Can a owner of a union company work on the equipment on the job?

It depends on the equipment. If working with the equipment is not covered under a collective bargaining union contract, then it would be allowed. However, if working with that equipment is covered by a collective bargaining union contract, then the owner could not work on the equipment unless he/she is a member of the union. But having the owner be a member of one of the unions working at his/her work place would be a conflict of interest during negotiations.
Therefore, if any union member saw the owner working on equipment that is covered by a collective bargaining union contract, that union member could file a formal grievance with the union.
I can think of two instances where the owner could work on equipment that is supposed to be worked on by union workers;
1 - when the union is on strike and the contract has expired
2 - when the union is locked out by the company and the contract has expired.

You mean like heavy equipment? If he is the owner he has every right to appoint anyone he wants to to work on it. If it's something like a telescopic boom, backhoe, skid loader to something of that nature, he also has the right to use it at his discretion. He would however, be better served to find a well qualified operator to that kind of work, so he could supervise other work at the site. Overall...it's HIS call.

It depends on the contract agreement. Every union shop has a book of laws and by -laws which are the agreement between the workers and management on how the shop will be run. Moreover, everyone should be given a book of the laws and by-laws on the day that they are hired. You will have to go through the book for your self to get that answer or, if you trust that you have a good union steward, ask your steward to explain it to you.

I have worked in several closed union shops as a manager, and it has been my experience in the ones that I worked in that management can not work on the equipment. In fact only certain classification of employees are allowed to use specific equipment. However, the shops I worked in were closed shops with very large corportations, that had very specific laws and guidelines.

generally, yes, unless there is something specific in the labor contract that forbids it. that would be pretty unusual, though, for a contract to forbid an owner to operate equipment which he owns.

his company his equipment