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.

Power Consumption

I decided to make the autonomous lawn mower fully electric for one big reason: If a person has to walk out to the mower with a gas can and refill the tank, is it really autonomous?

Ideally, you want the mower to do it’s job without any human intervention. If you have a gas engine, no matter how you cut it fuel has to be delivered to the mower in some fashion. With an electric design, you can have the mower automatically dock with a charging station when the battery gets low. No human required.

So from the get-go I have been trying hard to make the mower electric. I am encouraged by some electric riding mowers out there that use SLA batteries as their power supply. I like SLA batteries because they contain a lot of energy and are fairly cheap. Minimizing battery weight and volume isn’t a huge constraint for this project, thankfully.

Because these electric riding mowers cut grass and carry a ~200lb person on the mower, I have been operating under the assumption that as long as our batteries are larger capacity than those on this riding mower, we should be okay. That Ryobi mower features a battery bank that consists of four 12V, 25Ah SLA batteries.

I am beginning to question that assumption…

Power Consumption

Sizing the batteries ultimately depends on how much power the mower needs. The deck motors take the lion’s share of power consumption. Previously I estimated the mower would require motors that can output at least 5ft-lbf of torque to cut through thick grass based on typical gas engine torque output.

Examining the torque curves for the E30-400 motor I selected for our design shows that at 5ft-lbf or 3.7N-m torque, the motor consumes 1400W of power. If you assume all three motors pull this level of power, the deck motors collectively consume 4200W.

The drive I’m using on the mower design are stolen from the wheel chair. I suspect they are rated for 500W but I am not sure. The gearbox on them ensures they will generally be operating in an efficient area of their torque curves, so I am going to consume both motors consume 250W, and collectively consume 500W between the two motors.

The control electronics are almost negligible compared to the power consumed by the motors, but I will budget 100W for all the other little things on the mower, just to be safe.

That brings the total estimated power the mower needs during operation to 4200W + 500W + 100W = 4800W.

Battery Capacity

The batteries I’ve selected are four 12V, 35Ah SLA batteries. If you assume we intend to discharge these batteries 100% (and that doing so was physically possible), you could obtain (4)(12V)(35Ah) = 1680Wh of energy. If we were to draw 4800W of energy from these batteries, we would drain them in (1680Wh)/(4800W) = 21 minutes. Yikes.

But it gets worse. Because we’re pulling so much power out of these batteries, it looks like you have to discount the total amount of energy you can get out of them. I’m not entirely sure what that calculation looks like, but from the SP12-35 datasheet, it looks like a 1hr discharge rate only allows you to get 21.8Ah of charge out of each battery. That’s only 60% of the 20hr rate of 35Ah. I could be wrong about this interpretation of the datasheet, please correct me if I am mistaken.

Some Thoughts

Do the motors really draw that much power? Holy moly I hope not. At their most efficient, the motors draw 500W of power. Running the calculations above with this number gives you a run time of 48 minutes. Still not great.

The reality is somewhere between those two extremes. Taking the average of the two gives 35 minutes of run time. I was hoping for something more in the neighborhood of 2 or 3 hours. Going up to some 12V, 50Ah batteries could give us some extra oomph, but I don’t think it will be 3 hours of oomph.

Please let me know if these numbers seem way off base, it’s my best swag at them I can come up with. The last thing I want is a mower that can only cut grass for 10 minutes.

 

Progress

combine
The robot lawn mower design.

I’ve started doing some wiring diagrams for the robot lawn mower, as the mechanical portion is fairly well defined. However, there are a few things I’m still not sure about:

  1. Will four 12V 35Ah SLA batteries will provide the energy needed to run the mower?
  2. Should the battery bays be replaced with some off the shelf enclosures?
  3. Is there a better way to do the deck height adjustment mechanism?
  4. Are the motors sized appropriately, both for speed and torque?
  5. Is a pulley quick disconnect bushing really the best way to attach the cutting blade to the motor shaft?
  6. The sheet metal used on the weldments is 0.1875in thick aluminum. That is expensive and probably too stout. It should be changed to 0.125in thick.

I’m chasing my tail with these questions above, so I will take some time off from modeling the mechanical side of the mower and work on wiring for a while. Hopefully things will be more clear when I revisit these issues later.

Project Goals

Here are my goals for the robot mower over the next few months. I need to plan and execute well so that the mower will be ready to cut grass this spring.

December

Finish designing the robot mower, including wiring and planned integration of the RTK GPS module. The module should arrive at the end of December. I promise I will post more about the RTK GPS module soon.

January

Send the robot mower weldments out for quote. I’ll also start sourcing purchased parts for the project. Any design changes based on vendor feedback will be incorporated during January. I’ll also start playing with the RTK GPS module, getting a feel for performance and how to configure the base station.

February

Select a vendor to build the weldment. Start receiving in purchased parts. Implement the RTK GPS module on the wheel chair robot and take it out for field testing. If the weldments are completed in February, we’ll start assembling the robot mower.

March

Finish construction of the robot lawn mower. Conduct functional testing. Make any last minute changes to the design based on the testing results. Continue field testing the RTK GPS module on the wheel chair robot.

April

Integrate the RTK GPS module on the robot mower. Start working on making the mower truly autonomous, with my backyard as the test bed. It’s fully fenced in so it should be a safe area, and the trees and houses nearby provide a fairly challenging GPS environment, perfect for working out the kinks.

The Bottom Line

Shoot for the moon; even if you miss, you’ll end up among the stars.

-Some motivational kindergarten classroom poster

I realize this is a very aggressive schedule, but it’s been my experience that if you aim high but miss, you still will still achieve a lot more than you would have if you had set a more “realistic” goal. So we’ll see how far we get over the next few months.

Adjusting the Mower Deck Height

deck height adjustment
A simple height adjustment mechanism for the mower deck.

I’m trying really hard not to turn the height adjustment mechanism into a science project. All it needs to do is (1) support the mower deck and (2) allow the height of the deck above the ground to be easily adjusted.

You can find some exciting mechanisms out there to adjust the height of a mower deck. Google Scag Tiger Cat Height Adjustment if you want to see one of the more interesting ones.

A lot of mowers have a mechanism that lets you adjust the mower deck with one single lever. While I like these mechanisms I don’t think they’re necessary for the robot mower. How often do you typically adjust your lawn mower’s height? I do it once a year, if that.

For this project, having to adjust the height in four places versus one is a small price to pay compared to the time it would take to both engineer a mechanism that would work for our robot mower. Not to mention the cost to make it. Springs and linkages get expensive quickly, and the risk it won’t work right goes up fast when you start adding lots of moving parts.

I like simple. I’m not that bright, so I figure if can envision something working, chances are it will probably work okay in real life. To adjust the height of the deck, pull the quick release pin, rotate the lever to the appropriate height, and put the pin back in. Do that in four places and your done. Simple!

Concept #5 Refined

prlm-a50001-11-04-18.png
The autonomous lawn mower as of this evening.

The autonomous lawn mower design is coming along nicely. It turns out that the batteries fit nicely below the robot frame. I only had to raise it by 1.5in to give adequate clearance for the battery terminals. This keeps the center of gravity low, and makes for an all around good looking robot in my opinion.

I have an RTK GPS module arriving in December (more on that later), and I want to get the lawn mower design as mature as I can before I need to start investing my time testing that module with the wheel chair.

My list of open items on the design as of this evening:

  1. Latches for the battery compartments. Maybe I don’t need them, but it would be nice to have some way to hold the doors closed. Maybe just some screws would work.
  2. Control enclosure location. It needs to be far enough away from the deck motors to avoid the flux storm. But mounted in such a way that it doesn’t adversely affect vehicle performance or look goofy.
  3. Deck height adjustment mechanism. The robot needs to have a way to simply and quickly adjust the deck height as you would on a typical lawn mower.
  4. Safety shutoff and control system for deck motors. I think these should be powered by a separate set of relays so they can be independently turned off from the rest of the rover. They will still be wired into the master safety shutoff switch.
  5. RTK GPS antenna mount location. Wherever the control enclosure box gets placed, it will need to have enough real estate on it for the GPS antenna.
  6. General wiring. All the motors, the enclosures, everything. This will take a lot of time but as we saw earlier was very much worth it.
  7. Mower deck discharge chute. The mower needs a plastic chute where the grass clippings discharge. It’ll also need the hardware that attaches it to the deck.

 

xrlm-a10001-versus-prlm-a50001-isometric.png
The autonomous lawn mower versus our wheel chair robot.

The autonomous lawn mower measures 37.5in long X 36in wide X 17.5in tall currently. Not bad considering our grass cutting width is 35.5in!