Hi proton,
Here are some more comments from me.
So I just decided to give it a try on forum if someone of the older and more experienced members could deliver fast solution.
I think using this forum is a wise decision on your part, however beware of fast solutions
so the budget limit is 2000$
On the surface that appears to be enough to build a very nice project. But making hasty decisions and buying components before you have a well thought plan can eat a couple thousand in a hurry.
I have been searching on EV album for over a week...
Yard machines and specialty EVs are difficult search items. We have been trying to get the forum admin to start a section or sub-forum for such. You can find a number of examples linked on this thread
http://www.diyelectriccar.com/forums/showthread.php/express-your-interest-non-road-going-54835.html
And the Motenergy motor is the best I could find.
I am not saying that particular motor won't work for you, but it may not be your best bang for the buck. It is basically a redesign of the Briggs & Stratton Etek motor from 10 or 15 years ago. You can imagine what B&S had in mind when they spent a ton of money and introduced the Etek. Well, that didn't work out so well for them and they ceased production after a short time, really none of the Etek motors found application on commercial lawn equipment or otherwise and I bet B&S lost a bundle. Don't make the same mistake
By the Motenergy motor I have problems with relatively high voltage (48V) and high constant current (200A)
I think 48V is an excellent choice for vehicles of this nature. And your "constant current" statement leads me to believe you have a misconception about the way electric motors operate. A "constant current" would require a constant load, which is an unlikely situation.
because I want to install the Winstons LiFePo4 batteries with relatively low constant current and low voltage. After all I am rebuilding a garden machine not a car, so the budget limit is 2000$. So that’s why I can't afford to buy 2600 AH batteries, but just 500AH - 600AH it would be more than enough.
2600 Ah at 48V = 125 kWh

That would be enough energy to mow a golf course

When you put cells in series to make a battery, the charge (Ah) doesn't add. Even though you're not building an EV car, look over the EVInformation section here and see how energy usage and range are figured. This can be adapted to your machine and you can get a better idea of how to size your battery.
I am also interested in Kokam Lithium Polymer batteries, which would deliver enough current and voltage. But here is the problem of expensive battery controller. Maybe the solution would be Mini BMS, but as I said the Kokam Batteries are Lithium Polymer and the Mini BMS is intended for LiFePo4 batteries. Maybe someone had tried to use Mini BMS on Kokam batteries and would share the experience.
I use Kokam on my eTractor. Just for example, it was originally equipped with a 10 hp gas engine. I have an old floor sweeper electric motor powering it. I got the motor for free. It needed some TLC. It was originally rated at 3/4 hp. I run it at 48V and use an inexpensive Curtis controller. Been working for like 15 years. I do not mow with it, but do occasionally use it hard.
Stick around and read up on things. These smaller EV projects are great ways to get acquainted with the EV conversion process.
Regards,
major