What is Reddit's opinion of Simichrome Simichrome Polish 1.76oz 1.76 OZ TUBE?
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Vinegar is an acid - it has its uses but you have to be careful with it. If the usual bathroom cleaners aren’t removing it, you might consider trying a polish. But I wouldn’t use anything abrasive like powdered cleaners.

I had fantastic results with this one on chrome. Simichrome Simichrome Polish

If plan on keeping and restore it, may I suggest taking it all apart and cleaning everything. Re-grease the hubs and BB. Buy some SEMICHROME POLISH https://www.amazon.com/Simichrome-Polish-1-76oz-1-76-TUBE/dp/B00JDPS7Z8 to polish up all the chrome parts. As far as the worn out parts are concerned, either find them from a bicycle shop or online. It will a project as well as a mechanical learning process. It will really worth in the long run.

Regarding all those paint chips, scratches and white paint splatters, you can strip the paint off the bike and have it repainted with the same color or ? Have it soda blasted ? Before you do that you might want to take pictures of the all the decals and markings of the bike indicated that is a TREK 400 and have them reproduced https://velocals.com/ .

The bike is a 1984 400 Trek.

http://www.vintage-trek.com/Trek_timeline.htm

Hope this helps.