Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

This page supports the lesson note with a companion video and a short classroom-ready summary.

For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.

Performance objectives

• Define and differentiate between various types of gears.
• Calculate gear ratios, speed, and torque in gear trains.
• Explain the pros and cons of different gear types.
• Describe the basic principles of epicyclic gear trains.
• Sketch various gear arrangements accurately.

Lesson summary

This week, we delve into advanced mechanisms, with a particular focus on gear systems. Understanding these systems is critical because they are fundamental to many technologies we use daily, from the simplest hand drills to complex machinery used in South African industries like mining, manufacturing, and agriculture. Almost any device requiring controlled power transmission uses gears. As future mechanical technologists, a solid grasp of gear systems is vital for design, maintenance, and innovation in these sectors. This knowledge will also contribute to addressing challenges related to efficient energy use and sustainable technology development, important goals for South Africa's future.

Lesson notes

2.1 Gear Fundamentals Gears are toothed wheels that mesh together to transmit rotary motion. They are an essential part of mechanical systems, used to change speed, torque, and direction of rotation.

Gear Terminology: Pitch Circle: An imaginary circle on a gear used to determine the gear's size and tooth spacing.

Pitch Diameter (d): The diameter of the pitch circle.

Number of Teeth (N): The number of teeth on the gear.

Module (m): The ratio of the pitch diameter to the number of teeth: m = d/

N. The module is a crucial parameter for ensuring gears mesh correctly.

Addendum: The radial distance from the pitch circle to the top of the tooth.

Dedendum: The radial distance from the pitch circle to the bottom of the tooth.

Pressure Angle: The angle between the line of action (the line along which the force is transmitted) and the common tangent to the pitch circles. Common pressure angles are 14.5° and 20°. 2.2 Types of Gears Spur Gears: These have straight teeth parallel to the axis of rotation. They are simple, efficient, and commonly used for transmitting power between parallel shafts.

However, they can be noisy at high speeds. Imagine the gears in a simple gearbox driving a water pump in a rural South African community.

Helical Gears: These have teeth that are angled to the axis of rotation. They are quieter and smoother than spur gears because the teeth engage gradually. Helical gears can transmit power between parallel or non-parallel shafts.

However, they generate axial thrust, which requires thrust bearings. Consider the gears in a car's transmission system - helical gears contribute to a smoother and quieter driving experience, important on South Africa's often challenging road conditions.

Bevel Gears: These gears have teeth cut on a conical surface and are used to transmit power between intersecting shafts, usually at a 90-degree angle. Bevel gears are found in differentials of vehicles, allowing the wheels to rotate at different speeds during turns. Think about the gears inside the differential of a bakkie used on a South African farm, enabling it to navigate uneven terrain.

Worm Gears: These consist of a worm (a screw-like gear) and a worm wheel. They are used to transmit power between non-intersecting shafts at a 90-degree angle. Worm gears provide high gear ratios and are self-locking, meaning they can't be easily back-driven.

However, they are less efficient due to sliding friction. Consider their use in heavy-duty winches, like those used in mining operations, where high torque and holding power are required. 2.3 Gear Ratio, Speed, and Torque The gear ratio (GR) is the ratio of the number of teeth on the driven gear (output) to the number of teeth on the driving gear (input). It is also the inverse ratio of the speeds. ``` GR = N_driven / N_driving = Speed_driving / Speed_driven ``` Speed: If the driving gear has fewer teeth than the driven gear, the speed of the driven gear is reduced (speed reduction). Conversely, if the driving gear has more teeth, the speed of the driven gear is increased (speed increase).

Torque: Torque is inversely proportional to speed. If speed is reduced, torque is increased, and vice-versa.

Compound Gear Trains: These involve multiple gears in series, allowing for very high gear ratios. The overall gear ratio is the product of the gear ratios of each pair of meshing gears. ``` GR_total = GR_1 GR_2 GR_3 ... ``` Example 1: Simple Gear Train A motor drives a gear with 20 teeth at a speed of 1200 RPM. This gear meshes with a driven gear that has 60 teeth. Calculate the gear ratio and the speed of the driven gear.

Solution: Gear Ratio (GR): GR = N_driven / N_driving = 60 / 20 = 3 Speed of Driven Gear: Speed_driving / Speed_driven = GR => 1200 / Speed_driven = 3 => Speed_driven = 1200 / 3 = 400 RPM Interpretation: The gear ratio is 3, meaning the driven gear rotates 3 times slower than the driving gear. The speed of the driven gear is 400 RPM. This represents a speed reduction with a corresponding increase in torque. This could represent the speed reduction from an electric motor to the cutting blade in a bandsaw.

Example 2: Compound Gear Train A compound gear train consists of four gears. Gear A (driving gear) has 15 teeth and meshes with gear B (30 teeth). Gear C (20 teeth) is mounted on the same shaft as gear B and meshes with gear D (40 teeth). If gear A rotates at 1000 RPM, calculate the speed of gear

D. Solution: Gear Ratio 1 (GR_1): Gear A to Gear B: GR_1 = 30 / 15 = 2 Gear Ratio 2 (GR_2): Gear C to Gear D: GR_2 = 40 / 20 = 2 Total Gear Ratio (GR_total): GR_total = GR_1 GR_2 = 2 2 = 4 Speed of Gear D: Speed_A / Speed_D = GR_total => 1000 / Speed_D = 4 => Speed_D = 1000 / 4 = 250 RPM Interpretation: The total gear ratio is 4, resulting in a significant speed reduction. Gear D rotates at 250 RPM. Compound gear trains are useful for achieving high gear ratios in a compact space.