Coefficient of Friction and Prony Brake Dynamometers
written by Aaron Warsaw
This composite was compiled using my 50+ years of experience in the field of ‘Tribology” as related to the study of friction, friction brakes, and frictional Prony brake dynamometers. My background includes working with multiple friction brakes which are used in a wide variety of commercial applications and dynamometer configurations. I also have many years of analyzing brake performances and field service issues with Prony brake dynamometers, plus many years of manufacturing processes and production of thousands of Prony brake dynamometers. When combined, this was the basis I used in the designing and engineering process of three newly patented frictional Prony brake dynamometers.
The information contained in this article contains information that I have accumulated and used in creating formulas for calculating the coefficient of friction for both radial and axial force frictional Prony brakes. Calculations involving the coefficient of friction were used in my primary design criteria for the last three patents I have received, along with secondary functions including the ability to analyze and monitor the efficiency of wet friction brakes during dynamic operation. The coefficient of friction as related to mechanical friction brake efficiency is as important as apples are to apple pie.
Frictional Prony brakes have a wide range of absorption capabilities throughout a dynamic range of ½ rpm to 1300+ rpm. Prony brakes can be configured into a dynamometer using dry friction, semi-lubricated friction, and wet friction, per specific application. The coefficient of friction provides reliable baselines required for brake design, torque capacity, power ratings, product life, and operational analysis.
Using the coefficient of friction as referenced with mechanical friction brakes is operational efficiency. Values used are expressed using a measured numerical system representing a ratio of the amount of work a brake must produce to achieve a specific amount of resistance to an opposing force.
When frictional Prony brakes are used as a dynamometer, it is the coefficient of friction which represents a ratio between the amount of torque absorbed by the brake and the amount of braking force required to produce a defined amount of resistance. These values provide guidance to a brake’s operating efficiency during dynamic operation. With the ability to calculate the coefficient of friction during dynamic operation, a brake’s performance can be monitored while providing frictional conditions throughout the life of the brake.
The efficiency ratio expressed for the coefficient of friction is a numerical scale ranging from 1.00 to .001. This, without numerical limitations between. A ratio of 1.00 represents maximum coefficient of friction values such as that of a mechanical brake at stall or the complete restraint of an object from motion. Lower scale values such as .001 would represent the minimum amount of resistance such as water between two planes of glass.
Many coefficients of friction variables exist, even within the same model of brake, brake capacity and produced by the same manufacture. There are many factors which contribute to the variables. This requires a meaningful understanding for the basis which a brakes operating functions can be monitored during dynamic operation. Insuring accuracy requires the understanding of both radial and axial force friction brakes used in dynamometer applications. Understanding friction variables associated with friction brake dynamometers is a requirement in design criteria and the ability to monitor during operation.
The following criteria was used by myself in analyzing performance of both radial and axial force Prony brake dynamometers during my design process for the last three patents issued to me.
- Dry friction brakes
- Semi-wet friction brakes
- Wet friction brakes
- Temperatures at the kinetic point of friction
- Control of operating temperatures and availability
- Friction surface area
- Rotor surface feet per minute per revolution
- BTU exchange per square foot per revolution
- Mechanical and Power load
- Mating component materials
- Mating frictional surface porosity
- Mating surface finish [RMS]2.
- Rotor surface hardness
- Slip-stick friction
- Dynamic operation speed
- Static operation
- Friction material comprehensive strength.
- Friction material porosity.
- Friction material composite, asbestos, fiberglass, brass content, fillers
- Tensile and shear strength of friction material
- Material coefficient of friction rating
- Maximum surface feet per minute
- Maximum material operating temperature
- Hours of intended operation
- Establish a B10 life basis on operational load capacity
- Friction material wear rate
- Friction material burnout rate
- Apex loading
- Destructive analyzes
- Hermetically sealed brake vs Atmospheric exposure
- Availability of controlled ram or working force.
- Wet friction fluid maintenance basis
- Dry friction service intervals and adjustments
- Burnishing and or break-in procedures
- Maximum transfer of heat at the kinetic point of friction
- Lubrication vapor pressure
- Lubrication fluid viscosity
- Lubrication fracturing
- Lubrication fluid flash point
- Lubrication volume
During operation, wet friction radial force Prony brakes, used as a dynamometer, will not produce linear coefficient of friction values as resistance or torque loads are increased. The key being, the coefficient of friction recovery after repeated dynamic loads and heat cycles. This requires years of building knowledge specifically related to radial force Prony brake designs and usage in variable applications. There is much material written about friction, especially as it pertains the effect on roller bearings, and efforts to reduce energy robbing friction, but when it comes to wet friction brakes used as a load absorption unit as a dynamometer, information is limited in scope and not specific to brake design.
It is with many years of hands-on experience working with design engineering and manufacturing of both wet and dry frictional Prony brake dynamometers that has provided specific guidance to a design and the intended application.
Variables in the Coefficient of friction during a test of a prime mover results from several factors. These factors include frictional rotor surface feet per minute and the efficiency of heat transfer at the kinetic point of friction into a cooling media. Additional heat occurs as the hydraulic ram is increased to produce more torque load. When increasing the amount of hydraulic ram to produce greater resistance, a wet friction brake is also subject to compression of the friction material.
To compound issues is the use of lubrication fluid to protect frictional surfaces. Lubrication fluid acts much like a series of small ball bearings creating a microscopic barrier between the friction material and the rotor’s friction surface. By using lubrication fluids, the coefficient of friction is reduced, thus, to increase brake life and extend a brake’s usefulness between major repairs. With the use of lubricating fluids additional operational issues must be addressed such as viscosity, volume, and quality.
All extraneous forces must be removed from force readings such as oil shear, liner drag, cooling media skin friction, preloaded hydraulic or air pressure to ensure accuracy of coefficient of friction calculations.
The coefficient of friction for multi-sectional Prony brakes can only be calculated using the complete accumulation of the brake, as individual sections cannot be calculated nor monitored during dynamic operation. Only single chambered brakes can provide true coefficient of friction value calculations and monitored during dynamic operation.
Remember, unlike the intermittent usage of air-cooled brakes as used on a motorized vehicle, a frictional Prony brake dynamometer may be required to operate at high power loads for extended periods of time during test sessions. Under such conditions the Prony brake requires secondary cooling, normally water. The heat produced during extended operation can be calculated using the mechanical equivalent of heat and the quantity of power being absorbed. It is the heat being absorbed during dynamic operation that must be dissipated into the cooling media as effective as possible and removed as efficiently from the system as possible.
The chart below represents a range for coefficient of friction values used to monitor my newly patented radial force Prony brake dynamometer during dynamic operation. It is these values which represent performance efficiency during dynamic operation. With the ability to monitor these values, maximum brake life can be achieved. 
I have withheld the exact formulas for determining the coefficient of friction for radial and axial force brakes used. These calculations are highly proprietary to myself as I have spent 55+ years in this study. Included in this article is information which provides you the basis for coefficient of friction analysis of radial and axial force brakes, used as a dynamic absorption dynamometer. The use of variables is required to create reliable coefficient of friction values. The coefficient of friction should not be used to compare the performance relationship for different designs, or the size of the brake, as each design requires independent evaluation of brake configuration and application.
While using a Prony brake as a dynamometer, the cooling efficiency provides the ability to control the temperature at the kinetic point of friction, combined with efficient heat transfer, which extends the brake’s life. Finally, this amounts to the ratio of BTUs discharged, per square inch of frictional surface contact, per revolution, and the ability to monitor dynamic coefficient of friction.
In conclusion, many elements must be taken into consideration when comparing the relationship between the coefficient of friction of a water cooled, wet friction Prony brake to its performance. This is true when a friction brake is being used as a dynamometer.
Information contained in this article and the article are the property of Aaron Warsaw.