For that, you can simply relace your rim onto the new motor. It's pretty easy to do if you research it first, and practice at least once by unlacing and relacing a discarded wheel (which aren't too hard to come by). There are quite a few posts and threads around here about that, and websites like Sheldon Brown's that have tons of bicycle maintenance and build info, or online videos if you prefer that form of learning. Even if you are using motorcycle spokes and rim, the same info still applies as it's still a spoked rim using the same principles. (learning this skill also means you can fix your own wheels when stuff goes wrong, and you may even get good enough at it to earn money building wheels for others).
Normally, when a part keeps failing the same way on the same system under the same usage, there are a few potential causes of the failure:
--quality of the part
--suitability / design of the part for the usage scenario
--environmental conditions
The last one is often overlooked, especially with controllers, which are designed for sufficient airflow over the heat-generating parts, and are sometimes installed inside other parts of the bike where that airflow can't happen as it is required.
The first two are unfortunately fairly common problems, but I've abused crappy controllers for years at a time on heavy-cargo bikes and trikes without blowing them up as long as they have proper cooling. Take a look at my CrazyBike2 and SB Cruiser trike threads for examples.
Regarding capacitors, it is fairly easy to replace the usually low-quality ones in controllers for better ones (Rubycon, Panasonic, etc), if necessary with higher temperature ratings and higher capacitance and voltage ratings.
It's certainly a viable option--using something at less than it's max ratings means it has a safety margin not usually built into cheap(ly designed) ebike stuff. It also gives you some room for upgrading your system later without replacing that part. Most people are too cheap to do this, so you don't see it happen very often, unfortunately.
Don't forget that your battery also has to supply all the power of the system, so if you want to go faster, it will have to be able to supply the significant extra power it will take to do that work.
You can use the motor simulator at ebikes.ca to guesstimate the higher power usage (Watts) at whatever higher speed you wish to travel at under your specific riding conditions, and also guesstimate the higher usage rate (Wh/mile) you'll have at that speed. This will help you find a controller that can actually supply the power required to do the job you need done, and ensure your battery can also handle that job.
Not really. There's quite a few threads about doing this for various systems that you can look for and read up on that will help you depending on which system you go with.
Wiring is typically fairly simple as long as you have complete info on your bike's existing wiring, whether you get that from the manufacturer(s) of the bike/parts/etc., or determine it on your own and draw out your own complete system diagram for it, and you have complete info on the wiring for the new controller (and it's display that will come with it, if you want a display on the bike, since the new controller is unlikely to be compatible with your existing display).
If you are not sure which signals to connect together, you can post all the required info to do that here in this thread and we can then help you determine which signals match up, and which, if any, are to be left disconnected and unused.
If the connector styles don't match, you can usually cut the connectors off the part(s) you are replacing, after you have traced their pins back to the points inside that the wires are soldered to, so that you know which pins are whcih functions (unless you already have this info in your bike system diagram), so you can connect the correct wires together between connector and new part(s).
Keep in mind that some controllers' apps can't change all the settings that the computer based version can, so check out the app vs program settings to be sure the things you will want to change are available to you in the app. I don't know enough about the Sabvoton app to say, but Siaecosys is the source for manufacturer information on those.
As someone else has pointed out, it's pretty likely that yours does indeed have hall sensors, just that you haven't noticed the contacts for them on the connector shell. I think your motor has this
There are lots and lots of connector types used in the ebike industry, so many that it would be a very tall order to try and list them all. In our business, we focus just on aftermarket conversion kits and have tried to keep the connector styles down to a well chosen minimal set. This page...
ebikes.ca
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or some variant; it's what I've seen on the other Rad motors posted about. You can verify this, and even test the hall sensors for functionality if you like, using the info in the Learn Troubleshooting section at ebikes.ca.