A practical guide to calculating force, torque, rack travel and cylinder stroke

Unscrewing molded parts from injection molds requires careful evaluation of the force and torque needed to remove the threaded component, together with the number of cavities, thread geometry and the transmission ratio between the hydraulic cylinder, rack and pinions.

A common mistake is to size the hydraulic cylinder only according to the required stroke, or to select a commercially available unscrewing system without first verifying the actual force and torque required to remove the molded part.

A real Vega application involving a four-cavity mold with threaded cores provides a useful example of how this type of system can be engineered.

In this application, the customer had received a proposal from HASCO for a mechanical unscrewing system. The Vega distributor asked the Technical Department to evaluate the application and propose an alternative solution using a Vega hydraulic cylinder and rack-and-pinion system.

The technical evaluation resulted in the following values:

useful force required to unscrew each core: approximately 316 kgf;
number of cavities: 4;
total force: approximately 1,264 kgf;
recommended cylinder: CS050;
rack: module 2;
cylinder stroke and rack length: to be determined according to the pinion transmission ratio.

This application provides a useful framework for understanding how to size a hydraulic unscrewing system correctly.

1. Why Use an Unscrewing System in an Injection Mold?

When a molded part contains an internal or external thread that prevents simple linear ejection, the core or insert that forms the thread must rotate before the part can be removed.

The basic principle is therefore mechanical unscrewing.

During mold opening, the system must:

rotate the threaded core;
complete the required number of revolutions;
maintain synchronization between the cavities;
complete the required extraction movement;
return the system to its starting position.

A hydraulic unscrewing system can consist of:

hydraulic cylinder;
rack;
pinion;
intermediate gears;
shafts;
threaded cores.

This solution is particularly interesting when several cavities must be actuated simultaneously.

2. The Application: Four Cavities

The application analyzed by Vega involved four cavities.

The HASCO drawing shows four threaded cores arranged around the central area of the mold.

The original HASCO proposal included a mechanical unscrewing system with:

high-lead screw;
nut;
pinions;
intermediate gears;
bearings;
shafts and other transmission components.

The HASCO documentation specifies:

thread: 22.8 × 12;
thread diameter: 22.8 mm;
pitch: 1.5 mm;
thread length: 17.7 mm;
number of cavities: 4;
calculated rotations: 2.48;
required system stroke: 123.75 mm.

The HASCO drawing also specifies a right-hand high-lead screw and an intermediate gear with z = 40.

3. The First Question: How Much Force Is Required to Unscrew the Core?

Before selecting the hydraulic cylinder, the required unscrewing force must be determined.

This is the fundamental principle.

The calculation should not start with:

“Which cylinder can we use?”

It should start with:

“What force is actually required to unscrew the threaded core?”

In this application, Vega considered the thread surface for the sizing calculation.

The resulting useful force was:

316 kgf per threaded core.

This represents the useful force calculated by Vega for unscrewing each of the four cavities.

4. From the Force of One Cavity to the Total Force

The mold contains four cavities.

If each core requires approximately:

316 kgf

the total force, considering all four cavities simultaneously, is:

Vega therefore calculated a total force of approximately:

1,264 kgf for four cavities.

This is one of the most important points in the application.

When several threaded cores are actuated simultaneously, the system must be evaluated for the combined load rather than only for the force required by one core.

5. Why the Number of Cavities Matters

With only one threaded core, the required force would be the force of that individual cavity.

In this application, however, there are four cavities.

Therefore, if all four cores are actuated simultaneously, the common drive system must be capable of handling the combined load.

In this application:

1 × 316 kgf = 316 kgf

whereas:

4 × 316 kgf = 1,264 kgf

The difference is significant.

The number of cavities should therefore be one of the first pieces of information requested when sizing a multi-cavity unscrewing system.

6. The Hydraulic Cylinder Recommended by Vega

After determining the required force, Vega proposed:

CS050 cylinder with a module 2 rack.

It is important to understand that the cylinder is not considered independently.

The complete system is:

hydraulic cylinder → rack → pinion → transmission → threaded core

The cylinder produces linear movement.

The rack converts this linear movement into rotary movement through the pinion.

The resulting rotation is then transmitted to the threaded cores.

7. How a Rack Converts Linear Movement into Rotation

The principle is straightforward.

The hydraulic cylinder moves linearly.

The rack is connected to the cylinder rod.

When the rack moves:

linear rack movement

↓

pinion rotation

↓

shaft rotation

↓

threaded-core rotation

↓

unscrewing of the molded part

This system therefore converts the linear stroke of the hydraulic cylinder into a controlled amount of rotation.

8. Why the Rack Module Is Important

In this application, Vega specified:

module 2.

Module is one of the fundamental parameters defining the geometry of gears and racks.

It affects:

tooth dimensions;
pitch diameter;
load-transmitting capability;
overall transmission dimensions.

The module therefore cannot be selected solely according to the available space.

It must also be compatible with the load that the transmission has to transfer.

For this application, Vega proposed a module 2 rack.

9. Cylinder Force Is Not Directly Equal to Threaded-Core Force

This is an essential concept.

The force calculated at the threaded core:

316 kgf

should not necessarily be compared directly with the linear force available at the cylinder rod.

Between the hydraulic cylinder and the threaded core there is a mechanical transmission consisting of:

rack;
pinion;
intermediate gears, where applicable;
shafts.

The transmission ratio determines the relationship between:

linear cylinder force;
torque available at the pinion;
torque applied to the threaded core;
cylinder stroke;
number of revolutions of the core.

For this reason, Vega specified the CS050 cylinder while also stating that the cylinder stroke and rack length must be determined according to the pinion transmission ratio.

10. Torque Is the Key Parameter in Unscrewing

In a rotary unscrewing movement, the fundamental mechanical quantity is torque.

In simplified form:

where:

T = torque;
F = force;
r = lever arm.

In a rack-and-pinion system, the linear force of the rack generates torque on the pinion.

The pinion geometry therefore determines the relationship between rack force and available torque.

The torque is then transferred to the threaded core through the transmission.

11. Why the Pinion Ratio Is Important

When multiple gears are used, the ratio between their diameters or numbers of teeth determines:

rotational speed;
available torque;
threaded-core speed;
number of revolutions;
required rack travel.

This is precisely why Vega did not simply specify a standard cylinder stroke.

The technical documentation explicitly states that:

the cylinder stroke and rack length must be calculated by the customer according to the ratio between the pinions.

This is an important principle to retain for future applications.

12. Cylinder Stroke and Threaded-Core Rotation

The customer must determine how much linear rack movement is required to obtain the number of revolutions required by the threaded core.

In the HASCO system, the calculated values were:

2.48 revolutions

and:

123.75 mm required stroke.

However, these values belong to the specific HASCO transmission configuration shown in the original documentation.

They should not automatically be transferred to a Vega configuration without checking the transmission ratio of the Vega system.

The important principle is:

The required hydraulic-cylinder stroke depends on the actual kinematics of the transmission.

13. Do Not Confuse the HASCO System Stroke With the Vega Cylinder Stroke

The HASCO document specifies a required stroke of:

123.75 mm.

However, Vega specifies that the cylinder stroke and rack length must be calculated according to the ratio between the pinions.

Therefore, it would be incorrect to write:

“The Vega cylinder must have a 123.75 mm stroke.”

The technically correct statement is:

123.75 mm is the stroke specified for the HASCO configuration; the stroke of the Vega cylinder must be determined according to the transmission used in the Vega solution.

This distinction prevents a value belonging to one mechanical system from being incorrectly applied to another.

14. Thread Length Does Not Directly Determine Unscrewing Force

The HASCO documentation specifies:

thread diameter: 22.8 mm;
pitch: 1.5 mm;
thread length: 17.7 mm.

These parameters are essential for understanding the unscrewing movement.

However, Vega explicitly states that the thread surface was considered for the force calculation.

The thread length should therefore not be treated by itself as a direct measure of the required unscrewing force.

15. Thread Pitch and Unscrewing Movement

The HASCO document specifies a pitch of:

1.5 mm.

Pitch determines the theoretical axial movement of a screw for each revolution.

For a 1.5 mm pitch:

1 revolution → 1.5 mm theoretical axial movement

However, the actual unscrewing system must be designed according to the real geometry of the molded part and the movement required to completely release the thread.

The HASCO system calculated:

2.48 revolutions.

16. Why Four Cavities Can Be Arranged in a Line

In this application, the distributor proposed arranging the four cavities in line and using a Vega cylinder with a rack system.

Stefano Rogora agreed with this solution.

However, he made an interesting observation:

the HASCO system would have kept the mold more compact.

This demonstrates that unscrewing-system design is not only a question of force.

The designer must also consider:

cavity arrangement;
available space;
mold compactness;
transmission position;
accessibility;
installation;
maintenance.

17. Compactness Versus Transmission Simplicity

The HASCO system shown in the drawing uses a relatively compact arrangement of mechanical components.

The Vega proposal instead used a linear arrangement of the four cavities with a rack-and-cylinder system.

Both approaches can offer different advantages.

Compact mechanical system

It can reduce the overall mold footprint.

Rack-and-cylinder system

It can provide a relatively straightforward way of transmitting linear hydraulic movement to several threaded cores.

The final solution must therefore consider the complete mold architecture, not just the required force.

18. Sizing Must Start With the Actual Required Force

The application demonstrates a useful sequence.

First parameter

Determine the force required for one cavity:

316 kgf.

Second parameter

Multiply by the number of cavities:

316 × 4 = 1,264 kgf.

Third parameter

Select the cylinder and rack module:

CS050 + module 2 rack.

Fourth parameter

Determine the stroke according to the transmission:

pinion ratio → rack travel → cylinder stroke.

This is much more reliable than choosing the cylinder simply from the required stroke.

19. What Information Should Be Requested From the Customer?

When a customer requests an unscrewing system, it is useful to collect at least the following information.

Thread data

diameter;
pitch;
thread length;
thread type;
direction of rotation.

Mold data

number of cavities;
cavity arrangement;
distance between cavities;
available space;
possible cylinder position.

Process data

plastic material;
molding conditions;
required unscrewing force, if already known.

Movement data

required number of revolutions;
rotation direction;
required stroke;
time available for unscrewing.

Transmission data

number of teeth on the pinions;
module;
transmission ratio;
number of intermediate gears.

With these parameters, the unscrewing system can be sized correctly.

20. Number of Revolutions Is a Critical Parameter

One of the first values that should be determined is the number of revolutions required to completely release the thread.

In the HASCO configuration analyzed in this application:

2.48 revolutions were calculated.

This means that the threaded core must rotate almost two and a half turns before it is completely released from the molded part.

The number of revolutions directly determines the movement required from the transmission system.

21. From Number of Revolutions to Rack Travel

Once the required number of revolutions is known, the linear movement of the rack must be determined.

The relationship depends on the pitch diameter of the pinion.

In simplified form:

where:

s = linear rack displacement;
n = number of revolutions;
dₚ = pitch diameter of the pinion.

This relationship must be applied to the actual transmission configuration.

If additional pinions or gears are present, their transmission ratio must be included.

This is precisely why Vega stated that the cylinder stroke should be determined according to the pinion ratio.

22. Why Knowing Only That the Thread Is 22.8 × 12 Is Not Enough

The HASCO document specifies:

Thread: 22.8 × 12.

However, this information alone is not sufficient to design the Vega unscrewing system.

It is also necessary to know:

required unscrewing torque;
number of threaded cores;
pinion transmission ratio;
number of revolutions;
required stroke;
available space.

The thread defines part of the problem.

The mechanical transmission determines how the hydraulic cylinder movement is converted into rotation of the threaded core.

23. Why Vega Considered the Thread Surface

The Vega technical documentation is explicit:

“For the sizing I considered only the thread surface.”

Therefore, the force documented in the application refers specifically to the thread surface considered in the calculation.

Additional surfaces or undocumented correction factors should not simply be added to the calculation.

The documented Vega result is:

316 kgf per threaded core

and:

1,264 kgf for four threaded cores.

24. Why the System Must Be Sized for the Combined Load

In a four-cavity system, all forces must be considered together if all four cores are driven simultaneously by the same mechanism.

The overall system therefore needs to be checked against the combined load.

In this application:

4 cavities × 316 kgf = 1,264 kgf

This is the total force indicated by Vega.

The transmission system must therefore be evaluated not only for the individual threaded core, but also for the combined load transferred through the rack and gears.

25. The Cylinder and Transmission Must Be Designed as One System

This is an important concept.

The following should not be considered independently:

hydraulic cylinder

and

unscrewing transmission.

The correct engineering approach considers:

cylinder + rack + pinions + gears + threaded cores

as one transmission system.

A cylinder with sufficient force can still be unsuitable if:

the transmission ratio is incorrect;
the stroke is insufficient;
the pinion is undersized;
the rack is undersized;
the required number of revolutions cannot be achieved.

26. The CS050 Selection

In this application, Vega recommended:

CS050

with:

module 2 rack.

This is the technical solution documented for this specific application.

It should not be turned into a general rule such as:

“Four cavities always require a CS050.”

That would be incorrect.

The CS050 was the solution identified for this specific application, based on the calculated force and the mechanical configuration considered.

Another mold with:

four cavities;
different thread;
different diameter;
different friction;
different required torque;

could require a different cylinder.

27. What Can We Learn From the HASCO Comparison?

The customer had received a HASCO proposal and asked Vega to evaluate an alternative solution.

The HASCO document showed a complete mechanical solution with:

high-lead screw;
nut;
gears;
intermediate gears;
bearings;
shafts;
keys.

The Vega proposal introduced a different concept:

hydraulic cylinder + rack + pinions

to generate the same fundamental unscrewing movement.

This is an excellent example of how the same molding problem can be solved using different mechanical architectures.

28. When a Rack-and-Pinion Solution Is Interesting

A rack-and-pinion transmission can be attractive when the application provides:

sufficient linear space for the rack;
multiple threaded cores;
a need for synchronized movement;
hydraulic power as the source of movement;
high force requirements;
a relatively straightforward mechanical transmission.

The actual suitability must always be verified for the specific mold.

29. The Return Movement

An unscrewing system must not only perform the unscrewing movement.

It must also return to its initial position.

The hydraulic cylinder therefore performs the reverse movement and returns:

rack → pinions → threaded cores

to the correct starting position.

The direction of rotation must be compatible with the thread.

The HASCO documentation specifies a right-hand rotation direction and a right-hand high-lead screw.

This is another parameter that must be checked during system design.

30. Unscrewing-System Sizing Checklist

Before proposing a Vega hydraulic cylinder for an injection-mold unscrewing application, check the following.

Thread

Molded part

Material
Geometry
Thread surface
Unscrewing force

Mold

Number of cavities
Cavity arrangement
Available space
Possible cylinder position

Transmission

Movement

Force

31. Application Data at a Glance

Parameter	Value
Number of cavities	4
Thread diameter	22.8 mm
Pitch	1.5 mm
Thread length	17.7 mm
HASCO revolutions	2.48
HASCO required stroke	123.75 mm
Vega force per threaded core	316 kgf
Total force	1,264 kgf
Vega cylinder recommended	CS050
Rack module	2

The thread, pitch, length, revolutions and stroke values come from the HASCO proposal, while the force, CS050 cylinder and module 2 rack come from the Vega technical evaluation.

32. The Main Engineering Lesson

This application demonstrates that the sizing of an unscrewing system should not begin with the hydraulic cylinder.

The correct sequence is:

Thread geometry

↓

Required force for one cavity

↓

Number of cavities

↓

Total force

↓

Required torque

↓

Transmission design

↓

Rack and pinion module

↓

Transmission ratio

↓

Rack travel

↓

Cylinder stroke

↓

Final cylinder selection

In this application, this process resulted in the selection of a CS050 cylinder with a module 2 rack, based on approximately 316 kgf of useful force per threaded core, for a total of 1,264 kgf for four cavities.

33. Conclusion

Hydraulic unscrewing systems for injection molds must be designed by considering force, torque, number of cavities, number of revolutions, transmission ratio and cylinder stroke together.

A real four-cavity molding application provides a clear example.

The customer was looking for an unscrewing solution for four cavities and had received a HASCO proposal as a reference.

The HASCO proposal specified a 22.8 mm thread diameter, 1.5 mm pitch, 17.7 mm thread length, 2.48 revolutions and a 123.75 mm required stroke.

Vega analyzed the application by considering the thread surface and calculated a useful force of approximately 316 kgf per threaded core, corresponding to approximately 1,264 kgf for four cavities.

The proposed solution was a CS050 cylinder with a module 2 rack. The cylinder stroke and rack length were not arbitrarily fixed; Vega specified that they must be determined according to the pinion transmission ratio.

The most important rule to remember is therefore:

When sizing a hydraulic unscrewing system, do not select the cylinder based on stroke alone. First determine the required force and torque, the number of revolutions and the transmission ratio. Only then can the rack travel and hydraulic-cylinder stroke be correctly determined.

Useful Vega References

These official Vega pages are relevant to hydraulic cylinders and unscrewing applications:

Vega Cylinders – Hydraulic Cylinders for Molds — official overview of Vega hydraulic cylinders for plastic injection and die-casting molds, including the Unscrewing category.
Vega V210CS – Hydraulic Cylinders with Unscrewing Device — official page for the V210CS series specifically designed for unscrewing systems in plastic injection molds.
Vega Hydraulic Cylinders Catalog — official catalog organized by application, including Unscrewing, mechanical locking, ejection and other mold applications.
Vega Hydraulic Cylinders – Products — official product area with the current Vega hydraulic-cylinder range.
Vega Custom Hydraulic Cylinders — official information about customized hydraulic-cylinder solutions for applications requiring special configurations.