To prevent the mesting of water-based cooled lubricant by using a polymer based on an N-vinylacyl compound and acrylamidesulfonic acid to exhibit improved properties.

A copolymer bearing the structure units derived from compounds of formula I and formula II (R1 and R2 are each H or a 1-4C alkyl or the like; R3 is H or a 1-4C alkyl; R4 is a 1-6C alkylene; Y is an alkali metal, ammonium) is used in an amount of 0.01-2 wt.%. In a preferred embodiment, the molecular weight of the copolymer is 100,000-2,000,000 structural units. The contents of individual structural units are 2-50 wt.% in the units of formula I and 50-98 wt.% in the units of the formula II. The occurrence of the mist of water-based cooled lubricant can be inhibited by adding 0.01-2 wt.% of the water-based cooled lubricant including water, the common base materials of the cooled lubricant copolymer.