Calculation of Centrifugal Force and Amplitude

Centrifugal Force Generated by Vibration Motors

As illustrated in Figure X, a vibration motor generates centrifugal force in all directions on the vibrating body through the rotation of an unbalanced weight.

Figure X: Centrifugal force generated in all directions by a single vibration motor
Figure X

This centrifugal force F is expressed by the following equation:
F = m * r * ω²
When the angular velocity ω is expressed in terms of vibration frequency f, the force can be calculated using the following formula:

Formula for centrifugal force with frequency
Figure Y: Two rotating masses with rotational direction arrows and a vertical force vector shown at the center.
Figure Y
Symbol Meaning Unit
F Centrifugal force N
m Unbalanced mass kg
r Eccentric distance m
f Vibration frequency Hz

Controlling Vibration Direction with Two Motors (Principle of Linear Motion)

A well-known method is to install two vibration motors on the same rigid structure and operate them in opposite rotational directions using the same electrical circuit. Under the condition that the centrifugal forces generated by the two motors are equal ( F1 = F2 ), the following phenomena occur.

Figure Y-1: F₁ and F₂ synchronized downward, producing a combined force twice as large in the vertical direction
Figure Y-1
Figure Y-2: F₁ and F₂ synchronized horizontally, cancelling each other to produce zero horizontal force
Figure Y-2
Figure Y-3: F₁ and F₂ synchronized upward, producing a combined force twice as large in the vertical direction
Figure Y-3
Figure Y-4: F₁ and F₂ synchronized horizontally, cancelling each other to produce zero horizontal force
Figure Y-4
  • In Figures Y-1 and Y-3, the vertical components of F1 and F2 act in phase, resulting in a combined force that is twice as large.
  • In Figures Y-2 and Y-4, the horizontal components cancel each other, resulting in zero horizontal force.

The motion paths shown in Figures Y-1 through Y-4 produce linear vibration similar to that of a vertical piston mechanism.

An example applying this principle is the table vibrator shown in Figure Y-5.

Figure Y-5: Linear vibration generated by two motors (table vibrator).
Figure Y-5

By tilting the direction of the generated force, materials can be propelled horizontally while being lifted and advanced in small increments, enabling conveyor operation through vibration.

Vibratory conveyor with inclined motor arrangement

Calculation of Total Amplitude

For the single amplitude A0 generated by the resultant vertical centrifugal force (measured as the displacement from the motor center to one side), the total amplitude A is given by the following relationship:

A = 2 * A0

First, the general equation used to determine the single-sided amplitude A0 is shown below.

General equation for A0

The following transformed equation provides a simplified method for calculating amplitude using the vibration frequency f.

Transformed equation for amplitude using f
Symbol Meaning Unit
A Total amplitude (peak-to-peak amplitude) m
F Centrifugal force (combined centrifugal force) N
W Vibrating mass kg
f Vibration frequency Hz

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Applications＆Selection

Vibration Motor Applications and Installation Guide