# How much force is required to excite a vibrating machine with a load?

• slobberingant
In summary, the formula used to calculate how much force is required to excite a vibrating machine is based on Newton's second law and the acceleration of simple harmonic motion. If there is little material load relative to machine mass, then the force will be based on the machine weight only.
slobberingant
TL;DR Summary
Need help understanding a vibrating force formula that was given to me at work.
I have been given a formula at work to use for calculating how much force is required to excite a vibrating machine with load. Only a proportion of material load on a vibrating machine is considered.

The formula is
F = 2*S / (K*M)
Where:
S = stroke (mm)
K = (140/w)^2
M = (M1 + (M1 + M2)) / (M1 * (M1 + M2)) (1/kg)
M1 = machine weight (kg)
M2 = material weight (kg)

I've manage to derive that the formula is based on Newton's second law and the acceleration of simple harmonic motion.
F = ma
a = Aw^2 - simple harmonic acceleration formula
Where:
A = amplitude (mm) => Stroke = 2*A

Therefore
F = mAw^2

My formula above is different in the following ways.
- w^2 ((rad/s)^2) becomes K - (140/w)^2 (1/((rad/s)^2)) but is divided rather than multiplied.
- m (kg) becomes M (1/kg) and is also divided rather than multiplied.

What does the M variable in my formula above do? - It seems like a ratio between machine and material mass. However, in isolation, the values it produces can be lower than the machine weight which would result in incorrect force values.

Where does the 140 constant in K come from?

slobberingant said:
- w^2 ((rad/s)^2) becomes K - (140/w)^2 (1/((rad/s)^2)) but is divided rather than multiplied.
No. w^2 becomes 1/K

slobberingant said:
- m (kg) becomes M (1/kg) and is also divided rather than multiplied.
No. m becomes 1/M

slobberingant said:
What does the M variable in my formula above do? - It seems like a ratio between machine and material mass. However, in isolation, the values it produces can be lower than the machine weight which would result in incorrect force values.
Actually, if M1 >> M2, then 1/M tends toward 0.5*M1, which multiplied by the 2 in the equation really gives F = M1 * [acceleration].

If M2 >> M1, then 1/M tends toward M1, which gives F = 2 * M1 * [acceleration]. I'm not sure what it means though.

slobberingant said:
Where does the 140 constant in K come from?
Not sure, but I think it might have to do with some pre-calculated damping for the machine.

Thanks Jack.
Fantastic insight.
Regarding M, if there is little load relative to mass then use the mass of machine only. This makes sense as larger machines are less effected by material load. This logic works with M2 >> M1. This approach helps greatly.
I will do some more reading on damping.
Thank you.

## 1. How do you determine the force needed to excite a vibrating machine?

The force required to excite a vibrating machine is determined by the machine's mass, the desired amplitude of vibration, the frequency of vibration, and the damping characteristics of the system. This can be calculated using formulas derived from Newton's second law of motion and harmonic motion equations.

## 2. What factors influence the force required to vibrate a machine with a load?

Several factors influence the force required, including the mass of the machine and the load, the stiffness of the system, the damping coefficient, the desired amplitude of vibration, and the frequency at which the system is to be excited.

## 3. How does the frequency of vibration affect the required excitation force?

The frequency of vibration significantly affects the required excitation force. At resonance frequency, the force required is minimized due to the system's natural frequency matching the excitation frequency. Away from resonance, the force required generally increases.

## 4. What role does damping play in determining the excitation force?

Damping plays a critical role in determining the excitation force. Higher damping reduces the amplitude of vibration and thus requires a higher force to achieve the same amplitude. Conversely, lower damping means less force is needed, but the system may be more prone to oscillations.

## 5. Can you provide a basic formula to calculate the excitation force for a vibrating machine?

A basic formula to calculate the excitation force (F) for a vibrating machine is F = m * A * ω², where m is the mass of the system, A is the desired amplitude of vibration, and ω is the angular frequency (ω = 2πf, where f is the frequency). This formula assumes no damping; for systems with damping, the calculation becomes more complex and requires additional terms to account for the damping force.

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