Efficiency Calculations
- Efficiency measures how much input energy is successfully converted into useful output energy or work.
- In mechanical systems like gears and belts, some energy is always lost to heat, friction, or vibration.
- It is expressed as a percentage.
Key formula:
$$\text{Efficiency (%)}= \left(\frac{\text{Useful Output}}{\text{Input}}\right) × 100$$
For mechanical systems:
$$\text{Efficiency (%)}= \left(\frac{\text{Output Work or Power}}{\text{Input Work or Power}}\right) × 100$$
Efficiency is always less than 100% due to energy losses from friction, heat, and other factors.
Context: Gear & Belt Systems
- Gear-driven systems: Efficiency in these systems is influenced by:
- Friction: Between gear teeth.
- Material: Type and quality of the gears.
- Alignment: Proper alignment reduces energy loss.
- Belt-driven systems: Efficiency can be affected by belt slip, tension, and pulley alignment.
Typical efficiencies:
- Spur gears: ~95–98%
- Belt drives: ~90–96% (less if poorly tensioned)
A motor supplies 200 W of power to a belt system, and the output is measured at 180 W.
$$\text{Efficiency} = \frac{180}{200} \times 100 = 90 \%$$
Importance
- Higher efficiency = less energy waste = better sustainability
- Important in applications like automotive engines, conveyor systems, and manufacturing robotics
When analyzing efficiency, always consider external factors like temperature and load conditions, as they can significantly impact performance.
Calculate the efficiency of a gear system with an input torque of 60 Nm, output torque of 54 Nm, input speed of 1200 RPM, and output speed of 1000 RPM.
Solution
$$\text{Efficiency} = \left(\frac{54×1000}{60×1200}\right)×100$$
$$ = \left(\frac{54000}{72000}\right)×100$$
$$ = 0.75×100= 75\% $$
