### How to calculate vacuum suction force to find appropriate suction cups?

The use of industrial vacuum cups in automated production lines has become prevalent due to its convenience. To find the most appropriate suction cups for best performance, it is a must know how to calculate vacuum suction force.

**How to calculate vacuum suction force?**

The basic formula F=PxA is used to calculate the force of the suction cup with:

- F is holding force (or the vacuum force of the suction cup)
- P is pressure
- A is is the contact area (the size of the suction cup surface)

This is derived from the definition of pressure, which is P = F / A.

**Explain the vacuum force equation F=PxA**

**How does vacuum suction force work?**

Gravity and friction are the two main forces that make vacuum suction work. While gravity pulls molecules in the air toward the earth, creating an atmospheric pressure, the suction cup and vacuum pump cause a pressure difference, attaching both surfaces.

The suction cup contacts the workpiece’s surface, creating a sealed space. The vacuum ejection or vacuum pump takes the air inside the cup out.

By removing the air pressure inside the suction cup, the vacuum pressure on the surface of the workpiece is created. The air pressure difference is used to calculate the holding force of the vacuum cup.

**The holding force calculation**

Theoretically, the holding force calculation is affected by these factors:

- Type of workpiece’s material (steel, glass, or wood…)
- Properties of surface (smooth, even, rough or oily…)
- Dimensions of workpiece
- Mass of the workpiece m (by multiplying the length, width, height, and density)
- Acceleration of the system (m/s²)
- Acceleration due to gravity (9.81 m/s²)

Calculating the mass, holding force, and breaking force is the first step to help design suitable industrial vacuum suction cups.

The force calculation also requires attention to the friction coefficient μ, the safety factor S, the position of the gripper, and the directions of movement (vertically or horizontally).

**Safety factor S**

In the breakdown formula calculating the vacuum force, safety factor S or safety value S is added to prevent possible accidents during the operation of vacuum equipment.

Safety value S is regulated according to the characteristics of the workpieces’ surface and the position of the suction gripper, detail as follows:

- Minimum value is 1.5, applicable for smooth and closely compacted substance workpieces.
- Between 1.5 and 2.0 for a horizontal suction gripper position, where the applied load acts vertically on the suction cup.
- At least 2.0 for heterogeneous workpieces, porous materials, or rough surfaces.

The safety value S for oiled workpieces, vertical suction gripper position, or moving in swivel motions should also be 2.0 or higher.

**Friction coefficient μ**

Another critical factor that needs taking into account when calculating the vacuum force is friction defining the tangential forces.

The vacuum pressure calculation formula uses the friction coefficient μ to describe the resistance between the workpiece surface and the suction cup.

Not the same as the safety factor S, the precise specifications of friction coefficient μ can only be determined by suitable experiments.

This value alters depending on the material of which the workpiece is made and the properties of its surface.

The following are theoretical guide values for reference:

- For oily surfaces: μ equals 0.1
- For wet surfaces: μ varies from 0.2 up to 0.3
- For most materials (e.g. metal, wood, stone, glass): μ is equal to 0.5
- For rough surfaces: μ is equal to 0.6

**Load case**

Continuing from the tutorial on how to calculate vacuum suction force to select the right vacuum suction cups, the best way is to break it down into three specific cases where the position of the gripper and the directions of movement are different.

**Horizontal suction cup, vertical direction of force**

This is the simplest case when the suction cup is placed horizontally on the surface of a workpiece. Except for lifting the workpiece up and down, there is no other movement. Then the formula for force calculation is as follows:

**Force F = m x (g + a) x S**

Where:

- m is the mass of the workpiece
- g is the gravity (9.81 m/s²)
- a is the acceleration of the system (m/s²)
- s is the safety value

For example: m = 0.314 kg; a = 5 m/s²; S = 1.5

Force F = 0.314 x (9.81 + 5) x 1.5 = 6.97551 ≈ 7 N

**Horizontal suction cup, horizontal direction of force**

The next case is when the suction cup is placed horizontally on the surface of a workpiece.

Except for lifting the workpiece up and down, there is transverse movement. Then the formula for holding force calculation is as follows:

**Force F = m × (g + a ⁄ μ) × S**

Where:

- m is the mass of the workpiece
- g is the gravity (9.81 m/s²)
- a is the acceleration of the system (m/s²)
- μ is the friction coefficient
- s is the safety value

For example: m = 0.314 kg; a = 5 m/s²; μ = 0.1; S = 1.5

Force F = 0.314 x (9.81 + 5/0.1) x 1.5 = 28.17051 ≈ 28 N

**Vertical suction cup, vertical direction of force**

The final case is when the suction cup is placed vertically on the side surface of a workpiece and the workpiece is lifted up and down. Then the formula for holding force calculation is as follows:

**Force F = (m ⁄ μ) × (g + a) × S**

Where:

- m is the mass of the workpiece
- μ is the friction coefficient
- g is the gravity (9.81 m/s²)
- a is the acceleration of the system (m/s²)
- s is the safety value

For example: m = 0.314 kg; a = 5 m/s²; μ = 0.1; S = 2

Force F = (0.314/0.1) x (9.81 + 5) x 2 = 93.0068 ≈ 93 N

Selecting the right suction cups can be tricky by various categories and quality requirements. If your business is facing one, then after calculating the vacuum suction force correctly, the next step you can do is to contact EUROTECH to support your business in choosing the most appropriate suction cups for installation.

As a world-class vacuum suction cup spare parts and components provider, EUROTECH Vacuum Technologies has the knowledge and ability to recommend to their business clients the best cup for the application without bias.

Furthermore, if customers from different industries are unsure of how to calculate vacuum suction force, the company can also provide professional service with mass customization of vacuum solutions to fulfill needs or any portfolio.