Dear Munish Gupta,

I send to you a link about your question and  hope to be useful for you

Best Regards

http://www.okuma.com/hssc-and-vsst-prevent-cnc-lathe-chatter

 Hello Gupta,

This link would be really helpful

http://www.google.com.ng/url?sa=t&rct=j&q=&esrc=s&source=web&cd=6&cad=rja&uact=8&ved=0CDcQFjAF&url=http%3A%2F%2Fwww.moldmakingtechnology.com%2Farticles%2Fhow-to-eliminate-chatter&ei=CYliVOmdO8vLaLbRgvAK&usg=AFQjCNGg-8VbkCDB4kWl_euSR60RY5asuw&sig2=TAsu20dncK65hFq2Sb1WCQ&bvm=bv.79400599,d.d2s

http://www.google.com.ng/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&uact=8&ved=0CCEQFjAB&url=http%3A%2F%2Fwww.americanmachinetools.com%2Freduce_cutting_tool_chatter.htm&ei=CYliVOmdO8vLaLbRgvAK&usg=AFQjCNG_i8qNTU45xuUDxr5-kVJCN9sDRQ&sig2=0X310oWjIQXDXEPPszE0IA&bvm=bv.79400599,d.d2s

http://www.google.com.ng/url?sa=t&rct=j&q=&esrc=s&source=web&cd=5&cad=rja&uact=8&ved=0CDIQFjAE&url=http%3A%2F%2Fwww.okuma.com%2Fhssc-and-vsst-prevent-cnc-lathe-chatter&ei=CYliVOmdO8vLaLbRgvAK&usg=AFQjCNFqNvFYXD9ZMF1Xr3C52CgIVnf6cQ&sig2=mS4cCn_Ap1PGwe8qpffmBQ&bvm=bv.79400599,d.d2s

I think that this paper is good for you.

Normally relations between length bar / diameter bar minors to 10 are well.

In relations to cutting parameters, the highest incidence on chatter is made by depth of cut.

The paper Martinez has given is very good. 

Depending on the cutting operation either depth of cut or the cutting speed plays a big role.

If you are performing turning operation, then generally the depth of cut is critical because the stability lobes are very close to each other and playing with the spindle speed does not really put you in a stable pocket. So, the simplest way is to reduce depth. On the other hand, if you are cutting at higher speed, then changing the spindle speed may actually help you. Please note that it all depends on the structure of your machine tool and the cutting parameters. If your machine has a low frequency resonance, then your only chance is to reduce the depth.

Anyways, play first with the spindle speed, increase it and reduce it gradually to seek a stable pocket, if it does not really help you, then reduce the depth. That would be a good strategy to start with. 

The link about the Okuma would not help you. It has nothing to do with your application. If you have a Okuma machine then maybe you may use that functionality to troubleshoot your process. But, otherwise I would forget about that. Okuma has implemented a spindle speed variation method to disturb regeneration effect in chatter vibrations. You must change the spindle speed very quickly. Unless you have an open-CNC and you can control the spindle speed with a motion controller, you have no chance to suppress the chatter by following that link! So, forget about the Okuma. 

One more thing, if you are cutting hard material actually if you do not mind cutting at very low speed. Then, you can utilise process damping to increase your depth of cut. So, reduce the cutting speed very much. But, be careful about the tool chipping. If you reduce the speed a lot then you can actually increase the depth quite a bit! So, basically the total material removal rate would be same. But, as I said you have to be careful about the tool wear. 

Good luck and have fun with it! 

Thanks to all for providing the information.