Cold profiled ring rolling is an advanced local plastic deformation technology widely used to precisely manufacture various complex seamless ring parts.It plays an important role in many industrial fields such as aeronautics,astronautics,automobile,bearings,etc.In the cold ring rolling process,the ring radius expands gradually with the increase of the feeding amount(i.e.rolling reduction),and the expanding deformation of the ring radius is closely related to the rolling reduction.It is very important to investigate the expanding deformation of ring radius for the precise control of ring dimensions and the design of feeding movement.In this paper,the relation between the expanding deformation of the ring radius and the rolling reduction in the stepped ring rolling process,a typical profiled ring rolling process,is analyzed by using analytical method.The results show that the growth amount of the filling depth of groove can’t exceed the rolling reduction,that in the inner stepped ring rolling process,the curves of the outer radius and big inner radius with the rolling reduction are monotonous,ascending and concave,i.e.,the outer radius and big inner radius expand faster and faster with the increase of the rolling reduction,and that in the outer stepped ring rolling process,the curves of the inner radius and small outer radius with the rolling reduction are also monotonous,ascending and concave,i.e.,the inner radius and small outer radius expand faster and faster with the increase of the roll reduction. Cold profiled ring rolling is an advanced local plastic deformation technology widely used to precisely manufacture various complex seamless ring parts. It plays an important role in many industrial fields such as aeronautics, astronautics, automobile, bearings, etc.In the cold ring rolling process, the ring radius expands gradually with the increase of the feeding amount (ierolling reduction), and the expanding deformation of the ring radius is closely related to the rolling reduction. It is very important to investigate the expanding deformation of ring radius for the precise control of ring dimensions and the design of feeding movement.In this paper, the relation between the expanding deformation of the ring radius and the rolling reduction in the stepped ring rolling process, a typical profiled ring rolling process, is analyzed by using analytical method. results show that growth growth of the filling depth of groove can not exceed the rolling reduction, that in the inner stepped ring ro lling process, the curves of the outer radius and big inner radius with the rolling reduction are monotonous, ascending and concave, ie, the outer radius and big inner radius expand faster and faster with the increase of the rolling reduction, and that in the outer stepped ring rolling process, the curves of the inner radius and small outer radius with the rolling reduction are also monotonous, ascending and concave, ie, the inner radius and small outer radius expand faster and faster with the increase of the roll reduction.