Optimizing the motor and the CVT

Hi there – nice to have you reading this! My name is Dr. Antti Lehikoinen (just Antti will do), and I’m working as a special advisor for Revonte.

This post will take you through what our team has spent the last few weeks on – optimizing the Revonte drivetrain. It’ll cover the benefits and workings of the CVT drivetrain, some challenges we’ve faced, and finally the basics of modern optimization. I’ve tried to keep the amount of raw tech to a minimum, to make the text readable to anybody who understands bicycles.

Please let me know in the comments if I made it or not 😊

Why CVT?

As you might know, the Revonte drivetrain utilizes a continuously variable transmission, otherwise known as a CVT. As its name suggests, a CVT does not have a discrete set of fixed gears. Instead, any transmission ratio (within a certain range) can be reached.

But why use a CVT, you might be wondering. Why not simply have a traditional bicycle gearbox or wheel stack?

Well, there are several reasons for that.

First, a standard fixed-gear transmission has, well, fixed gear ratios. Anybody who’s ever ridden a plain 3-speed bicycle has certainly been climbing a moderate uphill where gear 1 was far too slow, while number 2 was already a tad too heavy. Of course, you could avoid that situation by riding a fancier 21-speed mountain bike, but then you’d be spending far more time going through gears once that uphill suddenly turns into even ground.

Which brings us to the next item: a 21-speed gearset obviously has lots of parts. It’s heavy, there are more parts to service and maintain, and a higher chance of one of them breaking down as they were never designed for e-bikes.

By contrast, the Revonte CVT through inside the pedal hub. All that comes out are the pedals, and then the chainwheel and the chain. It’ll be easy to keep it clean, and you’ll only have to oil the chain a few times a year or you can even choose to use a belt drive.

Furthermore, we only use robust components that have stood the test of time, like spur gears and electric motor. This makes the system extremely durable (especially compared to some other CVTs on the market), while also bringing the total number of moving parts down to the level of a standard 3-speed hub gearbox.

And obviously, it’s a CVT. You’ll be able to maintain a comfy cadence of 60, no matter how fast you’re going, or how steeply you’re climbing.

Challenges we’ve faced

Of course, it’s not all honey and no sting with CVTs.

CVT systems – all CVT systems – are by nature a little less efficient than regular gearboxes. For that reason, they usually adopt a configuration illustrated below (artwork by yours truly).

On the left side there are the pedals. (Obviously!) The power coming in from the pedals is split between two parallel paths. The majority is led along the lower path – a highly-efficient conventional shaft plus standard gears. The remainder is led above, through the actual variable part. Here, speed can be traded for torque, or vice versa. Finally, the powers are combined in a kind of differential, and led into the rear wheel.

As a result, biking happens. And, by changing the transmission ratio of the variable part, we can change the total pedals-to-wheel ratio. Handy, isn’t it?

Also, by using this kind of a power-split approach, the losses in the variable part can be minimized. After all, a big part of the total power goes through a conventional transmission, which is very efficient.

However, the optimal split ratio depends heavily on many factors, such as bike speed, pedalling torque, preferred cadence, the configuration of the conventional-gear path, loss characteristics of the variable path…you get the point. For instance, a drivetrain optimized for steep uphill riding at 8 km/h loses some of its efficiency when cruising around the countryside at 25 km/h.

To complicate things further, all of the above was assuming no assist coming from the battery. Once we consider that, we have even more choices to make. For instance, should we put the assist right after the pedals? Immediately before the wheel? The lower path? The upper path? Or some combination of these? You get the point. And then there are all the dimensions of the individual gears and motor parts to consider.

So, how to wrap all these together?

Optimization

We begin by defining a representative drive cycle – an imaginary cycling trip with both mountainous terrain and urban crosswalks included. Everything, from the gradients to the speeds to the time spent in different environments, was adjusted to best represent a typical cycling behavior of the Revonte end-user. This drive cycle is then coupled to models representing the various components – gears and electric motors – to evaluate the system as a whole.

Of course, this alone doesn’t exactly help in choosing all the dozen parameters discussed above.

Luckily, we don’t have to make all the choices ourselves. Thanks to the advances in computers and in the science of optimization, we can now (and did!) automatically analyse tens of thousands of configurations to find the best fit for our application.

Since a CVT is a rather complex system (you are probably starting to see this by now), something called multi-objective optimization is used. True to its name, the ultimate goal of multi-objective optimization is to find the solution that is best in the all possible senses: the lightest, the most affordable, the most efficient.

But, as you’ll undoubtedly guess, such a solution almost never exists. For that reason, the realistic goal is finding the best possible trade-offs between different targets.

These can be nicely visualized as something called the Pareto front. Despite the weird name, the Pareto front is nothing more than a curve (or surface) visualizing the best trade-offs attainable.

An illustrative example between price and weight can be found below (NOT representative of final Revonte results – just an example). What you can read out of the curve is that a 3-kg design would cost a bit over 200 Euros, while the price of a 1-kg solution would be close to 600.

Like mentioned, that is just dummy data, but you certainly get the idea. Indeed, the main benefit of Pareto optimization is to let the designer make the final choice between different trade-offs. Like if the price would suddenly explode below 2 kg of weight, you probably wouldn’t want to go there.

But how does the optimization work?

Alright, this part is not directly related to the Revonte drivetrain itself. But, it’s still such interesting information that I decided to include it nevertheless.

Namely, how does the optimization work? Like, really work?

Well, we used a specific genetic algorithm (SPEA2 for those really detail-oriented). Genetic algorithms work by maintaining a large set of different designs – called a population of individuals. See where the name ‘genetic’ comes from already?

The actual optimization then happens by creating new generations of individuals from the previous one, based on simple rules utilizing random numbers. Like in Darwinian evolution, the best individuals are favored in the process. This way, each successive generation tends to get closer and closer to the right optimal design.

This process can be seen in the animation below, illustrating a very early-stage optimization run of a then-scrapped design. Each dot you see is an individual drivetrain design. To tell the different generations apart, the first ones are illustrated in blue while deep red is used for the final one.

As you can see, each generation represents slightly better designs – lower losses and lower maximum internal temperatures.


Conclusion

Phew, that was a long one. As a reward for making it this far, you can read the highlights in a convenient list:

  • A continuously variable transmission (CVT) always lets you ride with the best possible gear.
  • The Revonte drivetrain combines CVT with simplicity, robustness and low maintenance.
  • Actually designing the system was a daunting task in the beginning…
  • …but we made it, with some state-of-the-art optimization techniques. And lots of sweat.

Thank you for reading! Please comment, share, and get in touch!

Dr. Antti Lehikoinen