Motorcycle Speed Wobble Troubleshooting
Troubleshooting speed wobbles can entail looking at quite a bit. Here are some bullet points on components you need to check on your bike for integrity and proper assembly.
Rear Wheel Alignment
Adjust your chain properly and ensure the real wheel is in alignment with your front. Common Issue, the wheels aren't lined up and you feel stable, then at a certain speed you get that oscillation. Chain adjustment and rear wheel alignment. You can get one of these tools. that will assist you getting the alignment proper.
Steering Head and Forks
Place the rear of the bike on a bike stand that lifts the rear of the bike on either side of the swingarm.
If you get clicking out of this test you will need to determine through feel if it's the fork in the slider or the steering head. I've never seen a speed wobble source be the slider and stanchion but I've heard of it.
Grab the bottom of the front forks and pull the bike toward you and then push the bike away as quickly as possible. You are trying to feel for a clicking in the steering head.
If you feel clicking, tighten the steering head spanner nut to factory specs. If it still clicks, replace the steering head bearing AND the race. Don't skimp, It's difficult to get the race out if you do it wrong. Tap around the edge from the inside using a long tap. Slowly and gently. If you have to wack it to get it out you will damage the frame. Gentle and easy.
Most speed wobbles start here oddly enough. I've fixed more speed wobble issues at the swingarm than at the steering head. Typically due to bad needle bearing getting water in them, which makes sense. They are closer to the road.
Have someone hold the front brake or use a zip tie on the brake lever to lock the front wheel. Grab either side of the swingarm and move it from side to side. A better method would be to use tie downs off the handlebars and secure the bike to either a bike bench or the ground and tighten them down to about half the travel of the forks. Jack up the bike under the oil pan so the rear wheel is just off the ground. Try and move the swing arm laterally by pulling on the left and pushing on the right side of it. Pull, push, pull, push.... Listen for the click. Best case scenario you take the shock out and do it. Then do side to side.
One of two things.
1 The swingarm shaft isn't torqued properly which allows the swingarm to move back and forth in the frame on the shaft. Make sure the end caps are on. They take up about 3-4mm of play. If they aren't there, get some and put them on.
2 Reach forward and grab the point closes to the motor on the swingarm and push pull to check you needle bearings. If you hear a click, that's it. Replace the needle bearings.
I recommend removing the swingarm shaft and visually inspecting the bearings. They are prone to water damage and seeing how your bike is now 10 years old I wouldn't be surprised.
Same test different shaft. Push the forks all the way to the right and grab the wheel while someone holds the forks against the stops. Try and get a clicking out of them. You will feel it but most likely not hear it. Do both wheels. Ensure you get enough leverage to feel the click. You can press the front of the wheel at it's furthest point away from the motor into the steering stop and press, let go, press, let go on either stop to detect the click. If you have a little bit of play, replace the wheel bearings. In fact, if it's used, replace them anyway. They are cheap. However, test them first so you know the state of them and if you are making progress.
Wheel Play on Axle
Test you lateral play. Put the front wheel in the air and see if you get lateral play, do the same with the rear. If you get any, then the wheels haven't been secured properly. You have the axle clamping style so follow the procedure to ge the front wheel centered properly if you encounter this. It's very common. Do the same with the rear. If you have lateral play, go through the adjustment procedure for you chain and test again.
If you still have play then you need to measure your bushing lengths and ensure they are the right ones for you bike. People love to use SV, TL and GSXR 1000 bushing on the 600. Probably from buying bushings at scrap yards. Use your shop manual that you bought for lengths.
You did buy an official Suzuki shop manual, right?
If you have flat spots, if they aren't round, especially the rear, you may be prone to speed wobbles. Don't screw around with old tires. Get new and have them balanced. Bubble balancing is fine. I have one at home and have never had an issue. If you need tire advice, please ask another question.
Check torque on the triple clamp pinch bolts for both upper and lower triple tree. Loose bolts there can cause some horrendous speed wobbles the only thing about these type of speed wobbles is that they typically happen under moderate braking into high speed sweepers. You don't want that one because recovery from it is often getting thrown off the bike. Why not swap the seals since this thing is 10 years old. You can change the fork oil AND inspect the bushings at the same time. I know, it's a great idea.
You indicated it didn't change a thing. That means one thing, the source is elsewhere. You have an adjustment on the end of it. It's a dial. Clockwise is more dampening, counter is less.
Take it off and push the shaft into the body and pull it out. If it gives resistance it's fine. If you feel points of no resistance in it when you pull the shaft in and out then you have air in it. Order a rebuild kit or better yet, send it out. They are hard to rebuild if you don't have the tools, you can't get air in it.
If it were my bike I would tear it down, visually inspect all the bearings, replace bearings and races as necessary, clean and lubricate all of the suspension components. This is just apart of the process for me. I suggest you take the weekend and do the same. It's worth and you get to know your bike more intimately as a result. It will pay dividends and it's proactive. Think about it.
To summarize, check torque values on all suspension and wheel components. Clean, lubricate, replace as necessary all bearing associated with wheels and chassis. Take your time. From your other posts, you have another bike that's pretty nice. This one can set for a bit while you sort it.
You need a special tool to remove the swingarm bolts. Here it is.