Supplemental Results obtained from the Study of Metal Distribution by Gating Design

Abstract

  The author carried out the study on the manifold type gate and has established the method of gating design from the theoretical formula derived by the author. He thinks that the method of calculation established by Berger & Locke is unsatisfactory and that of Ohira is unfavorable because of entirely experimental. And he derived entirely theoretical formula at his first step of work as follows :
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            α_x=(F/f_x)² (1+λ_x l_x/α_x +ζ_x
            β_x=λ_x L₂/D + ξ_x
  where     F_x : sectional area of channel
              L_x : distance between two ingates
              D : diameter of channel
              f_x : sectional area of No. x ingate
              α_x : diameter of No. x ingate
              l_x : length of No. x ingate
              ζ_x : coefficient of bend resistance
              ξ_x : coefficient of sudden change loss in viscosity
        λ_x, λ'_x : coefficient of pipe friction of ingate and channel
 This formula gives the distribution value of metal if the values of resistance at every part of ingate is given. The effects of pouring conditions such as pouring temperature and rate can not be supposed from this formula, but the effect due to the shape of ingate can be understood obviously.
  The author has ascertained the effects of these conditions by the experiment. Metals used in this experiment are cast iron and lead, and four and six ingates are used respectively.
  It has ascertained that the forementioned formula is applicable within the range of the pouring temperature of the metal is not so low as to cause solidification the metal in the channels and ingates.
  Satisfactory figure can be obtained when the normal values of coefficients of bend or pipe friction in case of water, are introduced in the formula. However, it is impossible to take a reasonable value of coefficient of pipe friction in the case of metal solidifies in gate.
  Some examples for gating design in which the metal distribution at each gate becomes equal, are also given in this article.
  The size of ingate can be determined from the following formula, because there is definite relation between the number of ingates and the size of each ingate.
            (F_i−1/F_o)²α_i+(n−i+1)²=(F_i−1/F_o)²α₃+(F_i−1/F_i)²(1+β_i)(n−i)²
  where     F_i : sectional area between ingate “i” and (i+1)
              F_o : sectional area to ingate 1
              n : number of ingate