How to Calculate the Pulling Force of Hydraulic Cylinders in Injection Molds with Mechanical Locks

Engineering Principles and Pulling Force Calculation

Selecting a hydraulic cylinder for an injection mold is often considered a routine design activity. In many projects, engineers choose the cylinder based on previous experience, available installation space or by simply reusing the same solution adopted in similar molds.

Although this approach may work in some situations, it frequently results in oversized hydraulic cylinders, unnecessarily high oil consumption, increased production costs and, in some cases, insufficient pulling force during mold opening.

A hydraulic cylinder should never be selected only by considering its bore diameter or stroke length.

The correct engineering approach always begins with an accurate analysis of the forces acting on the moving component throughout the entire molding cycle.

During injection molding, a hydraulic cylinder may perform several completely different functions:

resisting the pressure generated by the molten plastic;
holding a moving core or slide in position;
extracting inserts after cooling;
overcoming friction generated by guide elements;
ensuring dimensional repeatability for millions of production cycles.

Each operating condition generates different mechanical loads.

Consequently, every hydraulic cylinder must be sized according to its real working conditions rather than according to general design rules.

One of the most common mistakes in mold design is assuming that the cylinder must always resist the injection pressure.

In reality, many modern injection molds incorporate mechanical locking systems that completely change the engineering calculations.

This article presents a real engineering case handled by the Vega Technical Department, demonstrating how the extraction force of a hydraulic cylinder was calculated for an injection mold equipped with a mechanical locking system.

Rather than resisting injection pressure, the hydraulic cylinder only had to generate the pulling force necessary to extract the molded component after the molding cycle.

Why Mechanical Locking Completely Changes Cylinder Sizing

During the filling phase, molten polymer is injected into the mold cavity under very high pressure.

Depending on the material and the molding process, cavity pressure can easily reach several hundred bar.

If no mechanical locking system is present, this pressure acts directly on the moving insert.

The hydraulic cylinder must therefore generate sufficient force to keep the insert closed throughout the injection and packing phases.

However, many high-quality injection molds use mechanical locking systems, inclined wedges or mechanical shoulders.

These components absorb the injection loads directly through the mold structure.

Once the mold is mechanically locked, the hydraulic cylinder is relieved from resisting cavity pressure.

Its only task becomes moving the insert during mold opening.

This apparently simple design difference radically changes the engineering calculations.

Instead of calculating:

frontal surface;
injection pressure;
hydraulic holding force;

the engineer must calculate:

lateral contact surface;
plastic adhesion;
draft angle;
extraction temperature;
useful pulling force.

For this reason, understanding the function of the mechanical locking system is the first step in correctly sizing a hydraulic cylinder.

The Real Engineering Case

A mold manufacturer contacted the Vega Technical Department requesting the selection of two hydraulic cylinders for an injection mold producing a plastic elbow fitting.

The customer clearly specified that the mold already incorporated a mechanical lock.

Therefore, the hydraulic cylinders would only be required to generate the extraction force during mold opening.

This information immediately eliminated the need to calculate the pushing force generated during plastic injection.

Instead, the engineering analysis focused exclusively on determining the force necessary to overcome the adhesion between the molded plastic part and the steel insert.

Rather than selecting a cylinder directly from the catalog, Vega engineers first calculated the extraction force using the actual mold geometry.

This engineering approach minimizes oversizing while guaranteeing sufficient operating safety.

Engineering Data

The analysis started from the dimensional data extracted from the customer’s three-dimensional mold model.

The measured values were:

Parameter	Value
Lateral contact surface	177.66 cm²
Draft angle	1°
Plastic adhesion coefficient	20 kg/cm²
Estimated plastic temperature	30–40°C
Mechanical locking	Present

These values formed the basis of the entire hydraulic sizing procedure.

Step 1 – Determining the Lateral Contact Surface

Unlike conventional hydraulic calculations, the frontal surface exposed to injection pressure was not relevant in this application.

Because the mold incorporated a mechanical locking system, the injection pressure was completely transferred into the mold structure.

Consequently, only the lateral surface of the insert had to be evaluated.

The calculated lateral surface was:

177.66 cm²

This value represents the actual contact area between the molded plastic and the steel insert.

During cooling, the polymer shrinks around this surface, generating the adhesion force that the hydraulic cylinder must overcome.

One of the most common engineering mistakes consists of confusing frontal area with lateral area.

The frontal area determines the pushing force generated during injection.

The lateral area determines the pulling force required during extraction.

These two calculations are completely different and should never be mixed.

Step 2 – Evaluating the Draft Angle

The next parameter analyzed by the Vega Technical Department was the draft angle.

The mold incorporated a draft angle of only:

1°

Although apparently small, this geometric detail has a major influence on extraction force.

Draft angles reduce the contact pressure between the molded polymer and the steel surface.

As the draft angle increases, the contact pressure decreases, reducing the adhesion force.

Conversely, when the draft angle becomes very small, the plastic grips the insert more firmly.

This explains why components with draft angles close to zero frequently require larger hydraulic cylinders despite having relatively small dimensions.

Increasing the draft angle by only one or two degrees may significantly reduce the extraction force without modifying the hydraulic system.

For mold designers, optimizing draft angle is often one of the most cost-effective methods for improving hydraulic performance.

Step 3 – Estimating the Plastic Adhesion Coefficient

After evaluating the geometry, the next engineering parameter was the plastic adhesion coefficient.

Based on the material characteristics and previous industrial experience, the Vega Technical Department assumed an adhesion coefficient of:

20 kg/cm²

This value was considered appropriate for:

a draft angle of 1°;
extraction of a relatively cold molded part;
estimated part temperature between 30°C and 40°C.

Unlike hydraulic pressure, plastic adhesion cannot be measured directly during the design phase.

It depends on several variables, including:

polymer family;
filler content;
mold surface finish;
cavity texture;
mold temperature;
cooling time;
shrinkage characteristics;
lubrication conditions.

For this reason, experienced engineering departments often use experimentally validated adhesion coefficients developed through years of practical applications.

Step 4 – Calculating the Required Pulling Force

Once the lateral surface and the adhesion coefficient had been established, the extraction force could be calculated.

The engineering relationship is remarkably simple:

Pulling Force = Lateral Surface × Plastic Adhesion Coefficient

Substituting the values obtained from the mold design:

Lateral Surface = 177.66 cm²

Plastic Adhesion = 20 kg/cm²

Therefore:

Pulling Force = 177.66 × 20

Pulling Force = 3553 kgf

This result corresponds exactly to the calculation performed by the Vega Technical Department.

The calculated value represents the minimum useful extraction force that the hydraulic cylinder must generate to ensure reliable removal of the molded component.

Why This Calculation Is So Important

Many designers instinctively select larger cylinders whenever they are uncertain about the required force.

Although this approach appears conservative, it frequently introduces new engineering problems.

Oversized hydraulic cylinders require:

larger hydraulic power units;
higher oil consumption;
larger hydraulic valves;
greater installation space;
slower response times due to increased oil volume;
higher manufacturing costs.

On the other hand, undersized cylinders may fail to extract the molded part consistently, causing production interruptions and increased maintenance.

Accurate force calculations therefore provide the optimum balance between reliability, efficiency and manufacturing cost.

Engineering Considerations Before Selecting the Cylinder

The calculated pulling force of 3553 kgf should not immediately be interpreted as the cylinder force required in practice.

Before selecting the hydraulic cylinder, engineers must also evaluate additional operating conditions, including:

guide friction;
seal friction;
alignment accuracy;
possible contamination;
pressure losses within the hydraulic circuit;
pressure fluctuations;
wear occurring after millions of production cycles.

Only after evaluating these additional factors can the appropriate cylinder bore and operating pressure be selected.

Hydraulic Cylinder Sizing, Safety Factors and Engineering Analysis

In the first part of this article, we demonstrated how the extraction force of a hydraulic cylinder should be calculated when an injection mold incorporates a mechanical locking system.

Unlike conventional applications, the hydraulic cylinder does not resist the injection pressure. Instead, it only needs to overcome the adhesion between the molded plastic component and the steel insert.

Using the real mold geometry, the Vega Technical Department calculated a required extraction force of 3,553 kgf.

At this stage, however, the engineering work is only partially complete.

Knowing the required force does not automatically determine which hydraulic cylinder should be installed.

The engineer must now verify which cylinder diameter can safely generate the required force at the desired operating pressure.

This verification is the basis of every professional hydraulic sizing procedure.

Step 5 – Selecting the Hydraulic Pressure

One of the first engineering decisions concerns the operating pressure of the hydraulic system.

Higher hydraulic pressure allows smaller cylinders.

Lower hydraulic pressure requires larger piston diameters.

Neither solution is universally superior.

Instead, the designer must balance several factors, including:

available installation space;
oil consumption;
hydraulic pump capacity;
response speed;
seal life;
maintenance requirements.

For this reason, the Vega Technical Department proposed two different hydraulic solutions for exactly the same application:

Ø63 cylinder operating at 150 bar
Ø80 cylinder operating at 100 bar

Both cylinders generate sufficient extraction force, but they achieve this objective in different ways.

Step 6 – Calculating the Piston Area

The force produced by a hydraulic cylinder depends on two parameters only:

hydraulic pressure
piston area

The piston area is calculated using the standard engineering equation:

A = π × D² / 4

where:

A = piston area

D = piston diameter

Ø63 Hydraulic Cylinder

Cylinder diameter:

63 mm

Converting into centimeters:

6.3 cm

Piston area:

A = 3.1416 × 6.3² / 4

A = 3.1416 × 39.69 / 4

A = 124.69 / 4

A = 31.17 cm²

This represents the effective hydraulic surface generating the extraction force.

Step 7 – Calculating Cylinder Force

Hydraulic force is calculated using the classical hydraulic equation:

F = P × A

where:

F = force (kgf)

P = pressure (bar)

A = piston area (cm²)

Since the cylinder operates at:

150 bar

the available pulling force becomes:

F = 150 × 31.17

F = 4,675 kgf

This is considerably higher than the required extraction force of 3,553 kgf.

Step 8 – Safety Factor

Professional hydraulic design never selects a cylinder capable of generating exactly the required force.

A safety margin must always be maintained.

The safety factor is calculated as:

Safety Factor = Available Force / Required Force

Safety Factor = 4,675 / 3,553

Safety Factor = 1.31

In other words, the cylinder can generate approximately 31% more force than theoretically required.

This additional capacity compensates for:

guide friction;
pressure losses;
manufacturing tolerances;
seal wear;
hydraulic inefficiencies;
contamination over long service life.

For many injection mold applications, a safety factor between 1.2 and 1.5 is considered an excellent engineering compromise.

Alternative Solution – Ø80 Hydraulic Cylinder

The Vega Technical Department also proposed an alternative operating at a lower hydraulic pressure.

Cylinder diameter:

80 mm

Converted diameter:

8.0 cm

Using the same piston area equation:

A = 3.1416 × 8² / 4

A = 3.1416 × 64 / 4

A = 201.06 / 4

A = 50.27 cm²

Operating pressure:

100 bar

The generated hydraulic force becomes:

F = 100 × 50.27

F = 5,027 kgf

Safety Factor of the Ø80 Cylinder

The safety factor now becomes:

Safety Factor = 5,027 / 3,553

Safety Factor = 1.41

The larger cylinder therefore provides approximately 41% more force than theoretically required.

Although both cylinders satisfy the application, the Ø80 solution offers a larger operating reserve while working at a significantly lower hydraulic pressure.

Why Vega Proposed Two Different Solutions

Many engineers assume that there is only one correct hydraulic cylinder for each application.

In reality, hydraulic engineering often provides several technically valid solutions.

The final choice depends on the priorities of the mold manufacturer.

Ø63 Cylinder – 150 bar

Advantages:

smaller overall dimensions;
easier installation;
reduced hydraulic oil volume;
faster cylinder movement;
lower machine weight;
compact mold layout.

Possible disadvantages:

higher operating pressure;
greater seal loading;
increased sensitivity to pressure spikes.

Ø80 Cylinder – 100 bar

Advantages:

lower hydraulic pressure;
reduced stress on seals;
smoother operation;
longer component life;
greater safety margin.

Possible disadvantages:

larger installation space;
increased oil consumption;
slower movement if pump flow remains unchanged.

Neither solution is inherently better.

Both represent sound engineering choices depending on the overall hydraulic system.

The Influence of Plastic Temperature

One particularly interesting observation contained in the original engineering evaluation concerns the extraction temperature.

The Vega Technical Department assumed an extraction temperature of approximately 30–40°C.

However, the engineers also noted that extracting the molded part at a higher temperature would reduce the adhesion coefficient.

This would directly reduce the extraction force.

To better understand this effect, consider the following examples using the same lateral surface.

Adhesion coefficient = 20 kg/cm²

177.66 × 20

3,553 kgf

Adhesion coefficient = 15 kg/cm²

177.66 × 15

2,665 kgf

Adhesion coefficient = 10 kg/cm²

177.66 × 10

1,777 kgf

The difference is remarkable.

Reducing the adhesion coefficient from 20 to 10 kg/cm² decreases the required extraction force by almost 50%.

This demonstrates why extraction temperature, cooling time and polymer properties have such a significant influence on hydraulic cylinder sizing.

Common Engineering Mistakes

This case highlights several errors frequently encountered during hydraulic cylinder selection.

The first mistake is calculating the cylinder based on injection pressure even when a mechanical locking system absorbs those loads.

The second is ignoring the effect of draft angle on extraction force.

Another common mistake is assuming that plastic adhesion remains constant regardless of molding temperature.

Finally, many designers oversize cylinders simply to “be safe.”

Although this approach appears conservative, oversized cylinders increase oil consumption, reduce dynamic performance, require larger hydraulic power units and increase manufacturing costs without improving mold reliability.

A Practical Engineering Procedure

Whenever a hydraulic cylinder is used only for extraction, the sizing process should follow a structured methodology:

Confirm that the mechanical lock absorbs injection pressure.
Measure the lateral contact surface.
Determine the draft angle.
Estimate the plastic adhesion coefficient.
Calculate the extraction force.
Select the desired hydraulic pressure.
Calculate piston area.
Verify cylinder force.
Calculate the safety factor.
Validate the design during mold testing.

This systematic procedure minimizes design errors and ensures consistent hydraulic performance throughout the life of the mold.

Conclusion

This real engineering case demonstrates that hydraulic cylinder sizing begins with understanding the function of the mold rather than selecting a cylinder from a catalogue.

When mechanical locking systems absorb the injection pressure, the hydraulic cylinder becomes an extraction device whose sizing depends almost entirely on plastic adhesion, lateral contact surface, draft angle and operating conditions.

Using real engineering calculations, the Vega Technical Department determined a required extraction force of 3,553 kgf and demonstrated that both a Ø63 cylinder operating at 150 bar and a Ø80 cylinder operating at 100 bar provide reliable solutions with appropriate safety margins.

More importantly, this case illustrates a fundamental principle of hydraulic engineering: accurate calculations allow engineers to select cylinders based on objective mechanical requirements rather than assumptions.

The result is a hydraulic system that is more compact, more energy-efficient, easier to maintain and capable of delivering reliable performance over millions of injection molding cycles.