A mixed method which combines the recent developed finite analytical method and the boundary fitting coordinate transformation method was used first to calculate the temperature field and thermal stress field of the cold roller in this paper. The following results are obtained by the calculation: thermal stresses σr=0, σθ=σz are maximum tension stress on the inner surface of the cold roller and σr=0, |σθ|=|σz| are maximum compression stress on the outer surface of the cold roller in the steady and unsteady case. Effectiveness and validity of the mixed method are checked with steady coil roller problems having theoretical solutions. The results show that good agreement is achived between the calculated value and theoretical solution,and the mixed method used in the paper is very workable. The mixed method is also useful in solving the steady and unsteady thermal stress field proplems of the hot -rolled for the reversing rolling mill and the continous rolling mill.
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