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Your 3rd gear syncro is less than what it should be.
Going from 4th to 3rd it has to change the speed of the gears and clutch plate to the 3rd gear speed and if the syncro is bad, the gears grind.
If you take it out of 3rd to neutral, and let the engine slow down, the internal resistance of the clutch will slow down the clutch plate. Then when you try to shove it back into 3rd, the syncro has to try to speed the clutch plate back up to the 3rd gear speed and if it can't, the gears grind.
I'm surprised you haven't experienced 2nd to 3rd grind also. If you haven't yet, don't be surprised if it starts.
When I down-shift from 4th to 3rd, I hear synchro grind but no grind when going from 3rd to 4th - why for?
When I am in 3rd, push in the clutch, take the car out of gear, and then put the car back into 3rd, I hear synchro grind - again, why?
What's going out?
3rd gear uses a different blocker ring and cone then 4th gear even though they share the same syncro assembly.
Apparently the wear gap on the 3rd gear side is below min. specs and the cone clutch lacks the capacity to change the reflected inerita of the gears and the clutch disc in front of it.
Seek help immediately from a competent transmission tech.
Having chips of 60 rockwell steel floating around in your gearbox will do considerable damage to other componets very quickly.
Yeah you have a bad 3rd gear syncro, its not uncommon, just take it to the dealer. Best way not to grid 3rd gear is to blip the throtle and rev match when downshifting, but take it in cause it will only get worst.
I've tried the "blip" and it doesn't work. I guess the synchro is just going out, completely. It's stull under warranty, so I hope it will stand up until I can take it in.
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