Technically, there's no such thing as tax-free super contributions. Either you pay your normal income tax rate on the money and then add it from your bank to your super (personal after-tax contributions), or you pay the super contributions tax of 15% (salary sacrifice before-tax contributions).
Generally in 2022-23, you can add a total of up to $27,500 in concessional contributions before tax each financial year, and up to $110,000 per year in non-concessional (personal/voluntary/after-tax) contributions.
These are normally taxed at 15% (or 30% if you earn more than $250,000/year), or more if you haven't given your TFN to your super fund.
Find out more about the contribution limits.