How To: Swap the Rear Wheel on a Triumph Modern Classic
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Welcome to Ulterior Moto. Today I will be going over how to change your rear wheel. Here are the tools you’ll need:
Rear Stand
7mm socket
breaker bar
torque wrench
12mm and 13mm open end wrenches
5mm hex key wrench
ruler
lithium-based grease
degreaser
towels
If you prefer to watch rather than read, see below.
Step 1: Lift the Rear
Let’s get right to it. The first thing we need to do is get the rear tire in the air with our lift. As you can clearly see, I’ve pushed this tire well beyond its recommended lifespan. If you own a Bobber or Speedmaster you will likely need to lift the bike from the center about 7 inches.
Step 2: Remove Chain Guard
Let’s get the chain guard out of our way to start with. This may not be strictly necessary, but I like to give myself as much room as possible to operate. A 5 mm hex wrench is necessary. On the Bonneville T100, T120, and Street/Speed Twin 900, you will need to remove the mufflers as well.
Step 3: Remove the Axle
Use a breaker bar and 27 mm socket to loosen the axle bolt. Note the small holes in the swing arm behind the adjustment plates. Count how many are visible you’ll want to refer to this later.
Prepare to create chain slack by loosening the adjuster lock nut. Mine were only finger tight which is a bit loose for my liking. Do this on each side.
Fully remove the axle nut and the washer behind it.
Create chain slack by screwing in the chain adjuster and remove the adjustment plate.
Loosen the adjuster on both sides.
Support the wheel and push the axle out from the right side, then pull it out from the left when you can get a grip on it. 
Step 4: Remove the Wheel
Pull the chain off the sprocket and remove the wheel. Bobber and Speedmaster owners, you will need to remove the sprocket before you pull the wheel out and you’ll need to tilt the wheel to clear the rear fender. 
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Step 5: Disassemble and Reassemble
Remove the spacer and the sprocket from the wheel. If you’re taking your wheel to a tire shop, make sure you keep these parts so they don’t lose them.
Once you get your wheel back from the shop, it’s time to start reassembly. You’ll find the three spacers, note there is one inside the sprocket carrier, and bearing faces are covered in grease and dirt. You will want to clean those up as much as possible. Dirt is the enemy of all rotating parts.
Put the internal spacer and the cushions back into the wheel, then push the sprocket carrier onto it, making sure to line them up properly. It’s a great chance to get your sprocket all spiffy too. If you own the Bobber or Speedmaster, you’ll put the sprocket carrier on after you have the wheel under the fender.
Apply lithium grease to the inside of the bearings on each side and seat the spacers.
Place the rear brake bracket back onto the swing arm and roll the wheel up to it. As you roll it forward, align the brake disc between the brake pads.
Degrease the axle and left adjuster plate. Slide the left adjuster plate onto the axle and grease it back up. If you grease the axle before adding the plate, you end up with a mess. I can personally verify this sequence.
Step 6: Reinstall the Wheel
This is the most difficult part of the entire process. Support the wheel while aligning it with the brake caliper bracket and the hole in the swing arm. Slide the axle through all of them.
Replace the chain and extend the adjustment bolts back out a little less than where they started out. Do this on both sides. Add the right side adjuster plate, washer, and axle bolt. Slide the wheel forward until the adjustment plate butts up against the adjustment bolt. Finger tighten the axle bolt.
Measure the chain slack from the bottom to the top. It should measure 20-30mm, so 1” plus or minus two tenths.. I like to use a square ruler for this because I can leave it in one place. If you have too much slack, extend the adjustment bolt and recheck the slack until it is within the 1” window. Use a 13mm wrench as necessary. 
When you’ve gotten your chain slack to spec, tighten the lock nut with a 12mm while holding the adjustment bolt with the 13.
Check the location of the adjustment plate relative to the holes on the swing arm. Replicate this position with the adjustment plate on the left side to make sure the wheel is properly aligned. If not, turn the adjustment bolt until it is, then tighten down the lock nut.
Tighten the axle nut to 110Nm or 81 ft-lbs of torque. It doesn’t hurt to re-check the slack just to be sure. 
Replace the chain guard.
Pump the rear brake a couple of times to make sure it seats properly. You don't want to get down the road and have no rear brakes so do it now.
There. All finished. Aren't you glad you did that on your own and saved time and money?