Question about velocity and motors

In summary, the individual is seeking help with choosing an appropriate motor for a device that requires specific torque, power, maximum velocity, force, and acceleration. The motor specs provided are 0.304 Nm torque, 4000 RPM speed, 0.13 kW power, 60:1 gearing, and an inertia of .031 kg-cm^2. The individual is unsure of how to calculate the maximum velocity with the given parameters, but has come up with a potential solution involving kinetic energy and solving for velocity. They also mention a gearbox with 15:1 gearing and 1:1 pulleys with a 1" radius, and ask for tips or ideas to solve the problem. They also mention a deadline for
  • #1
_FES_
5
0
I'm working on choosing an appropriate motor. I have the calculations I need for the required torque, power, max velocity, force, and acceleration. Now I need to know the maximum velocity that a specific motor can move 159 kg 0.45 m across a horizontal plane.

In all of my calculations for which motor was needed, I neglected to take friction and inertia into consideration because I did not need to be so exact. The friction is quite minimal anyway. It is a seat moving along a metal rail.

The motor specs are as follows:

Torque - 0.304 Nm
Speed - 4000 RPM
Power - 0.13 kW
Gearing - 60:1 (15*4)
Inertia - .031 kg-cm^2

I don't yet know what the radius of the gear attached to the gearbox will be. I imagine something like 5 cm. I was told that the equation would involve something like (2pi*r(RPM))/15, but I don't know how that will work in with the power, mass, and distance when calculating the max velocity.

I was thinking if using 1/2*130*0.45 would be possible to use for the kinetic energy and then solve for v with 29.25=1/2*159*v^2. But again, I'm not sure how to work in the Speed and gearing of the motor.

I appreciate the help. If I'm missing any info, let me know.
 
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  • #2
Does anyone at least have some tips or ideas?

Thanks
 
  • #3
Update:

Gearbox is 15:1. Pulleys are 1:1.
Radius of pulley is 1"

The pulley's RPM speed is (circumference*RPM)/gearing, right? In other words, (2pi*4000)/15=1676 RPM. The torque would then be 0.304*15=4.56 Nm.

So then how do I get the maximum velocity of the 159 kg along 0.45 m that this setup can provide?
 
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  • #4
Hi FES, if this is your homework, it should go to the homework section.

Add a sketch or drawing if possible.

Think different, if you had to lift the same mass 0.45m in the vertical plane, frictionless and disregarding inertia, how would you solve the problem ? What would be the acceleration and kinetic energy ? And the maximum vertical speed ?

Now turn back to the horizontal plane and consider friction and inertia, what top speed would be attainable considering also the transmission efficiency?
 
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  • #5
Hi John,

Thank you for your response. No, this is not homework, this is real-world for my job. I simply am unfamiliar with working with motors and have not done physics in several years, so I am having a mental block. Unfortunately, I cannot disclose this device, but think of those Concept 2 rowers you would find in a gym.

I am running out of time. The motor guy will be in on Monday and I must have a spreadsheet complete with this same calculation for every motor in a certain class by then for my CEO.

Ergo, if you wouldn't mind feeding me a bit more than a crumb, I'd greatly appreciate it. I am thinking what I need to do is use Force=torque/radius and find the acceleration from there with F/m.

4.56 Nm/.0254 m=179.53 N
179.53 N/159 kg=1.13 m/s

1.13*0.45 m=0.51 s

Do the RPMs still need to factor in somewhere?

Thank you.
 
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  • #6
It looks like this is a gear\rack mechanism, a very simplified approach will be:

Considering the mass path is perfectly horizontal, negligible rotational inertia, no friction, starting at max power and max rpm...

Fmax = Tin x i x n / r

F -> Max Traction Force [N]
Tin -> Motor Input Torque [N.m]
i -> Gear ratio
n -> Efficiency
r -> Gear Radius [m]

amax = Fmax / m

amax -> Max Acceleration [m/s²]
m -> Mass

converting rpm -> rad/s => 1 RPM = 2*PI / 60s

w2 = w1 / i

w2 -> Gear speed [rad/s]
w1 -> Motor speed [rad/s]

vmax -> w2 x r

vmax -> Maximum Travelling Speed [m/s]

tmin = (2 x d / amax)^0.5

tmin -> Minimum Acceleration Time
d -> Travelling Distance [m]

P = Fmax x vmax / n

P -> Power [W]
 
  • #7
I typed up a lengthy reply that failed to post and is now lost, so all I will say is thank you for all of your assistance, John. I'm grateful!
 

1. What is the relationship between velocity and motors?

The velocity of a motor refers to the speed at which the motor can rotate. The higher the velocity, the faster the motor can rotate. This relationship is dependent on several factors such as the motor's design, power source, and load.

2. How does the voltage affect the velocity of a motor?

The voltage applied to a motor directly affects its velocity. A higher voltage will result in a higher velocity. This is because a higher voltage provides more energy for the motor to use, allowing it to rotate at a faster speed.

3. Can the velocity of a motor be controlled?

Yes, the velocity of a motor can be controlled through various methods such as pulse width modulation, changing the input voltage, or using a speed controller. These methods allow for precise control of the motor's velocity.

4. What is the difference between angular velocity and linear velocity?

Angular velocity refers to the rate of change of the motor's angular position, while linear velocity refers to the rate of change of the motor's linear position. This means that angular velocity measures how fast the motor is rotating, while linear velocity measures how fast the motor is moving in a straight line.

5. How does the load affect the velocity of a motor?

The load, or the force acting against the motor, can affect its velocity. A heavier load will require more energy for the motor to overcome, resulting in a slower velocity. Conversely, a lighter load will require less energy, allowing the motor to rotate at a faster velocity.

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