Pressure-Viscosity Coefficient vs Temperature for Base Oil Groups

[Gokhan]

Originally Posted by ZeeOSix
Per the charts posted, you have to get above about 250 MPa pressure region to see any (and slight at that) viscosity increase due to pressure.

No, see my post above. You get a 40 - 120% pressure-induced viscosity boost at only 40 MPa.

n/n0 = exp(alpha * P)

alpha ~ 0.009 - 0.02 1/MPa (or 9 - 20 1/GPa)

Go ahead and do the math for yourself.

 

[ZeeOSix]

Originally Posted by Gokhan
Originally Posted by ZeeOSix
Per the charts posted, you have to get above about 250 MPa pressure region to see any (and slight at that) viscosity increase due to pressure.

No, see my post above. You get a 40 - 120% pressure-induced viscosity boost at only 40 MPa.

n/n0 = exp(alpha * P)

alpha ~ 0.009 - 0.02 1/MPa (or 9 - 20 1/GPa)

Go ahead and do the math for yourself.


Looking at the graph again, it starts at 4 cSt (per the figure text). So even if there's and increase of a 100% it's still "in the mud" on the graph since the vertical scale covers a huge range. So yeah, would have to use the formula in that case.

 

[Gokhan]

Here is a much better plot of the pressure-induced viscosity boost η/η₀ vs. pressure P for pressure-viscosity coefficient α = 0.009-0.015 MPaâ»Â¹.

 

[Shannow]

Originally Posted by Gokhan
Here is a much better plot of the pressure-induced viscosity boost η/η₀ vs. pressure P for pressure-viscosity coefficient α = 0.009-0.015 MPaâ»Â¹.

Of course you are assuming that the behaviour is
* linear, throughout the entirety of applied pressures
* is linear as it passes through zero
* and thus at 40 MPa...it behaves the same as 2,000MPa.

Can't make those assumptions.

Anyway...the design curves of Sommerfeld et al...100 years ago through actual measurements of film thickness and viscosity automatically, because of their empirical nature take both PVC, and the variations in pressure along the bearing are already factored in...

(When we learned bearing design, everything was infinitely long (no side leakage) in the first pass before we went into the extra dimensions of side leakage).

 

[Gokhan]

Originally Posted by Shannow
Of course you are assuming that the behaviour is
* linear, throughout the entirety of applied pressures
* is linear as it passes through zero
* and thus at 40 MPa...it behaves the same as 2,000MPa.

Can't make those assumptions.

No, the y-axis is logarithmic. This is the semilog version of the same plot from the reference I posted.

 

[Shannow]

Originally Posted by Gokhan
Originally Posted by Shannow
Of course you are assuming that the behaviour is
* linear, throughout the entirety of applied pressures
* is linear as it passes through zero
* and thus at 40 MPa...it behaves the same as 2,000MPa.

Can't make those assumptions.

No, the y-axis is logarithmic. This is the semilog version of the same plot from the reference I posted.


OK...but like most things, the assumption that it passes through zero, and behaves predictably at near zero pressures (40 versus multiple thousands) can't be made...

for e.g. the Stribeck curve LOOKs linear when you look at one end of it...until it isn't

 

[Gokhan]

Originally Posted by Shannow
OK...but like most things, the assumption that it passes through zero, and behaves predictably at near zero pressures (40 versus multiple thousands) can't be made...

I used the equation from the book reference I had posted and they cited two references on that.

Are there correction terms to the simple exponential form? Perhaps there are. Nevertheless, this simple exponential form is common.

 

[ZeeOSix]

So is this viscosity increase due to increased pressure just from an increase in density due to the high compression of the oil, or are other factors involved? The plot Shannow posted has viscosity vertical axis units of mPa-s, which I believe has a density factor involved. cSt times density equals cP, which is the same as mPa-s (1 cP = 1 mPa-s).

And 40 MPa is still a pretty high pressure of 5800 psi. 10 MPa is 1450 psi, which is even in the 'mud' in Gohkan's logarithmic plot.

 

[Gokhan]

Originally Posted by ZeeOSix
So is this viscosity increase due to increased pressure just from an increase in density due to the high compression of the oil, or are other factors involved? The plot Shannow posted has viscosity vertical axis units of mPa-s, which I believe has a density factor involved. cSt times density equals cP, which is the same as mPa-s (1 cP = 1 mPa-s).

And 40 MPa is still a pretty high pressure of 5800 psi. 10 MPa is 1450 psi, which is even in the 'mud' in Gohkan's logarithmic plot.

The viscosity is increasing by many orders of magnitude (many factors of 10); so, it's definitely not the density. These are incompressible fluids and the density doesn't vary much with the pressure -- probably less than a few percent at gigapascal pressures. You can't really compress atoms and molecules together much. The colossal increase in the viscosity has to do with the increase of the attractive forces between the oil molecules when the pressure increases -- they get slightly closer together but that makes a large difference in the attractive forces.

Technically P = −∂E/∂V, with P, E, and V being the pressure, internal energy, and volume. In other words E = −∫PdV.

 

[ZeeOSix]

Wonder why they use the viscosity units of mPa-sec in the graph Shannow posted on page 1. Why not just use cSt, as they refer to the base oil in the graph at 100C having a viscosity of 4 cSt.

Maybe I missed it, but has this increased viscosity factor (PVC) actually been measured in the lab under those insanely high pressures, or is this all theoretical?

 

[Shannow]

Originally Posted by ZeeOSix
Maybe I missed it, but has this increased viscosity factor (PVC) actually been measured in the lab under those insanely high pressures, or is this all theoretical?


Yes, it's been measured.

Here's a paper with an example of the sort of machine that they use...this one's specifically on traction properties (went down that rabbit hole in the '90s with the aforementioned skidding bearing), which I think is more relevant to the OP's cam/lifter related issues than PVC per se.

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.1011.4363&rep=rep1&type=pdf

 

[Gokhan]

Originally Posted by ZeeOSix
Wonder why they use the viscosity units of mPa-sec in the graph Shannow posted on page 1. Why not just use cSt, as they refer to the base oil in the graph at 100C having a viscosity of 4 cSt.

Maybe I missed it, but has this increased viscosity factor (PVC) actually been measured in the lab under those insanely high pressures, or is this all theoretical?

Since we are looking at gigantic changes in the viscosity, less than a few percent change in the density Ï as a result of gigapascal pressures is not a concern as the results are nowhere near that accurate because of the exponential form; therefore, the same exponential equation with same pressure-viscosity coefficient α can be used for both the dynamic viscosity μ and kinematic viscosity ν.

μ = μ₀ exp(αP)

μ = Ïν

Excerpt from a paper:

2. VISCOMETER

The instrument used here to directly measure the limiting low-shear viscosity, μ, is a falling body viscometer which has been thoroughly described elsewhere [2,5., 6.]. Instruments of this type have provided most of the pressure-viscosity coefficient measurements and have made these measurements somewhat routine. The viscometer used here has been improved by strengthening the viscometer vessel and intensifier so that pressures of 1.6 GPa have been contained. The temperature limit is at least 165 °C and viscosities to 105 Pa•s can now be measured in reasonable time. The viscosities measured using this device for low molecular weight oils are comparable to those obtained using a high-pressure capillary viscometer for which the pressure transient is of the order of microseconds.

The pressure-viscosity coefficient at hertz pressure and its relation to concentrated contact traction
Scott Bair and Ward O. Winer
George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332
https://www.sciencedirect.com/science/article/pii/S0167892200801480

 

[Gokhan]

Originally Posted by Gokhan
Originally Posted by Shannow
OK...but like most things, the assumption that it passes through zero, and behaves predictably at near zero pressures (40 versus multiple thousands) can't be made...

I used the equation from the book reference I had posted and they cited two references on that.

Are there correction terms to the simple exponential form? Perhaps there are. Nevertheless, this simple exponential form is common.

Regarding the dependence of the pressure-viscosity coefficient α on the pressure P, here is an excerpt from the paper I linked in my previous post:

The local pressure-viscosity coefficient, α = ∂ℓn(μ)/∂p, has been assumed by many authors to generally decrease with pressure or remain constant over the high-pressure region of contact so that the parameters of the Eyring rheological model may be obtained from traction curves. However, viscosity measurements to 3 GPa have been available in the literature for at least fifty years [2] which refute these assumptions. The limiting low shear viscosity has been measurable to 1.2 GPa for at least seventy years. Figure 1 compares pressure-viscosity behavior obtained from viscometers against that derived from traction using a sinh law model [3., 4.]. Clearly there is a misconception among some tribologists concerning the nature of piezoviscosity at high pressure.

So, it could be roughly constant but it could also vary greatly over a large pressure range.

 

[Gokhan]

Originally Posted by Gokhan
Originally Posted by Gokhan
Originally Posted by Shannow
OK...but like most things, the assumption that it passes through zero, and behaves predictably at near zero pressures (40 versus multiple thousands) can't be made...

I used the equation from the book reference I had posted and they cited two references on that.

Are there correction terms to the simple exponential form? Perhaps there are. Nevertheless, this simple exponential form is common.

Regarding the dependence of the pressure-viscosity coefficient α on the pressure P, here is an excerpt from the paper I linked in my previous post:

The local pressure-viscosity coefficient, α = ∂ℓn(μ)/∂p, has been assumed by many authors to generally decrease with pressure or remain constant over the high-pressure region of contact so that the parameters of the Eyring rheological model may be obtained from traction curves. However, viscosity measurements to 3 GPa have been available in the literature for at least fifty years [2] which refute these assumptions. The limiting low shear viscosity has been measurable to 1.2 GPa for at least seventy years. Figure 1 compares pressure-viscosity behavior obtained from viscometers against that derived from traction using a sinh law model [3., 4.]. Clearly there is a misconception among some tribologists concerning the nature of piezoviscosity at high pressure.

So, it could be roughly constant but it could also vary greatly over a large pressure range.

Here are the results from the traction-rig rheometer Shannow posted, which provides an indirect measurement of the viscosity, vs. direct measurements using high-pressure viscometers ZeeOSix was inquiring about, the latter of which obviously capable of measuring the true viscosity values.

Traction-rig rheometers can be rather inaccurate because the pressure-viscosity coefficient α can vary greatly with the pressure P, which makes a good theoretical fit to obtain the viscosity very difficult.

So, the short answer to the question asked earlier is that the pressure-viscosity coefficient α does vary a lot with the pressure P in general and the simple exponential equation μ = μ₀ exp(αP) is only a first-order approximation.

 

[wpod]

The quality of the base oil blend,, it makes me wonder.