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Emilian Popa Injection Molding Design Guide Manual 2012

1- Temperature Control Basics

Temperature control for a mold refers to a control of receiving and releasing heat on the mold. In this

connection knowledge of heat conductivity is important for consideration of heat reception and heat dissipatio

Thus the basics if thermal conductivity will be reviewed as follows.

1.1 Heat transfer

When there is a certain temperature difference in an object or between objects, heat will transfer to keep

thermal equilibrium in a system. Heat will be transferred from high side to low side and the transfer modes are

classified as follows:

Heat transfer:

- Heat conduction- Convection heat transfer (Heat delivery)

- Radiation heat transfer.

Above three occur in a complex manner, but one normally dominates others.

1.1.1 Heat conduction

Characteristics of heat conduction is the conductor does not move. Thus heat transfer in a solid object is

considered to be the result of genuine heat conduction. To a certain extent heat conduction occurs in gas and

liquid but the conductivity there is prohibitively small in comparison with that of solid body. Transfer of heat made from high temperature area to low temperature area and the transfer rate is proportional to the

temperature gradient and the cross section area of heat passage. This is called Fouriers Heat Conduction Law

and the formula is shown below (Fig 1-1-1).

In the case of heat transfer from resin to mold in the molding process, both heat conduction and heat convectio

occur simultaneously during the injection process but heat conduction dominates during cooling process undeholding pressure after the injection process. Heat transfer from cavity surface t wall surface of cooling water

pipe is made under genuine heat conduction because it is a heat transfer in a solid body.

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Incidentally, heat conductivity of S50C steel, which is often used as mold material, is about 46

kcal/mh , while heat conductivity of HDPE, which has rather high heat conductivity among

resins, is 0.4 kcal/mh and that of GPPS, lower heat conductivity among resins, is about 0.1

kcal/mh . The ratio to S50C is 1:115 and 1:460 respectively (Fig. 1-1-1.2).

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1.1.2 Convection heat transfer (Heat delivery)

Looking into heat transfer between liquid and solid, effect of heat transfer along with movement of liquid ismuch greater than heat conduction. It is called convection heat transfer or heat delivery. The heat transfer rate

is proportional to temperature difference between solid and liquid and transfer area between the same. The

formula is shown below:

Difference between heat delivery and heat conduction is that in the heat delivery heat transfers along with

moving liquid media and heat transfer coefficient is not a specific constant for material like (formula1.3.8.1) and varies depending upon flow condition.

It is considered that there exists a stable film of liquid (or gas), named boundary film, between solid and flowmedia. This film is not subject to convection heat transfer but conduction heat transfer only. As heat

conductivity of flow medium is small in comparison to solid, this boundary film can be treated as a kind of

insulation layer made of flow medium (Fig. 1-1-2.1).

Accordingly if a flow makes the film thinner, the heat transfer coefficient becomes greater and the heat

transfer rate becomes faster. Generally in the case of slow flow velocity, the flow forms so called laminate flow

in which liquid is not mixed. In this case the boundary film is thicker. On the other hand the film is thinner if

the flow is under turbulent flow with high velocity where liquid is well mixed.

As explained, heat transfer coefficient is the one having a boundary film in between and influencedsubstantially by the film thickness. Thus it may be called as boundary film heat transfer coefficient. It is

important how to determine in the convection heat transfer. One way is to determine on the basis of Nusse

Number (Nu) which represents magnitude of heat transfer between solid and flow medium.

Convection heat transfer can be classified by two. One is natural convection heat transfer and another isenforced convection heat transfer. Heat discharge from mold to atmosphere is mainly influenced by natural

convection heat transfer together with radiation heat transfer to be explained later. While, heat transfer from

mold (internal wall of cooling water tube) to cooling medium (water or oil) is mainly affected by enforcedconvection heat transfer.

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1.1.3 Radiation heat transfer

Thermal energy from the sun is brought to the earth through a space without anytransfer media. This is because heat transfers as electro magnetic wave as same as lighand electric wave. This sort of heat transfer is called radiation heat transfer or simplyradiation.

Any material radiates heat unless its temperature is 0K (-273) in absolutetemperature. The radiation is mutually absorbed, reflected or passed trough. The heattransfer rate in radiation is proportional to difference of the 4th power of absolutetemperature (Kelvins temperature). It is shown below (Fig. 1-1-3.1).

Proportion constant k includes various elements. This k is not given based on physical

property like heat conductivity () but calculation like heat transfer coefficient (). In thcase of radiation from a mold, a formula is given below considering object a (mold) issurrounded by object b (air) and radiation area ratio (AA/AB) is negligibly small.

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In the formula (1.1.3.2), let us see the influence to heat flow due to radiation of moldtemperature by varying the temperature TA like 40, 80, and 120. Roomtemperature TB is assumed to be 25. Result shows when TA changes to 2 times and 3times, resultant Q changes 4.5 times and 9.3 times. This tells you that radiation transfecannot be ignored if temperature difference between room temperature and heated

objecttemperature is big when the object is exposed to atmosphere.

1.2 Received heat of a mold

In terms of received heat (QI) of a mold, the biggest source must be from resin (QA).Other received heat from hot runner manifold and hot tip area (QC) in the case of hotrunner mold (Fig. 1-2.1).

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Lets take up received heat from resin (QA). When W (kg/h) is resin weight injected perhour, received heat (QA) can be calculated by applying following formula.

In the formula (1.2.2), temperature at mold separation (TR) can be replaced by thermaldeformation temperature to assure the temperature in the center of the thickest portion

of the product to be lower than the heat distortion temperature. In this case, try to setthe temperature 10~30lower than the heat distortion temperature to entertain safetyconsideration. A part of the formula {CP(TP-TR) +LC} can be roughly estimated by resinmaterial, when the value is represented by total heat amount (Q), formula (1.2.2) can bshown as below.

Table 1-2.1 shows estimate values of Q by resin material in the safe direction(estimating q in the bigger side).

3) Released heat from a mold

If there is no temperature control device on a mold (natural radiation only), releasedheat from a mold (QO) should consist of transferred heat to platen of injection machine(QD) and radiated heat to atmosphere (QE) (Fig. 1-2.2).

QD is calculated as heat passing through composite wall surfaces, but estimation of hearesistance between mold clamping plate and platen of injection machine is very difficultQE is considered as a mixture of convection and radiation heat transfer. It is influencedby molding conditions such as mold temperature, airflow, mold open time, etc.

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1.3 Heat to be removed from a mold

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A mold reaches to thermally balanced condition through heat receiving and heatreleasing process. Thus theoretically speaking, molding can be made withouttemperature control device as long as the balanced temperature is suitable for theplastic molding. However it is advised not to precede molding without temperaturecontrol device because a long time will be needed before reaching to a balancedcondition and moreover mold temperature cannot be stable being influenced byenvironmental disturbances.

If receiving heat is more than releasing heat and thermal balanced point is higher thanbe required temperature range, cooling device is needed. On the other hand, if receivinheat is less than releasing heat and balanced temperature point is lower than requiredtemperature range, heating device should be arranged (Fig. 1-3.1).

Here in this section, condition QO< QI, in other words, condition required to cool off amold, will be taken and heat to be removed from a mold will be discussed. Removedheat QR can be expressed in a molding cycle where receiving and releasing heat are tobe balanced.

If you understand basics behind the formula (1.3.3), you may simplify the calculation asfollows. In the cold runner mold, QB can be traded off by (QD + QE) because (QD + QE) isusually bigger than QB. By trading them off, cooling calculation will come to safe side

(increased requirement for cooling). In this way, you may treat heat to be removed (QR)is equivalent to received heat (QA) from resin.

In the heat transfer calculation, you may apply formula (1.3.4) for approximate resultbecause q in formula (1.2.3) and table (1-2.1) are given in the safe side. However if youintend to apply formula (1.2.2), it is advised to incorporate 1.5 times safety factor takin

account of possible requirement of cycle shortening and expected deterioration in theheat exchanger performance.

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Assuming QR can be applicable to all kinds of cooling medium, following formula can bederived.

TL in formula (1.3.6) is average temperature of the cooling medium other than that in thboundary film. In the case of water as cooling medium, (TWTL) can be regarded as abou2~3. WL and VL, required volume of cooling agent can be expressed as follows:

Flow velocity V can be derived from formulae (1.3.4) or (1.3.5), (1.3.6), (1.3.7) and(1.3.8), as follows:

More accurate formula must be:

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Internal diameter of cooling tube (D) in above formulae should be picked up from Table

3.1 temporally, and confirm them if it falls in the range of 10,000~30,000 of Reynoldsnumber (RE) and then finalize the diameter. Be aware that unit of d is in m.

Next, Nusselt number (NU), important parameter in the convection heat transfercalculation, will be calculated. Prantle number (PR) in Nusslet number is defined as

follows.

Nusselt number is given as follows. Be aware NU formula varies slightly depending uponwhere to get the formula from.

Formula (1.3.13) is effective only for turbulent flow. In the case of laminated flow ortransition flow, in which Raynolds number is less than 10,000, re-evaluation of moldtemperature and cooling tube diameter must be carried out.

Once Nusselt number (NU) is decided, heat transfer co-efficient can be calculated byformula (1.1.2.1). And cooling tube surface area (AL) can be calculated by a convertedformula from (1.2.2).

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As cooling tube diameter (D) is known, cooling tube length can be calculated as follows:

As described, total cooling circuit length of cavity and core can be calculated.

So far, all formulae assumed that heat from injected resin W (kg/h) is transferredperfectly to a mold. Here we should evaluate if such assumption is reasonable or not.Bahlmans formula should be effective for the evaluation. It is to evaluate if W (kg/h) ispossible by estimating molding cycle from theoretical cooling time calculation.

This formula can be used as a guideline because all kinds of condition have to beassumed for calculation. Molding cycle should be evaluated by estimating injection timemold opening time duration, mold take-out time duration.

If you design temperature control system by applying above explained basics on theheat transfer thermal dynamics, you should be able to provide temperature controlsystem with improved heat exchanging efficiency comparing with traditional system,which was made based on past examples.

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Emilian Popa Injection Molding Design Guide Manual 2012In the end of basics on thermal transfer theory, a calculation example is shown below foyour better understanding. Try to solve the example before you read the answer tofollow.Mind units are to be carefully treated.

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Emilian Popa Injection Molding Design Guide Manual 20121.4 Design of Temperature Control Device

Coolant circulation method

Important point for the design of coolant circulation system is to optimize the design interms of coolant circulation channel, size and location in consideration of product qualitand productivity. For the design of pressurized water circulation system, basic designconcepts are the same but special attention should be paid for sealing and safety aswell. It is suggested to refer technical information supplied by the system suppliers.

Reduced pressure suction type of temperature control device will not be treated in thissection because of its specialty in the circuit design. Hereafter, we will discuss aboutdesign concept for standard temperature control device utilizing water, an excellentcoolant for heat exchanging.

1.4.1 Coolant channel diameter and flow velocity

Cooling efficiency is higher if coolant in the channel is under turbulent flow whereboundary film is thin. Thus it is important to decide proper diameter of coolant channelso as to make the flow stable turbulent with Reynoldss number RE 10.000~30.000.

As you may refer to formula (1.3.11), RE seems proportional to diameter d; in otherwords, a big diameter seems to give a big RE. This may be true if other factors stay thesame. But if flow volume is given constant, flow velocity is reversibly proportional tochannel cross section area, which is proportional to the 2nd power of channel diameter icase of round channel. Therefore if flow volume is given constant, flow velocity and REbecome small with big diameter D referring to formula (1.3.8) and formula (1.3.11).

Accordingly if channel diameter D is too big, heat-exchanging performance drops due tosmaller flow velocity, Reynoldss number, Nusselt number and heat transfer coefficient.

If the diameter is too small, the heat exchanging performance will also drop due to lessflow volume and increased pressure loss in the flow channel. Thus the channel diameteshould be appropriately designed referring to Formulae (1.1.2.2), (1.3.8) Table (1.1.2.1)

When passage is not of round shape, equivalent diameter should be applicable asexplained in the Gate Runner System. The equivalent diameter (DE) was as follows:

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1.5 Heater capacity

Heater capacity can be calculated as follows:

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Is a value due to heat transfer loss due to radiation loss or loss due to heatermounting, etc, and normally it is set as 0.5. If you utilize a heater with higher capacityand with adjustable power arrangement, you may ensure stable mold temperature byadjusting heating and radiation conditions in addition to shortened preparation time.

1.6 Clamping force

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Emilian Popa Injection Molding Design Guide Manual 2012In order to calculate required clamping force of a mold used for a product, we need toknow a force on the mold toward opening direction received from injected resin. Thismold opening force (FO) can be expressed as the product of total projected area of aproduct and a runner and average molding pressure (cavity inside pressure) as follows

Projection area is the area of a product projected in the mold clamping direction (usuallyperpendicular to PL). Total area is shown below (Fig. 1-6.1)

In the case of 3-plate mold, notice that projection of cavity and runner overlaps. If

separately calculated, overlapped area will be calculated twice. Assuming mold is oftransparent, project parallel light from nozzle side, and then figure projected area on thmovable platen surface (Fig. 1-6.2).

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Emilian Popa Injection Molding Design Guide Manual 2012Formula (1.6.1) shows that mold-opening force is proportional to projected area ifaverageclamping force is constant. Let us look into molding pressure.

Injected mold by injection machine fills a mold space against pressure loss caused bynozzle, sprue, runner, gate and cavity.

Thus there exists a big pressure difference between sprue area and a part of cavitywhere resin is filled in the end. Even after resin filling, molding pressure varies fromplace to place (Fig. 1-6.3). However, mind that you need to know average pressure, not ain different parts.

Although average clamping force varies depending upon product shape, moldingcondition, mold structure, etc., Table 1-6.1 can be practically used for your guideline. Ifyour calculation reveals clamping force exceeds average mold opening force, themachine should be well justified. In practice, the clamping force should be evaluated as80% of maximum clamping force against mold opening force compensating estimatedaverage of the opening force. Required clamping force (FC) then is shown as follows.

If your selected injection machine has a clamping force more than above describedforce, you will be able to mold products without burrs on PL surface. But be minded thattoo big a clamping force may cause you a trouble such as partial concentration of theforce in the center or ineffective clamping force due to excessive size of locating hole,etc. (Fig. 1-6.4). Rule of thumb is not to go beyond 20% of above formula.

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1.7Required injection capacity

A general injection machine provides 3 screw size options per clamping unit. Accordingyou should know which=0.h screw size is selected for evaluation of required injectioncapacity.

As screw size is given bigger, maximum injection capacity becomes bigger. But injectiopressure goes opposite direction. In other words, as screw size is given bigger,maximum injection pressure becomes smaller (Fig. 1-7.1) as long as diameter ofhydraulic cylinder is the same.

Thus under the same clamping force, injection machine with small screw is suited forprecision thin wall products and injection machine with large screw is suited for large

products with thick walls.

Injection capacity is a product of internal cross section area of injection cylinder (screwcross section area) and injection stroke.

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Maximum injection capacity shown in the specification of injection machine is calculatedby above formula. This means a capacity of an object (air for example) injected undernormal temperature and pressure by screw size.

Practically molding is operated by injecting plastic with viscosity and elasticity underhigh temperature and pressure. Therefore maximum injection capacity for injecting PS-GP (General purpose polystyrene) is usually given together with theoretical value.

Actually, internal pressure of injection cylinder is high, but density of the plastic there issmaller than that under normal temperature and pressure condition because plastic inthe cylinder is expanded due to high temperature (Fig. 1-7.2).

Calculation of required injection capacity has two folds. The first step is to calculateexpanded capacity of plastic per one shot for product, sprue and runner under highpressure and temperature condition, then the second step to compare it with maximum

injection capacity assigned for an injection machine. Specifically, total injection capacitycan be given as follows:

To figure volume expansion accurately, we need PVT data per plastic material, but in oupurpose it is not necessary to go to those details. Although there is some variations inpressure and temperature conditions, we may approximately estimate 90% of density(1.11 times volume expansion) for amorphous resin, of which specific volume is not

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Emilian Popa Injection Molding Design Guide Manual 2012much influenced by temperature, and 80% of density (1.25 times volume expansion) focrystalline resin, of which specific volume is much affected by temperature. Furthermortaking account of injection efficiency due to back flow and cushion amount, additionalsafety factor 80% shall be introduced. To make a formula applicable to all resin,regardless of crystalline and amorphous, density in the injection cylinder is nowassumed to be 85% of the value under normal pressure and temperature condition.Then required injection capacity (VS) will be as follows:

Injection machine with larger injection capacity than above can be utilized, but it shouldnot be too large. Expected problem is that resin starts decomposition in the cylinder if istays too long in the cylinder. As a minor problem, measuring accuracy drops due tosmall measuring stroke. Thus similarly to the case of clamping force, calculated injectiocapacity (VS) should not be less than 20% of theoretical maximum injection capacity ofthe injection machine. Accordingly formulae (1.7.4) and (1.7.5) can be expressed asfollows.

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1.8 .Mold Strength

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Emilian Popa Injection Molding Design Guide Manual 2012Mold strength should be evaluated to see if the deformation of the mold due to molding pressu(injection pressure or holding pressure) stays within allowable tolerance limit. Twoconsiderations must be highlighted. One is how to estimate molding pressure. Another is how todecide allowable tolerance limit.

Molding pressure comes from resin. With some exceptions, you need not take up a pressureduring injection but a pressure after injection. This is nothing more than the molding pressure

inside cavity pressure that was explained and calculated in the previous section for calculatingrequired clamping force. But in this section we choose 500 kgfcm2 with some margin.

Tolerable deformation varies depending upon product accuracy, mold structure, locations, etc.One practical reference is if the deformed amount results in generation of burr or not. Clearancto generate burr can be considered as the depth of air ventilation. If burr cannot be a referencethe allowable tolerance should be looked into from the aspect of allowable repeated stress onthe mold or product accuracy.

Generally allowable deformation amount is 0.1~0.2mm unless the mold is extremely small insize.

1) Side walls of rectangular cavity

There are two types. One is of split type consisting of sidewalls and bottom plate. Another ismade from one block, in other words one-piece cavity.

Split type can be machined easily with high accuracy but weaker in strength. Let us see thedifference in strength between split type and one-piece rectangular cavity.

1-8-1) Split type

In the split type, calculation disregards restraint of bottom plate. Actually sidewalls are boltedtogether with bottom plate or mounting plate. Thus calculation results in the value with safetyfactor by disregarding binding and friction influence from bolts (Fig. 1-8-1.1).

We apply a model of a beam both side fixed and with equal weight distribution to cavity walls fostrength analysis (Fig. 1-8-1.2). Be minded molding pressure uses cm unit, while strengthcalculation uses mm unit. The maximum deformation ( MAX) on the both side fixed beam appears in the middle as follows:

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Cross section of the beam is of rectangular, thus moment of inertia is as follows:

Wall thickness (H) is derived from formulae (1.8.1.1) and (1.8.1.2) as follows:

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Emilian Popa Injection Molding Design Guide Manual 20121-8-2) One-piece type

One-piece type cannot be simplified as split type. Table 1-8-2.1 shows coefficient (C)corresponding to ratio (L/A) of product length to height. Then allowable deformation( MAX) is calculated as below (Fig. 1-8-2.1).

Cavity wall thickness can be derived from formula (1.8.2.1) as follows.

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1-8-3 Wall thickness of cylinder type cavity

Thick wall cylinder is applicable in material strength analysis. Similarly to rectangulartype cavity calculation, we will try to make the clearance resulted from deformationsmaller than the clearance to cause burr for different resin materials. It will becomplicated if we try to calculate wall thickness of cylinder tube. Therefore we evaluateif the deformation is within allowable tolerance under a given wall thickness.

Deformation ( ) in Fig. 1-8-3.1 is given as follows.

1-8-4 Mold weight and center of gravity

Calculation for mold weight and center of gravity is required to determine size andposition of hook bolts for hoisting a mold. Normally the shape of a mold is of rectangulasections.Thus the volume can be easily figured, so as weight by multiplying specific weight of

mold material. In case of steel, apply 7.87.

Regarding center of gravity, it can be determined by estimating the position in thedirection of mold thickness. Mold is normally symmetrical with a centerline in theinjecting direction. The center of gravity should locate on the centerline.

Calculation proceeds firstly to calculate weight on the center of gravity of each plate ansecondly to find a point where each moment can be balanced.

Referring to Fig. 1-8-4.1, calculate each moment as a product of weight on the center ofgravity of each plate and distance based on fixed side clamping plate. The total momenshould balance with a moment as a product of total mold weight and distance from thereference point to the center of gravity.

`

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Distance from reference point to center of gravity can be derived as follows:

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1-8-5 Return force of ejector plate

Ejected ejector plate is normally returned to its original position by spring force of aspring installed on the periphery of return pin.

If the spring force is too weak, the ejector plate cannot fully return to its originalposition. If it is too strong, operational balance will be affected and galling may becaused on the return pin.

Thus we may define the return force of ejector plate should stand weight of ejectorplates (upper and lower) and their friction force.

Friction force is related to friction coefficient of ejector plates (upper and lower). As weknow the maximum friction coefficient is 1, it must be enough to estimate the frictionforce 2 times of the plate weight. Generally, number of springs to be installed on theperiphery of return pin is 4. Thus you should calculate the shared friction load per springis 1/2 of ejector plate weight (21/4).

The spring is better to have a smaller spring constant value to assure smoother loadtransfer to the spring while stroking (Fig. 1-8-5.1). In addition initial deflection of thespring is better not to exceed thread length of stripper bolt (normally 10~15), otherwiseyou will have a difficulty in installing stripper bolt to female thread hole because of thelong spring (Fig. 1- 8-5.2). Following checkpoints may be useful for selecting correctspring from available ones in the market.

- Internal diameter of the spring should be at least 1 mm larger than return pinoutside

diameter.- Maximum deflection in usage should be within allowable limit.- The spring should have enough returning force at the initial deflection.- When spot facing is made for the spring, clearance around return pin can be

secured(two times pin diameter) and there should be no interference with coolant channel.

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Calculation for the appropriate diameter of support pin and Deflection of Support pin

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Ejector Pin-Ejector Sleeve Strength Calculation

Ejector pins and sleeves are subjected to compressive loads when the cavity is filledwith molten plastic.When long thin objects are subjected to such compressive loads, buckling, bending of

the pin, or breakage can occur. In order to prevent buckling, we recommend that youselect an appropriate configuration by performing strength calculations beforehand

1. Computing buckling load P (kgf)

Eulers formula is usually used to calculate the bucking strength of ejector pins.

(2) Computing compression load P1 (kgf)

Compression load refers to load that is applied to the ejector pin during filling andpressurization with molten plastic.

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Emilian Popa Injection Molding Design Guide Manual 2012P1 = p x A

(3) Computing safety factor:

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(Considerations regarding safety factor values):

Safety factor (S) is affected by a wide variety of elements including those listed below.

- Inaccuracy of load estimates inconsistent strength of materials effect of heattreatment

- Notch effect finished roughness: abrasion and corrosion during use.- Expansion and contraction due to heat fatigue impact mold separation

resistance during ejection of the molded object etc.

In specific terms, we recommend that you decide in advance on an in company designstandard taking into consideration the empirical values of the various companies andthen use this to gauge the appropriateness of the computed results.

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