From working tool kinematics to new finishing-hardening processes

Rolls Geometry Calculating Mathematical Model for Rotational Bar Surface Drawing

“…From equation (20) it follows that the roll profile is bounded by a circle with the center coordinates 𝑑𝑑 𝑐𝑐 = 0, 𝑦𝑦 𝑐𝑐 = 𝑎𝑎 + 𝑓𝑓𝑘𝑘. The calculation of the roll profile, bounded by a circle, with the formula (10) gives almost the same results, which allows to make a conclusion about the validity of the assumptions made.…”

“…So β 𝑛𝑛 = 0, 𝑅𝑅 𝑛𝑛 = 𝑎𝑎. From equation (10) we obtain 𝑅𝑅 𝑥𝑥 = 𝑎𝑎, i.e. with 𝑓𝑓 = 0 roll profile is limited to a circle with a radius 𝑎𝑎.…”

“…Another way to improve the quality is plastic deformation of the surface layer by transverse rolling [9][10][11][12][13][14][15]. While transverse rolling on centerless lathes, the rolls perform a planetary movement around the cage that moves without rotation along its axis [16].…”

“…Equation (10) determines the rational profile of the roll in terms of rolls and supporting rings bearing surfaces uniform deterioration, as well as the balance of the rolls under one-sided load during rolling. The roll whose profile is configured on the curve calculated by this formula is shown in Fig.…”

“…profile evolute. The coordinates of curve curvature centers represented by equation (10) in the polar coordinate system…”