I suggest you check out
on your system for accurate details of your crontab set up.
Basically you write a shell script to copy and rename your file, and use crontab to run that script as specific times.
I can't help much more than that, because there are details about the job I don't know.
Things to consider -
Has the JVM got a lock on the log file preventing any other access while it's running ?
When is the quietest time to do the change ?
How long are you going to keep the backups ?
etc.