Machinery's Handbook, 31st Edition
DESIGNING PLASTIC PARTS 593 From the last box for Case 2, the maximum deflection at the beam center is given by y EI Wl Ebh Wl 48 4 3 3 3 = = Consider the example of a small beam whose width = 19 mm, depth (wall thickness) = 2.0 mm, and length between supports = 102 mm. The beam is to support a central load of 22.24 N (5 lb). This beam’s cross section is depicted in Fig. 17 . As it has very little depth, hence a low sectional modulus, it may not handle the job. The plastic’s flex modulus is 2069 MPa (300,000 psi). Using the formulas above, the four quantities to be calculated are . . . . . I Z mm mm MPa 3 4 3 σ = = = = = = ^ ^ ^ h h h 67 67
. 12 19 2 12 2 12 666667 2 12 4 19 2 6 22 24 102 44 77 4 20685 19 2 2224 102 . 2 3 3 ^ ^ ^ ^ ^ ^ ^ h h h h h h h
. 1877
mm
y
=
=
Both the stress and the deflection are too high. The wall thickness could be increased, but instead a rib will be added that will run along the underside and center of the beam, changing its cross section to that shown in Fig. 17. The rib will be 10 mm deep but only 1.0 mm thick, with a slight draft of 0.5 degree per side. Following the formulas given in the table Moments of Inertia, Section Moduli, and Radii of Gyration starting on page 241, see the third row of the T-sections for the one with the tapered rib; the new cross-sectional area is 47.548 mm 2 , and the location of the neutral axis is 9.87 mm above the most extreme material at the bottom of the rib. The new cross-sectional moment of inertia I is 339.6 mm 4 , 27 times greater than the original I . The section modulus Z = 339.6⁄9.87 = 34.4 mm 3 . The re- computed maximum stress is 16.5 MPa, and the maximum deflection is 0.70 mm, acceptable for both the material and the application. To achieve the same result from a heavier rectan - gular-section beam would require a thickness (depth) of 5.99 mm, tripling the beam’s weight and increasing molding difficulties, whereas the new rib adds only 25 percent to the total sec - tion weight. As shown in Fig. 17 , a fillet should be added at the bottom of the rib with a radius equal to half the nominal wall thickness to assist molding and avoid stress concentrations. Draft: Most molded parts have features that must be cut into the mold perpendicular to the parting line. Removal of these parts from the mold is easier if they are tapered in the direction of mold opening. This taper is called draft in the line of draw or mold movement, and it allows the part to break free of the mold by creating a clearance as soon as the mold starts to open. The drawing of Fig. 19 defines draft and the dimensions associated with it. Plastics materials shrink as they cool, so they grip mold projections very tightly and ejection can be difficult without sufficient draft. A draft of 1 ⁄ 2 degree on each side of a projection on the part is generally considered the minimum, although up to 3 degrees per side is often used. The exact relationship between the draft angle a and the dimensional difference from the top to the bottom of the draw depth D is given by (31) where tan is the tangent of the draft angle. An excellent approximation is (32) This is accurate to the nearest 0.001 inch (0.025 mm) for draft angles up to 5 degrees and draw depths up to 10 inches (254 mm). tan d D = α . d D 00175 = α
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