4.1 KiB
- Introduction
- Parameters
- Centrifugal forces for light and heavy sample
- Centrifugal forces as a function of the rotation speed
- Maximum rotation speed as a function of the mass
#+TITLE:Centrifugal Forces
Introduction ignore
In this document, we wish to estimate the centrifugal forces due to the spindle's rotation when the sample's center of mass is off-centered with respect to the rotation axis.
This is the case then the sample is moved by the micro-hexapod.
The centrifugal forces are defined as represented Figure fig:centrifugal where:
- $M$ is the total mass of the rotating elements in $[kg]$
- $\omega$ is the rotation speed in $[rad/s]$
- $r$ is the distance to the rotation axis in $[m]$
Parameters
We define some parameters for the computation.
The mass of the sample can vary from $1\,kg$ to $50\,kg$ to which is added to mass of the metrology reflector and the nano-hexapod's top platform (here set to $15\,kg$).
M_light = 16; % mass of excentred parts mooving [kg]
M_heavy = 65; % [kg]For the light mass, the rotation speed is 60rpm whereas for the heavy mass, it is equal to 1rpm.
w_light = 2*pi; % rotational speed [rad/s]
w_heavy = 2*pi/60; % rotational speed [rad/s]Finally, we consider a mass eccentricity of $10\,mm$.
R = 0.01; % Excentricity [m]Centrifugal forces for light and heavy sample
From the formula $F_c = m \omega^2 r$, we obtain the values shown below.
| Force [N] | |
|---|---|
| light | 6.32 |
| heavy | 0.01 |
Centrifugal forces as a function of the rotation speed
The centrifugal forces as a function of the rotation speed for light and heavy sample is shown on Figure fig:centrifugal_forces_rpm.
Maximum rotation speed as a function of the mass
We plot the maximum rotation speed as a function of the mass for different maximum force that we can use to counteract the centrifugal forces (Figure fig:max_force_rpm).
From a specified maximum allowed centrifugal force (here set to $10\,[N]$), the maximum rotation speed as a function of the sample's mass is shown in Figure fig:max_force_rpm.
F_max = 10; % Maximum accepted centrifugal forces [N]
R = 0.01;
M_sample = 0:1:100;
M_reflector = 15;