**4. Thickening of flange of disc-like parts with spinning**

The forming process and methods of typically disc-like part with thickened rim thickened by spinning are introduced in this section.

The following calculations in section 4.1. and 4.2. are based on the assumption of plane deformation which the meridian plane of the work-piece keeps planar during forming process. That is, the deformation can be treated as a process of axisymmetric radial compression.

#### **4.1. Design of multi-step process**

Thickening ratio is also a key factor during the process design of thickening spinning. It is defined as 1 / *n nn* λ *t t* <sup>−</sup> <sup>=</sup> , where *nt* is the thickness of the rim after the *n* time thickening step, *<sup>n</sup>* <sup>1</sup> *t* <sup>−</sup> is the thickness of the rim before the *n* time thickening step. The number of forming step required for rim thickening depends on the total thickening ratio 0 / *<sup>N</sup>* λ <sup>=</sup> *t t* , where *Nt* is the target thickness and 0 *t* is the initial thickness. Generally, the recommend value in a single thickening for low carbon steel is 1.4 *<sup>n</sup>* λ <sup>≤</sup> . If 1.4 *<sup>n</sup>* λ > , the thickening could not be obtained in one forming step, a multi-step thickening process will be needed.

In a multi-step forming, *nt* is decisive to the roller design and success of the process. Assuming the average strain in each forming step is equivalent, there is 1 0 <sup>1</sup> ln( / ) ... ln( / ) *N N tt t t* <sup>−</sup> = = . So, the *nt* equals to

$$t\_n = t\_N^{n/N} t\_0^{N-n} \tag{1}$$

where, *N* is the total number of forming steps, *n* is the number of forming step, 1≤*n*≤*N*.
