18/01/2018

# How to size Motors for Vertical Motion

#### The Hard Way or the Easy Way (Rule of Thumb Method)

Sometimes we make things harder than they need to be! SERAPID’s Chief Engineer, Bob Adams, explains the easy route for sizing motors for vertical motion.

Definition:

Horsepower is the rate at which work is done.  You may remember from high school science class that: 1hp=550 ft∙lbf/s. In other words, you can lift 1 lbf at a rate of 550 ft/s, or 550 lbf at 1ft/s. Both are equal to 1 horsepower. (In the metric system, we simply use Watts (W). 1hp ≈750W).

For purposes of calculating power requirements for lifting, the Horsepower model is easy to follow. If you know how much you are lifting, and how fast it is going, you have a starting point to determine the motor power requirements.

• The hard way

In many cases, documentation of calculations is vital. For reliability and safety, you may need to do fully documented math.  From the data above, you have the first part, how fast you are lifting and how much it weighs. A complete explanation is beyond the scope of this blog post, but as a brief overview, the forces you need to add:

1. Weight
2. Friction Force
3. Acceleration Force (Force = mass . acceleration)

As an example :

 Weight Wt:=550 lbf Friction Fμ:=50.lbf Acceleration (1 ft/s in 1 s)  ; 32 is for gravity and converts force to mass Fa:=550 lbf/(32.ft/s²).1.(ft/s²) = 17 lbf Total force required Ftot :=Wt + Fμ + Fa = 617 lbf
` `

This total force times speed defines your raw power. Still, you need to modify it by the efficiency of your drive system. This is often somewhere between 60% and 80% (0.60 and 0.80). For this example, ε=0.75.

One more thing, we need to use a safety factor (often SF=1.3 to 1.5). For this example,

Sf = 1.3. Putting it all together,

Sf . (Ftot . v) / ε = 1,945 hp

We would choose a 2 hp motor.

• Rule of Thumb Method

In many cases, we don’t need to spend all the time doing the full math.  We might need a good estimate or maybe we want a sanity check of the full math. We use modifier to the raw power of 2.

2. 550 lbf . 1 (ft / s) = 2 hp

Notice that both methods give us the same answer? They should. That’s why Rules of Thumb are used. They are approximately right most of the time.

Bob Adams, Responsable Technique USA chez SERAPID

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