# how much power is needed to move a linear axis

Ι need help calculating the power usage for a linear axis motor. it must move up and down at a maximum speed of 0.5 m/s a load of 50 kg

What I did so far:

The load (i.e. weight) acting on the motor is:

$$F = mg = 50 * 9.81 = 490.5 [N]$$

where:

• F-force [N]: weight of the mass

• m - mass [kg] mass of the arms + mass of the belt + estimate of the mass of the moving parts of the axis

• g - gravitational acceleration [m/s2]

Calculation of the power required to be performed by the engine

$$P = F * v = 490.5 * 0.5 = 245.25 W$$

where:

• P: work [W]

• F: force [N]

• v: linear speed [m/s]

Given an engine efficiency of 0.8 it will be obtained that the required power is:

$$P_{t,η} = \frac{P}{ η} = \frac{245.25 }{ 0.8} = 307 W$$

And when a safety factor of Ν=2 is taken into account it will be obtained that the required power is:

$$P_{t, s} = P_{t,η} \cdot N = 614 [W]$$

The problem that I have is how to take into calculations the inertia or the acceleration I need? What other formulas i need?

I searched the web and did not find what I need.

• You need to know the time or distance of the motion.
– r13
May 18 at 13:48

TL;DR: Given that you took into account the efficiency $$\eta$$, and added on top of that the safety factor $$N$$, in most cases you will be selecting a motor capable of performing the task you describe.

## Account for acceleration

You'd only need for acceleration and the mass moment of inertia, if you had significantly high values for acceleration.

For example, if you wanted to reach the maximum velocity of 0.5 m/s in 0.01 sec (i.e. you'd have an acceleration of a = 50 $$\frac{m}{s^2}$$), then the force acting on the motor (during the acceleration stage) would be equal to:

$$F = m\cdot (g + a) = 2990.5 [N]$$

NOTE: this acceleration value is extreme, and its only for illustration purposes.

In that case, you might want to consider also, the added torque required to accelerate the rotational masses of your system (e.g. the motor shaft etc).

However, as I said, the safety factor, gives you a safe margin, so I don't thing you need to overcomplicate things if you've found an appropriate motor (you might get away with 0.5[kW] motor if you are not too bother about the acceleration and the friction losses on your setup are small).

## why you can't find a more detailed analysis on the web

you mention that you couldn't find a detailed analysis/equations for this problem.

The main reason is that the parameters that will affect the problem (beyond the weight and the velocity), will have high fluctuations and be affected by the implementation and the assembly.

More specifically, -IMHO- the other parameter that will affect significantly the calculations is the friction losses on your setup, which will be depended on:

• alignment of assembly (small misalignment of sub millimeter can have a detrimental effect on the friction),
• condition of the bearings
• temperature
• dust on the assembly
• etc.

These are not easy to account for in a mathematical model, so the engineering way out is to use a safety factor (exactly how you did it).

A final note is that, -IMHO-, N=2 is a bit high for this purpose, given that the motor also has some margins of safety but then again, it won't hurt to have it, if you can control it.