terms of the geometric product as:

outer product: $(ab-ba)/2 = a \wedge b$

inner product: $(ab+ba)/2 = a \cdot b$

geometric product in terms of the inner and outer product: $$ab = a \cdot b + a \wedge b$$

And the outer and inner products are analogous to the cross products and dot products of normal vector math how ever they have some subtle differences that I wont go into right now.

More on the outer product:
The outer product is the antisymmetric part of the geometric product. Also from now on the outer product will be noted as $\wedge$ in equations. This property of antisymmetry has some useful effects, and results in something almost the same as a cross product. The cross product of two parallel vectors is 0. similarly the outer product of two vectors that are scalar multiples(a.k.a. parallel) will also result in 0.

$$a \wedge b = - b \wedge a$$
if  $$b = a$$
$$a \wedge a = - a \wedge a$$
$$\therefore a \wedge a = 0$$

If vectors are orthogonal then the following is true: $ab = a \wedge b$. The result of vector $vector2 \wedge vector1$ is not a vector, it is of greater dimension or 'grade', a vector is of grade 1, a plane is of grade 2 and a volume element would be of grade 3. When two things are wedged together their grades add as long as they are not linear multiples of each other.

$$a , vector, line$$
$$a \wedge b, grade 2 plane$$
$$a \wedge b \wedge c, grade 3 volume$$
$$a \wedge b \wedge a = - a \wedge a \wedge b = - 0 \wedge b, grade 0$$

This is to show some of the basic properties of geometric properties of geometric algebra but I don't have time to write a text book so I'm just going to show a few more things about the outer product right now.  Consider two vectors $a$ and $b$ with orthonormal bases (fancy terms for $\hat x$ and $\hat y$ ) $e_{1}, e_{2}$ and scalars $a_{1} , a_{2}, b_{1}, b_{2}$.

Consider the following:

$$a \wedge b = (a_{1} e_{1} + a_{2} e_{2}) \wedge (b_{1} e_{1} + b_{2} e_{2})$$
Remember in geometrric algebra stuff distributes over addition so:
$$a_{1} b_{1} e_{1} \wedge e_{1} + a_{1} b_{2} e_{1} \wedge e_{2} + a_{2} b_{1} e_{2} \wedge e_{1} + a_{2} b_{2} e_{2} \wedge e_{2} = a_{1} b_{2} e_{1} \wedge e_{2} + a_{2} b{1} e_{2} \wedge e_{1}$$

and the outer product anti-commutes so:
$$= ( a_{1} b_{2} - a_{2} b_{1}) e_{1} e_{2}$$

If you are familiar with the vector math this may be apparent but the outer product of two vectors results in a planar element with a magnitude of the parallelogram spanned by the vectors $a$ and $b$. This is the same as a cross product except that the cross product would produce a third vector perpendicular to the other two rather than a plane spanning the two vectors. This pattern continues with higher dimensions, the outer product of 3 vectors would produce a signed volume element with the magnitude of the spanned parallel piped. In fact this would hold to n-dimensional hyper volumes!

I mentioned before that one of my favorite properties of geometric algebra was how it treated imaginary numbers. Lets take a look at how 'imaginary numbers' occur as a result of the geometric algebra. Consider orthonormal vectors of magnitude 1, $a$ and $b$. The inner product is 0 for orthogonal vectors so in this case $ab = a \wedge b$.

$$(ab)^{2} = abab = -aabb = - (aa)(bb) = -1$$

That's right. $(ab)^{2} = -1$. The imaginary numbers naturally appear out of the geometric algebra. Part of the nifty thing is is that it does not require anything to define this besides the geometric product, and isn't actually dependent on a number of dimensions to exist besides having more than two. In this way you can construct multiple 'imaginary' planes and perform rotations higher dimensional systems in the same manner as a lower dimensional system. Some of you guys might note the possibility of the Euler equation to be applied here which does happen. Infact is allows us to construct the powerful rotor which allows arbitrary rotation across a vector. But that is for another time.

End of geomtric algebra for now next time I will talk about the inner product and general screw motion.