When I pursued my PhD in mechanical engineering, I went to the university library and looked for the programmes of various universities. Then I sent an application directly to the professor/institute of choice. In Europe, PhD studies in mechanical engineering are usually connected with part time employment and possibly with a temporary work permit. It might be a bit more difficult for a non-European, but if you have first grade credentials it is worth a try. Good luck.
there are many private university providing stipend for PHD scholars just go through the websites of the universities, you will get to know to about it.