Hello Mechatronitians,

Welcome to the latest post on the Sinadrives blog.

September 2022

In today’s post we’re going to discuss how to calculate static and dynamic moments of force. These simple calculations enable us to determine whether modules with selected linear motors are the most suitable for the application we’re developing.

Calculation of static force

Let’s start with the physics part of the calculation, where we’ll use formula 1:

F = m x g

Where:
F – force in N
m – mass in kg
g – acceleration of gravity m/s2

Example:
If we place a mass of 10 kg on a surface, the static force it exerts is 98N (10 x 9.8 = 98 N).

Calculation of dynamic force

To make the calculation of dynamic force, we replace g (gravity acceleration) with A (acceleration). It’s important to know that this acceleration has to act in the same direction as the mass.

F = m x A

Where:
F – force in N
m – mass in kg
A – acceleration in m/s2

Example:
If we place a mass of 10 kg on a surface and accelerate it in the vertical direction (A = 5 m/s2), the dynamic force it exerts is 50N (10 x 5 = 50N).

Calculation of static and dynamic forces together

Suppose we have to calculate the force an elevator exerts on the building structure when it moves vertically.

Data:

Elevator mass: 1000 Kg
Acceleration: 4.5 m/s2

F = m x A + m x g = 1000 x 4.5 + 1000 x 9.8 = 4500 + 9800 = 14300N

Calculation of static moment

To calculate the static moment, we’ll use the formula shown below:

M = m x g x X

Where:
M – torque moment in Nm
X – distance between the centre of mass and the clamp in m
m – mass in kg
g – acceleration of gravity m/s2

Example:
If we place a mass of 10 kg on a surface at a distance of 300 mm, the static moment will be 29.4Nm (10 x 9.8 x 0.3 = 29.4 Nm). Image 1 is an example of the application.

Calculation of the dynamic moment

To make the calculation of the dynamic moment, we’ll use the formula shown below.

M = m x A x X

Where:
M – torque moment in Nm
X – distance between the centre of mass and the clamp in m
m – mass in kg
A – acceleration in m/s2

Example:
If we place a mass of 10 kg on a mobile carriage at a distance of 300 mm and also move this carriage with an acceleration of 15 m/s2, the dynamic moment will be 45Nm (10 x 15 x 0.3 = 45 Nm).

Figure 2 shows an example of the application.

Calculation of static and dynamic forces and moments together

Let’s look at an example. We’re going to calculate the static and dynamic forces and moments. We’ll use the data from the two examples above and apply the order as shown in image 3.

In this case we have:

Static forces and moments:
Fz = 98N
Mx = 29.4Nm

Dynamic forces and moments:
Mz = 45Nm

Coefficient of maximum permissible force

Suppose we have selected an MLE30420 linear module for our application and we have to check the moments of force. The image below shows the catalogue values for the module with linear motor MLE30420HS:

If we use the formula shown in the catalogue, we have:

Fy/Fycat + Fz/Fzcat + Mx/Mxcat + My/Mycat + Mz/Mzcat ≤ 1

We put the values calculated in chapters 1, 4 and 5 on the top line, and the catalogue values on the bottom line, which gives us the following results:

98/1500 + 29.4/180 + 45/320 = 0.07 + 0.16 + 0.14 = 0.23

We can see that the result is ≤ 1, which means there is a good safety margin. According to the catalogue, a result of less than 1 guarantees a useful life of more than 30,000 km.

Some considerations

Separately calculated values can never exceed the maximum catalogue value. The lower this value, the longer the useful life will be. If the speed and acceleration exceed a value of 3 m/s and 30 m/s2, respectively, the total sum should not exceed 0.7, unless a shorter useful life is deemed acceptable.

If you have an application in which you’re keen to improve the performance of your machine, be it in terms of speed, dynamics, precision or simply reducing maintenance needs, please contact us.

Our specialists in Direct Drive technology and Linear Modules with linear motor technology will be happy to advise you free of charge.

Draw your own conclusions. Decide which innovation you want to implement in your machine to be competitive. We can help you.

Your SINADRIVES Team.