Calculation of Clamping force

It may be seen from the above analysis and that in Chapter 4 for the calculation of clamping force on an injection moulding machine the Mean Effective pressure (MEP) across the cavity may be obtained from 

Thus for any plastic where the Power Law constants are known, the clamping force can be calculated for a given radius, R, cavity depth, H, and fill time, /. 

For plastics other than polypropylene it would be necessary to produce a similar set of curves using equation (5.88) and the Power Law data in Table 5.2. 

However, in the non-isothermal case the pressure is also high at low injection rates. This is because slow injection gives time for significant solidification of the melt and this leads to high pressures. It is clear therefore that in the non-isothermal case there is an optimum injection rate to give minimum pressure. In Fig. 5.28 this is seen to be about 3.0 x 10 m /s for the situation considered here. This will of course change with melt temperature and mould temperature since these affect the freeze-off time, //, in the above equations. 

The viscosity flow curves for these materials are shown in Fig. 5.17. To obtain similar data at other temperatures then a shift factor of the type given in equation (5.27) would have to be used. The temperature effect for polypropylene is shown in Fig. 5.2. 

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The calculation of clamp force is considered in more detail in Chapter 5. 

Moulded part s projected area Calculation of clamping force ... 

In practice the clamping pressure will also depend on the geometry of the cavity. In particular the flow ratio (flow length/channel lateral dimension) is important. Fig. 4.42 illustrates typical variations in the Mean Effective Pressure in the cavity for different thicknesses and flow ratios. The data used here is typical for easy flow materials such as polyethylene, polypropylene and polystyrene. To calculate the clamp force, simply multiply the appropriate Mean Effective Pressure by the projected area of the moulding. In practice it is... 

Example 4.6 The mould shown in Fig. 4.35 produces four cup shaped ABS mouldings. The depth of the cups is 60 mm, the diameter at the is 90 mm and the wall thickness is 1.0 mm. The distance from the sprue to the cavity is 40 mm and the runner diameter is 6 mm. Calculate the clamp force necessary on the moulding machine and estimate how the clamp force would change if the mould was designed so as to feed the cups through a pin gate in the centre of the base (as illustrated in Fig. 4.38). The clamp pressure data in Fig. 4.42 should be used and the taper on the side of the cups may be ignored. 

Calculator An interactive process wizard that provides quick, effective material, design, processing, and cost solutions. This Engineering Calculator s capabilities include (1) Material, to select from a variety of GE Plastics materials (2) Design, which calculates minimum part thickness based upon allowable deflection (3) Processing, which calculates pressure to fill and clamp force and (4) Cost, which calculates estimated material and processing costs for the intended part. 

Since the longest flow path may exceed the radius of the projected area that causes mold separating pressures, we must also find the radius of equivalent projected area, Rp, to compute a more accurate mold clamping force. However, to perform the calculations to predict velocities and pressure fields, we assume a disc geometry of radius R and thickeness h, schematically depicted in Fig. 8.41. 

Sample application of the radial flow method. In this sample application, we are to determine the maximum clamping force and injection pressure required to mold an ABS suitcase shell with a filling time, tf=2.5 s. For the calculation we will use the dimensions and geometry schematically depicted in Fig. 8.49, an injection temperature of 227°C (500 K), a mold temperature of 27°C (300 K) and the material properties given in Table 8.8. 

Finally, Figure 14.5d shows a schematic of simple shear deformation. The specimen is clamped between steel blocks. The blocks must move parallel to each other in order to get a shear strain that is uniform along the waisted region. The shear stress is calculated as t = F/A, where F is the force applied to the plane of area A. In this test it is not necessary to distinguish between nominal and true stress because the shear strain does not affect A. The shear strain is defined as y = Ax/y, where Ax is the displacement of planes separated by a distance y. Ax being measured in the direction of the force applied, which is perpendicular to y. As in the case of the compression plane strain test, there is no change in the dimension of the sample along the z axis. 

Ah electrical fitting, injection-moulded in PES, will operate at 150 C. It will be bolted to a steel support, and the total clamping force must not fall below 10 kN after 10 seconds. Washers with inside and outside diameters of 10 mm and 20 mm, respectivety, will be used. The maximum allowable strain for PES at 15(PC is 0.7%. Calculate the number of bolts needed, using data given in Hgures 8.13 and 8.14. 

In our next project we have investigated with much effort and in great detail the mechanochemical hydrolysis mechanism of the simplest disulfide model system in aqueous solution—substitution at sulfur. For the first time in a calculation, the enigmatic biphasic behavior of the reaction rate as a function of applied force obtained from force-clamp AFM experiments, see [13], has been reproduced in silico [24]... 

The time-dependence of the force is determined by the protocol applied in the actual application of DFS. One common way to perform the experiments or simulations is the force-ramp mode, in which the applied force increases with a constant velocity, F t) = where k denotes the force constant of the pulling device. The other protocol, called force-clamp mode, crmsists in the application of a constant external force, F(t) = Fext- In the force-ramp case, one finds the logarithmic dependence of the mean rupture force and v quoted above. The simple model appears to work quite well for small pulling velocities but fails if one pulls fast. In this simation, more detailed calculations of the rupture force distributions via the computation of the mean first passage time in model free-energy landscapes give more reliable results [104]. 

In this equation, m. is the effective mass of the reaction coordinate, q(t -1 q ) is the friction kernel calculated with the reaction coordinate clamped at the barrier top, and 5 F(t) is the fluctuating force from all other degrees of freedom with the reaction coordinate so configured. The friction kernel and force fluctuations are related by the fluctuation-dissipation relation... 

The popular Izod impact tester can use different size specimens depending on the type of plastic and their method of fabrication. The specimen is usually 1/8 in. x l/2 in. x 2 in. other sizes are also used. Specimens can be notched or unnotched. A notch is cut in a specified manner on the narrow face of the specimen. The sample is clamped in the base of a pendulum testing machine so that it is cantilevered upward with the notch facing the direction of impact. The pendulum is released, and the force expended in breaking the sample is calculated from the height the pendulum reaches on the follow-through. The speed of the pendulum at impact is controlled. 

They are then forced through a narrow die to form a hollow tube called a parison. A chilled mold is then clamped around the parison and inflated from the inside by air. The air pressure presses the parison against the mold, and it hardens in the shape of the mold. The mold then opens and ejects the HDPE bottle. The bottle is then trimmed and conveyed to the milk filling station. The waste plastic is ground for reuse. GHG emissions associated with the embodied energy of the packaging machinery may be calculated but typically fall near the 1% cutoff line and can be excluded (Cashman et ah, 2009). 

The tensile force and birefringence were simultaneously measured as functions of the strain. In brief, the samples were suspended vertically between two clamps the lower clamp was fixed, and the upper clamp was connected to a force transducer (Statham strain gauge). The output of the transducer was monitored by a Hewlett-Packard chart recorder (7, 8). Values of the birefringence An were determined by using a single-frequency He-Ne laser according to well-established procedures (2, 7, 8). Values were calculated directly from the sample thickness and the relative retardation R, which was measured with a Babinet-type compensator. The measurements on the 660-21.3 X 10 samples were carried out at 0-90 °C, and those on the 880-21.3 X 10 samples were carried out at 25 °C. 

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