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.

velocity
The maximum angular velocity of a 21in mower blade for compliance with ANSI B71.1-1990. Don’t forget the calculation between radians and revolutions.

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:

  1. The need to minimize the number and size of steel or ferrous parts in the design.
  2. 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:

  1. 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.
  2. 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.
  3. 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

robot-mower-03-03-19.png
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.

Small Design Changes

mower 1-6-19
The robot mower design as of this weekend. Some wiring is completed.

I’ve decided to change a few things on the robot mower design. I have a tendency to get hung up on really small things by spending way too much time thinking about them. The deck height adjustment was turning into one of those things.

I’ve changed the design to include four simple clevis pins. They’re $0.50 a piece. You don’t need to adjust the deck height that often, and spending $100 on parts to do that in a fancy way is a waste of effort and money.

I modeled up a discharge chute because I think the mower will need one to look professional. I intended to 3D print it, but it turns out the dimensions are big enough that most hobby websites won’t take it. I know of a place nearby that does industrial 3D printing and they quoted me $290 for the part out of ABS. Yikes. Maybe I’ll try to adapt an off the shelf chute instead. That’ll be more reverse engineering but it will probably work better. And cost a few hundred less.

xt60
Some simple XT60 connectors for the motors. They’re rated for 60A and should be appropriate for this application.

I’ve started modeling up some wires and coming up with a way to neatly connect the motors was more challenging than I thought it would be. I found some “wall mount” XT60 connectors that will hopefully will work well. I’ll have some mounting plates NC machined and then attach the XT60 wall mounts to the plate.

Mower Positioning

5939749916dcd.image
A typical robot lawn mower on the market today. It’s basically a Roomba, but for your lawn. Have fun tearing up your lawn to bury cable!

When you google “robot lawn mower” you will find a bunch of Roomba looking robots like the one above. The missing ingredient between these robots and the one I’m attempting to make is one thing: positioning.

When you need your lawn mowed, you want it to be mowed 100%. You don’t want half the lawn cut and the other half not cut. You don’t want gaps of uncut grass between your stripes. You don’t want random paths cut through your lawn. You want nice, parallel, alternating stripes.

To accomplish that, you need to know the location of the mower throughout the process so you can keep track of areas that have been cut, and so you can cut the grass in a specific manner. Back and forth stripes, for example, or perhaps a nice circular spiral moving outward from a tree.

I’ve come to the conclusion that to really automate the mowing process, you need at least +/-1in of positioning accuracy. Historically, such a system required a $40,000 survey grade GPS system from Trimble or Leica and the equivalent of a master’s degree in computer engineering to integrate it into your robot.

So the Roomba mower guys, given these constraints, came up with the following solution:

Who cares where the mower is? Just fence it in and have it mow all the time. You’ll eventually cut all the grass. We gotta make a product that we can realistically sell to people at a profit, you know.

-Some engineering manager out at Roomba Mowers Inc, I’m guessing

Every robot mower has to compete with the neighbor kid that will mow your lawn for $20. He’ll even try to make the stripes in the front lawn mostly straight and parallel. That’s the price point and level of quality that you have to beat with any robotic mowing system.

The Roomba mower guys sacrificed quality and scalability to get there with their system. Those are probably decent tradeoffs if we’re honest. While these Roomba mowers are for the most part a novelty, for some folks they work okay. But in the scenarios where they do perform well, they’re probably not value added at their $2,000+ price point.

So for years, guys like me that dreamed of real robot lawn mowers were left with just that: dreams. I don’t have $40,000 laying around, and I’m a mechanical engineer, not a hardware guy or a computer engineer. And even if I had both of those things, such a system can never turn a profit in the market place.

Enter u-Blox with the ZED-F9P module….

Lithium Batteries

What would a composite lithium ion battery look like if we were to use one for the mower?

Untitled
What the performance of a hypothetical lithium ion battery could look like if we were to use one.

We need a nominal voltage of 24V, so if you string 7 18650 batteries with a nominal voltage of 3.6V you’d end up with 25.2V, which should work fine.

String 15 sets of those 7 rows of batteries connected in series together and you get a battery with 45Ah of charge. Not too shabby. This would be a 7s15p battery in lithium ion parlance, I think.

Two of those 7s15p batteries would fit in each of our two battery bays. You’d need a total of four to achieve the numbers shown above. They’d fit in our robot something like this:

Lithiums
How the lithium batteries would fit in the battery bays. Very compact. Very expensive.

The weight savings here are significant: 70lb. This is to be expected, but I’m surprised it’s this high. I don’t have a truck to haul this robot around in, so the lighter I can make it, the easier it will be to take it out for field testing. The reduced weight should also decrease the power consumption from the robot’s drive motors, making it more efficient, and possibly more agile.

The cost is still going to be over $1,000 though. Talking with some suppliers, I think the 18650 cells cost a little less than what Amazon will quote you, probably closer to $4.50 per cell. But you still need some fancy charging equipment, and there will be labor and material cost for building up the battery and coming up with a way to secure them in the battery bay.

I may start out using SLA batteries because the monetary risk is pretty low, about $300. They may perform better than I’m expecting. If they don’t, the lithium ion batteries appear to be a good plan B if we need more run time.

Power Consumption Revisited

I think I may have incorrectly estimated my power needs for the mower. A key assumption I’ve been making is that the motor will generally need to be capable of generating ~5ft-lbf of torque during maximum operation. I’m not sure this is really true though.

Do We Really Need 5ft-lbf of Torque?

The 5ft-lbf of torque figure comes from taking a typical gasoline push mower engine and looking at the gross torque output of the engine. But one variable I forgot to consider is that the torque curves I looked at are associated with an engine typically used with an 18in to 21in blade. Our mower uses a 12in blade.

Intuitively, the torque we need to cut through grass is going to be positively correlated to the amount of grass we’re trying to cut at once. So a smaller cutting blade should require less torque than a larger blade. There’s less grass for the blade to run into, sapping momentum from the rotating blade.

I have no idea what the relationship between blade length to required torque looks like. I am going to assume it is linear for simplicity, but I have no clue if this is a good assumption. The torque you need is also going to be related to the quantity of grass clippings circulating around under the deck impacting the blade. Good luck modeling that.

Given the smaller blade size, let’s say you only need 60% of that 5ft-lbf torque value, so 3ft-lbf or 2.2N-m of torque. That’s the ratio between a 20in blade and a 12in blade.

How Much Current Does the Motor Draw at 3ft-lbf of Torque?

The performance curves for the E30-400 motor say that the motor consumes 56A of current at 3ft-lbf of torque. I think this is a more accurate number for current draw from the motor.

E30-400_Chart
Performance curves for the AmpFlow E30-400 DC motor.

How Much Power Does the Motor Consume at 3ft-lbf of Torque?

Another mistake I made was pulling power numbers off this chart thinking they were power supplied to the motor, not shaft power output by the motor.

This is an important distinction, because no motor is 100% efficient. The input power should be the power supply voltage of 24V times the current consumed at a given point on the curves. At 3ft-lbf of torque, it’s (56A)(24V) = 1344W.

This jives with the chart above, because shaft output power at 3ft-lbf or 2.2N-m of torque is about 1040W. That would imply an efficiency of (1040W)/(1344W) = 77%. The chart says the motor is about 75% efficient at this torque, pretty close to this estimation.

So under maximum operating conditions, each motor should consume 56A of current and 1344W of power. The three motors collectively consume 168A of current and 4062W of power.

Is That a Good or a Bad Number?

The 168A number is acceptable because it is right at the limit of what the Mauch current sensor can handle. It’s rated for 200A of current and that leaves us 32A of current for drive motors and miscellaneous control electronics, which should be enough.

So assuming our three mower deck motors consume 56A, our two drive motors consume 12A and our control electronics consume 5A of current, you could have a maximum of 197A drawn from the batteries. Very little margin, but I think it should be okay because…

Maximum Versus Typical

One additional thing I’d like to mention is that I think these are maximum power consumption numbers. Previously I referred to them as typical power consumption numbers.

Do you need 3ft-lbf of torque while mowing the entire time? I doubt it. The calculations above prove that if our electric motors need to operate at 3ft-lbf of torque, they should be able to do it. Operating at 3ft-lbf of torque drops the rotation speed down to 4500RPM which results in a blade tip speed of 14100ft/s, which is a little lower than I’d like but should work.

Run Time Recalculated

Turns out I also miscalculated how battery charge adds when batteries are connected in parallel versus series. In series, battery voltage adds. In parallel, charge (your amp hours) add. Previously I assumed your total charge is the sum of each individual battery charge.

Since we have two sets of batteries connected in series, and then in parallel, our equivalent battery is 24V, 70Ah. This makes sense because I think the Ryobi lawn mower is advertised at 24V, 70Ah too. It’s the same battery set up, apparently.

If we were to run all three deck mowers with a load of 3ft-lbf torque on them, it would take (70Ah)/(197A) = 21 minutes to completely drain our batteries (again, assuming that’s even possible to do, in reality it isn’t).

At half this torque value, total current consumption would be 28A for each deck motor, resulting in 113A total. That results in (70Ah)/(113A) = 37 minutes of run time. The E30-400 motor consumes 29A of current at peak efficiency, so I’m hoping that I’ve sized these motors for the sweet spot of their performance.

If you were to bump up the battery size used on the mower to four 50Ah batteries, run time would be (100Ah)/(113A) = 53 minutes. Doing this would add 34lb to the mower, which would show up in the current consumed by the drive motors.

Thoughts

Even though I have more confidence in these numbers being correct, they’re still disappointing. I would like to shoot for a minimum 2 hours of run time. The only two ways I can think of to get there:

  1. More efficient motors and electronics.
  2. Larger batteries.

Using BLDC motors would increase our efficiency, but they cost 4 times the brushed DC motors I intend to use. Reduced run time is an acceptable trade off to save $700 in my opinion.

Larger SLA batteries start getting pretty ridiculous beyond the four 35Ah’s I’m using currently. The battery bay has to grow to accommodate the larger batteries, and that pushes the wheels out, increasing the wheel base and negatively affecting vehicle performance.

Additionally, the added weight makes me wonder if the 0.125in sheet metal battery bays are sufficient to support the weight of the batteries. Two 50Ah SLA batteries weigh 64lb. I’d probably want to reinforce it just to make sure.

We could switch to some Lithium Ion batteries, but here the cost is at least as bad as switching to BLDC motors.

Lithium Lead Acid Comparison
A brief cost and performance comparison of a composite lithium ion battery versus our current 12V, 35Ah SLA battery.

If you were to make a composite battery out of 18650 cells equivalent to the four 35Ah SLAs I’m using currently, it would cost just shy of $1,000 in 18650 cells alone. And that doesn’t even include labor to build the battery and a fancy charging system to go with it.

I found some guys that make custom 18650 batteries, and maybe they can do it for cheaper. I’m starting to understand why Tesla’s use lithium ion technology. If you need a boat load of power and have any kind of space or weight constraint, you kind of have to. Unfortunately, I drive a 2003 Honda Accord, not a Tesla Model X and so the mower project can’t afford some legit lithium ions.

I may have to get used to about 30 minutes of run time.