Acceleration resistance in crane design

In summary: I got it.In summary, the equation for calculating acceleration resistance in crane design is derived from the definition of power and uses units of torque, angular velocity, and acceleration time. The constant 3.65 x 10^5 is used for unit conversions to kW.
  • #1
Ridzuan
19
1
Hi everybody
Does anyone familiar with this equation?

Acceleration resistance,
= {(load MOI/mech. efficiency) + (motor MOI) x rpm^2} / {3.65 x 10^5 x acceleration time}
= {(kgm^2/ƞ) + (kgm^2) x rpm^2} / {3.65 x 10^5 x second}

= final value unit is in kilowatt (kW)

It used to calculate the acceleration power for trolley and gantry in crane design. I am looking for the origin/principal of this equation... thanks guys
 
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  • #2
First, I would guess your equation should read:

{(load MOI/mech. efficiency) + (motor MOI)} x rpm^2 / {3.65 x 10^5 x acceleration time}

It comes from the definition of power ##P = T\omega##, where ##T## is the torque and ##\omega## is the angular velocity (i.e. rpm).

The torque, if converted entirely to acceleration, is ##T = I\alpha##, where ##I## is the mass moment of inertia and ##\alpha## is the angular acceleration.

The angular acceleration is ##\alpha= \frac{\omega}{t}##, where ##t## is the time.

So, ##P = T\omega = I\alpha \omega = I\frac{\omega}{t}\omega = \frac{I\omega^2}{t}##.

Thus ##I## = (load MOI/mech. efficiency) + (motor MOI), ##\omega## = rpm/2 and ##t## = acceleration time.

The constant 3.65 x 10^5 = ##2^2 \times 1000 \frac{W}{kW} \div \left(\frac{\pi}{30}\frac{rpm}{\frac{rad}{s}}\right)^2##. So it is for unit conversions. The ##2^2## is from ##\omega## = rpm/2, because the acceleration time is measured from 0 to rpm, so we used the average rpm during the process, i.e. rpm/2.
 
  • #3
Dear sir, thank you for your explanation. it is very helpful. I appreciate it so much.
just wonder, what came out from the (kgm^2 x rpm^2) / t... to be specific, what unit it produce that enable it to be convert to kW?
 
  • #4
The basic SI units of your formula are:
[tex]\frac{kg.m^2 \left(\frac{rad}{s}\right)^2}{s}= \frac{kg.m^2}{s^3}[/tex]
The basic SI units that define the Watts are:
[tex]W = \frac{J}{s} = \frac{N.m}{s} = \frac{\left(kg\frac{m}{s^2}\right)m}{s} = \frac{kg.m^2}{s^3}[/tex]
So you can see that they have equivalent dimensions, i.e. ##\frac{mass \times length^2}{time^3}##
 
  • #5
jack action said:
First, I would guess your equation should read:

{(load MOI/mech. efficiency) + (motor MOI)} x rpm^2 / {3.65 x 10^5 x acceleration time}

It comes from the definition of power ##P = T\omega##, where ##T## is the torque and ##\omega## is the angular velocity (i.e. rpm).

The torque, if converted entirely to acceleration, is ##T = I\alpha##, where ##I## is the mass moment of inertia and ##\alpha## is the angular acceleration.

The angular acceleration is ##\alpha= \frac{\omega}{t}##, where ##t## is the time.

So, ##P = T\omega = I\alpha \omega = I\frac{\omega}{t}\omega = \frac{I\omega^2}{t}##.

Thus ##I## = (load MOI/mech. efficiency) + (motor MOI), ##\omega## = rpm/2 and ##t## = acceleration time.

The constant 3.65 x 10^5 = ##2^2 \times 1000 \frac{W}{kW} \div \left(\frac{\pi}{30}\frac{rpm}{\frac{rad}{s}}\right)^2##. So it is for unit conversions. The ##2^2## is from ##\omega## = rpm/2, because the acceleration time is measured from 0 to rpm, so we used the average rpm during the process, i.e. rpm/2.

Dear Jack Action
You mentioning the 3.65 x 10^5 is constant for unit conversions to kW. i am unable to figure out what unit to be converted to kW. can you help me? thx
 
  • #6
The units in your formula are all basic SI units (kg, m, s), except for rpm. Once you converted rpm to rad/s (see post #2), you have all SI basic units. In the end, the final SI unit is kg.m2/s3. In post #4, I showed that 1 kg.m2/s3 = 1 W. Then in post #2, W is converted to kW.
 
  • #7
jack action said:
The units in your formula are all basic SI units (kg, m, s), except for rpm. Once you converted rpm to rad/s (see post #2), you have all SI basic units. In the end, the final SI unit is kg.m2/s3. In post #4, I showed that 1 kg.m2/s3 = 1 W. Then in post #2, W is converted to kW.
Thanks Jack
 

1. What is acceleration resistance in crane design?

Acceleration resistance in crane design refers to the ability of a crane to withstand and safely operate under the forces of acceleration, which can occur due to factors such as wind, load changes, and sudden movements.

2. How is acceleration resistance measured in cranes?

Acceleration resistance in cranes is typically measured in terms of acceleration limits, which are specified by the crane manufacturer. These limits indicate the maximum acceleration that a crane can safely withstand without compromising its structural integrity or safety.

3. What factors influence acceleration resistance in crane design?

The main factors that influence acceleration resistance in crane design include the crane's structural design, materials used, and operational conditions such as wind speed and load capacity. Additionally, factors such as maintenance and wear and tear can also impact a crane's acceleration resistance over time.

4. How can acceleration resistance be improved in crane design?

To improve acceleration resistance in crane design, engineers can use stronger and more durable materials, optimize the structural design to better distribute the forces, and conduct thorough testing and analysis to ensure the crane can withstand expected acceleration forces. Regular maintenance and inspections are also crucial in maintaining a crane's acceleration resistance.

5. What are the consequences of inadequate acceleration resistance in crane design?

Inadequate acceleration resistance in crane design can lead to several consequences, including structural failure, operational malfunctions, and safety hazards for workers and surrounding structures. It can also result in costly repairs and downtime for the crane. Therefore, it is essential to ensure proper acceleration resistance in crane design to ensure safe and efficient operation.

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