According to the datasheet of this power supply, the output voltage goes from 0~60 VDC. If the output can't be negative, why does it have a negative rail beside ground? Why not just have ground?
In a circuit, should I connect my circuit's ground to the negative or to ground of this voltage?
The power supply itself has two output terminals, labelled \$\boldsymbol{+}\$ and \$\boldsymbol{-}\$, and produces up to 60 V between them. Remember that voltage is defined only as a difference between two points; neither of these has a defined voltage relative to earth.
It also has, for convenience, an earth terminal on the front, labelled ⏚. Neither of its outputs are connected to earth—almost all bench power supplies have a floating output—so if you need an earth-referenced output, you can tie either the positive or negative output to earth ground. It can also be a convenient place to plug in an antistatic wristband, or anything else you may need grounded. This terminal should, in a properly designed power supply, be connected via a low-impedance path to the ground prong on the mains plug powering the PSU.
The circuit being powered should always be connected between positive and negative; it's just that sometimes it's desirable to tie negative to earth. Or to tie positive to earth, in some cases (like telecommunications equipment), or even to have some other point entirely referenced to earth.
If the output can't be negative,...
Whether a voltage is positive or negative depends on how it is measured. The negative (black) terminal is the reference against which the positive (red) terminal is measured. placing meter probes such that the red probe is on the black terminal and the black probe is on the red terminal will measure the voltage as negative. So the output voltage can be negative.
why does it have a negative rail beside ground?
The word ground needs clarification. The green terminal is connected to the chassis and power earth. It is not a negative "rail". It is used to connect a circuit under test to a common mode voltage (not necessarily 0V) that is also common to the operator. It is commonly called zero volts, but be careful. It is zero volts only if used that way. Zero volts is arbitrary depending on where the black probe of the voltmeter is placed.
Why not just have ground?
This is a laboratory voltage supply. Having a separate power earth connection provides flexibility for circuit testing, with or without power earth a attached. It allows a static dissipative connection (if implemented properly) to power earth to an otherwise insulated circuit.
Test equipment (oscilloscopes for example) probes can have a power earth connection already, so a floating circuit may be convenient.
In a circuit, should I connect my circuit's ground to the negative or to ground of this voltage?
Here ground is being used to mean circuit common in one sense, and the negative of the power source in another sense. This is often used to represent zero volts in a circuit. The negative (black) terminal of a voltage source is not ground unless it is connected to ground. Be careful not to confuse negative with ground.
The phrase "ground of this voltage" is ambiguous. The red terminal is positive relative to the black terminal. It does not "have a ground" in any meaningful sense.
Either the positive or negative terminal may be connected to power earth. There is no general requirement that the negative terminal should be grounded.
simulate this circuit – Schematic created using CircuitLab
The red and black terminals should be considered like a variable battery connected between them, "floating in the air. When a conducting path is closed from the red to the black electrons will flow out of the black terminal and into the red terminal. The green terminal is not involved.
The green socket is in fact chassis earth and connects to the protective earth (PE) that comes into the power supply from the wall socket. That green socket is usually galvanically isolated from the red and blue socket circuit.
You may not want to tie your negative terminal to chassis ground when there is the possibility of picking up white noise off that ground. Floating the circuit and tying it to a different ground is sometimes better.
When using multiple supplies, you might want to tie all negative terminals to a "single point ground" and then tie that point to chassis ground.
As explained, the positive, negative, and Ground are electrically isolated. You can bond or reference either polarity to Ground. The ground terminal is the equipment chassis and AC Equipment ground feeding the power supply. In a DC system, you can float the output or make it a grounded system.
One primary reason you would use a grounded system is to provide simple, cost-effective over-current protection devices (OCPD) like fuses and breakers. Just like an AC grounded system, you bond one of the polarities to the Ground with a large enough conductor to safely handle any fault current likely imposed on the system. You install an OCPD on the ungrounded circuit conductor to protect all circuit conductors. The disadvantage of a Grounded System is they are dangerous and prone to unnecessary outages.
If you float the system, you must provide OCPD, which means you install an OCPD on each polarity or phase. An alarm or monitoring circuit is required to detect a Ground Fault and alert maintenance personnel to schedule an orderly shutdown to make repairs.
