E30-400 Motor Evaluation

The electric mower motor I got off craigslist had a 12in blade on it. That motor was rated for 24V, 4300RPM, 1.3N-m. I suspect it was pretty undersized for doing any real grass cutting, but whoever manufactured it had to size it at least somewhat appropriately.

Our three blade mower design has 12in blades on it. So in theory, any motor larger than the craigslist motor should be sufficient. But because I’m a perfectionist, I don’t want to just barely exceed these parameters. I want to knock them out of the park.

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

For the same torque values as the craigslist motor, the E30-400 motor will rotate at about 5000RPM, consuming 700W while operating at about 77% efficiency. That translates to a blade tip speed of 15700ft/min, or 80% of the maximum allowable tip speed.

At the same speed as the craigslist motor, the E30-400 outputs about 2.8N-m of torque. That’s more than twice what the craigslist motor is rated for. Not bad.

The best part? Three of these guys only cost $354.41. And that’s after shipping, with insurance. The holy grail indeed.

Mower Design: How Many Blades

There are a lot of variables to play with as we design the prototype autonomous mower from scratch:

  1. The deck dimensions and shape are entirely up to us.
  2. We get to choose the number of blades.
  3. The size of the blades.
  4. How the blades are driven: direct drive, through a pulley, chain, or timing belt.
  5. What standard lawn mower components we attempt to use.

This is not an exhaustive list, but these are the main variables I find myself tweaking as I try to optimize the design.

We have a lot of freedom to do whatever we want because we are custom making the mower deck. But this also creates a lot of questions. As we discussed previously, the deck geometry and the number of blades used on the mower lock down several of these variables. So before we go any further, I want to go into detail the advantages and disadvantages of a design with one, two, and three mower blades.

Single Blade Mower Design

dfsa
Dimensions of the top of the single blade mower deck. Length is 37.5in, width will 31in for a 30in blade.

The single blade design has one huge advantage: one blade, one motor. The motor can even be coupled straight into the blade if it is sized appropriately. This could minimize cost and complexity in a big way for our design.

Unfortunately, it also creates some disadvantages that aren’t immediately obvious:

  1. A single blade design results in the longest wheelbase, which will adversely affect the agility of the mower.
  2. It also results in the largest mower deck. That means it will be heavy and expensive compared to alternatives.
  3. The largest blade you can get is ~30in. So in addition to the negative performance and cost impact from the points above, you can only achieve a cutting width of ~30in with this design.
  4. And on top of all these issues, you also have to go with a minimum 3kW BLDC motor and controller to get the power you need to rotate the blade. That’ll set you back close to $700 after everything is said and done.

Yikes. Turns out a single blade actually creates more problems than it solves. If our target cutting width was in the neighborhood of 20in, this would be the way to go. But since we’re aiming for closer to ~36in, this design is unacceptable.

Two Blade Mower Design

2blade
Dimensions of the top of the two blade mower deck. Length is 25.5in.

The two blade design solves a lot of the issues that the single blade design faces. The deck length and resulting wheelbase are considerably smaller, and because there are two blades that need to be driven, two smaller, cheaper motors could be used. Or alternatively, you could use one large motor and have a pulley drive system transmit power to each blade.

The biggest drawback with a two blade design is related to geometry. In the picture above there are two dashed circles showing the path the tip of each blade with follow as it rotates. See how they overlap? If we leave the design as shown in that picture, the blades will crash into each other during operation. If space them apart, the grass between them doesn’t get cut.

There are two possible solutions to this issue:

  1. Use a chain or timing belt to link the two blade spindles together. This will ensure they are synchronized through their rotation paths and won’t crash.
  2. Separate the blades so their paths don’t intersect, but angle the deck. As the mower travels, it won’t leave a small tract of uncut grass.

Using chain isn’t a good option to synchronize the rotation of the two blades in my opinion. The blade drive system needs to be designed for shock loading, and also to minimize vibration for the Pixhawk. Chain doesn’t help any in this realm. It also creates maintenance issues, although those are secondary concerns. I suspect this is why V belt is used on commercial mowers most commonly, not chain.

A timing belt is a better solution, but this forces us to find a way to integrate timing belt sprockets into our design, which will invariably result in some expensive fabricated adapters to link an off the shelf timing belt sprocket to the mower spindle. So it’s a better solution than chain, but has it’s own set of problems. So option 1 is out.

Option 2 is an elegant solution, and you see it on commercial mower decks that feature two blades quite often. However, the tradeoff is that you increase the length of the deck because you are essentially moving one blade further forward than the other. See the picture below to see what I’m getting at.

offset 2 blade
The two blade mower deck, angled to where the blade paths overlap as the mower travels straight ahead.

Dimensionally, option 2 results in the same wheelbase as a single blade design, but with the headache of two motors. It may even be longer than a single blade design, because the swivel caster assembly on the front needs clearance to swivel.

Plus it just looks funky. So a two blade design is out, too.

Three Blade Mower Design

Initially I was hesitant to even consider a three blade design because of the number of parts it will require. Three blades, three spindles, three pulleys, a belt to connect all of the spindles, or three motors to direct drive the blades.

To complicate matters, the smaller the blade length, the faster it needs to rotate to achieve good grass cutting velocity. We previously discovered that a 21in blade requires 3500RPM in order to achieve a blade tip speed of 19000ft/min. For a 12in long blade, that number jumps to more than 6000RPM.

blade rotation speed
The relationship between blade tip speed and blade rotation speed. We’re aiming for a Vmax of 19000ft/min, or just below that.

This is a problem because most DC motors don’t operate at those speeds with any significant amount of torque. In fact, most of the motors I’ve seen have no-load speeds listed far below 6000RPM. That’s the bad news with a three blade design.

The good news? Other than these blade drive system constraints, the three blade design is geometrically very efficient. It results in the smallest wheelbase, and because it is triangular in shape, you get bonus clearance for the front casters to swivel. It requires the least amount of material to fabricate. That means cheap and lightweight.

three blade
The three blade mower deck design. It’s a very good combination of deck width and length.

The blades are separated by a small amount but because the center blade is slightly more forward than the outer two, you still get 100% cut coverage, similar to the angled two blade design.

The three blade mower design is by far the most efficient, and I like the way it looks, too. The only hurdle to making it works is finding a motor that won’t break the bank, but still get us close to the 6000RPM requirement for a 12in blade. If we can find a motor that works with this design it will by far be the best one of the three. Does such a motor exist?

The Holy Grail of DC Motors

We had previously considered BLDC motors to give us the power and efficiency we need to spin the cutting blade. But unfortunately that power and efficiency comes at a cost: BLDC motors require a controller to run them.

So even if you find a fairly cheap BLDC motor that meets your needs, tack on 50% of the motor price for the controller. Need three motors? Looks like you need three controllers, too. And the space to mount them somewhere. I’m sure they make combo controllers out there, but I can’t find them.

The other problem with these controllers is that you’re paying for a ton of features you don’t even need. Most are designed for electric scooters. I don’t need the ability to go in reverse, or to vary the speed. I just need a motor to spool up and stay there. With typical BLDC motor controllers, you get a bunch of these features, and boy do you pay for them.

So while BLDC motors fit our application requirements, they are costly. Ideally we’d like to use a simple brushed motor that operates at the speed and torque we need. Turn it on with a $3 relay. Keep it simple.

In my adventures across the interwebs, I had trouble finding anyone who makes a brushed motor that runs close to 6000RPM with significant amounts of torque, that also costs less than $400.

But that was before I found the folks out at AmpFlow. They make a really nice set of brushed, DC motors in the speed and torque range we need. They also appear to be US based, which is a plus. They post torque values in oz-in and dimensions in inches. And they have torque curves for their products. All around, these guys are awesome.

Next time I’ll go over the specifications for the E30-400 DC motor, which I think is perfect for this application.

Selecting a Motor

As I mentioned previously, I need to find a motor manufacturer that posts more than a picture of their product on an electric bike. I need torque curves and CAD models. I am surprised at how few of these manufacturers exist, or at least have websites that I can find. Maybe I just don’t know how to search for them.

Part of the problem is that I’m looking for a motor that has power output on the level of a small riding lawn mower. Finding smaller BLDC motors has been pretty easy, but finding something that operates efficiently at lawn mower speeds while still outputting decent torque has been challenging. Also, it has to cost no more than a few hundred dollars, because I’m cheap and I need some money left over for an RTK GPS module down the road.

So I’m starting out from behind the 8-ball to begin with. I wasn’t sure such a motor existed until I found the folks at Golden Motor. These guys are a little sketchy, and they need to hire a web designer from the 21st century. But they appear to have a wide selection of motors in some pretty epic sizes, with fairly comprehensive performance data, too.

But before we go looking at individual motors, let’s review our requirements.

Motor Requirements

At the moment I am leaning toward a single mower blade design. I’ve learned the hard way that complexity is not your friend, and simple designs are generally more robust.

To maximize the deck width, I am considering a 30in long blade. A 30in blade needs to rotate no faster than 2400RPM to be safe. Riding mowers with one single 30in cutting blade are equipped with engines that output about 10ft-lbf of torque.

The plan currently is to have four 12V 35Ah sealed lead acid batteries wired in series to power the motor. So it must be rated for 48V.

Evaluating the BLDC-108 Motor

This is a 1500W motor that Golden Motor makes. It’s also the only one that doesn’t have  a nice chart for all the relevant performance parameters, but they did give an excel spreadsheet with several data points. I graphed the data and here’s what it looks like.

BLDC-108 speed torque power
The speed and power versus torque curves for the BLDC-108 motor. The blue curve is speed and the red curve is power. Excel only lets you plot two separate y-axes, which is very frustrating. Get it together Microsoft, this is 2018!

The efficiency of the motor is greater than 85% between 1 to 3.5ft-lbf torque with a maximum efficiency of 88% at 3325RPM and 2.6ft-lbf torque. The motor consumes about 40A of current at the torque shown on the chart.

To achieve the maximum safe blade rotation speed of 2400RPM, we need to use two pulleys of different diameters on the motor shaft and the blade spindle. Taking the maximum speed the motor operates at of 4072RPM and dividing it by 2400RPM gives us the pulley ratio we’ll need, which in this case is 1.7.

If we use the motor with a pulley ratio of 1.7, we could obtain 5.9ft-lbf of torque at 1800RPM. Reducing the speed increases the torque.

Some thoughts about this motor:

  1. The torque is a little on the low side, even after you factor in the pulley ratio. I suppose you could go with a higher pulley ratio, but that reduces your speed even further, which I’m told affects the quality of your grass cut.
  2. I like that the current draw is only 40A. With four 35Ah batteries, you could in theory get 3.5 hours of operating time, neglecting current consumption from other electronics and motors. I like that number.
  3. The picture on the website is nothing like the CAD model you can download. So that’s something I’ll need to investigate if this is the motor I choose.

The motor is priced at $142 with $60 for shipping. BLDC motors require a separate motor controller, so that will be another $95 with $30 for shipping. So a system built around this motor will cost a total of $327. Not horrible. I wish I knew why the shipping was so high…

Next time I’ll evaluate the 3000W HPM3000B motor.

More Mower Musings

I’ve had some more time to think about our mower blade and the system that will be required to power it. To summarize what we discovered last time:

  1. A 21in blade is the maximum size we can use.
  2. A larger mower will be more efficient in general because a smaller portion of the mower width will be used to overlap the previous pass.
  3. Typical brushed DC motors are probably not a great way to power the blades.

Two Cutting Blades or One?

I think I need to retract statement (1) above. It turns out there are larger blades out there, the only caveat is that they have to be rotated at a slower angular velocity to maintain a blade tip speed of less than 19,000ft/min.

Using the math I outlined previously, a 30in blade needs to be rotated at just over 2,400RPM to achieve a blade tip speed of 19,000ft/min. This turns out to be a good thing too, because this slower speed can be achieved by using different sized pulleys on the drive motor and spindle, which will allow us to trade higher RPMs for more torque, which will be needed with a larger blade.

I was really hoping to avoid a mower with two blades for a few reasons:

  1. Complexity: two blades means two spindles, some idler pulleys, and more moving parts.
  2. Blade interference: the travel paths of the two blades need to overlap a little so you don’t miss any grass, forcing us to make sure the blades don’t get out of sync and crash into each other
  3. Vibration: I imagine two blades will result in more vibration, but this is speculation.
  4. Real estate: the mower deck needs to also house (4) 12V 35Ah batteries and a bunch of control boxes. Two spindles and a large belt with idler pulleys eat this space up really quick.
  5. Robustness: More parts means more opportunities for failure.
  6. Cost: More parts means more cost.

So seeing as we can use one blade while still achieving a cut width of about 30in, I think this is the preferable solution. There are mowers out there that use 30in blades, but the torque required for such a blade size is pretty high. This mower is equipped with a Briggs and Stratton engine that outputs 10.5ft-lbf of torque at 2,400RPM.

Keep in mind that’s engine torque output, not torque at the rotating blade, but that still means our electric motor needs to output at least 5.25ft-lbf at 4,800 RPM (see the pulley ratio math below). I’m guessing that will be a difficult number to achieve.

Motor Alternatives

Regarding (3) above, I think a brushless DC motor may be the way to go. I found this motor on an electric scooter parts store which seems promising, but I need to see a torque to RPM curve to be sure. Coincidentally, that motor is rated for 4800RPM, which results in a pulley ratio of about 2:1. Not bad.

On the down side though, most of those motors are designed to be used with sprockets and chain, which isn’t a great idea for mowers. There’s a reason mowers use pulleys and V belts. I suspect it is because they allow for a more fluid transmission of torque to the blade and also slippage if the blade hits something rigid, resulting in less strain on the drive motor or engine.

This will mean I’ll probably need to fabricate a custom drive pulley to adapt to the motor shaft and accommodate the V belt required by the blade spindle.

What Do The Other Engineers Think?

ryobi-rear-engine-riding-mowers-ry48110-64_1000
The Ryobi RY48110 electric riding mower. I wonder what’s inside?

This is the 21st century. Has anybody designed an electric mower with similar parameters to the ones we’re looking at here? Turns out the answer is yes. The specs for the Ryobi RY48110 riding mower:

  1. Looks like they’re using a few 12V 25Ah lead acid batteries for power.
  2. They use two BLDC motors directly connected to the cutting blade.
  3. Deck width is 38in which would imply a ~19in blade length.

Funny story, if you pull up the parts list and google their replacement motor part, you come up with this motor rated at 48V, 32A, 1800W, 4500RPM. So we’re at least in the neighborhood.

A few comments about this mower:

  1. They’re using this motor to drive a ~19in blade. We’re looking at using a motor that is actually rated at 1600W to drive a blade that’s more than 50% larger. Not good.
  2. Direct drive is interesting, it’s definitely simpler. I would be interested to see what kind of connection hardware they use.
  3. A 19in blade implies a maximum blade tip speed of 3800RPM. The motor is rated for 4500RPM. I wonder if the mass of the blade results in a equilibrium rotation speed of about 3800RPM. If not, the mower isn’t in compliance with ANSI B71.1-1990.
  4. How do the two motors stay in sync? I wonder if the blade paths overlap or if there is some kind of chain or belt between them to maintain their angular offset.
  5. Being BLDC motors, I also wonder what the controller looks like. I imagine it shoots for a fixed rotation speed. I would be interested to know what that rotation speed is.
  6. The Cadillac version of this electric riding mower only offers 100Ah of charge at 48V. That’s only 4.8kWh of energy. Our system with four 12V 35Ah batteries can store up to 6.72kWh of energy. This is interesting because not only does the riding mower need to cut grass, but it also has a possible 250lb person it’s driving around too. So I think we’re on the right track as far as power requirements go.

In Summary…

  1. I need to get some torque speed curves for these motors. Otherwise we’re just guessing about motor capability here.
  2. I think our power system is appropriately sized based on the RY48110 specifications.
  3. Torque output is still the big unknown here. The RY48110 gives us a baseline to work from though.
  4. It looks like BLDC motors are going to be the device that powers our blade, seeing as the folks at Ryobi arrived at the same conclusion we did.

Mower Musings

One of my goals for this winter is to design the prototype autonomous lawn mower. The rover V2 is coming along nicely, and while I have a few systems left to work on, the big ones are already implemented and working. So I spent some time this week thinking about the thing that makes a mower a mower: the cutting blade.

IMG_3958
The motor from Craigslist. The label says “24VDC 500W 4300RPM”.

A few months ago I purchased a small electric push mower off Craigslist. It had a DC motor and a 12in cutting blade that I disassembled for the mower project. I figured the “cutting grass” problem is essentially already solved and that there’s no sense in reinventing the wheel. But now that I’ve done some thinking, I’m not sure this problem is as simple as it seems.

Choosing the Right Sized Blade

Eventually I will attempt to integrate an RTK GPS system on the mower. Depending on who you ask, you’ll find that RTK GPS systems are accurate to about +/-1in. For the rest of this post I will be talking in terms of accuracy relative to the base receiver. Absolute positioning with any degree of accuracy is another can of worms altogether.

What +/-1in means is that at any given time, the mower could be 1in to the right, or 1in to the left of its reported position. Let’s say it’s 1in to the right while it’s mowing a row in your lawn. That +/-1in means when it doubles back for the next pass, it could be off by 1in in the other direction. Basically, +/-1in means there could be up to a 2in gap between passes.

So we will need to overlap passes by some amount. You would normally do this anyway if you were mowing your lawn manually. I overlap passes with my push mower by about 4in when I’m mowing my lawn to make sure I don’t miss anything, and we’ll want the robot mower to do this too to maintain a quality lawn cut. So we’ll need at least 6in of overlap: 2in to account for RTK GPS drift and 4in to account for normal overlap.

The issue I’m trying to highlight here is that the narrower your mower, the more critical it will be that it is positioned accurately. You can’t tolerate much drift because you’ll start missing passes if you’re mislocated by any amount. And to overlap such that you don’t miss passes requires overlap equal to 50% of your blade width, which is very inefficient.

This is why (in my opinion) RTK GPS works pretty seamlessly on big agricultural equipment. Those tractors and combines are a whole order of magnitude larger than our mower. They’re also out in big open fields with great GPS reception, but that’s a rabbit hole for another post.

So Pick the Biggest Blade Size, right?

Well, sort of. If you do much searching, you’ll find that the biggest blade you can get your hands on is about 21in. There’s a good reason for this: mowers cut best when the blade rotates at near-ballistic speeds, and if you make a blade much larger than 21in and then rotate it at 3600RPM, anything it hits turns into a piece of shrapnel. Not to mention what could happen if the blade itself shatters. Go look up some lawn mowing accident videos to see what I mean.

In my reading, I found that our friends at the American National Standards Institute (ANSI B71.1-1990) did some testing and recommended manufacturers keep the blade tip speed below 19,000ft/min, or 216mph. That’s linear velocity, not angular velocity. Remember that angular velocity is equal to linear velocity divided by the radius through which it rotates.

So How Fast Should We Spin the Blade?

So knowing that we want a big blade size and that we want to achieve a blade tip speed of just shy of 19,000ft/min, we can calculate the required angular velocity.

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.

Knowing the angular velocity, we can now calculate the required power if we know the torque the mower blade will experience spinning through thick grass. Unfortunately, that’s a very difficult figure to arrive at. So instead of doing some convoluted math to estimate the torque to cut through grass, we’ll just take the gross torque ratings listed by the folks out at Briggs and Stratton, as their mowers generally cut through grass with no problem.

e450 engine series gross torque
The gross torque versus RPM curve for a Briggs and Stratton 450e series engine.

This engine is one of their lower end models. Briggs and Stratton advertises gross torque at 2600RPM, so for this engine it would be 4.5ft-lbf of torque. If we take 5ft-lbf of torque as the required torque to cut through grass, we can estimate the power we’ll need for an angular velocity of 3450RPM.

Min power
The minimum power our motor needs to supply to keep a 21in blade spinning at 3450RPM.

Does the Craigslist Motor Cut It?

Electric motors aren’t like gasoline engines. Their torque to RPM curves are much simpler. With no load attached to the armature, the motor will spin very fast while outputting very little torque. If you apply a small load to the motor, the angular velocity will decrease slightly and torque will increase slightly. If you keep doing that until the motor stops turning, you’ll arrive at the stall torque. This is the maximum torque the motor can output.

So electric motor torque to RPM curves are linear. To draw them, you only need three pieces of information: the angular velocity and torque at a given point on the curve and the no load angular velocity. Using that information, you can draw a line for the torque curve.

motor specs
The best information I could find for the motor I salvaged.

The table here indicates the no load speed is 4300RPM and gives an operating point of 0.96ft-lbf (1.3N-m) of torque at 3700RPM. From this information you can find the stall torque and the maximum power the motor can output.

stall torque and max power
The calculation for the stall torque (top) and maximum power (bottom). The maximum power for a brushed DC motor occurs at half the stall torque and half the no load speed. This is why those variables are divided by 4 in the Power calculation above.

The manufacturer says that the rated power for the motor is 500W, but from my calculations I’m not sure that’s true. However, I am very surprised that the calculated power is this low. It’s very possible I have no clue what I’m doing here with these calculations. If that is the case, please call me out on it.

A motor that gets even close to the power levels we need would have to be a 2500W motor. We have a 24V power system, and we need the motor to spin at 3600RPM minimum. Doing a brief web search for those terms doesn’t come up with many promising alternatives. I’m not sure motors with those parameters are practical or even exist, at least in the PMDC variety.

So What Have We Learned?

I can think of a few things:

  1. If RTK GPS is our positioning technology, we’re going to want to make the mower as wide as we reasonably can.
  2. To keep our mower safe, the blade tip speed needs to be no faster than 19,000ft/min.
  3. Mower blades don’t come much larger than 21in long, so if we want a deck bigger than that we’ll be adding complexity to our design.
  4. We’re going to need a boat load of power to spin that 21in blade at power levels generated by gasoline engines.
  5. A permanent magnet DC motor may not be the way to go given these constraints.

I hope these musings about the mower make sense. I am always open to opinions and criticism about the evidence above, and what conclusions should be drawn from them.

Brushless DC motors, on the other hand…