Is my power calculation correct?

In summary, the goal of this design is to move a 1000 kg weight using a steel rope/pulley system. The power requirement is calculated to be 102 watts.
  • #1
FAlonso
112
4
I am currently working on designing a conveyor for feeding 1t material to a furnace. Not going into detail of how it works, I would just like to confirm my approach.

Goal: To move 1000 kilograms of mass using steel rope/pulley system. Determining power requirement

It would be a bucket mounted on two wheels running at a very low speed (0.3 m/s) over a mild steel I-beam. From literature around the internet, friciton values are:

mild steel on mild steel (0.74 static, 0.6 dynamic)
rail wheel on steel rail rolling resistance 0.0020

I am calculating power as follows:

Speed desired: 0.3 m/s
Time to achieve the speed: Not important but taking it to be 1s
Mass to be moved: 950 kg + bucket assembly (~50 kg) = 1000 kg

Friction to be overcome while driving: 1000 x 9.8 x 0.002 = 19.6N (2 wheels so 39.2N)
Force to move the mass from rest: F=ma > F=1000 x (0.3-0/1s) = 300N

Total force= 340N

Power required: F x v = 340 x 0.3 = 102 W or 0.13 hp

Am I missing something ? I am a bit skeptical about finding force required to move the mass from rest as it uses the static friction value of 0.72 which makes the required power go up by a large amount.

Regards
 
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  • #2
Stiction is a bear! That is the problem that you are facing here. If you want a realistic solution, you dare not use anything but the static coefficient of friction, and then give yourself a wide margin of extra power to overcome difficulties. Friction is extremely hard to prediction, and when it works against you, it can kill you!
 
  • #3
I went to market and found a winch with 5hp that according to the shopkeeper, people purchase for holding 1000 kg vertically. In my case, the load is moving horizontally. So the 5hp is surely more than my requirement I guess.
 
  • #4
It really depends. Can you tell yourself with certainty that μstatic ≤ 1? If not, then the frictional resistance could exceed the weight, and this winch may not be enough. A great deal depends upon the surfaces that are in contact - the material being moved and the stationary support surface - and you have not given much information about them. You are the design engineer. Just do what you have to do, and move ahead.
 
  • #5
Thanks for the advice. I will surely do some experimentation to determine the band of values in which the u(static) and u(rolling) falls. Rest I hope my approach is ok ? Just for counter-check
 

1. How do I know if my sample size is sufficient for my power calculation?

The best way to determine if your sample size is sufficient is to conduct a power analysis. This will take into account factors such as the effect size, alpha level, and power level to determine the minimum sample size needed to detect a significant effect. If your sample size is below the recommended number, you may need to consider increasing it to ensure adequate statistical power.

2. What is the significance of the alpha level in power calculations?

The alpha level, also known as the type I error rate, is the probability of rejecting the null hypothesis when it is actually true. It is typically set at 0.05, meaning that there is a 5% chance of falsely rejecting the null hypothesis. The alpha level is important in power calculations because it affects the required sample size and the probability of detecting a significant effect.

3. Can I use a power calculation to determine the sample size for any study?

No, power calculations are only applicable for studies that have a specific hypothesis and statistical test. They cannot be used for observational studies or studies with non-parametric tests. Additionally, power calculations assume that the data follows a normal distribution, so they may not be accurate for studies with skewed data.

4. How accurate are power calculations?

Power calculations are based on assumptions and estimates, so they are not 100% accurate. However, they provide a good estimate of the minimum sample size needed to detect a significant effect. It is important to keep in mind that other factors, such as the quality of data and variability in the sample, can also affect the power of a study.

5. Can I adjust the power level in my calculation?

Yes, the power level can be adjusted in power calculations. The most commonly used power level is 0.8, which means there is an 80% chance of detecting a significant effect if it truly exists. However, some researchers may choose a higher power level (e.g. 0.9) to increase the chances of detecting an effect, especially if the consequences of a type II error (false negative) are high.

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