Mechanical Design of InjectionMolds [10.1

If deformations and forces parallel to the direction of the clamping force are considered,the following equivalent diagram Figure 10.1 of the clamping unit including the mold is obtained

1 0 1 M o l d D e f o r m a t i o n

Injection molds are exposed to a very high mechanical loading but they are only allowedelastic deformation Since these molds are expected to produce parts that meet thedemands for high precision, it is evident, therefore, that any deformation of the moldaffects the final dimensions of a part as well as the shrinkage of the plastic materialduring the cooling stage Besides this, undue deformation of a mold can result inundesirable interference with the molding process or actuation of the mold

Effects on the quality of the molding:

- Mold deformation results in dimensional deviations and possible flashing

Effects on the function of the mold:

- Deformation of the mold, especially transverse to the direction of demolding and largerthan the corresponding shrinkage of the molding, results in problems in mold-opening

or ejection from jamming

- Thus, the rigidity of a mold determines the quality of the moldings as well as reliableoperation of the mold

- Common molds are assembled from a number of components, which as a wholeprovide rigidity to the mold by their interaction The components of a mold arecompact bodies and both bending and shear strains have to be considered in design.They are still sufficiently slender, though, that, with some exceptions, permissiblestresses need not be taken into account because of their small permissible deformation

1 0 M e c h a n i c a l D e s i g n o f I n j e c t i o n

M o l d s [ 1 0 1 ]

10.2.1 Evaluation of t h e A c t i n g F o r c e s

The acting forces are:

a) Closing and clamping forces exerted by the machine

b) The maximum cavity pressure It acts via the molding compound in the mold cavitiesand the runner system on the mold, which may deform mainly by bending

Two problems may arise:

1 The part is jammed in the mold when cavity pressure forces, acting perpendicularly

to the mold axis, bend the walls further than the molding compound at these pointsshrinks in thickness after cooling to demolding temperature

2 Under the effect of the cavity pressure forces in the direction of the mold axis,unpermissibly large gaps in the mold parting line could occur into which melt couldpenetrate and flash could form

The maximum cavity pressure in thermoplastics and normal operating conditions isalways the maximum injection pressure

With elastomers and thermosets, the maximum cavity pressure usually only occursafter filling because now the molding compound is heated further both by the hottermold wall and by the liberated heat of reaction, and it expands more Only whencross-linking progresses further does a more or less large reduction in volume occur.This volume expansion due to heating is also the reason that these moldingcompounds almost always leave behind flash on the parts While there are suitableappropriate controls for preventing this, they are rarely used Many molders stillafford themselves the luxury of expensive, very often manual finishing of every partproduced

To calculate the formation of such gaps more accurately, it is not sufficient to use thesimple calculations employing spring stiffness for the molds alone because thedeformations of the press (clamping unit) contribute considerably to overalldeformation

A great deal of work has been done in recent years that allows the formation of gaps

in mold parting lines to be calculated very accurately [10.3, 10.4] They alwaysconsist in adding up the deformations of the molds in the axial direction and those ofthe entire clamping unit These calculations are admittedly much more complicatedthan the simple calculation that will be described below An accurate calculationmoreover requires that the molder determines the deformation of the clamping unit,including all its elements To date, this deformation is usually not quoted by themachine manufacturers The method of measuring and calculating the deformation ofthe clamping unit is described in [10.4] There is, however, a relatively simple methodthat will be explained later This method yields results that lie on the safe side.c) Mold opening and ejection forces:

These forces are usually much smaller They only need to be considered whendesigning the ejection system If present, however, the ejector pins must also beallowed for, as there are two frequently ignored dangers here:

- the pins can buckle outwards and be destroyed,

- the pins can punch through the molded part

Calculations for these are provided in Chapter 12

1 0 3 B a s i s f o r D e s c r i b i n g t h e D e f o r m a t i o n

The mold forms a link in the closed system of the clamping unit

The following distinction has to be made to obtain characteristic deformations independence of the forces from injection pressure and clamping:

1 Which elements are relieved by the effects of the cavity pressure?

2 Which elements are loaded further by effects from the cavity pressure?

If deformations and forces parallel to the direction of the clamping force are considered,the following equivalent diagram (Figure 10.1) of the clamping unit including the mold

is obtained

Cavity pressureSpring characteristic of clamping unitSpring characteristic of mold

Figure 10.1 Equivalent diagram of clamping unit and mold [10.5]

The elements with the spring rate (load per unit deflection) CW1 and Cs are first stressed

by the clamping force and then, in addition, by the reactive forces from cavity pressure.Therefore, the machine platens exhibit the same deformation response as the tie bars

of the clamping unit, taking the parting line of the mold as reference line

That part of the mold with the spring rate CW2 (cavity area) is first stressed by theclamping force but then more or less relieved by the reactive forces from cavity pressure.With the simple calculation, it is assumed that the mold faces are just in contact withone another when the additional elongation of the clamping unit AL8 and the decrease incompression of the cavity ALW are equal

10.3.1 S i m p l e C a l c u l a t i o n f o r E s t i m a t i n g G a p F o r m a t i o n

(10.1)(10.2)

(10.3)

(10.4)(10.5)(10.6)Mold face

The resulting characteristic deformations are depicted in Figure 10.2 The cavitydeformation in the direction of clamping has a considerable effect on the quality of themolding It does not only depend on the rigidity of the mold but also on that of theclamping unit Under the reactive forces from cavity pressure a notable rigidity of theclamping unit results in

1 a small deformation of the cavity in the direction of clamping,

2 higher stresses in the clamping unit,

3 higher forces in the clamping surfaces

Cases 2 and 3 occur only if there is no overload protection (e.g., with a fully hydraulicclamping unit)

High rigidity of the mold results in

1 small cavity deformation in clamping direction,

2 lower stresses in the clamping unit

For these reasons it makes sense to design the mold with a high resilience

in direction of clamping [10.1, 10.5]

= Cavity pressure,

= Projected part area

= Deformation of clamping unit

= Deformation of mold

= Change in spring force

= Spring characteristic

= Index for clamping unit

= Index for mold

Forces on clamping unit

from cavity pressure

Cavity pressureProjected partareaClamping unit

1 Deflection of mold platens that are unsupported, primarily above the free space forthe ejector plate Particularly at risk in this respect are the molds for large-area parts,and multicavity molds.

2 So-called mold breathing, i.e the uniform opening of the mold faces due to acombination of inadequate pressure exerted by the clamping unit (press) anddeformation of the mold

Whereas mold deformation may be determined with sufficient accuracy by the simplemethod of spring stiffness of the mold elements (see Sections 10.4 to 10.6), no infor-mation is available about deformation of the clamping units This is usually not provided

by the machine manufacturers and is extremely laborious to determine

The clamping units, including toggle presses and locked hydraulic presses, areactually all very much softer than indicated in Figure 10.2 In effect, it is not, assuggested by Figure 10.2, just the tie bars that are placed under load but also a greatmany other elements, such as joints and link pins in the toggle presses and the lockingelements and plates, the compressibility of the oil etc in the hydraulic presses These allhave to be included because they are all much softer For this reason, the spring diagramfor a clamping unit is more like that shown in Figure 10.3 One can now use a programdeveloped by Krause et al [10.3] to make very accurate calculations or, to avoidperforming the tedious compilation work, use a simple, dependable method derived fromthe work of Krause et al

Flash is caused by deformation of the edge cavity in the mold For the gap formation, itsdeformation must be considered with that of the mold in a combined spring diagram.One such diagram is shown in Figure 10.4 Since the rigidity of the mold edge is veryhigh relative to that of the press, deformation diagrams like the example shown inFigure 10.4 are obtained There would be hardly any error involved in ignoring the slightslope of the spring characteristic of the press above its drop after the clamping force isexceeded and employing instead a constant holding force of the same magnitude as theclamping force (i.e., as for a hydraulic machine without locking in which a constantpressure of the same magnitude as the clamping force is maintained by the pumps) This

means that the mold-opening forces due to the mold cavity pressure must be smaller than the clamping force.

Figure 10.3 Realistic mold spring diagram

Cavity deformation Deformation

Force from opening by internal pressure

MoldPress

Locking force

Clamping force

Figure 10.4 Realistic spring diagram for two normal mechanical clamping units with a typical

mold [10.3]

1 0 4 T h e S u p e r i m p o s i t i o n P r o c e d u r e

A complete mold base is generally composed of different components, which areexposed to different loads It is useful, therefore, to dissect the mold into characteristicelements and consider their elastic behavior This results in a simple method fordetermining the total deformation (Figure 10.5)

10.4.1 C o u p l e d S p r i n g s a s Equivalent E l e m e n t s

The superimposition procedure represents a superimposition of individual deformations.All components of a mold base (plates, spacers, supports) are considered springs with acertain rigidity (Figure 10.6)

Mold height 310 mm Machine 2Mold height 336 mm

Loading case 1 Loading case 2

Figure 10.5 Dissection of a mold element [10.1, 10.5]

All cases of loading in any section of a mold have similar correlations This allows moldelements to be considered springs.

10.4.1.1 Parallel Coupling of Elements

With parallel, coupling, all components exhibit the same deformation under differentloads The total load is allocated to individual loads (Figure 10.7):

and the reaction of a plate to bending and shear, then the total deformation is

Bending Shear

As already mentioned, bending and shear have to be taken into account in this context

If we look at the mathematical relation which describes the spring behavior

(10.7)

(10.8)

(10.9)

a) b)

10.4.1.2 Elements Coupled in Series

All components are deformed by the same loads (Figure 10.8)

(10.11)Hence, all springs are loaded by the full magnitude of the acting force and not pro-portionately The resulting spring travel is

(10.12)The total deformation is the sum of the individual deformations

Thus, the possible number of loading cases can be reduced to three basic cases:

1 single load,

2 parallel coupling (Figure 10.7),

3 coupling in series (Figure 10.8)

Figure 10.8 System of elements in series [10.5]

Figures 10.5 and 10.6 demonstrate how the total deformation can be determined bycombining the basic cases

1 0 5 C o m p u t a t i o n o f t h e W a l l T h i c k n e s s o f C a v i t i e s

a n d T h e i r D e f o r m a t i o n

The configuration of all parts can be reduced to simple shapes If all possible cavity andcore configurations are analyzed with this assumption in mind, we can select thefollowing typical geometries with the goal of obtaining a method for estimatingdimensions:

1 circular cavities and cores,

2 cavities and cores with plane faces as boundaries

If the existing loading cases are analyzed, the causes of deformations can be reduced to

a few cases The basis for this simplified calculation is the dissection of the moldcomponent to be dimensioned into two characteristic equivalent beams as is done with a

Figure 10.7 Parallel system of elements [10.5]

plate with three edges built-in (Figure 10.5), or with a cylindrical cavity with integratedbottom (Figure 10.9).

Diagrams are supplied for various cases of loading based on equations from the theory

of elasticity (Figures 10.11 and 10.14 to 10.16) The required wall thickness - if steel isthe material of choice - for cavities, cores and plates can immediately be obtained fromthem if the permissible deformation is taken as a parameter To play it safe, thedeformations from both characteristic cases of loading have to be computed That wallthickness has to be chosen that results in the smallest deformation

10.5.1 P r e s e n t a t i o n of Individual C a s e s of L o a d i n g

a n d t h e Resulting D e f o r m a t i o n s

In Figure 10.10 the loading cases are presented schematically Suitable combinations can

be used to calculate the deformation of all occurring configurations and wall thicknesses.Formulae which result from the theory of elasticity were taken as basis for computingthe deformation:

Figure 10.9 Dissection of a cylindrical

mold component [10.1, 10.5] Loading case Il

Loading case I

and

Supported on twoopposite edgesFixed on twoopposite edgesFixed on one edge

Supported on fourcorners

Supported on two oppositeedges and fixed on theother two edgesFixed on all edgesFixed on three edges

Fixed circular plateCompressed rectangular plateCompressed circular plate

Expansion of circular cavity

Compression of round core

Expansion of circular cavitywith bottom

Figure 10.10 Basic cases of loading [10.6]

10.5.2 C o m p u t i n g t h e D i m e n s i o n s of Cylindrical Cavities

Krause [10.8] offers a very accurate method for calculating the necessary thickness ofthe walls of mold cavities (transverse deformation) that is also available as software.For the usual design in the absence of such software, the following dimensioningsuggestions are made These should be readily understandable and sufficiently accurate.The elastic expansion of a circular cavity can be taken from Figure 10.11 for the loadingcase I (Figure 10.9), which represents the following equation:

m = Reciprocal of Poisson's ratio

The elastic expansion of a cavity according to the loading case II (Figure 10.9) iscomputed from a relation presented in Figure 10.14 [10.9 to 10.11]

rCo = Outside radius of core,

r = Inside radius of core

The loading case of common injection molds is between case a and case b Friction acts

on the mating surfaces of the clamped mold This restricts the expansion of the cavitybut does not necessarily result in a rigid, inflexible condition

h I

(Figure 10.15) (10.19)a)

b)

Figure 10.15 Deformation of rectangular plates fixed on two edges

from deflection and shear [10.1, 10.5, 10.7]

f: DeflectionMaterial: Steel

Figure 10.16

Deflection of built-in

circular plates [10.5,

10.7]

h = Free length,

s = Thickness of core-retainer plate

1 0 6 P r o c e d u r e f o r C o m p u t i n g D i m e n s i o n s o f C a v i t y

W a l l s u n d e r I n t e r n a l P r e s s u r e

The following steps are necessary:

1 Computing of expected shrinkage

Before the wall thickness of the cavity can be established, the expected shrinkage inthe cavity has to be determined because it is the basis for the maximum permissiblecavity expansion According to Chapter 9, the theoretical shrinkage can be computedfrom the p-v-T diagram (Figure 9.4) A very good reference is the informationprovided by the material supplier It has to be noted, however, that those data are forlongitudinal shrinkage The shrinkage in thickness may be calculated with the aid ofthe following equation:

Where

Sw = Shrinkage of the wall thickness,

SL = Shrinkage in length (data provided by manufacturer)

2 Dimensioning the thickness of cavity walls

The elastic deformation of the cavity has to be smaller than the expected shrinkage.They are based on the maximum permissible deformation of a wall This requirement

is met by procuring the necessary wall thickness for a given deformation fromFigures 10.11, 10.12, and 10.14-10.16

1 0 7 D e f o r m a t i o n o f S p l i t s a n d S l i d e s u n d e r C a v i t y

P r e s s u r e

(See also design examples in Section 12.9)

Design formulae have been compiled not only by employees of the Institute forPlastics Processing (IKV) [10.6] but also by Krause et al., along with a software programthat allows easy accurate checking or simulation [10.12]

10.7.1 Split M o l d s

This special design of of injection mold permits large-area undercuts to be demolded and

is very common (see also Section 12.9) Figure 10.17 shows that the split mold has twoprincipal parting lines perpendicular to each other The one primary parting plane A is,

as usual, aligned perpendicularly to the direction of closing The second is locatedbetween the splits and is aligned parallel to the direction of closing With split molds, theclamping unit must take on much greater forces than in a mold with just one partingplane because, as Figure 10.22 shows, in addition to the force from the cavity pressure

acting on the clamping parting line there is the vertical component of the forces from thecavity pressure acting on the splits.

The first step in the calculation is to determine the minimum clamping force and then

to choose the machine

It is already necessary at this stage to decide on the type of splits because functionalityand flash-free parts require that the splits be closed so tightly and pre-stressed that nogaps can form under the internal pressure This is only possible if enough air is leftduring the vertical closing movement - Krause [10.2] calls this a "functional gap"(Figure 10.17, labeled a) - that the splits do not sit proud in the frame even after elasticdeformation under the locking force To carry out these calculations, a spring model ofthe split mold is made, as shown in Figure 10.21 (To perform a highly accuratecalculation, the program created by Krause et al [10.8] may be used This user friendlyprogram employs a step-by-step approach and contains the strength calculations for anybolted joints and the consequences of elastic deformation of these bolts.)

Figure 10.17 Section from a split mold

(principle) [10.6]

a = Functional gap

CADMOULD [10.13] which contains a program for designing split molds is somewhatsimpler to use but has proved to be of sufficient accuracy As shown below, thesecalculations can be understood by users, without their having to use the program itself*.The goal is to compute the load on a split mold (Figure 10.18)

The distribution of forces flows entirely through the split (element (I)), which isthereby compressed The counterforce is applied by the two locking mechanisms (2) and(3), which are both subjected to the same deformation Thus, elements (2) and (3) areconnected in parallel The split is connected in series with these two elements This is

Figure 10.18 Spring diagram

for deformation of a split mold

[10.6]

Extract from "Handbook for Computing Injection Molds", published by Kl-Verlag, 1985 [10.6]

X Y

shown in the equivalent circuit diagram on the right Deformations f { to f3 are

defor-mations under the total load, where f Y is pure compression, and f2 and f3 are deflections

of beams or plates clamped on one side

Aside from having to deal with the general dimensioning problems, the split molddesigner has to cope with problems involving the clamping forces because overpackinghas to be avoided in several parting lines This will now be explained (Figure 10.17) Inthis case, both the dimensions of the gap a and the angle a are important, the latter veryoften being pre-set at 18°

Section 10.2.1 discussed the basic deliberations for this special case; here, instead ofdeflection, the rigidities of the various elements are connected in series Thesedeliberations help to estimate the complex conditions obtaining in split molds

To make the following discussion clearer, the total clamping force will be divided intothe components F1 and F2

The clamping force in parting line A (Figure 10.19) is given by:

(10.23)where

Fcx = 2 - F2

p = Cavity pressure,

Fcx = Clamping force in the x-direction,

Ax = Area of the part in the x-direction

The clamping force in parting line B (Figure 10.20) is given by:

(10.24)

where

Fcy = Clamping pressure in the y-direction,

Ay = Projected area of part in the y-direction

The clamping force Fc computes to

(10.25)For the rest of the calculation, it is important to look at the interaction of the elements

To clarify this, the equivalent circuit diagram for the system is shown in Figure 10.21.The circled numbers represent the equivalent springs that are loaded in the clampingdirection x The numbers in the squares represent equivalent springs that are loadedperpendicularly to the clamping direction y

Figure 10.19 Loading on jaws in parting

line A (in clamping direction) [10.6]

Figure 10.20 Loading on jaws in parting line

B (right angles to clamping direction) [10.6]

Clamping force Fc

UnloadedLoading and deformation in the clamping

direction in a split mold

Figure 10.21 Loading and deformation in

clamping direction of split mold [10.6]

The stiffness values marked with ' are parameters that have been converted from thetransverse direction into the clamping direction

The following relationships may be derived from Figure 10.21

From Equations (10.28) and (10.29), it follows:

Substituting Equations (10.25), (10.26), and (10.28), the unknown parameter fx is givenby:

(10.32)

We now need to determine the individual stiffness values Clg and C2g

Figure 10.22 shows the deformation of the system in the y-direction (fy) on closing ofthe mold over the distance fx

Figure 10.22 Deformation at right

angles to clamping direction [10.6]

The spring constant that occurs in the y-direction is C This can be normalized by theconstant factor tan2 a to the x-direction

Thus:

(10.33)

Forces onelement 1

Forces onelement 2not deformed

deformed