Question about a dynamic equation of a crane model

In summary: The spring starts to oscillate when the tension in the wire rope is equal to the initial spring force.
  • #1
Iqbal94
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0
Hi guys,

I have a question on the fundamental dynamic equation as I am not sure if my equation is correct. I am doing an analysis on a portal crane to find its application factor, somehow I couldn't get the desired value for the velocity of each masses as I couldn't find the tension of the rope. The portal crane model is simplified to be (picture).

http://[ATTACH=full]200070[/ATTACH]
 

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  • #2
Since it's a dynamic situation you have to get an idea of the frequency of oscillation at the spring and the rope separately (two sine waves). Probably the two won't be in sync so there will be constructive and destructive interaction. So the load in both the spring and the rope will change over time. There are available equations for doing this calculation. The static tension in the rope is ML X G. The static tension in the spring is the sum of the masses X G. When you move the crane the tensions will increase (acceleration of the loads, which you'll have to know), then the "springiness" will start the loads oscillating.

Your sketch isn't very clear. Is the crane lifting the load, translating the load, or both?
 
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  • #3
OldYat47 said:
Since it's a dynamic situation you have to get an idea of the frequency of oscillation at the spring and the rope separately (two sine waves). Probably the two won't be in sync so there will be constructive and destructive interaction. So the load in both the spring and the rope will change over time. There are available equations for doing this calculation. The static tension in the rope is ML X G. The static tension in the spring is the sum of the masses X G. When you move the crane the tensions will increase (acceleration of the loads, which you'll have to know), then the "springiness" will start the loads oscillating.

Your sketch isn't very clear. Is the crane lifting the load, translating the load, or both?
The crane is lifting the load. Yes, I have the frequency of oscillation at the spring. From the tests and analysis that I've done, I found out that there is only 1 frequency peek which is for the spring. I used steel rope/wire during the tests and I assume due to its rigidity, the frequency due to load on the spring can be neglected. Anyway, I would like to confirm either the lifting velocity of the crane is equal to the difference of velocity of load(x'load) and crane body(x'm1)

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or

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  • #4
The tension on a reasonably "rigid" rope would be equal to ML X G. You have the velocity of the lift correct. That's at steady lifting speed. If the load starts out static then there's addition tension in the wire rope due to acceleration of the load. There will be a fluctuating component equal to the oscillation rate and magnitude of the spring. That's because the load accelerates and decelerates with the extension and retraction of the spring.
 
  • #5
Hi, thanks for your explanation. I have one more question, is it possible to know when the spring will start to oscillate? Is it right after the load is lifted, or is there any circumstance that I need to take note? I'm not sure if my idea is right. But I think the spring starts to oscillate (the load as well), when the rope tension is equal to the initial spring force?
 

1. How does the crane model's dynamic equation work?

The dynamic equation of a crane model is a mathematical representation of the forces and motions involved in operating the crane. It takes into account factors such as the weight and mass of the crane, the load being lifted, and external forces like wind and friction. By solving this equation, we can predict the behavior of the crane and ensure safe and efficient operation.

2. What variables are included in the dynamic equation of a crane model?

The dynamic equation of a crane model typically includes variables such as the mass and inertia of the crane, the mass and position of the load, the length and angle of the crane's boom, and external forces like wind and friction. These variables can be adjusted to simulate different scenarios and determine the crane's behavior.

3. How is the dynamic equation of a crane model used in real-world applications?

The dynamic equation of a crane model is used in real-world applications to design and test cranes, as well as to train crane operators. By inputting different variables and conditions, engineers can predict how a crane will behave in different scenarios and make necessary adjustments to ensure safety and efficiency. Crane operators can also use this equation to understand the physics behind crane operations and make informed decisions while operating the crane.

4. Are there different types of dynamic equations for different types of cranes?

Yes, there are different types of dynamic equations for different types of cranes. This is because the design and operation of cranes can vary greatly depending on factors such as their size, weight capacity, and purpose. For example, the dynamic equation for a tower crane may be different from that of a mobile crane, as they have different mechanisms and functions.

5. How does the dynamic equation of a crane model contribute to crane safety?

The dynamic equation of a crane model plays a crucial role in ensuring crane safety. By accurately simulating the forces and motions involved in crane operations, engineers can identify potential risks and make necessary adjustments to prevent accidents. Crane operators can also use this equation to understand the limitations and capabilities of the crane, helping them operate it safely and efficiently.

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