The Great Rigid Blade Experiment

[AimlessWanderer]

This all started with claims of forces pushing the blade away from the cap. While we do not have anything like agreement on what those forces are, we do seem to have a broad conceptual agreement, and progress towards understanding what kind of elements might contribute towards that force.

While Grant does his thing, I'll have a look at the other side of the assumption. I'll explore what forces are acting to keep the blade in contact with the cap. This will be somewhat simplistic, as I won't be factoring for the cut outs at the centre of the blade, but a standard beam deflection calculation (transposed) should tell us how much force is needed to bend the blade to the arc of any given razor. I can get some rough measurements off a Jagger head so there is something reasonably common to base an example on.

This should (hopefully) tell what force is being exerted upwards against the cap at either side, and how much force skin and everything else would need to exert to shove the blade off the cap. I'll put the formulas here too, so anyone can scrutinise this in case I have transposed it incorrectly (which is quite possible - I'm out of practice). If anything is unclear, give me a nudge and I'll try to simplify it.

 

[AimlessWanderer]

W = load on each end of cap (N)
y = deflection at each cap support (mm)
l = distance between baseplate supports (mm)
c = distance outwards from baseplate support to cap support (mm)
E = Modulus of Elasticity
I = Moment of Inertia

 

[SiBurning]

13) There are no other factors increasing normal forces on skin/hair and blade
14) There is nothing to reverse the nett loading of the blade, and push the blade away from the supporting surfaces on the cap

This sounds like a conclusion to me, and seems to be at the heart of the disagreement.

 

[AimlessWanderer]

This sounds like a conclusion to me, and seems to be at the heart of the disagreement.

Quite possibly towards the start of it all, yes - but I wouldn't call it a conclusion. I couldn't identify any other factors to bulk up the opposing forces. Believe me, I have been looking to identify all the forces on both sides of the blade. If you can spot any fundamental errors on either side to lend a little clarity, go for it! We've got two strong characters here, both with differing experiences, not quite talking the same jargon, probably sometimes arguing about bits that we actually agree on, and both wondering why the other can't see what we see.

 

[AimlessWanderer]

View attachment 843342
W = load on each end of cap (N)
y = deflection at each cap support (mm)
l = distance between baseplate supports (mm)
c = distance outwards from baseplate support to cap support (mm)
E = Modulus of Elasticity
I = Moment of Inertia

I HAD transposed the equation wrong (I told you I was out of practice) and was scratching my head wondering why my calculation said that I needed 64N (6.5kg) to flex a razor blade

I figured it out eventually (the brackets should have been 6EI over c^2), and the force comes out at around 2.15N (roughly 220grams force), so that's approximately 110grams force per side of spring tension ...

... however ...

... once the blade is fully flexed, it is then clamped which complicates things further. We can ignore that for now though, and working purely on spring tension, you'd need to generate 1.08N of force (110 grams) on the outside of the blade to equalise the pressure on the cap, before the blade starts moving away from it. (if discounting the additional rigidity from the clamp).

DISCLAIMER: That's 110g/1.08N distributed evenly over the whole blade length. A smaller localised force might make part of the blade flex away in one area.

So far, we have identified about 8g

Also, I did a rough verification with kitchen scales. Sat the cap on the scales with thread upwards, placed the blade on top, and zeroed the scale. Placed the baseplate on and applied pressure to flex the blade, and the 220g is in the right ballpark. It was slightly less due to the cutouts in the middle, but I couldn't press accurately enough with my fingers to get a decent reading. As the clamp will significantly increase this anyway, I reckon 110g is a good enough start figure.

 

[SiBurning]

I find the whole question vastly complicated.

From "Cutting Characteristics Of Beard Hair"
"Blade angle did not affect the cutting stress noticeably."
This implies that any force from pulling on the hair would need to be either exactly perpendicular to the cutting direction, or negligible in comparison with the forward stress. The first seems hard to reconcile with a pulled hair. The second implies this is an insignificant effect. We seem to be left with a strictly geometric question: where is the blade clamped?

From "Observations on the Cutting of Beard Hair"
"The fact that the cutting force is less dependent on relative humidity than the shear or tensile modulus suggests that these moduli--even at a rate of 0.5 in./min--are not the predominant factors in beard hair cutting. Instead, the force to cut might be more closely related to stress propagation or to the creation of new surface area, than to the viscoelastic properties of the fiber."
He's anticipating a later result from chemistry that suggests chemical bonds across the width are reduced more than along the length as the hair gets wet. In other words, dry hair pulls easier, wet hair cracks easier. So there's other evidence to implicate stress propagation as the main mechanism of cutting hair, both mechanical and chemical, though that doesn't necessarily rule out the possibility that work is required to produce new surface area. Soft, pliable materials can cause significant friction along the back face, partly due to plastic deformation, and we haven't ruled out this possibility.

In many modes of cutting,including those mentioned above, both the rake face and back face do work.

The most likely mechanism of cutting is deformation followed by a crack that then leads the blade through wedge action. Once the cut forms, the stress changes suddenly, which could cause the blade to bounce. Since the change is usually a reduction in the force, this bounce would be in the opposite direction of the stress in the deformation phase.

We don't actually know which way the stress occurs once the cut starts.
There are three ways of applying a force to enable a crack to propagate:
Mode I crack – Opening mode (a tensile stress normal to the plane of the crack)
Mode II crack – Sliding mode (a shear stress acting parallel to the plane of the crack and perpendicular to the crack front)
Mode III crack – Tearing mode (a shear stress acting parallel to the plane of the crack and parallel to the crack front)

Here are some other considerations.
Deformation (longitudinal bending & pulling) and torsional behavior caused by the hair being unsecured.
Relief and application of stress due to the blade being unsecured.
We don't know the cutting mechanism: orthogonal, oblique, guillotine, slice-push.
Many of the parameters are affected by the speed of the cut, which can alter not only the magnitude of many of the forces, but also the mechanisms in some cases.

 

[Dovo1695]

I'm still trying to wrap my head around why my devette blade makes so much noise. It seems like it does not stay absolutely still against the cap, though I have as to what force might cause it. I posted a youtube clip a few pages ago of a nutcase shaving with a razor blade on a bolt to you a sense of the the sound, but the audio wasn't great. I realized that I had a pretty good Samson mic, so I figured I might try to capture the sound as I hear it when I'm shaving with my devette.

The link below is the sound my devette shaving about the same distance from the mic that it is from my ears. Sorry about the breathing, I tried to hold my breath as best I could. In the last 20 seconds when I slow down around the beard area, you get a much better sense for the metallic "tink" notes that sound less like vibration and more like the blade leaving the cap, and then springing back to clink against it. This usually happens when the razor gets to parts where the hair density increases around my chin area.

Sound of a devette - Clyp

I don't what, if anything, to make of it, but it does sound like the blade is not staying absolutely still against the cap. I don't have a clue what part is moving, or where, or by what force. Just thought I'd post it in case it makes sense to anyone else.

 

[WalterK]

C'mon guys, I just need an excuse to buy one of these things:

Or perhaps instead of going the deflection measurement route, some sort of "blade plucking" jig could be made and the vibrations measured with one of those musical instrument tuning tools (there are a bunch of smartphone apps that do this, but I have no idea how truly worthwhile they are)

I remember years and years ago on woodworking sites, guys were plucking their bandsaw blades until they got to a certain musical note to determine if they put the correct amount of tension on the blade.

 

[Raven Koenes]

I'm still trying to wrap my head around why my devette blade makes so much noise. It seems like it does not stay absolutely still against the cap, though I have as to what force might cause it. I posted a youtube clip a few pages ago of a nutcase shaving with a razor blade on a bolt to you a sense of the the sound, but the audio wasn't great. I realized that I had a pretty good Samson mic, so I figured I might try to capture the sound as I hear it when I'm shaving with my devette.

The link below is the sound my devette shaving about the same distance from the mic that it is from my ears. Sorry about the breathing, I tried to hold my breath as best I could. In the last 20 seconds when I slow down around the beard area, you get a much better sense for the metallic "tink" notes that sound less like vibration and more like the blade leaving the cap, and then springing back to clink against it. This usually happens when the razor gets to parts where the hair density increases around my chin area.

Sound of a devette - Clyp

I don't what, if anything, to make of it, but it does sound like the blade is not staying absolutely still against the cap. I don't have a clue what part is moving, or where, or by what force. Just thought I'd post it in case it makes sense to anyone else.

The physics is certainly interesting, but once again I'll point back to field experience. I agree all pressure tends to the cap. Perhaps it tends towards the cap? Tend being the opertive word in a razor that's not fully supported equally from the baseplate and top cap at an equal distance? I would think that would increase the possibility of any vibration causing flutter however small.

 

[Esox]

Is there any agreement about any force that could move the blade away from the cap?

I've been thinking on this a while now, a great while actually lol.

While not the same forces at work, the same principle applies I think. One may not think the cutting edge of a DE blade would flex and/or deflect as it passes through a hair. One may also think that a high velocity rifle bullet will not deflect while it passes through a pane of window glass, but they do. Sometimes with drastic results and a complete miss.

For sniper training in urban environments its taught of out necessity that when shooting through glass at a target, the aiming point must be adjusted for angle as well as thickness of the glass pane the bullet will be passing through along with other factors such as, bullet velocity, weight, sectional density and ballistic coefficient, target distance from glass etc, none of which really applies to razor blades.

The closer to 90 degrees the less adjustment needs to be made. The further from 90 degrees the more adjustment needs to be made, because as angle increases, the effective thickness of the glass increases and so does the resistance met increasing that deflection.

Since I never had any thoughts of shooting through glass at anything, its not something I've really explored, but I did many years ago learn about it.

In the above diagram, think of the bullet fired from outside as the blade edge and the pane of glass the hair. The cap being above the blade and the blade edge deflecting downwards as it passes through the glass or hair where the resistance is highest.

Gunfighting Science: Shooting Through Glass

http://www.dtic.mil/dtic/tr/fulltext/u2/a283575.pdf

If a high velocity bullet can deflect like that, so can most anything else when it meets, and travels through, resistance. How much that may matter relating to DE blades and shaving I cant say. The physics is real however.

Mike needs the blade to be rigidly held, and so do I. Rigidity increased a great deal when my P-BOCS handle was very tight. If that doesn't matter to you, it's fine.

Of course, I could have an atypical P-BOCS. I've only tested the one I own.

The thing about the PAA BOCS is its basically plastic. I dont know how their made, injection molded whatever, but I'm sure because of the material they're made from and the process of making them, the razors will vary. I'm not thinking those razors to be especially precisely made to the same tolerances of say a Fatip. Each will be an individual and one may need a really tight handle and another may not.

 

[Dovo1695]

Sound of a devette - Clyp

I don't what, if anything, to make of it, but it does sound like the blade is not staying absolutely still against the cap. I don't have a clue what part is moving, or where, or by what force. Just thought I'd post it in case it makes sense to anyone else.

Does anybody else hear that metallic "ting" or "ping" note? It's not the hairs making that sound. I can change the volume and pitch of it by changing just the base plate (hairs stay constant). The blade is moving. Sound can't occur with movement.

So here we have empirical evidence that the blade is moving, however minutely, in however small an area, for however short a period of time. Let's work with that. What empirical test could be undertaken to better understand what is causing the sound, and therefore the movement?

@WalterK has proposed at least one interesting tool. How could we use it, or something else to make sense of the only empirically observable and quantifiable phenomenon related to blade movement?

I'm not knocking physics or geometry in the least, or suggesting we shouldn't use it, I'm just trying to figure out how else we might approach the problem empirically in conjunction with the physics.

Or perhaps instead of going the deflection measurement route, some sort of "blade plucking" jig could be made and the vibrations measured with one of those musical instrument tuning tools (there are a bunch of smartphone apps that do this, but I have no idea how truly worthwhile they are)

I remember years and years ago on woodworking sites, guys were plucking their bandsaw blades until they got to a certain musical note to determine if they put the correct amount of tension on the blade.

 

[Esox]

Pogonotomy? It's not a word.

Oh but it is, and quite relevant too! LOL.

"pogonotomy in British. (ˌpəʊɡəˈnɒtəmɪ) the cutting or shaving of a beard."

Pogonotomy definition and meaning | Collins English Dictionary

 

[Chan Eil Whiskers]

Pogonotomy? It's not a word. That's the sound a cry for help makes as one slips down the rabbit hole of RAD. Perhaps it's an onomatopoeia? I'm not the first to use it though since some poor soul before me uttered something similar once, and it was recorded by Mssrs. Merriam & Webster...

Definition of POGONOTOMY

Word or sound, it proves we're not the first members of .

Happy shaves,

Jim

 

[SiBurning]

For me, the important question is whether the blade is singing in ecstasy or screaming in agony? And in what key?

Could we do something with a high speed camera? We could record the sound at high resolution and run the file through a software analyzer. That might give us an idea of the physical movement. By ear, the sound seems too high to capture on a normal camera, so we might need a very high speed camera to capture the actual movement. This could be done on an artificial surface at first to get a feel for things.

 

[SiBurning]

Does anyone have a razor where some appropriate damping material could be used between the blade & cap? I'd like to know how the sound and the shave changes. Perhaps a few milimeters of rubber?

 

[SiBurning]

From "Cutting Characteristics Of Beard Hair"
"Blade angle did not affect the cutting stress noticeably."
This implies that any force from pulling on the hair would need to be either exactly perpendicular to the cutting direction, or negligible in comparison with the forward stress. The first seems hard to reconcile with a pulled hair. The second implies this is an insignificant effect. We seem to be left with a strictly geometric question: where is the blade clamped?

Now that I've gone over my old notes, and had some time to think this over, I'll put out my first thoughts.

The main force is going to be the cutting force because it almost always is: lateral and tangential forces are typically half or less for most forms of cutting. The quote above seems to suggest that these forces are negligible. It then becomes a question of geometry. Apply the force along the direction of the cut and it's pretty clear where it goes.

But if we're talking about blade rigidity, do we really care about the steady-state? I think not. So all the other considerations could come into play. Or am I confusing rigidity with real-time stability?

 

[AimlessWanderer]

Now that I've gone over my old notes, and had some time to think this over, I'll put out my first thoughts.

The main force is going to be the cutting force because it almost always is: lateral and tangential forces are typically half or less for most forms of cutting. The quote above seems to suggest that these forces are negligible. It then becomes a question of geometry. Apply the force along the direction of the cut and it's pretty clear where it goes.

But if we're talking about blade rigidity, do we really care about the steady-state? I think not. So all the other considerations could come into play. Or am I confusing rigidity with real-time stability?

If we take my earlier calculations, and call it a nominal 1N of spring force (discounting actual clamping), I can't see how greater forces in the opposing direction are going to happen.

Add in your comments here, and we can be pretty sure the blade isn't going to be shoved off the cap. If we're fairly confident of that, it means we only need to look at the blade beyond it's last support point - or do we?

What does this leave as potential effects of "lack of rigidity"? Vibration? Flex after last support point? Edge flex vs full thickness flex?

It might also be worth considering the shaving angle of the razors claimed to be rigid vs less rigid, or blade gaps, as these might be increasing blade loading in comparison to the others - higher load rather than less support, or more vibration from "strumming" angle.

 

[SiBurning]

It's not clear to me that the blade can't wobble off the cap. As analogy, I'm thinking how you can move a heavy box by wiggling it. Maybe one point of the box always remains on the floor, or maybe not, but some of it does come off. I don't know quite how to relate this to a typical DE. Maybe the blade just vibrates about some point where it touches the cap, but if the contact is larger than a point, the blade can at least partly come off the cap just like the box. If it does wobble, either it either leaves every point that touches the cap (at various point in time), or there's a specific pivot point. I could see this depending on exact design of the razor. Either alternative would affect the singing question, though I suspect one would have a purer pitch.

BTW, it's not clear to which questions we're trying to answer--it's a very long thread.

 

[AimlessWanderer]

It's not clear to me that the blade can't wobble off the cap. As analogy, I'm thinking how you can move a heavy box by wiggling it. Maybe one point of the box always remains on the floor, or maybe not, but some of it does come off. I don't know quite how to relate this to a typical DE. Maybe the blade just vibrates about some point where it touches the cap, but if the contact is large than a point, the blade can at least partly come off the cap just like the box. If it does wobble, then it either leaves every point that touches the cap at some point, or there's a specific pivot point. That might depend on the exact design, and could affect the singing question.

BTW, it's not clear to which questions we're trying to answer--it's a very long thread.

I think we're both of the same (or similar) thinking here. As I mentioned above, 1N would be needed to shove the whole blade off, but a localised (smaller) force could certainly shove some of it off. That said, vibration might be more likely to disturb full contact.

The question as I understand it, is what does a lack of rigidity do? If the effect of not being rigid is known, it's easier to determine what is rigid and what isn't .... or at least that was a question somewhere along the line. There was talk about razors that rely on spring tension not being as rigid as clamped blades, and of the blade coming away from the cap. Based on the exercise with the Jagger head, the whole blade coming away from the cap is highly unlikely - but may be possible in localised areas, but if so, how? Vibration might be more feasible, but you'd still need a heck of a lot of vibration to get the blade off the cap. That might not happen at all, and maybe it's just the distance forward of last support that's vibrating.

 

[SiBurning]

Don't think of it as physically coming off the cap. Rather as a wave going through the blade, maybe causing increased & decreased pressure, maybe causing almost microscopic localized separations. Either way, I'd think it would act as if it wasn't rigid. And either way should be enough to produce sound. Maybe there wouldn't be any sound at all at 20N, at least none caused by that part of the blade, corresponding to a highly rigid state. And maybe even at 1N the sound only ever comes from the part that sticks out, but I doubt that.

High speed cameras? Fourier transform of the sound? A fourier transform converts from amplitude to frequency, so we can see the set of frequencies at each point in time. From there we might be able to figure out which piece of metal is vibrating. There's software that can do the transform on a WAV file.