Derrailleur Pulley Efficiency Test Equipment

The Reactive Torque Pulley Tester (RTPT) is a simple, yet highly accurate piece of equipment designed to measure the frictional losses seen in a derailleur pulley at a given RPM.  The tester measures torque in gm∙cm. Knowing this torque and the RPM of the pulley, the energy consumption in watts is calculated. The shaft of the pulley is rotated via a variable speed AC motor.  This allows a user-definable range of pulley RPM from 1-705RPM.  The pulley under test is slid onto the spindle shaft and tightened down, and the inner race of the pulley bearing rotates with the spinning shaft.  A custom machined weighted wheel is centered and affixed to the teeth of the pulley.  This weighted wheel is 4.5lbs, which is the average force to which a pulley is subjected by the chain spans in a bicycle drivetrain with a stock rear derailleur.  A load cell transducer is connected to a lever arm on the weighted wheel by a fine elastic cord.  When the shaft is spun, the friction from the pulley bearing attempts to rotate the weighted wheel in the same rotational direction as the shaft.  This force (torque) to attempt to rotate the weighted wheel is measured as a linear force by a load cell (the weighted wheel itself does not actually spin).  The load cell is connected to a strain gauge signal conditioner, which converts the force from the load cell to an analog signal.  The strain gauge conditioner is connecter to an analog-to-digital data acquisition device, which is then connected to a PC running DAQ software.  The DAQ software performs all calculations to convert the force to watts.  The software typically averages the data over 1-minute intervals, with a 25 samples/second sampling rate.

Additional notes

  • The weighted wheel was designed to accommodate multiple diameter pulleys. Adapter rings were machined which will accept pulleys with varying tooth counts. An adapter ring is placed in the center of the weighted wheel, the pulley placed in the adapter ring, and a hub locks the weighted wheel to the pulley.
  • The weighted wheel is not only balanced on the plane perpendicular to the shaft, but also balanced laterally along the shaft line. This balance must occur to ensure the weighted wheel places only radial loads, and not axial loads, nor twisting loads on the pulley.
  • A very fine elastic thread connects the load transducer to the wheel. This is done to allow the weighted wheel to exhibit small rotational displacement while a minimal change in force seen on the load transducer. Many of the pulleys tested are not perfectly machined . Some exhibit small amount of runout (center line of the bore not perfectly centered with the outside of the teeth). Some exhibit a non-perpendicular alignment of the shaft and plane of rotation. Because of these minor imperfections, when some pulleys are brought up to speed during a test run, the weighted wheel may vibrate slightly. The elastic thread allows slight wheel vibrations without affecting torque measurements.
  • The accuracy of the RTPT is +/- 0.001 watts

Design Of RTPT

Three unique methods were considered for measuring the frictional losses in a derailleur pulley. These are 1) direct axial torque measurement with the shaft spinning and pulley (teeth) held static, using a rotating torque transducer. 2) Axial reactive torque measurement with a shaft held static and the pulley spinning, using an axial reactive torque transducer, or 3) reactive torque measurement with shaft spinning and pulley held statically using a load cell to measure the reactive to torque of the pulley.

  • The first method described above uses a weighted member attached to the pulley and held rigidly. The shaft is spun at a given RPM and a rotating torque transducer is attached to the shaft to measure the torque required to spin the shaft. With a known RPM, frictional losses can then be calculated. However, the shaft must be supported by bearings as part of the test apparatus, and the power to rotate these bearings will also be seen by the torque transducer. Since the support bearings would most likely consume more power to rotate than the actual bearings in the pulley, the accuracy of this method is limited. Additionally, the cost of rotating torque transducers is an order of magnitude higher than simple load cell transducers.
  • The second method described above uses a static shaft, with a reactive torque transducer fixed to the shaft. A weighted balanced wheel would be firmly attached to the pulley, and that wheel would be spun up to the test RPM by an external source. The reactive torque seen in the shaft would be measured by the axial transducer. This method has similar drawbacks to the first method, as the shaft needs to be supported by apparatus bearings, and the power to rotate the apparatus bearings would overshadow the pulley bearings.
  • The third method described above uses a spinning shaft, and a static balanced weighted wheel firmly affixed to the pulley. The shaft is spun at a given RPM, and the reactive torque is measured in the weighted wheel. A load cell is attached to the wheel. The reactive torque is measured in gm-cm, at a given RPM to determine power. This method is superior to the other two methods, as it does not have the apparatus bearings in line with the torque measurement, and also uses a simple, relatively inexpensive load cell. Also, the weighted wheel does not have any moving parts to create system friction, as opposed to, for example, hanging weights from the pulley to achieve the pulley loading. The weighted wheel with adapter rings is a more expensive approach, with a fair amount of custom machining, but allows for more accurate measurements. The accuracy of this equipment is +/- 0.001 watts. Friction Facts uses this third method of testing to determine pulley efficiency.