- #36
Al_Pa_Cone
- 143
- 0
For this I hav tried to make my answer clear by adding a statement to the bottom of the graph, The statement is as follows:haruspex said:For ii), you write that increasing the angle reduces the power. Again, it does not necessarily reduce the actual power; it reduces the maximum power.
For the graph, you need to be clear on what is kept constant. E.g. if the geometry is fixed then the tension sum is fixed.
Here is a plotted Graph showing the results of the changes effected by the coefficient of friction and the change in pulley groove angle on the ratio of tension. The middle results 24.13 and 15.06 represent the original measurements taken prior to changes. Then to the left is a positive change to the coefficient of friction which reflects a rise in maximum power transmitted. To the right represents the change in groove angle as increasing this decreases the maximum power transmitted. They both run parallel to the final power transmitted proving therefore, a negative change to the ratio of tension reflects a negative change to the power transmitted to the second pulley and a positive change will also reflect a positive power output.
haruspex said:15057.02W should be rounded to 15.06kW, not 15.05
Good spot, I should have noticed that one!
haruspex said:For the calculation of max torque without changing friction, and limited by breaking tension/2:
It follows from my preceding remarks that in order to achieve this maximum the geometry would have be adjusted so that the sum of the tensions is 8000+331.54N. That is, under zero load, the tension would be (8331.54/2) N throughout.
From the question:
(b) What would be the effect of the following factors on the maximum power which can be transmitted (give reasons for your answer):
(i) increasing the coefficient of friction
(ii) increasing the included angle of the pulley groove.
I have tried to follow an example question in the lesson and work through my results by substitution of the known figures:
I have Highlighted in the red boxes, The figure which is given to me as the ultimate strength of the belt? So 8000N in my case. Following the method provided for working this out:
In my method I substituted the coefficient of friction, and increased the pulley groove angle to obtain the results. Would I have been better off reworking the soloution without using the ultimate strength as my starting value?
and finally:
haruspex said:Sorry for the delay, wanted to get my thoughts clear on this...
I still have a quibble with the answer to b. Increasing the friction coefficient does not in itself increase the tension ratio; it only increases the maximum ratio that can be obtained. I.e. it allows you to increase the load.
The belt is elastic. The total of the two tensions is governed by that coefficient and the ratio between the belt's relaxed length and its path length around the pulleys. If the load is increased it will increase the difference in the tensions, keeping the total constant, and thus increase the ratio.
Note that if the higher tension is already at its max to avoid breaking, but there is plenty of friction coefficient, the way to increase the load that can be handled is to slacken the belt.
Likewise, in your answer to d, the causality is not quite right. You write it as though increasing the ratio makes the slack side slacker. You also imply that the stronger frictional grip makes the slack side slacker. Neither is the case. The stronger friction increases the maximum possible ratio, not the actual ratio. That allows you to increase the load. The increased load increases the tension difference, and hence the actual ratio.
I'll take a closer look at your equations.
I have changed my statement, included some of your text and I think It may now be ok?Solution:
The coefficient of friction is governed to a mainly by the fact that a pulley
surface has to be mostly smooth or the belt would wear too quickly.
There are semi-liquid compounds available which can help preserve belts and to make the belt surface 'sticky' so that the coefficient of friction will remain at a reasonable value.
If the coefficient of friction was improved by this change, as it increases resistance in the contacting surfaces of the belt and the pulley, it increases the maximum ratio of tension that can be obtained. I.e. it allows you to increase the load. This would reflect a positive increase in the effective tangential force
The total of the two tensions is governed by that coefficient and the ratio between the belt's ‘slack’ side and its ‘tight’ side around the pulleys. If the load is increased it will increase the difference in the tensions, keeping the total constant, and thus increase the ratio.
It is understood that more power is transmitted if the 'effective tension', i.e. the difference in tension between the tight and slack sides of the belt (F1 - F2) can be increased