A equation computing exact dimentions of cylindrical risers with consideration of the contact area of riser to casting is derived as follows :
F
ct=(π/4)+πK ⁄ ((πK/4)
2/3)⋅(V
r/V
c)
2/3 ⁄ ((1−
β)(V
r/V
c)−
β) + (π/(4))
1/3(1/(K) V
r/(V
c))
2/3⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(1)
where; F
ct=A
ct/V
c2/3, a shape factor of casting
A
ct=Total surface area of casting including riser-casting contact area.
V
r, V
c=Volume of riser and casting, respectively
K=height of riser/diameter of riser
β=fraction of solidification shrinkage (0.05 for steel).
The value of K corresponding to the minimum value of V
r/V
c, which gives the most efficient riser, varies as a function of F
ct, but the K can be practically regarded as a constant 0.75 for any values of F
ct. It is found that Bishop-Pellini's diagram showing the relation between the simplified shape factor (L+W) / T (L, W, and T : length, width and thickness of casting) and the minimum effective riser volume as a fraction of casting volume V
r/V
c can be derived from equation (1). From the results of experiments on cube and T-shaped test castings, it wsa found that the risers determined from equation (1) behaved as the optimam riser.
Nomograms for rapid determination of heights and diameters of the minimum adepuate risers having K=0.75, 1.0 and 1.5 from volume and modulus (V
c/A
ct) of any given castings are presented, which are derived from an approximate formula against equation (1). These nomograms have sufficiently high accuracy for practical use. In applying the nomograms for a casting consisting of a principal part (the most massive section) and appendages (the thiner sections), the modulus of the casting must be calculated from the volume and surface of the principal part alone, but the casting volume can be calculated from the sum of the volumes of the principal part and the appendage.
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