STEM Principles

The holding force produce by the suction cup is completely dependent on the surface area of the sealing lip, which is given by the circle equation (π r2 ). Additionally, the difference in pressure outside and inside the cup is a factor in the holding force. This equation was verified by John Ballentine, a physics instructor at Glenelg High School.

In other words...

FTH  = ΔP * A

ΔP - Difference in pressure inside and outside of the cup (kPA)

A - Surface Area of the sealing lip (in² or m²)

Flat suction cups are optimal for smooth, flat surfaces due to their quick attach/release ability and their ability to retain shape. They also work very well with vertical surfaces. On the contrary, bellowed suction cups work very well with curved, angled surfaces due to their versatility in depth. This information was verified by Schmalz, a vacuum automation company based in Germany.

The absolute pressure rating of a vacuum pump denotes the measured air pressure inside the pump container. Because it is impossible to reach a pressure of 0 Pa, this value must always be positive. In contrast, the relative pressure rating denotes the difference between the air pressure inside and outside the container. Because the air pressure inside the container is always less than regular air pressure, this value will always be negative. It is important to understand the difference between these two metrics as relative air pressure is used in determining the holding force of the solution. For the unit of measurement (kPA) used to measure vacuum pressure, the kwadropus team consulted Nicholas Formica, an engineering instructor at Glenelg High School. 

Newton's second law states that the sum of the forces acting on an object in a given direction is equal to the product of its mass and acceleration. For our design to be successful, it must be able to attach to a wall without moving. As a result, the sum of all the forces acting on the cup must equal zero. When attached to a wall, there are three forces acting upon the suction cup: holding force, gravity, and static friction. Additionally, a safety factor must be added to the equation to account for the orientation of the cup and the surface type. The net force diagrams were reviewed by John Ballentine, a physics instructor at Glenelg Highschool.

• "Minimum value is 1.5, applicable for smooth and closely compacted substance workpieces"(EuroTech).

• "Between 1.5 and 2.0 for a horizontal suction gripper position, where the applied load acts vertically on the suction cup"(EuroTech).

• "At least 2.0 for heterogeneous workpieces, porous materials, or rough surfaces"(EuroTech).

This is the general equation for a suction cup on a vertical surface:

FTH =  (m ⁄ μ) × (g + a) × S 

m - mass (kg)

μ - coefficient of friction

g - gravity (9.81 m/s²)

a - acceleration of the system (m/s²)

S - Safety Factor

This is the general equation for a suction cup on a Horizontal surface:

FTH =  m  × (g + a/μ) × S