For example, on PLC cabinets, the negative side of 24Vdc power supply may be tied to earth. Siemens S7-300 cpu's for one, has a sliding tab to optionally connect/disconnect the negative side of 24Vdc power supply to earth.
What are the reasons for tying the two together?
Under which conditions should the two not to be tied together?
This is a topic that comes up from time to time. There's no easy answer. However to ground the negative is my preference for the following.
If the negative is not grounded and the positive gets grounded by accident, no fuse will blow but all the signals that were floating around zero will now be at -24 which some input cards won't be able to read, i.e,. the signal input will be -23 to -19 instead of 1 to 5. If the card shares the power supply it's probably OK however quite often they are separate.
If the short to ground is only intermittent, it might be very hard to find the fault. wheras if you blow a fuse or pop a breaker on just the faulty loop, it's much easier to find.
I have also seen two 24V lamps in series across the 24 with the center point grounded (+/- 12V). The lamps normally glow equally with a bright lamp to indicate either supply rail shorted. Here again it's quite easy to find a fault but my preference is to solidly ground -24
I'm sure there will be a lot of opinions but one of the best reasons to tie the negative side of the 24V supply to ground is so that a wire short won't successfully tie it to line voltage which is dangerous to man and machine. It also is good practice to avoid noise and weird problems from interaction with 24V devices that do have the negative side grounded or are other wise sensitive to floating systems.
Some folks tell it the other way, that floating it solves problems, but I've found that if you have problems that go away when you unground the power supply, you haven't solved anything and they should be fixed rather than floating the DC system. Some of the weird problems that happen with floating power are bits flipping, outputs latching up requiring a power down before they will work and stuff that stops working when you interconnect.
Also, you won't get too far along before you hook up a piece of gear that ties the negative side to ground and that may be a bad place to ground for noise and ground loops. It makes chasing a problem a lot easier if you know where the ground is and you return everything within reason to that point. Complex systems have a great deal of attention paid to the grounding system and with good reason, fixing the grounding has solved as many problems as good power and good connections.