How is the friction multiplier important and applicable to load cases and how without friction in case of rotating equipment connections? Can anyone describe the significance of this?

The friction multiplier is just a quick way to adjust friction for the whole job, on a "per load case" basis.

For exmaple, assume you've defined "mu" as 0.3 on all your restraints. Suppose you now want to consider a higher value, say 0.4. You can set the friction multiplier to 1.33 to accomplish this (0.3 * 1.33 = 0.4).

You can do the same if you want to reduce "mu", say to 0.2. Here you would use a friction multiplier of 0.67.

Setting the multiplier to 0.0 effectively removes friction from that load case.

Friction may or may not be conservative in doing static analysis, but with dynamic analysis higher the friction means reduced stresses of system and more stable system. so for dynamic load cases avoid using higher friction values for stress qualification.

But for static analysis with rotating machinery, it may sometime help you reduce your nozzle loads. Dont remove friction from the whole system as it is unrealistic(Remember even glass to glass surface have a friction value).Just reduce the friction value from the nearest support to the nozzle by keeping an antifriction PTFE pad (check temp feasibility, dont use for more than 210 C)

An exception is Pipe rack system where a conservative check would be to make friction zero as said by richard above and making a run for maximum displacements and stress check for failure at elbows.

Refer attached file for more clear idea