The demoulding force

The demoulding force is the overall force that is needed to take out a foam piece from its mould (Fig. 70.) and is also the force that has to be transmitted by the gripper. The task of determining the demoulding force of a real seat foam is a task that cannot be done analytically. This is due to the complexity of geometry of the seat and the difficulty of solving the equations (96)-(100) even for the simple case that was described in Chapter 4.2. To have an idea of the force, finite element analysis may also be used.

The whole force is difficult to determine, so for the first attempt the deformation of the foam will be considered. This means to calculate the force that is required to deform the undercuts of the foam to the size of the mould opening. Demonstration of the deformation of undercuts during lifting the foam out of the mould can be seen on Fig. 2. The deformation of the foam is principal for the calcu-lation. The first assumption is that the deformation energy is constant in every foam. This means that no matter how and in what sequence the foam is deformed (e.g. first the small undercuts are taken out, then the large ones) the same energy is needed for the whole foam to be lifted out of the undercuts.

Fig. 69: The deformation of undercuts in the foam during demoulding

Model for the Calculation

When calculating the demoulding force the following components should be taken into considera-tion:

Fdem:= µFdef + Fstr + Fg + Fad (158)

Where :Fdem Demoulding force.

Fdef Deformation force It is a projection of the compression force perpendicular to the wall of the mould issued from the compression of the foam in cross direction. (it is used for the calculation).

µ Friction coefficient

Fstr Stretching force arisen from the elongation in the lifting direction.

Fg Mg, where M is the mass of the foam, g is the gravitational constant 9.81 m/s2.

Fad The adhesion force acting between the foam and the mould when production parameters are not set properly. It is not taken into consideration in this model

The deformation force can be calculated by knowing the geometry of the foam, the size of the mould opening the material function (16) and its parameters from Chapter 2.3.5.3. µ is also a mate-rial parameter of the foam and the mould that can be acquired from measurements, literature or fac-tory standards. Fg can be easily determined from the geometry of the foam and the density of the foam. Fad in precise production can be neglected straightaway; otherwise in less careful manufac-turing this force can give the design a great uncertainty. Fstr will not be calculated. It causes just a small addition to the overall force since the foam is pierced all over with needles that cause the foam to act rigid in the direction of the pull by having the frictional force grip on all needle sides from “inside” the foam in a large volume. By neglecting this force causes an error, but taking it into the calculation would make it impossible to solve.

If it is presumed that the foam is demoulded by making the whole undercut volume deformed to the size of the mould opening, as a first approach then the stretching force can be neglected so this will be our first assumption.

For all force calculations the geometrical foam parameters are the base data. Usually in the facto-ries the precise geometry of the foam is documented in a 3D CAD model (e.g. ProE^®), this model is used for designing the seat, making the mould for the foam, calculating storage space, transport, etc.

The solid model of the foams can be used to derive features and size measurements for the calcula-tions and may be the base for further finite element studies.

Required deformation

The foam has to be compressed until all its parts are smaller than the free surface. On Fig. 71 a section of a sample seat cushion with real life parameters can be seen. Usually these values do not differ much on different seats therefore a general rule can be set. It means that the needed deforma-tion on all seat-like foams may be less than 30% of the whole size of the foam secdeforma-tion.

Fig. 70: Model of foam in the mould, with

illus-trated demoulding force Fig. 71: Cross section of a seat foam

Simplifications for the Calculation

The most serious assumption that σ acts in one directional only and this direction is collinear with the direction of the compression. On sharp corners the σ is three directional. These corners however take up less then 1% of the foam and they are well rounded for proper foam design. At first ap-proach we disregard them.

The next three assumptions are technical. The inserts in the foam that are parallel with the com-pression are not taken in consideration for the calculation. The inserts that are collinear with the pulling out force (normal to the compression) do not affect the calculations. Although almost every seat have some inserts in them. Fortunately these inserts never reach into the undercut parts of the seats; otherwise the demoulding would be impossible. The compression causes a sliding stress along the surface of the inserts in the foam. The sliding stress is the largest at the part nearest to the side of the seat and zero at the middle. At present this stress is neglected, but further investigations should be made to include it in a later model.

Sometimes the seat cover is polymerised onto the foam. This makes the production simpler cheaper and gives a better securing for the cover. In the calculations the cover is not taken into con-sideration. This is because there are too many different material used for the covers (almost every

car seat has a different cover) that by taking it into consideration would make calculations too spe-cific. The last simplification is about the starting pressure of the foam inside the mould. The pres-sure is inside the foam from the residue gas of the polymerisation. This is an initial value of the de-moulding force calculation. This means that at mould opening the foam would like to be bigger than the mould so it presses the mould apart. Since the mould does not extend a pressing force acts in-side the mould. This can be seen when trying to demould a foam that has no undercuts. The force is larger than just the weight of the foam, because the force for the pressure acting on the side of the mould times the frictional constant acts as a counter force to the pull. This has to be taken into con-sideration at the calculations by calculating the difference of the foam’s size (at demoulding) and the adequate size of the mould. It can be also calculated from the chemistry of foaming (See: Chap-ter 2.3).

Calculating the Demoulding Force

For the determination of the demoulding force first let us consider a one-directional problem, when the foam shape does not change along the contour. In this case a section of the foam can be described by a single variable function like y=f(x) (Fig. 72.).

Fig. 72: Section of a part of a simple foam

The compression stress and the size of the area where the compression stress acts, changes with the variable x. This can be formulated as (See also Chapter 5.3.1.2):

∑

^∆

i

i i

C= (x ) A(x )

F σ (159)

where: σ(x_i) is the stress acting in the direction of x.

) x ( A _i

∆ is the infinitesimal area where the stress acts. By performing the limit on (159) we get the integral for the force as:

∫

²

1

X

X

dA(x)

σ(x) (160)

To convert the integral to a Riemannian integral the dA(x) is converted to d(x) by the formula:

(x)dx A

= x dx

A(x) /

d

d (161)

By substituting (161) to the value of the integral and multiplying it by the friction coefficient the

‘one-dimensional’ demoulding force problem is:

∫

²

1

X

X

/ C = (x)A (x)dx

F µ σ (162)

By taking these results into consideration the more complex problem of a real life foam can be presented.

On a general foam the surface of the undercuts can be given by a binary function Z= f(x,y) (Fig.

73).

Fig. 73: An infinitesimal section of a foam

where:

S: is the base area are where the double integral has to be calculated. On a real part it is the area of the middle section of the foam.

dx,dy: is the elementary rectangular area. By summing these small areas and performing the limit we obtain A.

dA (xi,yj): is the elementary surface area of the foam

z(xi,yj): is the height if the small parallelepipeds that has dxi*dyj for the base area.

The stress σ(x,y) and the area dA(x,y) can also be considered as functions of two variables.

Since the foams are symmetrical these calculations may be done only to one side of the foam. So the middle split section of the foam may be the base area (A) of the XY plane from where the lation of the integral can be calculated. With these parameters the deformation force can be calcu-lated by the same way as were seen in the one dimensional problem but using the method for the double integrals:

∑

^{∆ ⇒}

j i,

j i j

i

S = (x ,y ) A(x ,y )

F µ σ by performing the limit (163)

∫

S

S = (x,y)dA(x,y)

F µ σ (164)

where µ is the stationary frictional coefficient.

In this case there is no problem of the contact surfaces that were encountered in Chapter 4.2 for the needle forces. This is because the foam surface that is in contact with the mould is more or less continuous. During the foaming and polymerisation a skin is formed on the outer surface of the foam that takes on the shape of the mould (It is like the crust of a bread). This way the outer surface has a dimension of mm² as a very good approximation.

When calculating the sometimes rather difficult

∫

S

dem = (x,y)dA(x,y)

F µ σ integral, several methods can be used. Symbolic programming languages are available (Maple) to get a closed form or nu-merical results of these integrals. The first three variables of Taylor formula may be used for simpli-fying the σ(ε)function. If the surface of the foam cannot be presented by one function then it has to be broken down to smaller surface parts until these parts can be written down by an analytical func-tion [109]. Another method is to use a larger bounding surface that can be presented by a simple function. By calculating with this containing surface a larger force for the deformation is obtained.

This pushes the results of the calculation to safer values, because the real deformation will always be smaller than the calculated ones. For more precise results finite element analysis may be used with some of the suggested material models. The procedure of demoulding force calculation can be followed on the chart of Fig. 74. The inputs are the foam hardness, the foam’s geometry and the pa-rameters from previous tests. The result of the process is a value of the demoulding force for the given foam part [108].

S

DEMOULDING FORCE MATERIAL MODEL

F-dL FUNCTION CURVE PARAMETERS

(a, b, c)

FOAM'S GEOMETRY

FOAM HARDNESS

PARAMETERS FROM PREVIOUS TESTS

Fig. 74: The process of demoulding force calculation

Conclusion

The method described in this section is just a simple model. It has much neglection and may only be used for certain foam geometry with a lot of criterion: small undercut-foam size ratio, small seat foams, no inserts, foams with at least one symmetry in the direction perpendicular to the demould-ing. This means that the method described is not at all general, and further investigations are needed before it can be widely used.

However for simple foams it can be used effectively, especially in the pre-design stage of process planning and for acquiring initial data for gripper design. To see how to use the method a simple example of the calculation of a cylindrical problem will be presented in the next Chapter (5.3.1.2).

In Chapter 5.3.1.3 the calculated force will be determined by tests with the same dimension and pa-rameter foams.

In document Budapest University of Technology and Economics Department of Manufacturing Engineering (Pldal 108-112)