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Re: Measuring the diameter of fans can be tricky..
Jack,
Thanks for your email response to my question above. I tried to respond by email but was bounced by your email server. This forum appears to be the only venue to address your explanation. In fairness to you, the following is a quote from your email.
__________________________________________________ _______________
quote:
Geometric symmetry isn't a hard requirement for balance and there are two aspects to balance: (1) in the plane of rotation, and (2) orthagonal to the plane of rotation.
You can trim for both even with blades spaced asymmetrically around the circumference of the spider. If fact, if you don't, you wind up 'beating' the water pump's shaft against its bearing and/or causing the shaft/impeller to 'thump'.
The offsets to asymmetric blade placement around the hub are twofold: (1) skew the length of selected blades to adjust individual moment arms from the rotational center and compensate for asymmetric blade placement,
and (2) skew the pitch of selected blades so their slightly different air 'drag' contributions compensate for the asymmetry.
end quote
__________________________________________________ _______________________
I don’t pretend to be brilliant and I probably should just take Mikie’s advice and chill on the couch and forget the whole thing… but I'm still struggling. I respect your contributions here. You are a very smart person. My “cred” on this board is way less than the cube root of your “cred”, but I’m afraid I don’t follow your logic on this. Your statements above are just…statements? Admittedly, it’s been a very long time since I took a class in analytical geometry but here is my take on the topic.
Bear with me, this is long and I’ve tried to keep it easy simple enough that my 6 grade daughter could understand.
The question here is about finding the center of gravity (cg) for the entire fan assembly and what affect grinding material off of any given fan blade has on its rotational balance. To break this down, let’s call each of the 5 blades on a fan assembly an “individual blade arm”. Each of these 5 blade arms have an individual weight that rotates about the fans center. We will call this the “rotational mass” for these blade arms. Because we have 5 blade arms, we have 5 individual rotational masses. When we add all 5 together, we have the total weight or mass of the fan.
Additionally, with each blade arm there is a single point that we can call its own individual cg. Where as in theory, if we were to remove the blade arm from the assembly and place it on the head of a pin, it would rest in a state of equilibrium. Let us mark this point, reinstall the blade arm to the assembly, and then we measure the distance from the cg to the fan assembly’s rotational center. (hard to do because it is a point in the center of the hole) This distance is the “moment arm” for this particular blade arm’s rotational mass. Because we have 5 blade arms, we have 5 individual moment arms. (one for each rotational mass).
We now draw a representation of our fan assembly on a X, Y grid coordinate system with the rotational center of the fan at X=0, and Y=0. The cg of each blade arm would be represented by a point clocked about the center of the grid (point 0, 0) as it is on the actual fan and at a distance from (0, 0) that is equivalent to the moment arm of its respective blade arm. We now have 5 points on the grid, each with a representative value for X and Y. Some points will have negative X or Y value and at least one will likely have both a negative X and Y value.
To determine the cg for the entire fan assy, we must add all values of X for the 5 points and all value Y for the 5 points. The resultant summation of the X, Y coordinates is considered the center of gravity for the entire fan assembly. The distance that this point is from (0, 0) represents the value for the rotational mass of the “out of balance” weight for the fan.
In your email response you stated that a person could “skew the length of selected blades to adjust individual moment arms from the rotational center and compensate for asymmetric blade placement”.
I would contend that no small amount of material removal from any given blade arm assembly (alteration of both rotational mass and moment arm) or no small amount of material removal from any given combination of blade arm assemblies would result in a “balanced” fan whereby it’s center of gravity would now reside at X=0 and Y=0 on the grid.
What this means is there will always be some constant final “rotational mass” whirling about the water pumps center shaft on some constant “moment arm”. Furthermore, this out of balance condition will produce a rotational side loading of the bearing rather than a “beating or thumping” condition as you described. (imagine a ball bearing on the end of a string of fixed length whirling around and around about your hand).
When all the calculations are complete, this side loading will have less affect on bearing wear than an over tightened fan belt. Bearings are designed to accommodate some degree of side loading.
You also stated that a person could “skew the pitch of selected blades so their slightly different air 'drag' contributions” to compensate for the blade asymmetry”.
I would contend the increasing or decreasing the pitch or drag element would have no affect on the rotational side loading of the bearing or the balance of the fan. The rotational mass “is what it is” and alteration of the blade drag will only affect the amount of horsepower consumed during the rotational process.
Thanks for reading I feel better.
tc
Jack,
Thanks for your email response to my question above. I tried to respond by email but was bounced by your email server. This forum appears to be the only venue to address your explanation. In fairness to you, the following is a quote from your email.
__________________________________________________ _______________
quote:
Geometric symmetry isn't a hard requirement for balance and there are two aspects to balance: (1) in the plane of rotation, and (2) orthagonal to the plane of rotation.
You can trim for both even with blades spaced asymmetrically around the circumference of the spider. If fact, if you don't, you wind up 'beating' the water pump's shaft against its bearing and/or causing the shaft/impeller to 'thump'.
The offsets to asymmetric blade placement around the hub are twofold: (1) skew the length of selected blades to adjust individual moment arms from the rotational center and compensate for asymmetric blade placement,
and (2) skew the pitch of selected blades so their slightly different air 'drag' contributions compensate for the asymmetry.
end quote
__________________________________________________ _______________________
I don’t pretend to be brilliant and I probably should just take Mikie’s advice and chill on the couch and forget the whole thing… but I'm still struggling. I respect your contributions here. You are a very smart person. My “cred” on this board is way less than the cube root of your “cred”, but I’m afraid I don’t follow your logic on this. Your statements above are just…statements? Admittedly, it’s been a very long time since I took a class in analytical geometry but here is my take on the topic.
Bear with me, this is long and I’ve tried to keep it easy simple enough that my 6 grade daughter could understand.
The question here is about finding the center of gravity (cg) for the entire fan assembly and what affect grinding material off of any given fan blade has on its rotational balance. To break this down, let’s call each of the 5 blades on a fan assembly an “individual blade arm”. Each of these 5 blade arms have an individual weight that rotates about the fans center. We will call this the “rotational mass” for these blade arms. Because we have 5 blade arms, we have 5 individual rotational masses. When we add all 5 together, we have the total weight or mass of the fan.
Additionally, with each blade arm there is a single point that we can call its own individual cg. Where as in theory, if we were to remove the blade arm from the assembly and place it on the head of a pin, it would rest in a state of equilibrium. Let us mark this point, reinstall the blade arm to the assembly, and then we measure the distance from the cg to the fan assembly’s rotational center. (hard to do because it is a point in the center of the hole) This distance is the “moment arm” for this particular blade arm’s rotational mass. Because we have 5 blade arms, we have 5 individual moment arms. (one for each rotational mass).
We now draw a representation of our fan assembly on a X, Y grid coordinate system with the rotational center of the fan at X=0, and Y=0. The cg of each blade arm would be represented by a point clocked about the center of the grid (point 0, 0) as it is on the actual fan and at a distance from (0, 0) that is equivalent to the moment arm of its respective blade arm. We now have 5 points on the grid, each with a representative value for X and Y. Some points will have negative X or Y value and at least one will likely have both a negative X and Y value.
To determine the cg for the entire fan assy, we must add all values of X for the 5 points and all value Y for the 5 points. The resultant summation of the X, Y coordinates is considered the center of gravity for the entire fan assembly. The distance that this point is from (0, 0) represents the value for the rotational mass of the “out of balance” weight for the fan.
In your email response you stated that a person could “skew the length of selected blades to adjust individual moment arms from the rotational center and compensate for asymmetric blade placement”.
I would contend that no small amount of material removal from any given blade arm assembly (alteration of both rotational mass and moment arm) or no small amount of material removal from any given combination of blade arm assemblies would result in a “balanced” fan whereby it’s center of gravity would now reside at X=0 and Y=0 on the grid.
What this means is there will always be some constant final “rotational mass” whirling about the water pumps center shaft on some constant “moment arm”. Furthermore, this out of balance condition will produce a rotational side loading of the bearing rather than a “beating or thumping” condition as you described. (imagine a ball bearing on the end of a string of fixed length whirling around and around about your hand).
When all the calculations are complete, this side loading will have less affect on bearing wear than an over tightened fan belt. Bearings are designed to accommodate some degree of side loading.
You also stated that a person could “skew the pitch of selected blades so their slightly different air 'drag' contributions” to compensate for the blade asymmetry”.
I would contend the increasing or decreasing the pitch or drag element would have no affect on the rotational side loading of the bearing or the balance of the fan. The rotational mass “is what it is” and alteration of the blade drag will only affect the amount of horsepower consumed during the rotational process.
Thanks for reading I feel better.
tc
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