If your eye lashing is only on curves you are probably speeding up as you make the curve. I call it the swoosh factor. Try to keep your speed even over the curves.

Thanks everyone for the input. Ok I have just purchased a used Liberty APQS. I am teaching myself and it's been fun but challenging. So far I have just done a couple of practice pieces with sheets and muslin and of course cotton batting. I am using Superior "so fine" thread. The eyelashes are on the top! It seems I was doing pebbles that did not have eyelashes on every pebble before but do now. Today I am going to slow down. That could be the problem. I am now thinking after reading all these suggestions that it could be the top tension as last night when I was fussing with it I noticed the disc on the top tension was opened! Which would mean there was no top tension, right? So I will mess with that. I cleaned the bobbin case several times, I checked for dust or threads in the bobbin spring and honestly I did not notice any lint. The bobbin tension appeared right as it did turn on its side and I could pull the thread evenly! So when I go up today I will try all these suggestions! Oh by the way I used a turbo winder to wind my bobbins! The bobbins appeared to be hard so I thought that they looked pretty good but that turbo winder is almost scary when it winds it's so powerful! Anyway ladies thanks for input...in about one hour I will be up there using and going over each suggestions given to me by you all!

One other cause which hasn't been mentioned (I think) is having the quilt sandwich too tight. You should be able to grab (with your other hand) the end of your finger with the quilt sandwich overtop of it if you push it up from underneath the quilt sandwich.

OK here is my update: I changed bobbin cases, oiled machine, adjusted top tension, loosened quilt on frame and slowed down and the result was positive! My pebbles are not making the eyelashes on top, how ever the thread broke twice. I readjusted the tension just a smidge and all looks well. Thanks now I will go back and practice with anxiety that it will mess up again. Now to longarm it seems there are going to be those cases of repeated problems and new problems arising which puts me on guard just waiting for another hill to climb! When does it get easy? When will I be able to travel back and not fall off the track? Oh my maybe 64 years old is too old to start longarm quilting! We will see!

Jude, don't give up! I have just started longarming and also have had tension problems and thread breakages. I finally found out that my inexpensive Janome 1600 is a thread snob!! Darned thing only likes Aurifil thread!!

lol Susie, i an starting to see that these machines do everything even think for them self! How long have you ben long arming? Are you teaching yourself? Good luck with your adventure of long arming. We are lucky to have this board with so many talented folks to help us when we are in a pinch!
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Eyelashing in my case was caused because I did not floss my thread in the tension disks. Once I did this, it sorted it shelf out. BTW, my machine was a used longarm also. Good luck.

OK I am new at this so I have to ask.: what does flossing your thread in tension disks mean?

You. Also might check how tight your quilt ison the frame. After you put yout three layers on I find it helps to put one finger on the underneath side and poke it with your finger if you can pinch all three layers with your other hand the tension of your quilt on the frame is not to tight this allows the thread to penetrate the fabrics when quilting
Also some fabrics have a higher thread count.

Another trick is to shorten your stitch length.