Well Sameer,
I have tried out the same and could not realize the problem. My climb rates were:
230 kts, 1000 fpm until FL50
250 kts, 1500 fpm until FL100
280 kts, 2500 fpm until FL150
300 kts, 2000 fpm until FL200
320 kts, 1500 fpm until FL250
320 kts, 1000 fpm until FL300
320 kts, 500 fpm until FL350
There was not any problem, except 1 that is not aircraft specific, I think:
At me, and only sometimes, when I want to push over the job to autopilot (everything setted correctly) at about 2000-3000' it pushes the nose down and I have to fight with the autopilot to keep the aircraft in the air ...

But after the situation stabilized within 20-40 seconds, everything went well again.
I recommend to check sometimes the aircraft from outside. I usually hit my joystick unwantedly and later realized that I am flying with gears out, or with speedbrakes... I know it sounds dumb, but sometimes worth to look around the plane from outside.
Anyway, I do not know what Y/D is for, so I never use it. If you still have problems, try out
this FDEHope it helped.