Calculation of the Shape and Size of Rectangular Parts
Calculating the shape and dimensions of rectangular blanks is a crucial step in drawing process design. Its core principle is to adhere to the law of conservation of volume while simultaneously considering the plastic flow characteristics of the material and the shape characteristics of the part. Unlike rotating parts, rectangular parts typically have straight edges and corners, so the blank shape is not typically a simple circle. Instead, it must be designed with irregular shapes based on parameters such as the part’s aspect ratio and corner radius to ensure uniform material distribution during the drawing process and minimize defects such as wrinkling and cracking.
The shape of rectangular part blanks must be determined based on the part’s geometric characteristics. For low rectangular parts (height less than or equal to half the minimum side length), the blank shape can be rectangular or rectangular with rounded corners. By adjusting the corner radius and straight side length, the blank area can be equal to the part’s surface area. For example, a low rectangular part with a length of 100mm, a width of 80mm, a height of 20mm, and a corner radius of 10mm can be designed as a rectangle with a length of 120mm, a width of 100mm, and a corner radius of 25mm. This ensures sufficient material while avoiding excess material at the corners. For tall rectangular parts (height greater than half the minimum side length), the blank shape must be elliptical or a “runway shape” consisting of a rectangle and two semicircles to supplement the material required for corner drawing and prevent overstretching of the straight sides.
The calculation of rectangular part blank dimensions is based on equal surface area. The surface area of each part must be calculated separately, then converted to the blank area before determining the specific dimensions. The part’s surface area includes the base, four sidewalls, and the fillet transition area. The calculation formula is: S = base area + 2 × (long side × height + short side × height) + 4 × (part fillet radius × height × π/2). For example, a rectangular part with a length of 150 mm, a width of 100 mm, a height of 50 mm, and a fillet radius of 15 mm has a surface area of S = 150 × 100 + 2 × (150 × 50 + 100 × 50) + 4 × (15 × 50 × 3.14/2) = 15,000 + 2 × (7,500 + 5,000) + 4 × (1,177.5) = 15,000 + 25,000 + 4,710 = 44,710 mm². If the blank is in a “racetrack shape”, the blank area S=π×R² + 2×a×b (R is the radius of the semicircle, a is the length of the rectangular part, and b is the width of the rectangular part). The blank size can be obtained by solving the equation.
The blank’s corner radius and straight side length need to be adjusted based on the characteristics of deep drawing deformation. The blank’s corner radius should be larger than the part’s corner radius, typically 1.5-2 times the part’s corner radius, to provide sufficient material for deep drawing deformation of the corner. The straight side length should be determined based on the ratio of the part’s long and short sides. The blank’s straight side length corresponding to the long side should be appropriately increased to compensate for the flow of material toward the corner during deep drawing. For example, for a rectangular part with an aspect ratio of 2:1, the blank’s straight side length corresponding to the long side should be 10%-15% longer than that of the short side to ensure even material distribution on the straight side. For asymmetric rectangular parts, the blank shape needs to be adjusted accordingly to match the material supply on both sides with the deformation requirements to avoid distortion of the part after deep drawing.
Correction of blank dimensions must be based on the test punching results. Theoretically calculated blank dimensions often need to be adjusted based on actual drawing conditions. If cracks are observed at part corners after a test punching, this indicates insufficient material at the corners and the corner radius should be increased. If wrinkles appear on straight edges, this indicates excess material and the length of the straight edges should be reduced. For example, if a part exhibits significant cracks at corners after a test punching, the corner radius can be increased from 30mm to 35mm to increase the available material. If wrinkles are severe on the straight edges, the length can be shortened by 5-10mm to reduce excess material. For high-precision parts, two to three test punches and subsequent corrections are required before final blank dimensions are determined.
Blank calculations for special rectangular parts (such as those with flanges or stepped shapes) require additional considerations. The blank for flanged rectangular parts must include the material of the flange, increasing the flange surface area during calculations. The blank shape can be rectangular or elliptical with large rounded corners. The flange width must be 5%-10% larger than the part flange, allowing for reshaping. Blank calculations for stepped rectangular parts must be performed in stages, first calculating the surface area of each step and then determining the overall blank size. Blank shapes are often complex and irregular, so finite element simulation software (such as Dynaform) can be used to analyze material flow and optimize blank dimensions when necessary. Scientific calculations and trial punching corrections ensure the proper shape and size of rectangular part blanks, providing a sound foundation for the deep drawing process.
