Press forming method and tool of press forming

A tool of press forming for forming a press-formed product having no flange portion, the press-formed product including at least a top portion and a side wall portion continued from the top portion via a connecting portion, and the press-formed product being structured so that either all or a part of the side wall portion curves toward an outside of the press-formed product to form a convex shape in a planar view, the tool of press forming comprising:

• a punch that has:
• (i) a forming top portion that is configured to support a blank, (ii) a punch shoulder portion that is continued from the forming top portion and that is configured to extend along a curvature of the press-formed product, and (iii) a forming wall portion continued from the punch shoulder portion;
• and
• a die that has a side wall forming portion that is configured to form the side wall portion of the press-formed product by moving the die relative to the punch,
• wherein:
• in an X-Y coordinate system in which an origin is a point serving as a center of a radius curvature of a curvature on the forming top portion:
• (i) an X-axis corresponds to a horizontal direction, (ii) a Y-axis corresponds to a vertical direction, (iii) an optimal curve is a curve drawn by a formula presented below, and (iv) an optimal inclination angle is an inclination angle of a tangential line of the optimal curve at an arbitrary X-coordinate position,
• the side wall forming portion of the die has a cross-sectional shape expressed with a curve where an inclination angle of a tangential line at the arbitrary X-coordinate position with respect to the horizontal direction is equal to or greater than the optimal inclination angle, and
• the formula of the optimal curve is:
• X
• =
• pr
• -
• R
• +
• (
• R
• +
• t
• )
• ⁢
• sin
• ⁢
• ⁢
• θ
• +
• {
• br
• -
• (
• pr
• -
• R
• )
• -
• (
• R
• +
• t
• 2
• )
• ⁢
• θ
• }
• ⁢
• cos
• ⁢
• ⁢
• θ
• Y
• =
• -
• ∫
• 0
• θ
• ⁢
• [
• t
• 2
• ⁢
• sin
• ⁢
• ⁢
• θ
• -
• {
• br
• -
• (
• pr
• -
• R
• )
• -
• (
• R
• +
• t
• 2
• )
• ⁢
• θ
• }
• ⁢
• sin
• ⁢
• ⁢
• θtan
• ⁢
• ⁢
• θ
• ]
• ⁢
• d
• ⁢
• ⁢
• θ
• ⁢
• }
• where:
• pr:
• a radius [mm] of the punch;
• R:
• a radius curvature [mm] of the punch shoulder portion;
• br:
• a radius [mm] of the blank;
• t:
• a thickness [mm] of the blank;
• and
• θ:
• a contact angle (0≤θ≤π/2) [rad] of the blank with respect to the punch shoulder portion.