**ISO 17025 When Calculating Torque Measurement Error Cosine Error should be considered**

A ‘vector’ is known as a quantity that is defined by its size and direction. Every time the effect of a known force is evaluated on a static or dynamic system, all applied and resulting forces should be determined by both their magnitude and direction. For instance, if one says that a 100 lbf force is applied at ‘point X’ on a table, without fully defining the applied force direction, an infinite number of solutions each with its own set of results can be generated.

One method of measuring torque is through applying a known force to the end of an arm with known length. One end of the arm is normally fixed to the point of interest where the torque is measured, and the known force is applied to the other end of the arm. The applied torque is then determined by multiplying the applied force by the torque arm length. If done correctly, this simple method can be the most accurate method of torque measurement. Most high accuracy torque measurements by National Metrology Institutes such as PTB and also by Morehouse are done by this method. Numerous details must be considered in the setup of such torque measurement machines, and they are typically made to highest manufacturing precision standards available. The known force in these machines is induced by deadweights accurately calibrated and adjusted for local gravity, material density and other factors that may affect the gravitational forces applied on a known mass. In deadweight torque machines, the system allows the gravity forces to align the applied force; however, the fixed point where the torque transducer is installed is precisely manufactured and maintained during calibration to produce a 90° angle between the applied force and torque arm direction. In other words, the force vector in the machine is defined by the number of deadweights (calibrated for force) and gravity direction.

For general industrial purpose, however, some accuracy might be sacrificed for faster and more efficient torque measurements. When accurately calibrated torque wrenches are not available, some users may try to use alternative methods such as the one shown in Figure 1 to measure torque. Although this method might look feasible at the first glance, it is very difficult to maintain all requirements of a proper torque measurement with it. One potential issue could be the determination of applied force assuming the device was calibrated using force and not mass weights as discussed in our previous post. If we assume the dynamometer used in Figure 1 shows the applied force with 100% accuracy (which does not exist in real life), still without knowing the complete characteristics of the force vector, this method could lead into highly erroneous torque measurement values. By having a second look at Figure 2, you will realize that the angle between the wrench direction and the applied force is not close to 90°. Only this one factor can result in major errors in the measured torque value if it is not accounted for.