Functionality of the Collapsible Spacer

SydneyRoverP6B

Well-Known Member
Staff member
#1
The spacer is a mild steel tube with an outside diameter of 49mm, a wall thickness of 1.25mm, and a length of 38mm. Mild steel is linearly elastic which means it behaves according to Hooke's law. For calculation purposes, we assume the material is both homogeneous and isotropic. In other words, the material has the same physical composition throughout, and its mechanical properties are the same in all directions. The collapsible spacer that I removed from one of my rear hubs some while ago had suffered compressive deformation, with a change in length of 1mm. If I assume that the yield strength of the material is 250MPa and its elastic modulus is 200GPa, then the axial force applied to the spacer is 962kN. You might be wondering what does a force of 962kN feel like? If you place two 50g snickers on the palm of your hand, then the force that you feel pushing on your hand is one Newton. The applied axial force is 962,000 times that :oops:. When you apply a torque to the nut, an axial force perpendicular to the lever arm is applied to the spacer. The spacer is captured between the bearing cones with no axial force applied directly to the bearings as the nut is tightened. When the applied axial stress (stress = the axial force divided by the cross-sectional surface area) passes the yield point of the tube, compressive deformation takes place. Prior to reaching this stress, the tube was behaving elastically. After the yield point, the tube behaves plastically. This means that it has sustained permanent deformation, which is precisely what it has been designed to do. In reducing the length of the spacer, the frictional force experienced by the bearings increases. This ensures that the right amount of friction is experienced by the bearings. Too little or too much will shorten their life.

The reduction in length of the spacer is called strain, which is a unitless measurement of deformation. Up until the yield point, both the applied stress and strain were in a linear relationship. If the load had been removed during this time, the spacer would return precisely to its original length. After the yield point, this no longer happens. The strain remains and any further axial force applied will shorten the spacer with a lower level of applied axial force relative to the strain. The stress and strain are no longer proportional, with the strain increasing at a much greater rate. It is for this reason that the spacer is a one-use-only device. Do not confuse compressive deformation with buckling, they are quite distinct. Buckling is a phenomenon that impacts slender tubes, with slenderness ratio a function of tube length and radius of gyration. The images illustrate the placement of the spacer and a comparison between a new and old spacer. The compressive deformation is quite obvious.

Ron.
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SydneyRoverP6B

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Staff member
#3
That was beautifully written and laid out. Have you considered teaching mechanical engineering (assuming you don’t already?)
Thank you sdibbers, that is very kind of you to say, I appreciate it! I don't teach mechanical engineering, but I used to teach mathematics. Now I am a civil engineer, specialising in both hydraulics and structural engineering. I will complete my master of engineering degree in June, so not long now :D
Mechanics of materials is a core area for both mechanical engineers and civil engineers. It is an area that I have always found interesting.

Ron.
 
#4
I would still call Snickers, Marathon's. As they used to be called here in the U.K. :LOL:

But as much as l like them l think 962,000 Newtons-worth would be a little indulgent.
 
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jp928

Well-Known Member
#5
As I understand the need for such spacers....tapered roller bearings are very sensitive to loading if they are to have long useful lives when they are up to working temperature. In the P3 and P4 models (at least) the front hub adjustment had a 52 point vernier embodied - a round nut with 4 holes, and a washer keyed to the stub axle with 13 holes , and the manual specified an end float figure (.003-5" ?) aimed at achieving a correct loading when warmed up. Some makes of differential pinions use these spacers to set their bearings up.
 

GRTV8

Well-Known Member
#6
I would be interested on your take of the Twin Towers 9/11 destruction.
I worked with explosives in the mines at Tom Price/Parapurdoo Hammersley Iron back in the 70's.
The way those buildings came down -Id say a controlled blast.
 

SydneyRoverP6B

Well-Known Member
Staff member
#7
I would be interested on your take of the Twin Towers 9/11 destruction.
I worked with explosives in the mines at Tom Price/Parapurdoo Hammersley Iron back in the 70's.
The way those buildings came down -Id say a controlled blast.
Hi Gerald,

That is an interesting theory and in a way you're right, but not in the way that you would think. The reality rests with temperature and the expansion and contraction of structural steel. When designing a structure, the engineer will use what is known as limit states with factored loads that encompass both permanent and imposed actions. The design capacity of the structure will be lowered using capacity reduction factors. Doing so accounts for material imperfections and potential variations in construction. The intent is to produce a design that carries a significant factor of safety given the loads are greater than the worst-case scenario, and that the design capacity still exceeds the amplified loads. So far so good. The problem now though with World Trade Centres is the impact of increasing temperature from fire. The burning fuel both from the aircraft and from within the building raised the temperature to levels that far exceeded the load-carrying capacity of the structural steel beams. Structural steel will see a 40% reduction in yield strength at only 550 degrees C. By 1000 degrees C it essentially has no strength left at all. Structural steel beams supported reinforced concrete floors. The beams were attached to columns that were displaced outwards by the initial expansion of the steel beams as the temperature increased. As the temperature increased further, their capacity to carry the load imposed by the concrete floor was compromised and they began sagging. In so doing, the beams now pulled the columns inwards. Reinforced concrete has a unit weight of circa 2400 - 2500kg per cubic metre. Although extremely strong in compression, it is very weak in tension without the contribution from reinforcement. The reinforcement that is placed within the tension zone of the concrete due to the increased temperature has also yielded. The compressive strain at the concrete surface has reached its maximum of 0.003 strain, which means the concrete is now crushing in compression whilst the tension side is cracking significantly. The reinforced concrete floor now collapses onto the soft and sagging steel beam pushing the beam downwards whilst simultaneously pulling the columns in on top of it. It is now a domino effect where one floor falls upon another, columns are pulled in and the whole building collapses.

Ron.
 
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SydneyRoverP6B

Well-Known Member
Staff member
#9
I an not a Structural engineer but a Environmental engineer M&E.

You have a knack of explaining very difficult concepts and make then easy to understand.

I wish I had a lecturer like you when I was at Uni!
That is very nice of you to say Betsie, I appreciate that.

Ron.
 
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