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# Clamping force calculation

## Clamping force calculation in injection moulding

Injection moulding is a manufacturing process that fabricates plastic parts (thermoplastics/thermosetting plastic materials) or components by injecting molten material into the mould cavity. Raw plastic melts in the injection moulding machine and gets injected into the mould for cooling and solidification, and the cooled part gets ejected out.

Please refer to figure (i) for the injection moulding process diagram. The magnitude of clamping force in the injection moulding process is quintessential to maintaining the part’s quality and mould life. This article will aid you with the Clamping force formulas in the Injection moulding process.

What is clamping force in injection moulding?

The clamping unit should close the two halves of the mould before injecting molten plastic during the injection moulding process. The hydraulically powered clamping unit exerts a force on the mould halves, closing and clamping the mould. The force applied to the mould during the operation is the clamping force. It should oppose the separating force that results from the injection of molten plastic into the mould. When the molten material fills the mould cavity, the clamping force F must resist rapid thermal expansion and contraction.

What factors impact the clamping force?

Consider the below factors that influence the clamping force calculations before proceeding:

• Depending on the viscosity, fluid properties, and temperature of the mould material, the pressure injection units exert on the mould varies. Injection pressure alters the clamping force depending on the mould material.
• Melt Flow Index is the ease of the mould flow per unit area within the hot mould, which affects the clamping force. For instance, thin-walled parts are more restrictive and require more pressure. Melt Flow Index measures the relative viscosity and remains a significant factor while calculating clamping force.
• Resin density is yet another consideration that changes the clamping force. High-density resins need low clamping force and vice-versa.
• The ratio of flow length to the wall thickness, known as the Aspect ratio, is directly proportional to clamping force.

Why is clamping force calculation necessary in injection moulding?

A small clamping force can lead to poor geometrical symmetry and flashes. In addition, hotshots, loose packing, and air bubbles result from that force.

A large clamping force can cause insufficient air venting during mould filling/packing, premature ageing of hydraulic components, and mechanical structural wear. Also, it leads to cavities, cracked cores and vents, wall cracks, and parting lines. Moreover, too much clamp force increases machine energy, hikes energy costs, deflects the platen and reduces mould life.

Hence, an accurate clamping force is necessary to shape the product and appropriately pack the material.

How to calculate the clamping force in injection moulding using the formula?

A simple formula to calculate clamping force is cavity pressure (material injection pressure in kg/cm2) multiplied by the total projection area(cm2). The resulting clamping force is in kg.

Force (kg)= Cavity Pressure(kgf/cm2) ✕ Total Projected Area(cm2)

It is often divided by thousand to get the value in Tons {Force(tons)= Force(kg)/1000}. For instance, a 100 Tons machine can produce a maximum clamping force equivalent to 100 tons.

Step-by-step calculation:

1. Total projected area calculation

The projected area is the largest area along the mould opening and closing when you see the moulding from the clamping force application direction, denoted by S.

The total projected area equals the sum of the projected areas of the cavities and runners with the parting surface. To calculate the total projected area, get the dimension and layout of the impression (according to the component geometry), diameter, and length of runners (to calculate runners’ area). Remember to include moulds with a runner system. You can ignore hot runner moulds as they eliminate runners.

Remember, if the component geometry is a square, use the below formula:

Area (cm2) = L cm ✕ W cm

If the component geometry is a circle, use the below formula:

Area (cm2) = (3.14) D2/2 or (3.14) R2

Also, multiply the number of cavities by the projected area.

Total projected area = Projected area ✕ Number of cavities

Consider this example to calculate the projected area:

Calculate the Total Projected Area for the Polypropylene container mould, which has a moulding diameter of 70 mm at the top, and 50 mm at the base, with a height of 48 mm. It consists of a hot runner mould tool of 8 impressions. The cavity at the split line has a diameter of 70 mm, a cavity depth of 48 mm, and a cavity diameter at the base is 50 mm. The mould cavity base has a thermal gate in the centre. The component’s wall section is 1.6 mm.

Solution: Total Projected Area= Area of one cavity ✕Total number of impressions

One cavity area = 3.14✕D2/4= 3.14✕7✕7/4=34.49 cm2

Total projected area= 34.49 cm2✕8=307.92 cm2

2. Cavity pressure calculation

To determine the cavity pressure, consider the gate size, location as well as the number of gates, the product’s wall thickness, viscosity of the plastic, and injection speed.

• Thermoplastic flow characteristics grouping has GPPS HIPS TPS PE-LD PE-LLD PE-MD PE-HD PP-H PP-CO PP-EPDM in Group 1, PA6 PA66 PA11/12 PBT PETP in Group 2, CA CAB CAP CP EVA PEEL PUR/TPU PPVC in Group 3, ABS AAS/ASA SAN MBS PPS PPO-M BDS POM in Group 4, PMMA PC/ABS PC/PBT in Group 5, and PC PES PSU PEI PEEK UPVC  in Group 6.
• The group multiplication constant (k)  for Group 1 is 1, for Group 2 is 1.3~1.35, for Group 3 is 1.35~1.45, for Group 4 is 1.45~1.55, for Group 5 is 1.55~1.70, and Group 6 is 1.7~1.9.

For cavity pressure calculation (represented by P), identify the group of thermoplastic flow characteristics to which the plastic belongs and the viscosity grade. Get the multiplication constant (k) from the relationship between cavity pressure and wall thickness and process/wall thickness ratio (P0). Then, cavity pressure P = P0✕k.

Let us understand the cavity pressure concept with an example for easy understanding.

Consider this example question: The round lamp holder has an outer width or diameter of 220 mm with a wall thickness of 1.9-2.1 mm. It has a pin-shaped centre gate design with the longest parts flow at 200 mm. Calculate the cavity pressure for the polycarbonate (PC) lamp holder. Refer to cavity pressure graph (ii) for reference.

Calculations:

•   ratio = Longest part flow/ thinnest part of the wall thickness range= 200 mm/1.9 mm= 105:1
• Calculate the cavity pressure from the cavity pressure/ wall thickness graph. The figure shows that for 1.9 mm cavity thickness and 105:1 ratio, it is 160 bar.
• Data is for the Group 1 of plastics, so multiply by a constant k for other groups. The flow properties of polycarbonate belong to the Group 6 of viscosity. Hence, the Viscosity of polycarbonate is 1.7~1.9 times  that of Group 1.

Cavity pressure = 160 bar ✕ k

= 160 bar✕1.9

= 304 bar (however, due to safety reasons, choose 1.9)

3. Clamping force calculation

Clamping force (T)= P(kgf/cm2 or bar)✕S(cm2)

= P0✕k(kgf/cm2 or bar)✕S (cm2)

If you want to calculate the clamping force for the above example,

P=304 bar, S=?

It is a circular polycarbonate lamp holder,

Hence, S=(3.14)D2/4

=(3.14✕22✕22)/4

=380 cm2

Therefore, Clamping force = 304 bar ✕380 cm2

=115520 kg

=115520/1000 Ton

= 115.5T

You can use a 120T machine for the given dimensions of the polycarbonate lamp holder.

The benefits of this calculation method to determine clamping force are as follows:

• It is an accurate calculation method that does not consider rough values.
• No need for professional CAE software for clamping force calculations.

Theoretical calculation using clamping force constant (Kp)

If the Kp value is in the question, use the below empirical formula:

Clamping force(T) = Clamping force constant (Kp) ✕ Projected Area (S in cm2)

Consider this example: Kp experience value for a PE material is 0.32 with a projected area of 410 cm2. Calculate the clamping force.

Solution: Clamping force = Kp✕S=0.32✕410=131.2T

Wrapping Up

Clamping force in injection moulding is a significant factor that affects parts quality because a meagre force produces defects, and an intensive force generates short shots. Use the formulas mentioned in this article for accurate clamping force calculations.

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