Continuous casting mold and continuous casting method of round billet

1. A mold for continuously casting a round billet with a curved type continuous casting apparatus, in which the mold has an upper edge, a lower edge, and a cooled mold surface extending between the upper and lower edges, the mold also having an inner diameter D 0 (m) at the lower edge thereof, and an outer curvature side thereof is configured to have a curvature radius R 0 (m) at the lower edge thereof, wherein D is a mold inner diameter at a distance x away from the upper edge of the cooled mold surface and dD/dx represents a change in D with respect to a change in x, and R is a curvature radius of an outer curvature side at a distance x away from the upper edge of the cooled mold surface and dR/dX represents a change in R with respect to a change in x,

the mold being characterized in that:

given that a rate of change Tp (%/m) in mold inner diameter per unit length along a casting direction is expressed by Formula 1, and a rate of change Rp (%/m) in curvature radius of an outer curvature side per unit length along the casting direction is expressed by Formula 2, the rate of change Tp in mold inner diameter and the rate of change Rp in curvature radius satisfy a relationship expressed by Formula 3;

Tp =(1 /D 0 )×( dD/dx )×100(%/m),  Formula 1

Rp =(1 /R 0 )×( dR/dx )×100(%/m),  Formula 2

Rp =( Tp/ 2)×( D 0 /R 0 )  Formula 3.

2. The round billet continuous casting mold according to claim 1 ,wherein the mold is divided into three regions along a casting direction, the rate of change Tp in mold inner diameter ranges from 12 to 16%/m in a first region, the first region being allocated from an upper edge of a cooled mold surface to a zone of 50-100 mm, the cooled mold surface being the side which molten steel is poured to, the zone of 50-100 mm being between the positions of 50 mm and 100 mm away from the upper mold edge, the rate of change Tp in mold inner diameter continuously varies from 12-16%/m to 0.8-1.4%/m in a second region, the second region successively following the first region and being allocated from said zone of 50-100 mm to a zone of 250-300 mm, the zone of 250-300 mm being between the positions of 250 mm and 300 mm away from the upper mold edge, and the rate of change Tp in mold inner diameter ranges from 0.8 to 1.4%/m in a third region, the third region successively following the second region and being allocated from said zone of 250-300 mm to the lower mold edge.

3. The round billet continuous casting mold according to claim 1 , wherein the mold is divided into three regions along the casting direction, the rate of change Rp in curvature radius ranges from 6×(D 0 /R 0 ) to 8×(D 0 /R 0 ) (%/m) in a first region, the first region being allocated from an upper edge of a cooled mold surface to a zone of 50-100 mm, the cooled mold surface being the side which molten steel is poured to, the zone of 50-100 mm being between the positions of 50 mm and 100 mm away from the upper mold edge, the rate of change Rp in curvature radius continuously varies from 6×(D 0 /R 0 )-8×(D 0 /R 0 ) (%/m) to 0.4×(D 0 /R 0 )-0.7×(D 0 /R 0 ) (%/m) in a second region, the second region successively following the first region and being allocated from said zone of 50-100 mm to a zone of 250-300 mm, the zone of 250-300 mm being between the positions of 250 mm and 300 mm away from the upper mold edge, and the rate of change Rp in curvature radius ranges from 0.4×(D 0 /R 0 ) to 0.7×(D 0 /R 0 ) (%/m) in a third region, the third region successively following the second region and being allocated from said zone of 250-300 mm to the lower mold edge.