What are benefits to persue PHD by mechanical engineer ?

I earned my Ph.D. in systems engineering about 3 yrs ago as an older student (late 40s). The benefits are both professional and personal.
Let’s hit the professional first. It depends on your field and your peer group. I know in the federal government, degrees and certifications are valued, so it can help to conduct engineering services and to consult. Also, if your peers have advanced degrees, then a Ph.D. helps not only set you apart but helps establish you with inherent authority in your field.
In some fields, like academia, a Ph.D. is expected for tenure track positions. However, an MS will normally be acceptable at the community college level. In engineering, an MS or a professional engineer degree is more acceptable.
Personally, you can get a lot of personal satisfaction from a Ph.D. degree. It is one of the things in life that you really need to want.