Forces: Resistance and Torque

Force is a push or pull on an object that tends to change its motion by producing acceleration in the direction of the applied load. Thus, force is defined as a vector with a specific magnitude and direction. Resistance is any force that tends to oppose or retard movement. Friction is the resistance to motion when bodies slide against each other. Friction is a major factor in system inefficiency. Efficiency being the ratio of useful output to total input of the system.

Torque is a rotational force created when a linear force is applied on one end of a lever while the other end is held steady. Torque is equal to the product of the force and the distance between the fixed axis and the point where the force is applied. Thereby, if we know how much torque is applied to something, a resultant force can be determined at any point along the lever by measuring the distance from the axis centerline. Thus, a measurable force in one part of a rotating system can be easily compared against input and resistive forces at other points in the system. This relationship is the basis for computing the influence an individual component has on overall system performance.

Figure 1: Schematic Presenting Torque as a Rotational Force

When a force operates on an object through a distance, work is done. Energy defines a system's ability to do work. Power is the rate of doing work, or of producing or transmitting energy. Some commonly referenced units of power are horsepower and kilowatts. One horsepower is equal to 550 ft-lbs per second and is a convenient reference when relating torque to power. One kilowatt equates to approximately 1.34 horsepower. These are the basic measures used for analyzing the influence of turning resistance to fuel consumption.

Locomotive power provides the pulling (pushing) force for the railcars. As the train moves much of this generated power is dissipated by the various parts of this complex mechanical system. Engine power is lost in the transmission, in overcoming motion resistance, and in vehicle slip. Major factors contributing to this loss of motive force are equipment selection, track conditions, train handling, and the climatic situation. No control exists over several of these resistive forces such as wind speed or direction, the established track grade, and physical effects due to outside temperature. Other factors directly relate to the operating requirements or practices for example rate of acceleration, rail lubrication, and braking forces. And a third group depends primarily on equipment design features such as engine operating efficiencies, the equipment's aerodynamic features, and achieved traction versus undesired drag. This publication is limited to exploring design features; thus it should be mentioned that much of the analysis presented herein does not account for very sizable efficiency losses from environmental influences, track curvature and grade, braking effect, etc. This Technical Forum specifically focuses on the contributions from the roller bearings of a Railroad wheel set. Therefore, the sources of bearing turning resistance will be examined.

Railroad Roller Bearing Turning Resistance

The Association of American Railroads (AAR) Research and Test Department conducted research to characterize the turning resistance of a journal bearing. The outcome of this research was incorporated into their Train Energy Model (TEM), now owned by the Transportation Technology Center Inc. (TTCI). TEM established a standard means by which to estimate individual component contribution to overall train resistive force at the draw bar. TEM's input parameters were derived from empirical findings. Unfortunately, very limited investigation has taken place to confirm the model's actual fuel usage estimates. None the less, TEM simulations offer valuable insight into areas of potential savings. Several fuel consumption examples for bearings with various premium features are presented later in this text, but first these bearing features will be better defined.

Figure 2: Exploded View of the Tapered Roller Bearing Assembly

Roller-Raceway Forces

Sliding friction occurs at the roller-to-raceway interface. Friction exists if roller and raceway profiles do not identically match, flanges are not frictionless, or there is any off-apex condition. Component geometry directly affects sliding or skidding in the system. Lateral forces from track curving or rail car hunting result in roller end sliding contact on the flanged rib of the inner race. Sliding may also occur during rotation of the inner race as rollers enter the load zone due to misalignment forces such as oil wedging or encountering debris.

Rollers and raceways are intentionally ground with crowned surfaces to avoid stress concentration at the end of their rolling surfaces. During loaded conditions, the components deforms and pure rolling only occurs at two locations. All other points are in relative motion. Friction resulting from the motion between these parts is dependent on their surface roughness, conditioning, coating, and lubrication. Therefore, it is important to select the proper surface finish for areas of rolling contact. Research has found that smoother is not necessarily better but rather balance is sought between the conditioned surface structure, applied surface coatings such as phosphate compounds, and proper selection of lubricant qualities such as viscosity and extreme pressure additives.

Cage Interaction

The cage's major function is to separate and properly space the rollers around the inner raceway. By its nature, the cage will interact with all of the other members of the cone assembly. The pocket design is important to avoid undesired roller skewing. When a roller is not in the load zone gravity will tend to pull it down and into contact with the cage bar. Under dynamic conditions, the cage essentially floats between the races; however, inertial changes will alter part acceleration in the system and routinely initiate contact. A rib-riding cage minimizes part movement by allowing cage contact on the flanged rib of the inner race. This containment helps to lower impact forces but is another point of interaction. All cage interactions result in frictional losses. One third of the total bearing rolling resistance can be attributed to rolling and sliding contact generated by race to roller effects and cage contact. Although influenced by load, speed, and temperature, the contribution of rolling and sliding contact does not vary dramatically as operating conditions change.

Lubrication Effects

Roller bearings employ grease to reduce friction on moving components. The main purpose of any lubricant is to establish a film between moving surfaces and keep them separated under applied load. In ideal conditions, the moving parts will ride on the fluid lubricant and make no contact with each other. Although maintaining ideal conditions is unrealistic, proper grease selection will diminish friction and minimize any resulting wear. Therefore, system performance depends heavily on matching the correct lubricant with the expected operating conditions.

Many characteristics must be considered when selecting the best bearing lubricant. The main ones are oil viscosity (flow resistance), grease consistency (hardness), additive chemistry, operating temperature, leakage tendencies, bearing diameter and rotational speed. The right combination of these features creates the desired fluid film between the moving parts. For railroad bearings, the desired outcome is a hydrodynamic film formed by rotation and pressure which squeezes the grease between parts in relative motion. As the bearing rotates, grease continuously circulates. Shear friction and viscous drag occur as the oil film is forced between the loaded surfaces, as a result rolling resistance is encountered and motion is converted into heat. This energy loss exhibits itself by raising operating temperature.

The bearing system temperature has been observed to play a vital role in its proper function and reliability. Thermal extremes can cause intermittent performance issues. As temperature drops, oil viscosity greatly increases. Therefore, when ambient temperature decreases, resistance to flow can grow dramatically and correspondingly affect grease drag. Cold start-ups can cause excessive energy consumption, functional difficulties, and account for a major portion of the initial bearing resistance. Meanwhile, under typical sustained operating conditions the lubricant is responsible for around one sixth of the total bearing rolling resistance.

Seal Drag

Roller bearings' seals serve two main functions, to retain lubricant and to exclude contaminants. This is accomplished through a barrier established by a mechanical structure and a fluid boundary. Although designs vary substantially, the radial lip seal is commonly used in Railway applications since it works reliably and is low cost. Its sealing action is achieved through constant contact pressure of a rubber lib, or series of lips, onto a sealing surface. The contact area, material, and pressure determine a seal's efficiency. Under typical operating conditions the seals are responsible for about half of the total bearing rolling resistance.

Non-contact (light contact) seals do exist. These seals offer lower frictional resistance. The drawback is they are more expensive to produce. They utilize small clearances, typically in a labyrinth arrangement, to create their barrier.

Grease is often the fluid used to fill clearance spaces, enhance sealing, and lubricate contact surfaces. Shear friction and viscous drag occur in seal lubricant just as they do in the bearing grease. Any resistance to rotation, whether physical contact or lubricant drag, will elevate the seal temperature. Over time, high temperature can have detrimental effects such as hardening of rubber seal elements and initiation of grease deterioration or oil leakage. Therefore, it is important to minimize seal drag as much as practical to reduce heat generation.

The sources of bearing resistance mentioned above are always present but contribute in varying amounts depending on the system specifics. A typical operating scenario was calculated for a journal roller bearing running at an ambient temperature of 90º F. It found the resistance caused by seal drag, rolling/sliding contact, and lubricant effects equated to 50, 36 and 14 percent respectively. This relationship is shown graphically below.

Figure 3: Sources of Tapered Roller Bearing Frictional Resistance During Operation

Bearing Collective Frictional Forces

As detailed above, rotational resistance in the roller bearing system can be assigned to three basic contributors: seal drag, rolling/sliding contact, and lubricant effects. The overall level of resistive forces from these bearing features is dramatically affected by several specific environmental and operational factors. The four main factors being load, rotational speed, operating temperature, and service time. So let us evaluate the influences experienced from each one of these four factors.

Increased loading will apply more pressure to components, reduce lubricant film thickness, and moderately increase rolling/sliding contact resistance. Variations in speed alter system vibration, acceleration, and viscous shear. After start-up, it is typical to experience an increase in frictional resistance with higher rotational speed with this loss of energy showing up as system heat. Meanwhile the factors of temperature and service time play the most critical roles in determining a bearing's efficient performance.

As temperature goes up, the bearing's rolling components will expand; however, due to design clearances this has a minimal effect on their imparted rolling resistance. Sealing elements are typically made from rubber that can stiffen or harden if exposed to thermal extremes for extended periods. Such temperature extremes can make them less pliable and has been recorded to double their resistance. In the worst case scenario, seal friction can be one order of magnitude higher than the roller-raceway forces. Oil viscosity is heavily influenced by temperature change. Railway bearing greases are targeted at the typical operating environment. Extreme temperatures will adversely affect their performance. At low temperatures, the oil will stiffen and eventually solidify (freeze), which has been recorded to increase bearing resistance 100-fold at start-up. In the worst case scenario, grease friction can be two orders of magnitude higher than the roller-raceway forces. Research has identified that both high viscosity indexes and extreme pressure additives will enhance lubricant performance and reduce bearing damage during cold starts. Therefore, one is encouraged to use grease with these attributes in cold climate conditions since it has such a profound influence. Figure 4 relates the effect and magnitude that cold-operating temperature has on the basic components of a standard freight journal bearing.

Figure 4: Typical Bearing Start-Up Torque vs. Temperature Relationship

Time in service also plays a noteworthy role in the frictional resistance of a roller bearing. During their initial service period, the loaded bearing components undergo a surface conditioning. As high points of the surface roughness are burnished to a smoother finish, its frictional resistance marginally decreases. The seals also undergo a run-in period in which wear occurs on the high contact points and the rubber elements take a thermal set. The duration of this run-in period is dependent on the seal's design features, as well as, the operating conditions. It is not uncommon to observe a seal's frictional resistance steadily decrease over a period of several years. The reduction percentage can be quite significant. As for lubrication, during the bearing assembly process, grease is fully packed between the rollers and raceways. At start up, energy is consumed moving this grease into other regions of the bearing assembly. After initial grease redistribution is complete, the frictional characteristics of a bearings lubricant generally change very little during its service life. Figure 5 relates the effect that service mileage has on new journal bearings containing various seal types.

Figure 5: Bearing Torque vs. Service Mileage Relationship for Various Seal Types

Train Fuel Consumption

Now that the sources of bearing rolling resistance have been defined, they can be related to turning resistance of the wheel set and ultimately to the fuel consumption of a train. As explained earlier, once a force is measure in one part of the rotating system it can be compared against force experienced at other locations by measuring its generated torque. In this manner, bearing torque divided by the wheel radius equals its contribution to wheel turning resistance. For example, using two Class F bearings that each generates 72 inch-pounds of rolling resistance on a 36-inch wheel set produces an equivalent axle drag force of 2 X (72 inch-pounds/18 inches) or 8 pounds.

Power is equal to the product of torque and angular velocity. It can be defined as the rate of doing work or as the rate of consuming energy. Locomotive fuel consumption can be expressed either in terms of power per fuel volume or energy per fuel volume. Generally speaking 15% of the generated power is lost during transmission within the locomotive. Locomotive fuel consumption in terms of work delivered to the drawbar has been estimated by previous industry studies such as the AAR Train Energy Model. The TEM model evaluates the vehicle's resistance parameters under various operational scenarios. For example, on a typical fully loaded western coal train running at 50 mph on level tangent track, wheel-to-rail rolling resistance, aerodynamic drag, and journal bearing rolling resistance account for 56, 28, and 16 percent of a railcar's losses respectively. In comparison, on a typical unloaded western coal train operating at 50 mph on level tangent track, wheel-to-rail rolling resistance, aerodynamic drag, and journal bearing rolling resistance account for 18, 60, and 22 percent of a railcar's losses respectively. Figure 6 shows this comparison graphically.

Figure 6: Vehicle Rolling Resistance Parameters for Unloaded and Loaded Scenarios

Bearing torque change of 2 ft-lbs [T]
Operating speed of 50 mph [S]
36 inch wheel diameter [d]
Fuel cost of $1.00 per gallon [$]
Train energy-to-fuel ratio of 14.0 kW-hrs/Gal [R]

Power = 0.04772 (TS/d) = 0.04772 (2 X 50/36) = 0.133 kW.
Fuel consumed per mile = P$/RS = 0.0133 X 1.00/14.0 X 50 = 0.00019 $/mile.

In this simplified example, use of low torque bearings would result in fuel savings of 19¢ per 1,000 miles per bearing. By knowing these savings and the railcar' standard service mileage, one is provided with justification for deciding whether to purchase premium components. Figure 7 depicts this relationship between torque reduction, fuel costs, and calculated savings.

Figure 7: Savings per Bearing vs. Fuel Cost

Operating Efficiency and Life Cycle Cost

This Technical Forum has presented information on bearing rolling resistance and its direct effect on the operating efficiency of a train. It has provided the conceptual building blocks and offered some key examples. Of the many aspects that need to be considered when attempting to minimize operating expenses, a few specific attributes of the journal roller bearing were shown to offer potential cost savings. To summarize these, the three most critical items are grease selection for cold climates, seal selection for high utilization services, and high reliability bearing components to eliminate unscheduled train stoppage.

This Technical Forum also recommends using both theoretical and empirical fuel analysis techniques to evaluate efficiency gains from enhanced components or new designs. Under the right service conditions, fuel savings can greatly exceed the initial cost of premium bearing components such as high viscosity index grease or low drag seals. Meanwhile, the tapered roller bearing is only one part of a complex mechanical system that offers many opportunities for lowering a vehicle's rolling resistance. Calculating overall life cycle costs can provide the needed justification for the introduction and use of better equipment. The widespread use of more efficient operating practices and premium rolling stock promises the accumulation of sizable savings throughout the Railroad Industry.

The Technical Forum is an information resource for the rail industry and is provided as a courtesy of Amsted Rail Group. Suggestions, inquiries or comments are welcomed and should be directed to:

Editor, Technical Forum
BRENCO, Incorporated
P.O. Box 389
Petersburg, Virginia 23804
804-863-1713

Additional copies provided upon request.

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