Minimizing manufacturing costs for thin injection molded plastic components(降低制造成本射出成型了薄

DOI10.1007/s00170-003-2023-1

Int J Adv Manuf Technol(2005)26:517–526

J.K.L.Ho·K.F.Chu·C.K.Mok

Minimizing manufacturing costs for thin injection molded plastic components

Received:11June2003/Accepted:14November2003/Published online:8December2004

?Springer-Verlag London Limited2004

Abstract Minimizing the cost of manufacturing a plastic com-ponent is very important in the highly competitive plastic injec-tion molding industry.The current approach of R&D work fo-cuses on optimizing the dimensions of the plastic component, particularly in reducing the thickness of the component during product design,the?rst phase of manufacturing,in order to mini-mize the manufacturing cost.This approach treats the component dimensions established in the product design phase as the given input,and uses optimization techniques to reduce the manufac-turing cost of mold design and molding for producing the com-ponent.In most cases,the current approach provides the cor-rect solution for minimizing the manufacturing cost.However, when the approach is applied to a thin component,typically when miniaturizing products,it has problems?nding the true minimum manufacturing cost.This paper analyses the shortcomings of the current approach for handling thin plastic components and pro-poses a method to overcome them.A worked example is used to illustrate the problems and compare the differences when using the current approach and the new method proposed in the paper. Keywords Miniaturization of plastic parts·Minimization of manufacturing·Plastic part design and manufacturing cost Nomenclature

B Plastic material dependent constant

C l Material cost for single cavity insert=$557

Cs Speci?c heat of polymer=2.5kJ/kg K

C w Labor cost of mold making machine=$2.0/h

D1Diameter of hydraulic cylinder of molding machine D2Diameter of hydraulic cylinder of molding machine D R Diameter of runner

D S Diameter of screw of molding machine

J.K.L.Ho(u)·K.F.Chu· C.K.Mok

Department of Manufacturing Engineering&Engineering Management, City University of Hong Kong,

P.R.China

E-mail:mejohnho@https://www.wendangku.net/doc/4a8570888.html,.hk

Tel.:+852-********

Fax:+852-********H G The thickness of gate

H r The thickness of the rectangular channel

i m Latent heat of fusion of PP=130kJ/kg

L G The length of gate=0.5–1.3

L C The length of circular channel

L r The length of rectangular channel

m(T)the consistency index

m1/Poisson ratio of PP=0.35

n p Plastic material constant,

Q The volume?ow rate

Q r The volume?ow rate inside the rectangular channel Q runner The volume?ow rate inside the runner

Q C The volume?ow rate inside the circular channel

R C The radius of the circular channel

S Distance of piston movement

t Loading time=31536000s

t CC Time for making single cavity mold insert=15h t dc Dry cycle time=16.5s

t ej Ejection time=0.009s

t in Injection time=0.5s

T b Plastic material dependent constants

T E Demolding temperature of PP=70?C

T M Melt temperature of PP=190?C

W G The width of gate

W r The width of the rectangular channel

ηthe viscosity

εstrain of materials

σstress of materials

λs Thermal conductivity of steel=45W/mK

τShear stress of plastic material

τ?Plastic material dependent constant

γShear rate of plastic material

?P sprue Pressure drop of sprue

?P runner1Pressure drop of secondary runner

?P runner2Pressure drop of tertiary runner

?P gate Pressure drop of gate

?P cavity Pressure drop of cavity

?P C Pressure drop of circular channel

?P r Pressure drop of rectangular channel

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1Introduction

In most industrial applications,the manufacturing cost of a plas-tic part is mainly governed by the amount of material used in the molding process.Thus,current approaches for plastic part design and manufacturing focus primarily on establishing the minimum part thickness to reduce material usage.The assump-tion is that designing the mold and molding processes to the minimum thickness requirement should lead to the minimum manufacturing cost.

Nowadays,electronic products such as mobile phones and medical devices are becoming ever more complex and their sizes are continually being reduced.The demand for small and thin plastic components for miniaturization assembly has considerably increased in recent years.Other factors besides minimal material usage may also become important when manu-facturing thin plastic components.In particular,for thin parts, the injection molding pressure may become signi?cant and has to be considered in the?rst phase of manufacturing.Em-ploying current design approaches for plastic parts will fail to produce the true minimum manufacturing cost in these cases.Thus,tackling thin plastic parts requires a new approach, alongside existing mold design principles and molding tech-niques.

1.1Current research

Today,computer-aided simulation software is essential for the design of plastic parts and molds.Such software increases the ef-?ciency of the design process by reducing the design cost and lead time[1].Major systems,such as MoldFlow and C-Flow, use?nite element analysis to simulate the?lling phenomena,in-cluding?ow patterns and?lling sequences.Thus,the molding conditions can be predicted and validated,so that early design modi?cations can be achieved.Although available software is capable of analyzing the?ow conditions,and the stress and the temperature distribution conditions of the component under vari-ous molding scenarios,they do not yield design parameters with minimum manufacturing cost[2,3].The output data of the soft-ware only give parameter value ranges for reference and leaves the decision making to the component designer.

Several attempts have also been made to optimize the param-eters in feeding[4–7],cooling[2,8,9],and ejection[10].These attempts were based on maximizing the?owability of molten material during the molding process by using empirical relation-ships between the product and mold design parameters.Some researchers have made efforts to improve plastic part quality by reducing the sink mark[11]and the part deformation after mold-ing[12],analyzing the effects of wall thickness and the?ow length of the part[13],and analyzing the internal structure of the plastic part design and?lling materials?ows of the mold de-sign[14].Reifschneider[15]has compared three types of mold ?lling simulation programs,including Part Adviser,Fusion,and Insight,with actual experimental testing.All these approaches have established methods that can save a lot of time and cost. However,they just tackled the design parameters of the plastic part and mold individually during the design stage.In addition, they did not provide the design parameters with minimum manu-facturing cost.

Studies applying various arti?cial intelligence methods and techniques have been found that mainly focus on optimiza-tion analysis of injection molding parameters[16,17].For in-stance,He et al.[3]introduced a fuzzy-neuro approach for au-tomatic resetting of molding process parameters.By contrast, Helps et al.[18,19]adopted arti?cial neural networks to pre-dict the setting of molding conditions and plastic part quality control in molding.Clearly,the development of comprehensive molding process models and computer-aided manufacturing pro-vides a basis for realizing molding parameter optimization[3, 16,17].Mok et al.[20]propose a hybrid neural network and genetic algorithm approach incorporating Case-Based Reason-ing(CBR)to derive initial settings for molding parameters for parts with similar design features quickly and with acceptable accuracy.Mok’s approach was based on past product process-ing data,and was limited to designs that are similar to previ-ous product data.However,no real R&D effort has been found that considers minimizing manufacturing costs for thin plastic components.

Generally,the current practical approach for minimizing the manufacturing cost of plastic components is to minimize the thickness and the dimensions of the part at the product design stage,and then to calculate the costs of the mold design and molding process for the part accordingly,as shown in Fig.1.

The current approach may not be able to obtain the real mini-mum manufacturing cost when handling thin plastic components.

1.2Manufacturing requirements

for a typical thin plastic component

As a test example,the typical manufacturing requirements for a thin square plastic part with a center hole,as shown in Fig.2, are given in Table

1.

Fig.1.The current practical approach

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Fig.2.Test example of a small plastic component

Width (Wp)and length (Lp)Wp =15mm,Lp =15mm Diameter of center hole (Dp)Dp =?1.2mm

Creep de?ection at the center

Minimized,0.01–1.47mm after 1y of usage Plastic,material density and maximum stress PP,0.96g /cc,2～6.9MPa Order batch size Ls =200000units Delivery lead time

t l =21d Desired mold temperature

Tw =25?C Labor cost for molding machine C l =$1.19/h Working hours per day T D =21.5h /d Plastic material cost (PP)C M =$HK3/Kg

Mold type

Two-plate mold,without stripper plate The constant loading at the center W =5N

Table 1.Customer requirements for the ex-ample component

The component thickness (H P )is required to be determined in order to obtain the minimum manufacturing cost,where the value of H P should be within the range of 0.01–6.00mm.

These given requirements for the plastic component will be used to illustrate the differences of using the current practical approach and the new proposed approach in this paper.

2The current practical approach

As shown in Fig.1,the current approach consists of three phases:product design,mold design and molding process parameter setting.A main objective in the product design is to estab-lish the physical dimensions of the part such as its thickness,width and length.The phases of mold design and molding subse-quently treat the established physical dimensions as given inputs to calculate the required details for mold making and molding operations.

When applying the current practical approach for tackling the given example,the key variables are handled by the three phases as follows:Product design

?Establish the minimum thickness (height)H P ,and then calculate the material cost.H P is then treated as a pre-determined input for the calculation of the costs of mold design and molding operations.

Mold design

?Calculate the cooling time for the determined minimum thickness H P in order to obtain the number of mold cavities required.The mold making cost is then the sum of the costs to machine the:

–Depth of cutting (thickness)H P –Number of cavities n –Runner diameter D R –Gate thickness H G Molding process

?Determine the injection pressure P in ,and then the cost of power consumption

?Determine the cooling time t co ,and then the cost of ma-chine operations.The overall molding cost is the sum of the power consumption cost and machine operating cost.

The total manufacturing cost is the sum of the costs of plas-tic material,mold making and molding operations.Note that,in accordance with typical industry practice,all of the following calculations are in terms of unit costs.2.1Product design

This is the ?rst manufacturing phase of the current practical approach.The design minimizes the thickness H P of the plas-tic component to meet the creep loading de?ection constraint,Y (<1.47mm after 1year of usage),and to minimize plastic ma-

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terial usage cost C m .Minimizing H P requires [21]:

Y =0.139W εL 2p m 2

?1 m 2σH 3p (1)and minimum C m =ρC M (W P ×L P ×H P )/1000

(2)

Figure 3plots changes in H P through Eqs.1and 2.The graphs show that the smallest thickness that meets the 1.47mm max-imum creep de?ection constraint is 0.75mm,with a plastic mate-rial cost of $0.000483558/unit and a batch size of 200000units.This thickness will be treated as a given input for the subsequent mold design and molding process analysis phases.2.2Mold design

2.2.1Determination of cooling time

The desired mold temperature is 25?C.The determined thick-ness is 0.75mm.Figure 4shows the cooling channels layout following standard industry practices.The cooling channel diam-eter is chosen to be 3mm for this example.From [22],the cooling time t co :

t co =

3.45×10?2[(T M ?T E )C S +i m ]ρH P d 0.2×

21.4d 0.8+S e λs

λs (T W ?15)

(3)

Fig.3.De?ection and plastic materials costs ver-sus part

thickness

Fig.4.Cooling channel layout

And the location factor,S e =

2π

ln 2x sinh

2πy x

πd

(4)

By solving Eqs.3and 4,and substituting H P =0.75mm and the given values of the cooling channel design parameters,the cooling time (3.1s)is obtained.

The cycle time t cycle ,given by Eq.5,is proportional to the molding machine operating costs,and consists of injection time (t in ),ejection time (t ej ),dry cycle time (t dc ),and cooling time (t co ).

t cycle =t co +t in +t ej +t dc

(5)

In the example,the sum of t in +t ej +t dc is treated as a given constant of 17s.Therefore,t cycle =3.1+17=20.1s,when H p =0.75mm.

2.2.2Determination of the number of mold cavities

In general,the cost of mold making depends on the amount of machining work to form the required number of cores/cavities,runners,and gates.The given example calls for a two-plate mold

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that does not require undercut machining.Therefore,the ma-chining work for cutting the runners and gates is proportional to the work involved in forming the cores/cavities and need not be considered.In the example,mold making cost C mm is governed by (n ,H P ).

Generally,the minimum number of cavities,n min ,is cho-sen to allow for delivery of the batch of plastic parts on time (i.e.n n min )[1].n min =

L S t cycle

3600t D t L

(6)

After substitution,n min =200000×20.1

3600×21.5×21=2.64,which is rounded to n =3,since the mold cannot contain 2.64cavities.

The machine operation capacity and the lead-time of produc-tion in the example are given as 21.5h /d and 21d,respectively.Moreover,as mentioned in the previous section,the cycle time is directly proportional to the part thickness H P .A curve of batch size against thickness is plotted in Fig.5.As shown,at H P =0.75mm,the production capability (batch size)is 242470units.Thus the production capability of n =3is larger than the re-quired lot size (200000units).

For simplicity,the time taken for machining the depth of a thin component 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]:

C mm =2

C W t CC n 0.7

+nC l

(7)When n =3,C mm =2× 2×20×30.7+55×3

=$503/

200000units.2.3Molding process

In the molding process,the cycle cost and power consumption cost are used to establish the molding operations cost as de-scribed in the following

sections.

Fig.5.Mold making cost versus part thickness

2.3.1Cycle cost

The cycle cost C P is de?ned as the labor cost for molding ma-chine operations.The calculation of cycle cost,given by Eq.8,mainly depends on the cycle time and number of mold cavities:C P =

C L t cycle 3600n

(8)

For the example,the value of labor cost per hour,C L ,is given

as $1.19/h.Also,C P can be calculated,as t cycle =20.1s and n =3when H P =0.75mm,as found earlier.And so C p =$0.0022147/unit.

2.3.2Power consumption cost

Typically,within the operating cycle of a molding machine,max-imum power is required during injection.Hence,longer injection times and higher injection pressures increase the power con-sumption cost.

For the purposes of this example,an injection time of t in =0.5s is selected and applied for the molding process.

The required hydraulic power P H ,power consumption E i ,and cost C PC for injection can be found from the following expressions [23]:P H =

P in D 2

S 0.8× D 21?D 22

(9)E i =π×D 21×P H

×S 4×102×2×t in

(10)C PC =C E ×t in ×E i /3600n

(11)

In Eq.9,0.8is the mechanical advantage of the hydraulic cylin-der for power transmission during molding,and the result-ing electric power cost of C E =HK $1.0476/kWh is given in Eq.11.To ?nd C PC ,the sum of the required injection pressures P in in the feeding system and cavity during molding need to be found.

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Required injection pressures.Based on the mold layout design,the volume ?ow rate Q in the sprue is equal to the overall ?ow rate,and the volume ?ow rate in each primary and sec-ondary runner will be divided by the separation number,N i ,according to:Q runner =

Q N i

(12)

The volume ?ow rate in a gate and cavity equals to that of the runner connecting to them.Tan [24]derived simpli?ed models for ?lling circular and rectangular 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 expressed as:

?P C =2m (T )L C R C (3n p +1)Q C

n p ×πR 3C n p

(13)2.Cavity and gate (rectangular channel)

The pressure drop of cavity and gate is expressed as:

?P r =

m (T )L r H r (2n p +1)Q r 2n pW r H 2

r

n p

(14)

Further,the temperature-dependent power law viscosity model can be de?ned as:

η=m (T )γn ?1= B n τ? 1?n exp

nT b

T γn ?1(15)Based on the values of the volume ?ow rate and consistency index m (T )for each simple unit,the pressure drop ?P can be found by using Eqs.12to 15.Thus,the required ?lling pressure is the sum of pressure drops ?P in the sprue,primary runner,secondary runner,gate,and cavity:

P in =?P sprue +?P runner 1+?P runner 2+?P gate +?P cavity

(16)

Fig.6.Molding process cost versus thickness

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 from Eqs.12to 15,and are substituted into Eq.16.The required in-jection pressure P in is calculated and substituted into the https://www.wendangku.net/doc/4a8570888.html,bining Eqs.10and 11,the power consumption cost C PC is calculated and depends on the variation of injection pressure,which is indirectly affected by the thickness of product as shown in the following Eq.17.

C PC =1.0476×0.53600×4×π×0.2032×0.05

4×102×2×0.5×0.0462

0.2032?0.0462

×

?P sprue +?P runner 1+?P runner 2+?P gate +?P cavity

(17)

After substitution,this becomes:C PC =

1.0476×0.53600×4×

π×0.2032×0.05

4×102×2×0.5

×

0.0462

0.8× 0.2032?0.0462

×(36.7069+30.1765+23.2935+0.3670+3.7289)And C PC =0.003755Then the molding cost C molding =C P +C PC

(18)

After calculation,C molding =$0.0022147/unit +$0.003755/unit,when H P =0.75mm,n =3.

2.4Remarks on the current practical approach

Based on Eqs.8to 18it can be shown that as the part thickness,H p ,increases,the necessary injection pressure (and thus power

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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 Fig.6for the example in this study.As can be seen the minimum molding process cost is H p=2.45mm.

If the test example part thickness,H p,were increased from 0.75to2.45mm,the plastic material cost is increased by 230.1%;however,the total molding process cost decreases by 20.6%to$0.004741/unit.Moreover,the total manufacturing cost for the part falls by9.54%,a saving of$0.0001174/unit.

Thus,applying the current practical approach does not give the true minimum manufacturing cost.The current practical ap-proach mainly focuses on minimizing the thickness of the part to reduce the plastic material usage and achieve shorter cool-ing times.When the part is thin,higher injection pressures are needed during the molding process,which substantially in-creases the molding process costs and consequently shifts the true minimum manufacturing cost for the part away from the minimum thickness solution.

3The proposed approach

To overcome the shortcoming of the current practical approach, a concurrent approach is proposed for minimizing the manufac-turing cost for plastic parts made by injection molding.

3.1Framework of the proposed approach

Three parallel phases of product design,mold design,and mold-ing process setting are undertaken for the proposed approach shown in Fig.7.The parallel phases handle individual cost func-tions for material cost,molding cost,and mold making

cost,

Fig.7.Framework of the proposed approach 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 op-tions for combinations of the thickness of the part,the number of mold cavities,and the minimum manufacturing cost that meet all the given requirements.

3.2Cost functions

The cost functions of the individual parallel phases to achieve the aim of manufacturing cost minimization,are as follows:?Plastic material cost against thickness,subject to the min-imum creep de?ection and including the allowable dimen-sions,functional performance,and limitations of plastic ma-terial properties.

?Mold making cost against thickness,subject to batch size, cooling rate and delivery lead-time.

?Molding cost against thickness,subject to the power con-sumption and labor costs and injection capacity,shear stress, and other material properties.

3.3Product design phase

The graphs of both functions of creep de?ection and plastic ma-terial cost are plotted as shown in Fig.8.The possible solution is bounded within the area of the dotted line STU.To satisfy cus-tomer requirements inside this possible zone,the thickness can range from0.75mm to2.21mm with creep de?ection from1.47 to0.00575mm,respectively.In addition,it is possible to achieve design with plastic materials cost from$0.00048356/unit to $0.00142488/unit.

3.4Mold making phase

The mold making cost for different numbers of mold cavities, n,is calculated and indicated in Fig.9.The X and Y axes rep-resent the thickness and batch size,respectively.Eight curves are plotted.The curve n=1has the lowest mold making cost and the most expensive cost is curve n=8.The horizontal dotted XY line corresponds to a batch size of200000units and divides Fig.9into two portions.The upper portion has possible solutions that are able to meet the given production delivery requirements,while the lower portion has no solu-tion for meeting the production batch size on time.The XY line intercepts the curve n=3at point A(thickness1.91mm), curve n=4at point B(thickness3.91mm),and curve n=5 at point C(thickness5.91mm).This means that all three in-tercepting points with n=3,n=4,and n=5can produce the batch size200000units on time.However,from among the three solution points,the curve n=3with thickness1.91mm yields the lowest mold making cost($503/200000units).If n=3is used for mold making,the thickness of the plas-

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Fig.8.Creep de?ection and plastic material cost versus

thickness

Fig.9.Mold making cost versus part thickness (n =1–8)

tic part should be less than 1.91mm to minimize the cool-ing time and increase the production rate.Thus,the opti-mal solution will lie in the range 0.01mm to 1.91mm with number of cavities n =3,and the mold making cost will be $503.3.5Molding phase

The molding process cost is the sum of cycle cost and power con-sumption cost.Each number of mold cavities has its own curve of molding cost as shown in Fig.10.Each curve is inversely proportion to the thickness of the plastic component.The low-est point of the curve is the minimum https://www.wendangku.net/doc/4a8570888.html,ually,when the curve has no sharp turning point and asymptotes,it means that enlarging the thickness cannot reduce molding cost very much.If the thickness of product is increased,lower injection pressure

is required during molding,thus the power consumption cost is reduced,but the cycle time is lengthened and the cycle cost is increased.

As in Fig.10,assuming an eight cavity mold,the thickness of the plastic part should be less than 2.81mm,with minimum molding cost less than $0.00475676/unit.mold 3.6Determination of manufacturing cost

As discussed,the results obtained in sections 3.3,3.4,and 3.5can be combined to yield a total manufacturing cost that is the summation of the part design,mold making,and molding pro-cess costs.Eight different curves have been drawn in Fig.11,for the different numbers of mold cavities.The minimum manufac-turing cost is obtained from the lowest point among the eight curves in this study.From Fig.11,the thickness of the plastic

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Fig.10.Molding process cost versus part thickness (n =

1–8)

Fig.11.Manufacturing cost versus part thickness (n =1–8)

component is 1.44mm,with minimum manufacturing cost of $0.00843177/unit and n =3.

The lowest manufacturing cost is obtained after inputting all values of thickness and numbers of cavities within the allowable range,0.01mm to 6mm and 1to 8,respectively.

Table https://www.wendangku.net/doc/4a8570888.html,parison of results for the different approaches Result parameter Current approach

Proposed approach

Thickness of product 0.75mm 1.44mm Creep de?ection 1.4705mm 0.2078mm Mold temperature 25?C 25?C Cooling time 3.1s 5.96s Cycle time

20.1s 22.97s Number of cavities 33Total pressure drop

94.27MPa 61.74MPa Manufacturing lead time 21d 21d Batch size 200000units 200000units Material cost

$0.000483558/unit $0.000928432/unit Mold making cost $0.002513/unit $0.002513/unit Molding cost

$0.00597053/unit $0.00499027/unit Manufacturing cost

$0.00890716/unit

$00843177/unit

3.7Comparison of the approaches

The results for the current and proposed approaches are summa-rized in Table 2.

When the thickness is increased from 0.75to 1.44mm,the plastic material cost increases by 92%,but reduces total manu-facturing cost by 72.4%.An improvement of 85.9%for the creep de?ection is also obtained in the functional design.Fur-ther,with the 1.44mm part thickness,34.5%less electric power is spent.

4Conclusions

The problems of the current approach to optimize the design parameters for a small plastic part,its mold and the correspond-ing molding process for the minimization of the manufacturing costs have been investigated.A new approach to overcome the problems has been proposed and tested.The relationships be-tween power consumption and thickness of small plastic parts

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for design and molding have been set up.The criteria for the proposed approach to manufacture a small plastic part with min-imum manufacturing cost have been discussed and veri?ed by a test example.In conclusion,the proposed approach will ensure that the minimum cost solution can be obtained when manufac-turing small plastic parts.

Acknowledgement Assistance from Dr.Richard Whit?eld in preparing this paper is gratefully acknowledged.

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