Vibration Issues

Before using the robot mower, I always power the blade motors on in my garage for a few minutes to make sure everything is working right. I pulled our vehicles out of the garage, told the missus to expect some loud noises, and made sure that Mr. Mower Jr. was safe inside the house.

The nice thing about the new motor controller I’m using on the blade motors is that I can vary the rotation speed of the blades. So instead of commanding full throttle from the get-go like I had been doing with a relay, I decided to slowly ramp up the speed. It’s pretty incredible listening to the crescendo of the blades as they spool up.

About halfway to full throttle, I started to get a ridiculous amount of vibration. It was extraordinarily loud. The vibration was so intense that it peeled open the eye of one of my deck support eyebolts.

The eyebolt on the turnbuckle supporting the mower deck. The vibration was so intense it peeled it open.

At first, I thought this was just a fluke, or that perhaps the eyebolt was already close to failure, so I replaced it with a spare and repeated the process. I’m not very smart. The result was identical.

When I was in engineering school, I had a choice to take Design of Heat Exchangers or Vibrations and Acoustics for technical electives. As you can probably guess by looking at my mower deck design, I chose Design of Heat Exchangers. It was a fun class, but pretty useless for anything mower related.

So to work through this issue, I’ve had to do some homework. Lucky for me, I managed to stumble upon a copy of Timoshenko’s Vibration Problems in Engineering at the Goodwill a few years ago, which has proven a valuable resource in my vibrations education.

Timoshenko says it better than I can, so I will quote him directly:

By an impulse or sudden application and removal of an external force, vibrations of the [spring mass] system can be produced. Such vibrations are maintained by the elastic force in the spring alone and are called free or natural vibrations.
Vibration Problems in Engineering, page 1

The mower deck is a kind of spring mass system, though geometrically more complex. There is a frequency at which it will vibrate if you were hit it with a hammer, just like a tuning fork will vibrate at 440Hz if you strike it against a hard surface. That unique frequency is called the system’s natural frequency, or frequency of free vibration.

Unfortunately, we’re not just hitting the mower deck with a hammer once. We’re hitting it with a hammer 4800 times per second. That oscillating force does not allow the mower deck to vibrate freely. That’s not free vibration. It’s forced vibration.

In the case of the mower deck, the frequency of that forced vibration is whatever speed the motors are spinning at. Because the motors go from zero to 4800RPM, the mower deck experiences vibration at every frequency along the way. Chances are good that the motors will create forced vibration at the natural frequency of the mower deck at some point as they spool up to operating speed.

A very curious thing happens when you force a structure to vibrate at it’s natural frequency. You get resonance. And the amplitude of vibration becomes very large at resonance. Absent damping it will become infinite. Timoshenko includes a chart that illustrates this phenomenon very well.

Resonance, and the Magnification Factor, from Timoshenko’s Vibration Problems in Engineering, page 42.

When I was spooling up the mower deck motors, I consciously decided to do it slowly to minimize electrical current spikes. This created a problem that didn’t previously exist with the relay, where we rapidly turned on the motors. Timoshenko explains:

The amplitude of vibration [at resonance] increases indefinitely with time… This shows that, while we theoretically obtain infinite amplitude of forced vibration at resonance in the absence of damping, it also takes time to build up these large amplitudes.
Vibration Problems in Engineering, page 48

In other words, if we maintain forced vibration at the natural frequency of a structure, the amplitude of vibration will increase continuously to the extent allowed by any damping present in the system.

By slowly increasing the speed of the motors, I was allowing the mower deck to experience resonance and the accompanying large vibration amplitudes for a period of time long enough to damage the turnbuckle eyes. Who’d have thought?

Something else I noticed was that I had trouble getting the motors to speed up once they were at speeds close to the mower deck’s natural frequency, when it started vibrating really bad. Timoshenko has something interesting to say about that, too:

Experiments show that if any vibrating system is once allowed to reach a steady state just below resonance, it then becomes difficult to accelerate the machine through the resonance condition. Additional power supplied for this purpose is simply used up in increasing the amplitude of vibration rather than the running speed of the machine.
Vibration Problems in Engineering, page 48

I think I have a good grip on what the problem is. Next post I’ll discuss some things that can be done to mitigate this surprising issue.

Mower Blades: More Complex Than You’d Think

ego-lawn-mower-blades-ab2000-64_1000 — A typical mower blade.

While designing the robot mower, I spent a lot of time working on the chassis, electronics enclosures, and wire routes. I tried hard to select components I could easily acquire at a reasonable cost, and that effort paid big dividends when I went to get everything built.

Unfortunately, I didn’t spend nearly as much effort on how the mower blades would attach to my motors, or even what the mower blades would look like. I assumed I could easily find any mower blade size I would need, or that making my own custom blades wouldn’t be difficult.

Now that the blades are the only thing missing on the robot mower, I’m realizing how mistaken that assumption is. I designed the mower deck for three 12in long blades, thinking that surely such a size exists. But most blades are generally in the neighborhood of 20in long.

Small gasoline powered mower engines operate at speeds in the range of 2,500RPM to 3,000RPM, and to achieve an appropriate blade tip speed slightly less than 19,000ft/min, the math forces you to use a blade that is between 19in to 22in long. Blade sizes outside this range aren’t common.

Initially I decided this wasn’t an issue: I’ll just make my own blade. It’s just bar stock with two sharp edges, right? Well, kind of. There’s a fair amount of metallurgical considerations that go into mower blade fabrication. On the one hand, you want a soft, ductile blade that doesn’t shatter when it hits a rock or tree stump. But on the other, you want the blade to be able to keep a sharp edge for a long time, which means making the blade, at least near the sharp edge, more brittle.

Cutting grass creates an inherently moist environment under the deck, so mower blades are usually painted or feature some kind of corrosion resistance. And on top of all this, a good blade will have a small bend opposite the cutting edge to create a little wing so that the grass clippings can be pulled upward resulting in a nice, even height cut.

The more you learn about mower blades the more you start to realize that buying one is really the way to go. In your research you’ll come across horror stories of guys who made their own mower blades and either welded them poorly or jury rigged them to work and then got hurt or even killed by the shrapnel from a blade shattering. Just this video alone should give you pause: there’s a lot of energy under a mower deck.

So off I went to find a 12in long mower blade. The closest I could find was one that was 12.125in long, which leaves 0.375in between the blade tips when they rotate past each other instead of the 0.625in I had designed for. We’re about to find out how accurately the mower deck weldment was made. I really hope I don’t have to grind the ends of the blades down because they crash into each other.

Finding a blade is only half the battle. How do you attach it to the 0.5in diameter keyed shaft on the E30-400 motor? The crankshaft on most push mowers I’ve seen has a threaded hole in the shaft for bolting the blade on. The E30-400 has nothing of the sort.

Could you drill and tap a hole in the end of the shaft? Possibly. But a #10-24 threaded hole is about the biggest you could drill and tap, and that only gives you 0.083in of edge margin from the major diameter of the threads to the keyed portion of the shaft. Too close for comfort in my mind.

The first solution that I came up with was to take a piece of 1.5in long, 2in diameter round stock, bore a 0.5in hole in it, key the hole, and then drill and tap holes for mounting the blade and some set screw holes to clamp the key up against the shaft. But in this scenario, the set screws are the only thing that holds the blade on the shaft. Better than nothing, but not by much.

combined — My first idea for a mower adapter: a machined piece of round stock. Expensive and heavy, not what you want in a blade adapter.

I got a few quotes on three of these parts and the keyway really kills you on cost. I got several no bids because of the keyway alone. And the quotes I did get back were pretty high. Because I don’t like spending $300 on blade adapters, it was back to the drawing board.

What I really need is something with a keyway already in it. Initially I looked into some keyed pulley bushings, but they too have no way to hold themselves on the shaft. That and they have to match your hole pattern on the blade, and none of them met that criteria. They’re cheap, which is nice, but don’t really work for this purpose.

Eventually I got turned onto the idea of using solid shaft couplings. They’re keyed and include set screws. But the outer diameter for most half inch couplings is 1.5in or larger. That leaves no clearance for the bolts to mount the mower blade, which are 1.625in apart.

A 0.5in ID X 1in OD solid shaft coupling with four set screws. McMaster has them for $16 apiece, but if you search on eBay you can find them closer to $6.

After some more digging, I found these smaller OD shaft couplings. And on top of their 1in outer diameter, they come with 2 pairs of set screws offset by 90°. Not bad! Take one of them and weld it to a plate with a hole pattern matching your mower blade, and you’ve got a custom mower blade adapter for ~$30 a piece after material and labor. The result looks like this:

the best option — The 1in OD shaft coupling welded to a plate. The cotter pin keeps the coupling on the shaft.

The nice thing about the plate is that you can get a lock nut on the back side. I’m less worried about things vibrating loose compared to the machined adapter where the bolts run straight into a threaded hole.

But even with four set screws clamping up against the shaft, you really need some positive retaining feature to make sure the blade stays on the shaft. To meet this design objective, I figured it’s best to keep things simple: drill a small hole perpendicular to the coupling and the motor shaft, and then run a small hairpin through it. You don’t need a big one to keep it on the shaft.

The hairpin will add a little bit of eccentricity, as will the set screws. How much? I guess we’ll find out soon. Once the parts get back from the shop I’ll post some graphs and pictures.

Finishing Touches

Drawing pictures in a CAD program is fun, but when the rubber meets the road and you start fabricating something, you quickly notice some areas that weren’t too well thought out. Lately I’ve been backfilling those issues as we discover them at the shop. Here are some things I’ve tweaked over the past few weeks. Hopefully we’ll have a finished robot lawn mower soon!

Mower Deck to Chassis Interface

When the deck is stationary in my CAD program, chains look like a great way to support it. I can flip the model upside down and they don’t even move! But when the robot lawn mower starts rolling in reality, what keeps the deck from swaying all over the place? Well, if it hangs from chains, the answer is nothing.

The turnbuckle that will replace the chain used to attach the mower deck to the chassis.

Unfortunately, the chassis weldment and the mower deck weldments are pretty much complete. So whatever fix we come up with has to interface with those features like the chain did. The solution? Turnbuckles! Some really small turnbuckles, to be exact.

The eye on these little guys is 0.26in ID, perfect for the 1/4-20 screw I had planned on using. The length is adjustable from 3.375in to 4.625in long. They’re rated for 36lb, a strangely specific number, but with three of them they should work fine. The mower deck weighs just over 30lb.

Steel Mower Blades

Another issue the shop made me aware of was the mower blades. I don’t remember if I mentioned it or not, but the reason I designed the robot lawn mower out of aluminum was to avoid any compass interference issues. You may recall I ditched the compass a few months ago, but I never went back and changed the design to steel.

The shop thought that aluminum mower blades were a goofy idea. They’re not wrong, but at least I had a reason for making them that way. Kenny Trussell discovered that when the blades spool up to speed, they interact with the earth’s magnetic field in a way that skews your apparent compass heading.

Making them out of aluminum would avoid that issue, as they’d be non-ferrous. But since we’re not using the compass anymore, it seemed like a reasonable change to make. Besides, all the mower blades you see out in the wild are made from steel.

And if there’s one thing I’ve learned working with fabrication guys, if they make a suggestion that doesn’t impact your design significantly and doesn’t cost much, change it. It’s an easy way to show them you value their input, and they’ll do whatever it takes to get your design working now that their finger prints are on not just the physical parts, but the design, too.

A Legit GNSS Antenna Enclosure

On the wheelchair robot, I had the two GNSS modules velcroed to the top of the robot. That doesn’t seem befitting of a robot I’ve spent a year and a few thousand dollars making. So I designed a small 3D printed enclosure for the RTK GNSS antenna and the UBlox M8N module. It sits on top of a small ground plane disk, mounting to the lid of the electronics enclosure.

gnss enclosure — A 3D printed GNSS antenna enclosure. The larger GNSS antenna is for the Ardusimple RTK GNSS module. The smaller one is a UBlox M8N.

Everybody I talk to says you need a really good ground plane for your antennas. That’s what the circular disk is below the enclosure. The screws for the lid of the enclosure are plastic. Hopefully this doesn’t create any reception issues. I also hope that the antennas don’t have to be perfectly concentric with the ground plane. If anybody has experience with ground planes, I’ll take any advice or feedback you can give me!

Mower Deck Discharge Chute

For some reason I had it on the left side of the mower deck. The shop mentioned that most mowers have the discharge chute on the right side of the deck. I don’t want people latching on to minor quirks of my design, so changing it to the right side seemed like a good idea.

Mower Deck Progress

Here’s the progress on the mower deck last time I visited the shop. We’re a few roll formed parts short of a robot lawn mower!

Innovators in the Autonomous Lawn Mower Realm

As I’ve been working on the mower project, I find myself returning to a few blogs and websites to see how other people are trying to automate lawn mowers. It’s fun seeing different solutions to the problem, and I use their successes and failures to spur my own creativity.

This is a list of innovators that I’m aware of in the autonomous lawn mower realm. If you know of some folks that I haven’t found yet, post a comment and I’ll add them to this list!

MowBotix

These guys had automated a fully autonomous riding lawn mower back in 2017, so I think they win the prize for first large scale autonomous lawn mower. They went silent about a year ago and recently posted on their blog that they’re moving toward a more holistic terrestrial software solution that isn’t just for mowers.

Greenzie

Every once in a while I’ll do a Google search for “autonomous lawn mower” to see what I can find. That was how I found the folks out at Greenzie. They appear to be taking the same approach MowBotix did: start with a riding lawn mower and retrofit it with a suite of electronics and sensors. Their solution looks a lot more robust than MowBotix’s, but also quite a bit more expensive. Their Twitter account is a fun time, lots of cool demonstration videos.

Left Hand Robotics

As far as I can tell, the folks over at Left Hand Robotics started out trying to make an automated snow plow. Based in Longmont, Colorado, I’m sure that’s a very welcome solution. It appears they took their snow plow platform and put a mower deck on the front. Voila! Instant mowing platform.

The downside? It appears these bad boys cost an arm and a leg. Or perhaps just a left hand? I’ll show myself the door. This source says their snow plow solution costs $55,000 and has an annual subscription fee of $4,250. However, for that price I’m sure the system works very well. Their videos are quite impressive.

Deep South Robotics

Robo Robby over at Deep South Robotics has a full up riding mower automated with linear actuators to run the steering arms. With his software and hardware chops it appears to be a very robust solution. I admire his willingness to share his methods along with his successes and failures. The comments on his blog are quite informative. Every time he posts, I learn something new.

Evatech

Well, kind of. Evatech makes a series of radio controled lawn mowers, and BitDog from the ardupilot forums took one and added some special sauce to automate it. I admire the simplicity of this solution. It seems to be quite plug and play. But I’m left wondering why Evatech doesn’t take the leap and automate their platform themselves. Their machines are on the pricy side, but being gas powered are probably pretty reliable.

Kenny Trussell

Kenny was the first person I know of (other than possibly the folks at MowBotix) that used an RTK GPS system on a riding lawn mower. He continues to improve his mower, and I look forward to some updates of his progress soon! Kenny shared a very useful waypoint generation program for creating a mower mission in Mission Planner. If I ever get my mower finished, I will likely be trying it.

The Ardupilot Forum

There are quite a few folks on the Ardupilot forum that are working on their own solutions. I won’t post names here, but a cursory search will bring up several of them.

Mean Green Mowers

autonomous_mower_fmt — Mean Green Mower’s autonomous mower. Great minds think alike?

These guys have partnered with a company called Kobi to build an autonomous robot whose anatomy looks surprisingly familiar. I think the solar panel is a bit over the top though. When your deck motors pull multiple kW’s of power, a 200W solar panel isn’t going to be very helpful in my opinion. But it’s great marketing, especially when your company has “green” in the name.

One thing is for sure, it’s an exciting time to be working on autonomous lawn mowers!

A New Addition to the Mr. Mower Family

68993112_10157592162359312_6153332179632914432_n — The Mr. Mower family is growing! Timing both a lull in the Kansas wind with a smile on Mr. Mower Jr.’s face for a picture is quite challenging.

The lack of activity here on MowerProject.com hasn’t been due to a lack of autonomous lawn mower development. This June we were blessed with a baby boy, and he has been taking up a lot of our time! Posting to the blog in the meantime has been difficult.

Juggling my 8 to 5, the mower project, and making time for Mr. Mower Jr. has been quite challenging. I owe a special thanks to my wonderful wife for letting me run errands for the project and work on it in the evenings. She is truly something special! Having her to bounce ideas off of and to encourage me along the way has been invaluable. I love you so much Mrs. Mower!

As I’ve done in the past, I find it’s good to set goals. Even if I don’t achieve them, they focus my mind and give me a sense of accomplishment and purpose as I work toward them. Below are some goals I have for the next few months.

Finish Procurement and Begin Assembly

I have all of the parts to build the prototype robot lawn mower except for two more SLA batteries and new enclosures for the electronics. The SLA batteries are so cheap that I think it’s worth a gamble on them instead of ponying up the $1,000+ I’d need for some good quality LiFePo4’s.

Once those items arrive I will start to wire up the enclosures and get the subassemblies put together. I will probably need to make another wiring diagram showing how everything connects and functions before I get too far along.

Support Fabrication of the Prototype Weldments

Originally I had planned to fabricate a lot of the robot lawn mower components myself. The idea was that it would be cheaper to purchase my own tools and make the parts myself. Unfortunately, that plan requires a lot of time, a resource I’m very much short on these days with Mr. Mower Jr. in the picture. The economics of paying someone to make the parts suddenly looks attractive again.

To this end I’ve found a local gentleman who is helping me make the weldments. I find myself over at his shop every week or so answering questions about the design, and working with him has been very productive. His feedback has been quite helpful in helping simplify and refine the design so that it is easy to fabricate.

Functional Testing

I have a litany of questions I need to get answered about the performance of the prototype before we even cut grass. A few questions I need to get answered:

How long can the mower run on four 12V, 35Ah SLA batteries?
How well does the prototype handle pivot turns?
How much current does the entire robot draw at typical operation?
We need to verify emergency stop and safety features function correctly.
How much air flow does the current mower deck and blade design create?

Once I’m satisfied the design adequately answers these questions, we can start cutting grass. Stay tuned for some pictures of the fabrication so far!

The Sky is the Limit

Manned Versus Unmanned — An MQ-9 Reaper military drone comparted to the T-6 Texan II. Both aircraft are similar in size.

The primary advantage of autonomy is obvious: the removal of a human from the machine. But that’s not where the benefits stop. Think about what a military drone looks like compared to a fighter jet. If you can get rid of the pilot, you can get rid of the seats, the yoke, the visual instruments in the cockpit. You don’t have to pressurize the cabin anymore. Shoot, now you can change the whole configuration of the aircraft to gain efficiencies you never even imagined when you had to design around a human in the cockpit. Notice how the propeller is on the back side of the drone, whereas it’s on the front of the manned aircraft?

I’ve been watching several folks develop autonomous lawn mowing solutions over the past few years. Back in 2014, Alligator over at the Rusty Nails Workshop attempted to make an autonomous lawn mower using an electric push mower deck with a Piksi RTK GNSS module, the cutting edge in positioning technology in 2014.

More recently I’ve watched the venerable Kenny Trussell and Robby over at Deep South Robotics fully automate a ZTR mower for their acreages. I’ve also been paying attention to the folks out at MowBotix who are attempting to commercialize their solution, which appears to be similar to what Kenny and Robby have come up with.

Each one of these solutions begins with an off the shelf mower. That seems to be a logical place to start: cutting grass is kind of a solved problem. And if you use a riding mower, you get the drive wheels for free, eliminating the need to come up with a way to propel your mower like Alligator and I had to.

Along the way I have questioned whether making a clean sheet design was the right way to approach this problem. There’s no doubt it will be more expensive in the short run. I’ve spent close to 300 hours designing the robot lawn mower over the past year and a half, and once everything is finished I will probably have close to $4,000 tied up in it.

But there is one thing that you can’t beat with a clean sheet design: The opportunity to toss out all the baggage that existing mowers come with and explore what an autonomous lawn mower could look like if you take the person out of the equation.

The Baggage

61XTWHN+JRS._SL1000_ — A typical 36in zero turn radius riding lawn mower.

If you look at a typical ZTR riding mower, you see many familiar features: a nice plush seat to sit in, foam covered control handles, a deck to place your feet on with a nice grippy surface.

Look closer and you’ll find some very deliberately designed safety features, such as a dead man switch under the seat and some guards placed in areas you might get your foot too close to the mower blade.

If you look even closer you’ll discover that because of all the features described above, you kind of have to put the engine far away from the deck spindles. And that forces you to have an intricate pulley system to transmit power to the mower blades.

And your wheel base has to be pretty large in order to create room for a person to drive the thing. Your tires and engine have to be oversized in order to support the weight of an operator that could possibly weigh 200lb+.

Long story short, mowers manufactured today are designed with a significant constraint in mind: the operator. If you remove the operator, you can eliminate those constraints, and you end up with a machine that is much more efficient in almost every respect. The table below is just the weight and size differences between the prototype robotic lawn mower and the mower pictured above.

compare — A comparison of size and weight between the prototype robotic lawn mower and the 36in Swisher ZTR mower.

The prototype robotic lawn mower is half the weight and less than half the foot print of the ZTR mower, while featuring a deck that is the same width. With the right deck motors and batteries, the 14.5hp power rating could be matched, too. However, I suspect part of the reason you need so much power on a riding mower is because it’s larger, and you have to have a person sitting on it the whole time.

The biggest advantage to automating lawn mowers is obvious: you don’t need a person controlling the mower anymore. But if we’re going to remove the person from the equation, let’s take that leap all the way to it’s conclusion. There are huge design efficiencies you can gain by eliminating the operator. Let’s redo the whole system to take advantage of all of them.

Combined Battery Bays

version 5 and 6 compare — Version 5 compared to version 6 of the robot lawn mower.

I started drawing up what the robot lawn mower would look like if we didn’t care about separating the compass from the electric motors. Removing this constraint allows several design efficiencies, some of which I was not expecting.

I decided to use two battery bays on version 5 because I had to mount a mast smack dab in the middle of the chassis. I didn’t want to mount it on a removable lid because it would be cumbersome to remove to get access to the batteries. Instead, I put hinged doors on both bays.

It looks neat in the picture above, but what you don’t see is all the wires running through my chassis tubes between bays to connect the batteries and all the signal wires run through the mast weldment up to the control enclosure. It started getting ridiculous drawing all of that up.

A separate design constraint I’ve been trying to achieve is to keep the wheel base of the robot to a minimum for handling reasons. Unfortunately, the mower deck design I settled on has a motor in the middle of the deck that is a pain to locate such that it doesn’t interfere with the battery bays.

Because I was splitting the battery bays anyway, I positioned the mower deck the way you see in the version 5 picture above. One downside to doing this is that the mower deck is pointing backward from what you see on virtually every riding mower.

bottom compare — The bottom view of version 5 and version 6.

Combining the battery bays let me rotate the mower deck 180º. In the back of my mind I have been worrying the backward orientation of the mower deck might cause performance issues. Now we won’t have to find out.

Additionally, both power and control enclosures can be mounted directly to the battery bay, which will drastically shorten the wire runs I’ll have to make. I’m actually excited to start drawing wires again. Things aren’t so claustrophobic anymore.

And on top of all the benefits above, the chassis weldment went from having 28 total parts to 15. Not too bad!

Where Does All That Power Go?

I’m estimating the electric deck motors on the robot lawn mower will use about 168A of current collectively, and at 24V that means they consume just over 4kW or 5.3hp of power. Even in a worst case scenario, saying that aloud sounds ridiculous. Really? Where is all of that power going?

Remember that power is equal to torque times angular velocity. The angular velocity of the mower blade is governed by the blade tip speed limitation of 19,000ft/min. The linear velocity of the blade can’t exceed this value. If we know the blade length, we can do the math and determine the necessary angular velocity to achieve that blade tip speed.

So we have a very good handle on angular velocity. The mystery variable in the power equation is then torque. The amount of torque we need when the blade is spinning is going to determine how much power the motors are going to consume.

In my previous power calculations, I made a huge assumption:

I have no clue how much torque a mower blade needs. Let’s just use whatever my 21in Toro push mower outputs. It mows grass pretty good. Close enough.

-Me, making poor decisions

The engineer in me loves that assumption. Find the appropriate RPM, pull up the power curve for the engine and boom, there’s your torque value on a silver platter.

The problem is that the robot lawn mower and my Briggs and Stratton push mower are two different animals. I should have made this chart a long time ago, but here is the performance curves for the E30-400 electric motor compared to a Briggs and Stratton 450e gasoline engine, typical of a push mower with a 21in wide deck:

Gas Versus Electric Comparison

The chart above makes more sense when you remember that the 450e gasoline engine is paired with a 21in long blade, but the robot lawn mower has 12in blades. This is why the electric motor curves go all the way to 5,700RPM whereas the gasoline engine curves end at 3,600RPM. Their respective blade length gets you close to the allowable blade tip speed.

Remember that these curves represent the maximum torque and power created at a given speed. When you’re mowing your lawn, how often does your mower bog down? Not much, hopefully. If it’s designed well and your grass isn’t a foot tall your mower probably isn’t operating at it’s maximum torque or power.

Because you shouldn’t often need the maximum torque or power out of your mower engine, the guys that engineered them installed a cleverly designed throttle governor, which varies the amount of fuel and air fed into the engine in such a way that its speed stays in a narrow RPM band.

Instead of letting the engine spool up to the fastest speed it can achieve under a given load, the governor limits speed of the engine, and subsequent power output, making it more efficient. If you need more torque or power, it adjusts the air and fuel mixture accordingly. The governor also ensures the blade tip speed stays safe.

This is where my power calculations go off the rails. I’m using the maximum torque values from these curves (measured in laboratory conditions no less) and sizing an electric motor such that it can achieve this torque value. This is inflating the estimated current these motors will consume.

Remember the motor from the electric push mower I got off Craigslist? It doesn’t appear quite so undersized now, given that our gasoline engine is likely operating somewhere below those maximum torque and power curves.

Our E30-400 electric motor, on the other hand, has no throttle control. This makes the analysis simple: it will always be operating at the curves on the chart above. A brief look at the chart shows that it should still perform very well.

Under no load, it will spin at 5,700RPM. As the required torque increases, the motor speed will drop, but the total power output from the motor increases until the motor is spinning at 2,900RPM. At this power output, one single motor is almost generating the power created by the 450e gasoline engine. Nice!

So realistically, the 168A of current for all three motors is probably on the high side. By how much, I am unsure. But I suspect it’s a significant amount. The robot lawn mower uses three of these motors. Collectively, I would imagine they won’t need too much torque to spin through whatever resistance they encounter.

This is looking more and more like a problem best solved by experimentation, not analysis…

Is a Compass Even Necessary?

bad compass health — My favorite Mission Planner error message: Bad Compass Health.

The compass drives two very costly design constraints into the robot lawn mower:

The need to minimize the number and size of steel or ferrous parts in the design.
The need to separate the compass from the motors to prevent electro-magnetic interference.

To address the first constraint, I selected a 5000 or 6000 series aluminum for the robot chassis and deck. That is quite costly both from a material standpoint and from a fabrication standpoint. And ultimately, you’re going to have some amount of steel in your robot. You can’t avoid it.

The second constraint requires the compass to be raised above the motors to a level high enough to get it out of the magnetic field created by the motors. Because I’ve placed the flight controller and other electronics in the same control box with the compass, several wires have to be run between this box and the power box. Shielding those wires is going to be tricky. Long story short, it creates lots of secondary design inefficiencies.

Reading through the forums and in my own research, I’ve come across a few interesting anecdotes:

Kenny Trussell reports that when steel mower blades begin to spin at high RPMs, the compass heading begins to drift by some amount, about 20º.
Christopher Milner had to place a 4ft tall mast on his vehicle to sufficiently separate his compass from the noise created by two drive motors and one brushless DC motor.
Unplugging and disabling all compasses on my wheelchair robot doesn’t cause any EKF errors, and after traveling a few feet in the wrong direction, the robot corrects its heading somehow, without the compass. I suspect the wheel encoders aid this process.

In light of this information, I am beginning to question whether I even need a compass. It seems to be creating more problems that it solves. The bad compass health error messages in Mission Planner are starting to get very annoying, even though they don’t usually seem to impact the robot wheelchair’s ability to navigate properly.

According to U-Blox, you can use two ZED-F9P modules configured as a moving base-rover combination to calculate the vehicle’s heading. Even with a spread between the antennas of 10in, U-Blox says the heading accuracy is 0.8º. Some folks on the Ardupilot forum are starting to investigate using the modules in this way, and I suspect it will be a much more accurate way to obtain the vehicle’s heading.

I’ve had enough bad luck with compasses that I’m willing to get rid of them altogether and use the ZED-F9Ps for heading exclusively. This allows some significant improvements to the robot design. I guess I’ll head back to the drawing board for the time being…

Weather

Weather in Kansas during February can be pretty awful, and this year is no exception. We’ve had a lot of snow lately, and the temperatures have been 30’s or lower on the days that I could take the robot wheelchair out for some more testing.

A few months ago I listed some goals I had for the robot mower prototype. I’ve made progress toward some, and overall I feel pretty good about where I’m at for now. Here’s an update of the progress.

Prototype Robot Mower Design

The robot mower design as of this evening.

The robot mower design is about 70% finished. I am working on getting the wires modeled in my CAD software currently, and this has been time consuming but I know it will pay off down the road.

I need to revisit how I’m attaching the mower blade to the motor shaft. I had considered using some cheap QD pulley bushings because they have a nice keyway in them that matches the motor shaft and holes that would mount easily to the blade, but I’m not sure this is the best way to do things.

I wish I could find these bushings without the split in them. I’m not sure they make them that way. The split makes me worry that it will be difficult to get good clamping force around the shaft. Also, nothing but a set screw keeps the key and bushing clamped up against the shaft. Because the motor is mounted vertically, all heck could break loose if the set screw loosens up. The bushing could conceivably slide off the shaft while spinning at stupid high RPMs. Not good.

At any rate, CAD work is about the only thing I can work on when there’s 4 inches of snow on the ground outside.

Sourcing Weldments

I’ve been very disappointed with some of the local weld shops I’ve sent drawings to for quote. I live in an industrial town and there are lots of mom and pop shops that I figured would jump at the chance to pick up a small job like mine. I’ve received 5 no bid quotes so far, and haven’t heard back from 3 other shops. Very frustrating.

I tried one of those online weld shops and they quoted the mower deck at $4,500. That’s definitely not in the budget, and I know this weldment is worth no more than several hundred dollars. If you can weld 0.125in thick aluminum sheet metal, leave a comment and I’ll send you over some drawings and maybe we can make a deal.

Purchased Parts

I’ve purchased one of the E30-400 motors to evaluate, but haven’t had time to play with it yet. It’s a lot smaller than I expected. I hope to do a write up on it here in the next few weeks.

I also purchased some high current automotive relays for switching power to the deck motors. The wheelchair design has all of the current running through a 20A switch which in hindsight is a really crappy design. It works for the wheel chair, but to power three 50A motors requires a better solution.

RTK GPS Integration

The Ardusimple RTK GPS boards are working far better than I expected. There’s really very little integration left to do. I will try to take the wheelchair robot out to a large parking lot here when the weather warms up to get a better idea of it’s performance in a decent GPS environment. I’m very excited to see how it does without a ton of trees and buildings around. Its performance so far has been pretty awesome.

Rebuilding the Wheel Chair Robot

I haven’t rebuilt the wheel chair robot yet in light of our crash a few weeks ago. This is also on my to do list. Hopefully we’ll have a chance to do that this next weekend. It’s really hard to get motivated work on a lawn mower robot when it’s 20 degrees outside and there’s snow on the ground.

New Goals

Because RTK GPS integration isn’t going to take nearly as long as I anticipated, I need to spend more effort on getting the robot constructed, under budget and by May if possible. I may try some weld shops in surrounding towns, or possibly the old Craigslist method where I just post drawings and see who replies.