"What are the advantages of using zinc-free hydraulic oil? Some hydraulic oils don't contain zinc, so what would be the reason to make them zinc-free?"

Zinc has been a key additive constituent in hydraulic oils, as well as the majority of oil types, for decades. It primarily is used as an anti-wear agent or as an antioxidant.

These zinc-based additives are sacrificial, which means they are used up and depleted as they do their job. However, it's not simply the metal zinc added to the oil that performs this function. There is a chemical reaction between zinc oxides and an organic thiophosphoric acid that produces an effective resultant known as zinc dialkyldithiophosphate (ZDDP).  

Zinc-based hydraulic oil is widely used for a number of reasons. Under boundary conditions, a sacrificial layer of anti-wear additive (typically zinc-based) is established on the load-bearing surface of machine components to help protect against the results of friction. Anti-wear additives are most effective in moderate to severe load applications, while oiliness agents are utilized in mild conditions. Extreme-pressure (EP) additives are best in severe applications.

ZDDP (as well as other additive compounds) use phenolic and aminic compounds to neutralize free radicals and disengage the oxidation reactions. This in turn will prevent any harmful acidic byproducts from corroding equipment parts and changing the base oil's lubricating capability.

Another hidden advantage of ZDDP is that it has the capacity to perform several key functions at once. Without ZDDP, multiple additives must be employed and typically at higher concentrations and cost.

The disadvantages of zinc-based additives include their corrosion of certain metals and environmental impact. Oils with zinc levels that are too high have a history of leading to the corrosion of some metals, such as yellow metals, as they chemically attack the metal surfaces. A number of components even include instructions to avoid zinc-based additized lubricants for this reason.

In addition, these additives not only are non-biodegradable, but research has indicated that they are aquatically toxic.

The variety of ZDDP compounds also differ in their effects on hydrolysis and thermal degradation. Achieving high-quality levels in both of these categories can be a challenge. Additive alternatives to zinc have the potential of obtaining these benefits separately.

Keep in mind that zinc-based hydraulic oils have historically performed well and should continue to do so. If no underlying reason exists for utilizing a zinc-free oil, such as the metallurgy of a component or the environmental/operating factors, then there is a strong case to use zinc-based additives like ZDDP. The benefits typically outweigh the risks.