11.6:
Mechanical Efficiency of Real Machines
A machine's mechanical efficiency is the ratio of output to input work.
For an ideal machine, the ratio is one, implying that the input and output work are equal.
For instance, in an ideal toggle vise that compresses wood, the output work due to the reaction force equals the input work due to the applied force.
In contrast, a real machine experiences friction force.
The frictional force can be obtained from the normal reaction force.
The total virtual work due to the contributing forces, when applied in the principle of virtual work, gives output work as the difference between the input work and the work due to frictional force.
Dividing output work by input work gives the mechanical efficiency. The efficiency in the absence of friction is one. However, for a non-zero coefficient of friction, the efficiency is zero when the toggle angle equals the friction angle and negative for toggle angles less than the friction angle.
This implies that a vise should be used only for a toggle angle greater than the friction angle.
11.6:
Mechanical Efficiency of Real Machines
The mechanical efficiency of a machine is a fundamental concept that describes how effectively a machine can convert input work into output work. According to this concept, the efficiency of a machine is equal to the ratio of the output work to the input work. An ideal machine, meaning a machine that has no energy losses, has an efficiency of one. This implies that the input work and the output work are equal.
However, in reality, no machine can be truly ideal, and all of them experience some form of energy loss. One of the primary sources of energy loss in machines is friction. For instance, consider a toggle vise used to compress wooden blocks. In the absence of friction, the output work of the vise is equal to the input work of the applied force, making it an ideal machine.
However, in reality, the sliding block of the vise experiences a frictional force against the horizontal plane. To determine the mechanical efficiency of a real vise, first, calculate the normal reaction and corresponding frictional force. Then evaluate the total virtual work of all the forces during the virtual displacement. Applying the principle of virtual work, the output work of the vise comes out to be the difference between the input work and the work of the frictional force.
Consequently, the net reaction force can be calculated, which is zero when the angle of the vise is equal to the angle of friction and negative, when it is less than the angle of friction. This means that the vise should only be used when its angle exceeds the friction angle.
The mechanical efficiency of the vise in the absence of friction is one. However, when friction is present, the efficiency can become zero or less than one, depending on the coefficient of friction. The lower the coefficient of friction, the closer the efficiency will be to one—conversely, the higher the coefficient of friction, the lower the efficiency.
The mechanical efficiency of a machine is an essential concept that explains how effectively a machine can convert input work into output work. In reality, no machine can be entirely ideal, and they all experience some form of energy loss due to friction. When analyzing the efficiency of a machine, it is crucial to consider the effects of friction and its coefficient because they play a significant role in determining the net reaction force and the overall efficiency of the machine. While an ideal machine can achieve perfect efficiency, real machines will always have less than ideal efficiency due to energy losses, especially from friction.
Suggested Reading
- Beer, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. and Self, B.P. (2016). Vector Mechanics For Engineers. Eleventh Edition, New York: McGraw-Hill Education. Pp. 580-581.