Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

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Performance objectives

• Explain the principles of belts, chains, and gears.
• Calculate velocity ratio, speed, and power in these systems.
• Describe the different types and their applications.
• Analyse factors affecting system efficiency.
• Compare and contrast the three drive systems.

Lesson summary

This week, we delve into the fascinating world of power transmission systems. These systems are crucial for transferring mechanical power from an engine or motor to the part of a machine that does the actual work. Whether it’s a tractor ploughing a field, a conveyor belt in a mine, or a bicycle taking you to school, power transmission systems are at work. Understanding how these systems function allows us to design, maintain, and troubleshoot machines effectively. Imagine a farmer's tractor breaking down during harvest season – a mechanic skilled in power transmission systems is essential to get it running again, ensuring food security.

Lesson notes

2.1 Introduction to Power Transmission Systems A power transmission system is a mechanism that transfers mechanical power from a power source (like an engine or motor) to the driven unit (e.g., wheels of a car, rotating shaft of a machine). The three primary types we'll focus on are belt drives, chain drives, and gear drives. 2.2 Belt Drives Definition: A belt drive consists of a belt wrapped around two or more pulleys to transmit power. The driving pulley (connected to the motor) rotates, which in turn moves the belt, causing the driven pulley (connected to the load) to rotate.

Types of Belts: Flat Belts: Simple, inexpensive, but can slip easily. Suitable for low power applications.

V-Belts: Trapezoidal shape fits into grooved pulleys, providing more grip and higher power transmission capability. Commonly used in automotive engines and industrial machinery.

Timing Belts (Toothed Belts): Have teeth that mesh with corresponding grooves on the pulleys, providing positive drive (no slip). Used where precise timing is crucial, like in engine camshafts.

Velocity Ratio (VR): The ratio of the speed of the driving pulley to the speed of the driven pulley. VR = N1 / N2 = D2 / D1 Where: N1 = Speed of driving pulley (rpm) N2 = Speed of driven pulley (rpm) D1 = Diameter of driving pulley D2 = Diameter of driven pulley Belt Speed (v): The linear speed of the belt. v = π D1 * N1 / 60 (m/s)

Where: D1 is in meters N1 is in rpm Power Transmitted (P): P = (T1 - T2) v (Watts)

Where: T1 = Tension in the tight side of the belt (N) T2 = Tension in the slack side of the belt (N)

Advantages of Belt Drives: Simple, inexpensive, absorb shock loads, relatively quiet.

Disadvantages of Belt Drives: Can slip, less efficient than gears or chains, require proper tensioning.

Example 1: Belt Drive Calculation A motor drives a pump using a V-belt. The motor pulley has a diameter of 150 mm and rotates at 1440 rpm. The pump pulley has a diameter of 300 mm. a) Calculate the velocity ratio. b) Calculate the speed of the pump pulley. c) If the belt speed is 11.3 m/s, and the tensions in the tight and slack sides are 800 N and 300 N respectively, calculate the power transmitted.

Solution: a) VR = D2 / D1 = 300 mm / 150 mm = 2 b) VR = N1 / N2 => N2 = N1 / VR = 1440 rpm / 2 = 720 rpm c) P = (T1 - T2) v = (800 N - 300 N) 11.3 m/s = 500 N * 11.3 m/s = 5650 Watts = 5.65 kW 2.3 Chain Drives Definition: A chain drive uses a chain that meshes with toothed sprockets to transmit power.

Types of Chains: Roller Chains: Most common type, used in bicycles, motorcycles, and industrial machinery.

Silent Chains (Inverted Tooth Chains): Quieter than roller chains, used in high-speed applications like camshaft drives.

Velocity Ratio (VR): Similar to belt drives, but based on the number of teeth on the sprockets. VR = N1 / N2 = T2 / T1 Where: N1 = Speed of driving sprocket (rpm) N2 = Speed of driven sprocket (rpm) T1 = Number of teeth on the driving sprocket T2 = Number of teeth on the driven sprocket Advantages of Chain Drives: Positive drive (no slip), higher power transmission capacity than belts, suitable for longer distances than gears.

Disadvantages of Chain Drives: Noisier than belts, require lubrication, more complex than belt drives.

Example 2: Chain Drive Calculation A chain drive connects a motor to a conveyor belt in a mine. The motor sprocket has 20 teeth and rotates at 1000 rpm. The conveyor belt sprocket has 40 teeth. a) Calculate the velocity ratio. b) Calculate the speed of the conveyor belt sprocket.

Solution: a) VR = T2 / T1 = 40 teeth / 20 teeth = 2 b) VR = N1 / N2 => N2 = N1 / VR = 1000 rpm / 2 = 500 rpm 2.4 Gear Drives Definition: Gear drives use meshing gears to transmit power. Gears are toothed wheels that transmit rotational motion and torque.

Types of Gears: Spur Gears: Teeth are parallel to the axis of rotation. Simple and efficient for transmitting power between parallel shafts.

Helical Gears: Teeth are angled to the axis of rotation. Quieter than spur gears and can transmit more power.

Bevel Gears: Teeth are cut on a conical surface. Used to transmit power between shafts that are not parallel (usually at 90 degrees).

Worm Gears: Consist of a worm (screw-like gear) meshing with a worm wheel. Provide high gear ratios for speed reduction.

Velocity Ratio (VR): VR = N1 / N2 = T2 / T1 Where: N1 = Speed of driving gear (rpm) N2 = Speed of driven gear (rpm) T1 = Number of teeth on the driving gear T2 = Number of teeth on the driven gear Torque (T): T = Power / (2 π * N/60) (Nm) Where N is in rpm.

Advantages of Gear Drives: Positive drive (no slip), high efficiency, compact size, can transmit high power.

Disadvantages of Gear Drives: Noisy, can be expensive to manufacture, require lubrication.

Example 3: Gear Drive Calculation A motor rotating at 1750 rpm drives a machine through a gear train. The motor gear has 25 teeth, and it meshes with a larger gear having 75 teeth. a) Determine the velocity ratio. b) Calculate the speed of the driven gear.