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t thickness HP. A curve of batch size against thickness is plotted in Fig. 5. As shown, at HP =, the production capability (batch size) is the production capability of n =3 is larger than the required lot size (202000units). For simplicity, the time taken for machining the depth of a thin ponent is treated as a given constant and added to the required time t CC for making a cavity insert. The C mm can then be calculated by n as expressed [1] process In the molding process, the cycle cost and power consumption cost are used to establish the molding operations cost as described in the following sections. . Mold making cost versus part thickness Cycle cost The cycle cost C is defined as the labor cost for molding machine operations. The calculation of cycle cost, given by E q. 8, mainly depends on the cycle time and number of mold cavities For the example, the value of labor cost per hour, L, is given as $, Cp can be calculated, as t cycle = n = 3 when HP = , as found earlier. And so Cp =$ Power consumption cost Typically, within the operating cycle of a molding machine, maximum power is required during injection. Hence, longer injection times and higher injection pressures increase the power consumption cost. For the purposes of this example, an injection time of tin = applied for the molding process。 The required hydraulic power PH, power consumption E i, and cost CPC for injection can be found from the following expressions [23] 9 In E q. 9, is the mechanical advantage of the hydraulic cylinder for power transmission during molding, and the resulting electric power cost of CE = HK$, the sum of the required injection pressures Pin in the feeding system and cavity during molding need to be found. Required injection pressures. Based on the mold layout design, the volume flow rate Q in the sprue is equal to the overall flow rate, and the volume flow rate in each primary and secondary runner will be divided by the separation number, Ni, according to: The volume flow rate in a gate and cavity equals to that of the runner connecting to them. Tan [24] derived simplified models For filling circular and rectangul a r channels that can be employed for the feeding system design in this study 1. Sprue and runner (circular channel) The pressure drop of sprue and runner is express e d a s: 10 2. Cavity and gate (rectangular channel) The pressure drop of cavity and gate is expressed as: Further, the temperaturedependent power law viscosity model can be defined as: Based on the values of the volume flow rate and consistency index m (T) for each simple unit, the pressure drop P can be found by using E q s. 12to15. Thus, the required filling pressure is the sum of pressure drops P in the sprue, primary runner, secondary runner, gate, and cavity: Required power consumption. Given the shape and dimensions of the part and feeding channel, the pressure drops of the sprue , runner, gate , and cavity are obtained through the calculation froE q s. 12 to 15, and are substituted into E q. 16. The required injection pressure Pin is calculated and substituted into the E q. E q s. 10 and 11, the power consumption cost CPC is calculated and depends on the variation of injection pressure, which is indirectly affected by the thickness of product as shown in the following E q .17. After substitution, this bees: 11 Then the molding cost After calculation, C molding = $+$,when HP =, n =3. on the current practical approach Based on Esq. 8 to 18 it can be shown that as the part thickness,Hp, increases, the necessary injection pressure . Molding process cost versus thickness consumption cost) decreases but the cycle time (and thus labor cost) increases and so there is a minimum total molding process cost, as shown in for the example in this study. As can be seen the minimum molding process cost is Hp =. If the test example part thickness, Hp, were increased from to , the plastic material cost is increased by %。 however, the total molding process cost decreases by % to $, the total manufacturing cost for the part falls %, a saving of $Thus, applying the current practical approach does not give the true minimum 12 manufacturing cost. The current practical approach mainly focuses on minimizing the thickness of the part to reduce the plastic material usage and achieve shorter cooling times. When the part is thin, higher injection pressures are needed during the molding process, which substantially increases the molding process costs and consequently shifts the true minimum manufacturing cost for the part away from the minimum thickness solution. 3 The proposed approach To overe the shorting of the current practical approach, a concurrent approach is proposed for minimizing the manufacturing cost for plastic parts made by injection molding. of the proposed approach Three parallel phases of product design, mold design, and molding process setting are undertaken for the proposed approach . The parallel phases handle individual cost functions for material cost, molding cost, and mold making cost, Which add to yield the total manufacturing cost . The product shape and dimensions (the possible range of thicknesses) are considered as the main design inputs at the beginning of design phase, as shown in Fig. 7. The proposed approach will provide a possible solution by considering the three phases simultaneously. The outputs are options for binations of the thickness of the part , the number of mold cavities , and the minimum manufacturing cost that 13 meet all the given requirements. . Creep deflection and plastic material cost versus thickness . Mold making cost versus part thickness (n =1–8) Molding phase The molding process cost is the sum of。
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