# B Force at which a cutting disk comes off from an angle grinder

#### jra12222

Hi all,
This is not exactly a homework question, more like for my own safety
So I have a project going on and I need to use an angle grinder without the safety guard which will be enclosed in a box (made from plastic most probably).
So I decided to check if the plastic box would be able to withstand the impact of the cutting disk (6'') should it break.

I decided to assume a worst case scenario where the whole disk comes off at 12000rpm.
I am assuming it has a mass of about 50g.

After converting this to angular velocity I got 1256 rad/s
I was considering F=ma where a=r⍺
⍺= change in angular velocity/ change in time.
Now this is where I got stuck, should I consider a change of 1256 rad/s in 1s?
thus having an angular acceleration of 1256 rad/s^2?

Also as for the radius, should I consider the distance which the disk will need to travel until it hits the box?

Thanks a lot

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#### gneill

Mentor
Grinding wheels typically shatter when they fail. So think lots of bits flying off tangentially, some larger, some smaller.

If you consider a worst case scenario where the disk miraculously splits in two, half the disk will fly off in one direction and the other in the opposite direction. You might estimate their "departure" speed as the speed of their centers of mass at the time of fracture. You'll need to find the center of mass of a half-disk to determine the radius at which the center of mass lives, hence it's tangential speed.

Also as for the radius, should I consider the distance which the disk will need to travel until it hits the box?
Probably not. The speed of the projectile is not going to change much over a relatively short distance (what, a half meter or so?). If the box is kilometer sized, my answer will change

Your problem is going to be dealing with the actual impact. I don't have any experience in materials strength with regards to impacts. Perhaps another forum member will jump in.

#### sophiecentaur

Gold Member
Unfortunately the thread title is a bit of a non-starter. Things flying through the air do not have a "Force". They have Momentum and they have Energy due to their speed (and rotation). The Force involved in any collision will depend on what they collide with; the longer it takes to bring an object to a halt, the less the impact force. You could absorb the energy of the flying parts in a totally safe way by having a thick padded jacket or (as in a ballistics lab) a tank of water. A containment case, consisting of just a skin of plastic or metal would take a long time to dissipate the energy of the flying parts and they would probably emerge from the gap where the disc is exposed with hardly any reduction in velocity (bearing in mind they would impact the shield almost tangentially.
Careful Machinists always stand aside from a bench grinder when it is first switched on because that's the time when grinding wheels tend to shatter. Using a disk for the purpose it's supplied for is also a good idea. Some discs are specified for cutting only so you need to avoid lateral pressure on them. (I am point this out as the usual PF Health and Safety response.)

#### jra12222

Thank you both for the reply,

speed of the projectile is not going to change much over a relatively short distance
With respect to the distance it has to travel this will be even less so I'll take it as negligible.

Things flying through the air do not have a "Force". They have Momentum and they have Energy due to their speed (and rotation).
As both of you pointed out it's the impact force which I need to take into consideration, and to be honest with you I did think about it, however when going through a datasheet of a certain perspex (just for reference) what you are given is the Charpy impact test which is given in the form of energy, i.e. in KJm^2

However can I just compare this to the kinetic energy which is measured in Joules?

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#### sophiecentaur

Gold Member
However can I just compare this to the kinetic energy which is measured in Joules?
Calculating a ballpark figure for Kinetic Energy is straightforward but the Force on a guard will depend on how much the guard will move / distort when hit.
Kinetic Energy is converted to Work (force times distance). There's another issue and that is what happens to the energy that's converted. The energy needs to be dissipated - probably by distorting the guard.
The problem has been addressed many times before by machine tool manufacturers and I would suggest looking at existing designs and finding the materials they use. To be sure of investigating this from scratch and of getting a safe arrangement, you would need to do some actual testing which would be long winded and expensive. This will be a rare occurrence so assuming the guard is damaged / destroyed would be reasonable. That would absorb loads of energy.

#### gneill

Mentor
Calculating a ballpark figure for Kinetic Energy is straightforward but the Force on a guard will depend on how much the guard will move / distort when hit.
I notice also that the units of the Charpy Impact Strength are kJ per square meter. So how the chunk hits (flat on, rounded edge, pointy bit) can have a big influence.

#### jra12222

OK so just a small recap;

1. I need to find the center of gravity and the tangential velocity,
2. I need to determine the kinetic energy
3. Look into possible case studies of how this energy can be dissipated
4. Finally I need to find materials which can be used for a worst case scenario where the cutting disk hits the guard on a pointy edge.
Just a side note, and currently not based on any research, I doubt that plastic (such as perspex) would be able to withstand such force right? I'm asking this because preferably the guard is not opaque such as metal.

Thanks a lot to both of you!

#### sophiecentaur

Gold Member
Bottom line here is that, in a matter of safety (of sight or of life even) you should learn from the experts who can expect court proceedings if their designs lead to injury.
The KE calculation can be reduced to, say 1/4 the mass of the disc, travelling at around the tangential speed of the disc. That's easy peasy. You could see hows your calculations tie in with the numbers in that table of yours if you had, say a 10mm square contact area. I found a good evening's worth of links with a quick google search of ISO 179. Happy reading.

#### berkeman

Mentor
So I have a project going on and I need to use an angle grinder without the safety guard which will be enclosed in a box (made from plastic most probably).
Why did you remove the safety guard from your angle grinder? I know why I removed it from my table saw, but I don't see an advantage to doing it on an angle grinder. And will your hands be in the box? Or will there be some other way to support and guide the angle grinder while it is in the box?

https://cdn2.tmbi.com/TFH/Step-By-Step/display/FH03JUN_UTANGG_11.JPG

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#### Steelwolf

From experience with the equipment, having been a Navy trained Welder and ran a swordmaking business myself, but a 6" grind wheel, anglehead grinder like that, the wheel is typically 1/4 inch thick, and 3" of that 6" is hub with paper and metal backing holding it solid. When it breaks it tends to do so in 1/3 to 1/6 of the diameter of the wheel chunks, only about 1 1/2 inch wide.

So, at 12000 rpm with 6" dia is:

12000 X (.5 X Pi) / 60= ~314 ft/sec for a piece of grindstone that is about 1/4 inch thick by 1 1/2 inch by 3 or 4 inches long at around 314 ft/sec

Something like 1/2 inch sheetrock like for housing would help protect plastic in areas you dont Have to see thru, and will absorb the impact with minimal damage and bounceback. High temp sheetrock is available as well.

Keeping hold of the grinder while unstabilised due to the broken wheel is a fun trick too, so please use all safety precaution for what you are grinding on and with.

#### sophiecentaur

Gold Member
@jra12222 Be a good boy and listen to your uncle Steelwolf.

#### jra12222

its not that simple :P

Ok so I actually need to remove the guard because I was thinking of using a 6'' cutting disk on a 5'' angle grinder, meaning that it wont fit. I need to do this because I plan on cutting a PVC pipe held in place with jaws whose diameter is 40mm. However the gearbox eats up about 20-30mm by itself thus a 5'' cutting disk would not suffice.

And will your hands be in the box?
No my hands will not be in the box, I plan to use a pneumatic cylinder and 2 linear rods to guide the angle grinder in a downward movement.

I understand this may seem a bit too complicated just to cut a piece of PVC pipe however I need a bit in large quantity so this would help to make it faster.

#### sophiecentaur

Gold Member
Would it be suitable to use a coarse saw blade rather than a disc. PVC is very soft and it could melt with a disc. (Or even a jabsaw?

#### jra12222

That did cross my mind but any kind of saw (i tried jigsaw, oscillating multitool as well) would not result in a clean cut, while on the other hand a saw blade does not fit on an angle grinder...its inner diameter is slightly smaller

Mentor

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#### jra12222

I just wish to avoid performing any debarring.
Initially that's how I was cutting them but now I just need many more so this would be a good investment for me.

Also a side question, do you think it is wrong to use a 6'' cutting disk on a 5'' grinder? I tried searching the web for some information but got nothing, also in my opinion I think at most, I will be damaging the bearing but I dont believe there's any other problems.

#### sophiecentaur

Gold Member
6'' cutting disk on a 5'' grinder?
You could experiment dropping the volts a bit to reduce the speed of the oversized disc. I guess you've already tested the disc method under normal circs. I'm surprised the plastic doesn't melt. Angle grinding is a pretty savage process but I guess it works for you. A slower disc could be better for plastic in any case.

I'm sorry if all these suggestions are annoying you but it's PF style to (virtually) take over peoples projects. Sometimes it's actually helpful.

#### 256bits

Gold Member
I just wish to avoid performing any debarring.
Initially that's how I was cutting them but now I just need many more so this would be a good investment for me.

Also a side question, do you think it is wrong to use a 6'' cutting disk on a 5'' grinder? I tried searching the web for some information but got nothing, also in my opinion I think at most, I will be damaging the bearing but I dont believe there's any other problems.
Well yes. there is a danger since the 6-inch is rated for a lessor rpm than the 12000 rpm the 5-inch grinder puts out.
Which they usually are.
Overspeed of the disk, which is what you are attempting to do, is a setting up for disaster even with the enclosed box, since you are actually doing an experiment with no prior indication of how fragments will behave, fly off, and shatter, until they do. The centrifugal force on the disk increases with diameter.

from this site,
you will notice that the maximum grinding speed that they posit at the peripheral is 80m/s.

Larger wheels have lower maximum operating rpm in order to keep the grinding speed a the peripheral at the 80m/s.
The maximum operating rpm of the 5-inch ( 125 mm ) wheel is 12,200 rpm.
The maximum operating rpm of the 6-inch ( 150 mm ) wheel is 10,200 rpm.

If you do decide to go ahead, and any 6-ich disks are still operable after completion of your task, take the 6-inch disk(s) and break in two, so that it(they) will not be used again.

while on the other hand a saw blade does not fit on an angle grinder
Probably worse if the blade as a whole flies off at 12000 rpm.
You want to lose a whole foot??

Why don't you use the 5-inch wheel, and rotate the PVC pipe to have all the circumference cut?

#### jra12222

First of all a big thanks to everyone, you've been a big help!

I'm sorry if all these suggestions are annoying you but it's PF style to (virtually) take over peoples projects. Sometimes it's actually helpful.
Oh dont worry, I wouldn't have asked if I didn't want the suggestions! I did try to cut PVC with the cutting disk and it cut just fine, however no I have yet to test it with a 6'' cutting disk.

Thanks @256bits I honestly could not find any information! (In case that there is no such information written on the disk, I'm guessing these are universal right? they dont really depend on the brand of the cutting disk used)

I will test it with lower voltages as @sophiecentaur suggested.

Since I have no means to measure the RPM at which it is revolving, should I try to supply it with say 200V instead of 230V?

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#### gneill

Mentor
You might try a motor speed control, as they have for routers and table saws.

"Force at which a cutting disk comes off from an angle grinder"

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