Feel free to continue open access, but place a social stigma on using the equipment without recording your use.
For example, imagine that when you sit down at the desk, a light goes on that says "Thanks for logging in" (if you have). Now, tomorrow, you find three other people in the lab who don't have the sign lit. You say "Hey, I can see that you didn't sign in to indicate that you're using the system-- here, let me help you"
Another way to encourage self-policing from the users is to tie maintenance or upgrades to the logged use of the system. Say "Sorry, we're not going to upgrade that oscilloscope because nobody logs that they use it. We're going to spend grant money on the bench power supply in room 6B that has lots of log entries."
Put these two things together, and the people who care about using the equipment will help you keep the other users under control.