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Basics of Rheology
Basics of Wear

Viscosity is the resistance to flow of a fluid, in our case, a lubricating oil.

Why is it important to understand viscosity? Because viscosity is central to the performance of lubricated machinery, such as your car:

  • If you use a high viscosity engine oil in your car, the oil puddles in your driveway will be smaller, but your engine will run hotter and it probably won’t start on a cold winter morning.
  • If you use a low viscosity engine oil in your car, the piston rings may wear out in a few thousand miles, the crankshaft bearings may seize, and the puddles in your driveway will amaze your neighbors!
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Hydrodynamic Films

One of the functions of a lubricant is to transfer loads from one surface, such as the crankshaft in your engine, to another surface, such as the engine block. However, this only happens when the crankshaft is rotating. When one surface moves and the other is stationary, oil is carried through the gap between the two surfaces. As the oil moves through the gap, it supports the vertical load, as shown below:


Before a shaft begins to rotate, it rests on its supporting bearing. When rotation begins, the shaft climbs up the bearing, as shown above. It also carries a thin film of oil into the contact region. As the shaft rotates faster, it carries more oil into the wedge shaped area that is just above the contact region. As the shaft rotates even faster, the oil in the wedge region becomes pressurized such that it supports the shaft. The fluid pressure also moves the shaft over slightly to the right. The fluid film supporting the shaft is thinnest just to the right of center. When the shaft is rotating fast enough to be riding on a stable film of oil, full hydrodynamic lubrication has been achieved.

The minimum film thickness in most journal bearings is about 0.001 inches. The pressure in that region ranges from 40 to 400 psi.

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Lubricant Film

This graph shows how the friction torque in a journal bearing changes with lubricant viscosity and other variables. Remember that friction torque is wasted energy that heats the oil, shaft and bearing. The friction torque is shown on the vertical axis and we see that it is highest on the left side of the graph where the arrow points to Boundary Lubrication. The friction torque decreases in the area called Mixed-Film Lubrication and it is at its lowest value across the bottom of the graph in the region marked Hydrodynamic Lubrication. This diagram is called a Stribeck Curve.

Across the bottom of the curve, we have a new parameter - mN/P . In this parameter, m is oil viscosity, N is shaft speed in rpm and P is the external load carried by the bearing. The parameter is found by multiplying the viscosity by the shaft speed and dividing by the external load.

For our bearing, we can change the friction torque, or wasted energy, by changing one, two, or all three of these variables.

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Thickness and Friction Torque

Shaft Speed changes Friction Torque: As the shaft speed (rpm) increases from zero, the friction torque is initially high since there is metal-on-metal contact with Boundary Lubrication. It drops as oil is carried into the contact zone by the rotating shaft, creating Mixed Lubrication where we alleviate the metal-to-metal contact with an intermittent film of oil. At a slightly higher speed, the shaft is fully supported on a fluid film and full Hydrodynamic Lubrication is achieved.

With higher speeds, the friction torque increases again. Does this seem logical to you?

The reason that the friction torque increases again is that more oil has to be pumped, with the attendant pumping losses.

Lubricant Viscosity changes Friction Torque:

If an oil with a higher viscosity m is used, the journal can to move through the Lubrication regimes with smaller increases in shaft speed. In the Hydrodynamic Lubrication regime, an increase in viscosity results in a proportional increase in friction torque loss.

If a journal must be operated at low shaft speeds, the lubricant viscosity should be high if we want to achieve full Hydrodynamic Lubrication. Does this seem logical to you?

Load Effect on Friction Torque:

As the load P increases, the Stribeck Diagram shows that the shaft speed or the lubricant viscosity (and sometimes both) must increase if we want to maintain a low friction torque.

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Definition of Viscosity

The simplest definition of viscosity is resistance to flow. Sir Isaac Newton (the guy with the three laws and an apple on the ground) defined it as “the resistance that arises from lack of slipperiness in a fluid.” Cold maple syrup is thick and not slippery, but cold water is thin and slippery.

Words such as thick, slippery, thin and sticky are not distinguishing when we have to describe dozens of different oils. Instead, we use numbers to compare different lubricating oils. Consider the experiment shown in the sketch. The force F that is applied at the edge of the top plate, divided by the area of the plate A, is defined as Shear Stress. The movement of the fluid between the plates that results form the application of the force is the Shear Rate. Shear Rate has to do with the speed with which the layers of fluid between the plates move. The top layers, the ones closest to the moving plate, move the fastest and the layer nearest to the stationary plate moves the slowest. Thus, there is a velocity gradient from fastest to slowest. This gradient is the Shear Rate for that fluid at a given shear force.

We use these two relationships to describe the resistance to flow:

Two types of viscosity measuring instruments are in common use. They are described on the next two sections.

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Capillary Viscometers

We can measure the viscosity of lubricants quite easily by measuring the time required for a known amount of oil to flow through a small diameter (capillary) tube at a known temperature. This turns out to be a lot easier to do than the moving plates model described in the previous slide. The test measures the kinematic viscosity (moving-fluid-viscosity – get it?) and the units of measure are called centistokes. (George Stokes was an English mathematician who published his ground-breaking work in fluid mechanics during his early 20’s and thus deserves to have the units for viscosity named after him)

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Rotational Viscometers

Rotational viscometers measure viscosity by sensing the torque required to rotate a spindle at constant speed while immersed in a fluid. The torque is proportional to the viscous drag on the immersed spindle, and thus to the viscosity of the fluid. This type of viscometer is widely used for fluids that contain suspended particles, such as paint. It should also be used for lubricating oils that contain significant volumes of soot particles.

There are many other methods used to measure viscosity, such as measuring the time that glass marble needs to fall through a lubricant – a falling-body viscometer. The marble falls more slowly in a viscous lubricant. This method has a huge disadvantage – the marble disappears if the lubricant is cloudy or opaque. Several indirect methods have been developed to allow continuous monitoring of viscosity by process control computers. These devices provide a current or a voltage that is proportional to viscosity; they must be calibrated with oils that have been previously measured with a rotational or capillary viscometer.

The units of viscosity can also be confusing. If we go back to our first experiment to measure viscosity (the two parallel plates separating a film of oil) the experiment measures viscosity relative to the shear stress, which has units of force divided by area. The metric unit for force divided by area is the pascal (Pa) or the millipascal (mPa). One pascal is equivalent to one Newton per square meter. The shear stress is divided by the velocity over the film thickness. This yields the metric unit for kinematic viscosity - the pascal-second (Pa-s). Sometimes you may also see viscosity units in poise or centipoises (cP). Fortunately, centipoise and millipascal-second (cP and mPa-s) are equivalent.

People in the lubricants industry use kinematic viscosity. This is the dynamic viscosity (millipascal-second) divided by the density of the fluid. The units of kinematic viscosity are called stokes or, commonly centistokes (cS). For those of you who like equations:

Notice how the kinematic viscosity accounts for the observation that a more dense fluid will move more quickly through the capillary tube.

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Newtonian Fluids

Recall that viscosity is equal to the shear stress / shear rate. What happens if we stir a can of oil at different speeds? Does it seem obvious that more effort is required to stir at a faster speed? More effort is required, but for some oils it is not proportionally more effort.

We can determine the effect of stirring rate with a rotary viscometer by rotating the spindle at different speeds. For each of these speeds, we calculate the shear rate (related to the rotation speed of the spindle) and measure the shear stress (related to the torque needed to rotate the spindle). Then we make a plot of the shear stress and shear rate as shown below. The data might fit a straight line starting from zero. The slope of that line (or its steepness) is the viscosity for that oil at the temperature of the oil.

Remember from a few screens back that mathematically

An oil whose viscosity remains constant as we increase or decrease the shear rate is a perfect fluid. The term Newtonian is used to designate this behavior. Water, gasoline, and most unmodified mineral oils display Newtonian viscosity curves.

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Non-Newtonian Fluids

Most fluids, including motor oils, are not perfect, or Newtonian. The shear stress is not directly proportional to the applied shear rate such that when the shear stress is plotted against the shear rate, the points are not in a straight line. Often, the points do not begin from zero shear stress and zero shear rate. Certain other fluids are sensitive to the length of time that the fluid is being sheared, resulting in changes in viscosity with the duration of the experiment.

  • These kinds of fluids have interesting names:
  • Pseudoplastic fluids - The viscosity of pseudoplastic (soo doe plastic) fluids decreases with increased shearing. Molten polymers have this characteristic, which is used to advantage in injection molding when the material flows through small cross section gates. Paper pulp suspensions also display pseudoplastic viscosity behavior.
  • Bingham plastic fluids - The viscosity curve for Bingham plastic fluids does not go through the origin. As shown in the figure below (which figure?), the shear stress can be substantial even at a small shear rate, but once the fluid is moving, the shear stress is directly proportional to shear rate in exactly the same manner as for Newtonian fluids. Water suspensions of rock particles behave in this manner. More familiarly, mashed potatoes, a suspension of tasty solids in a liquid, flow in the bowl when you stir, flow harder when you stir harder, and assume a mountain peak shape if undisturbed.
  • Shear Time Dependent Fluids – for these fluids, the shear stress changes with time of shearing. This behavior is related to breaking bonds between particles or molecules or to changes from the at-rest shape of long molecules,
  • Thixotropic Fluids that are thixotropic are not simply small molecules aggregated together, such as water. They include molecules that have a longer range structure that can be altered with mechanical shearing. For most of these fluids, the viscosity decreases at higher shearing rates. Mayonnaise has this characteristic. It is not a Bingham plastic fluid because its viscosity decreases with higher rates of shearing, but only after a minimum amount of shear is reached. Yogurt (without the tasty fruit addition) is also reputed to have this behavior. Finally, g Parahead 2

The non-Newtonian fluids discussed on the previous page have important behaviors. For example, in Pseudoplastic fluids, flow does not begin until a minimum shear stress level is reached. This is important for printing ink rheology where we would not like the ink to move until it is deposited on paper. Once the minimum shear stress has been reached, the fluid thins with increasing shear rate and penetrates the structure of the paper. When the shear stress goes back to zero, the ink does not move. Similarly, with Thixotropic fluids, flow can vary with applied shear stress and/or rate, becoming rapidly thin with increasing shear time, but when the shear forces are removed the fluid rapidly becomes thicker or more viscous. Paint is usually compounded to be thixotropic - it applies easily (high shear stress and rate) but it doesn't sag or run when the brush is removed, yet has the time to flow and level out before thickening. At low temperatures, wax particles in lubricating oils can cause the non-Newtonian Thixotropic behavior of the oil to become even more pronounced.

How does a Pseudoplastic oil behave in a hydrodynamic bearing?

At startup, the shear rate is slow and the oil has a high viscosity such that the transition to mixed lubrication is facilitated. As the shaft speeds up, the viscosity decreases but hopefully the increased speed compensates and the system remains in the mixed lubrication regime or transitions into the hydrodynamic regime. On the other hand, with a Thixotropic fluid, at start up, if the shear rate is slow the oil initially supports the bearing. If the shear rate remains constant, the oil will eventually thin and not support the bearing.

A Dilatant fluid is the opposite of a Pseudoplastic fluid in that its viscosity increases with shear rate. This would be very bad for a paint system, as it would be very difficult to spread the paint evenly. If a lubricating oil was dilatant, its viscosity would increase with speed and friction losses would increase, not a good outcome when the general objective is to decrease energy consumption.

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Changing Viscosity with Additives

VI improvers change oil blends so that they maintain a more constant viscosity over a wide temperature range. The additives that act as VI improvers are generally long polymer chains that are coiled like a spring. When an external shear stress forces the blend of oil and polymer chains to flow, the coiled polymer chains that are suspended in the oil become stretched and distorted to an extent that they impede the oil flow. But impeding oil flow has the same effect as increasing the oil viscosity and thus the blend has a different viscosity curve from the unmodified oil.

A polymer that changes the viscosity index is called a VI Improver. They most commonly are long polymer molecules with a molecular weight of about 100,000. When a suspension of these polymers in oil is heated, the polymer molecules expand and make the oil behave in a more viscous manner. When the same suspension is made to flow under the action of a shear stress, the molecules interfere with flow as explained above. This also causes the blend to behave in a more viscous manner.

  • Summarizing, the polymer and oil behaves:
  • In a more viscous manner
    • As the temperature is increased
    • As the shear rate is increased
  • In a less viscous manner
    • As the temperature is decreased
    • As the shear rate is decreased.

Note from the diagram below that this yields a High VI oil, which is desirable for most applications.

Some additives, particularly those with smaller molecular size, can change the viscosity index or change the viscosity curve in a manner that can be negative to the system performance.

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Types of Viscosity Index Improvers

When the shear rate decreases to a low level or to zero in a blend that includes a VI improver, the viscosity returns to its original state. This is called temporary viscosity loss (TVL).

In the diagram above, VI Improver A shows less temporary viscosity loss than VI improver B. Generally, linear straight chain polymers show more temporary viscosity loss than more highly branched chains. Unfortunately, VI Improvers can also undergo permanent viscosity loss (PVL). This happens when the polymer chain breaks as it is distorted. This is highly undesirable. Therefore, the key in developing a polymer that will act as a good VI improver is to find a polymer that shows minimum breakage as the polymer coils distort under high shear. In most instances, a compromise between minimum breakage and cost is usually necessary.

Typical VI improvers are of the following chemical polymer types:

Olefin Polymers

High Molecular Weight Polymethacrylate

Low Molecular Weight Polymethacrylate

Linear Styrene Isoprene

Styrene Isoprene

Would you predict that dust particles and soot particles might affect viscosity? Yes, the viscosity will increase as these particles become suspended in the oil. This has the effect in increasing the friction torque, and thus overall system efficiency will decrease.

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Viscosity at High Pressures

As stated above, the properties of oil are also sensitive to pressure. While oil is largely incompressible, its viscosity increases at very high pressures. Further, this change is somewhat time dependent. This behavior is used in the lubrication of ball bearings where the instantaneous load between a ball and the two races is extremely high. The oil, now very viscous under the high pressure, does not flow out of the contact area and the ball and races are separated. This behavior is called elasto-hydrodynamic lubrication.

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Clearly, viscosity and rheology are very important to the proper operation of mechanical equipment. An equipment design engineer designing a bearing or gearbox, or a lubricant dispensing device, needs to understand the implications of rheology on her design. If she knows the conditions under which the ?converging wedge? is operating, the rotating speed, the load, and the possibility of any intermittent changes in pressure with time, and if she can predict the range of operating temperatures, she can specify a viscosity and viscosity index for effective lubrication. Conversely, if she knows the viscosity profile of a lubricant, she can design a mechanical system to operate reliably.

Lubricant formulators keep all of these concepts in mind and under control when developing new products.

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