ClassX Video Lessons Youtube Channel The Engineering Mindset Gear Train Design – How to calculate gear trains mechanical engineering
In this article, we’ll explore how to calculate the RPM (revolutions per minute) and torque of simple gear trains. These calculations are crucial in mechanical engineering for designing systems that require precise control of speed and force. You can also find an Excel sheet for these calculations in the video description linked to this article.
To understand gear train dynamics, we use the following formulas:
Let’s consider a simple gear train with two gears, Gear A and Gear B. Suppose Gear A has 8 teeth and Gear B has 10 teeth. The gear ratio is calculated as 10/8, which equals 1.25. If Gear A rotates at 150 RPM, then Gear B will rotate at 150/1.25, which is 120 RPM. If Gear A has a torque of 20 Newton meters, then Gear B will have a torque of 1.25 × 20, resulting in 25 Newton meters. Gear B will rotate in the opposite direction to Gear A, slower due to its larger size, but with increased torque.
Now, let’s add Gear C with 20 teeth. The ratio between Gear B and Gear C is 20/10, which is 2. The RPM output from Gear B is 120 RPM, so Gear C will rotate at 120/2, which is 60 RPM. The torque for Gear C will be 2 × 25 Newton meters, equaling 50 Newton meters. Gear C rotates in the same direction as Gear A but slower and with more torque due to its size.
If we introduce Gear D with 8 teeth, the ratio between Gear C and Gear D is 8/20, which is 0.4. The RPM from Gear C is 60 RPM, so Gear D will rotate at 60/0.4, which is 150 RPM. The torque for Gear D is 0.4 × 50 Newton meters, resulting in 20 Newton meters. Gear D rotates in the opposite direction to Gear A, matching its speed and torque due to its size.
In real-world applications, it’s important to consider potential losses due to friction and other factors that can affect the efficiency of gear trains. These calculations provide a theoretical understanding of how gears manipulate speed, torque, and direction.
In a compound gear train, multiple gears are mounted on the same shaft, sharing the same rotational speed and torque. For instance, if Gear A has 8 teeth and Gear B has 10 teeth, the ratio is 1.25. Gear A’s RPM is 150, so Gear B’s RPM is 150/1.25, which is 120 RPM. Gear B’s torque is 1.25 × 20 Newton meters, equaling 25 Newton meters.
If Gear C, mounted on the same shaft as Gear B, has 20 teeth, its RPM remains 120, and its torque is also 25 Newton meters. Gear D, with 8 teeth, has a ratio of 0.4 with Gear C. Its RPM is 120/0.4, which is 300 RPM, and its torque is 0.4 × 25 Newton meters, equaling 10 Newton meters. Gear D rotates in the same direction as Gear A, faster but with less torque.
When designing gear trains, it’s essential to consider the number of gears, their sizes, and the required torque and speed for your application. Understanding these principles will help you create efficient mechanical systems.
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Engage with an online gear train simulator. Adjust the number of teeth on each gear and observe how it affects RPM and torque. Reflect on how these changes align with the formulas discussed in the article. This hands-on experience will deepen your understanding of gear dynamics.
Work in small groups to solve a series of gear train problems. Each group will be given different gear configurations and must calculate the resulting RPM and torque. Present your solutions to the class and discuss any challenges faced during the calculations.
Create a project where you design a gear train for a specific application, such as a clock or a simple machine. Calculate the necessary gear ratios, RPM, and torque to achieve the desired performance. Present your design and calculations to the class.
Analyze a real-world case study where gear trains are used, such as in automotive transmissions or industrial machinery. Discuss how the principles from the article apply to these systems and identify any additional factors that engineers must consider.
Use the provided Excel sheet to perform gear train calculations. Input different gear configurations and observe the changes in RPM and torque. This exercise will help you become proficient in using tools for engineering calculations.
Here’s a sanitized version of the provided YouTube transcript:
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Let’s look at how to calculate the RPM and torque of simple gear trains. By the way, you can download an Excel sheet of these calculations; links can be found in the video description.
We’re going to use the following formulas:
1. Ratio = T of the output gear divided by T of the input gear
2. RPM output = RPM input divided by the ratio
3. Torque output = Ratio multiplied by the torque input
For example, if Gear A has 8 teeth and Gear B has 10 teeth, the ratio is 10 divided by 8, which is 1.25. If Gear A rotates at 150 RPM, then 150 divided by 1.25 equals 120 RPM. If Gear A has a torque of 20 Newton meters, then 1.25 multiplied by 20 gives us 25 Newton meters. This gear will rotate in the opposite direction to Gear A; it will rotate slower because it is larger, but it will have more torque.
If we add Gear C with 20 teeth, the ratio is 20 divided by 10, which gives us 2. The RPM output is 120 RPM from Gear B divided by 2, which gives us 60 RPM. The torque will be 2 multiplied by 25 Newton meters from Gear B, resulting in 50 Newton meters. This gear will rotate in the same direction as Gear A, but it will rotate slower because it is larger, although it will have more torque.
If we were to add Gear D with 8 teeth, then the ratio is 8 divided by 20, which gives us 0.4. The RPM is 60 RPM from Gear C divided by the ratio of 0.4, which gives us 150 RPM. The torque is 0.4 multiplied by 50 Newton meters, resulting in 20 Newton meters. So this gear will rotate in the opposite direction to Gear A, but it is the same size, so it will rotate at the same speed and have the same torque.
However, this doesn’t take into account any losses that we would see in the real world. This setup lets you visualize how gears manipulate speed, torque, and direction.
What if we had a compound gear train like this, which has the same size gears, the same input torque, and the same rotational speed? Again, links in the video description for the Excel sheet calculator for this.
With this setup, we have four gears: A, B, C, and D, but B and C are compound. If Gear A has 8 teeth and Gear B has 10 teeth, then the ratio is 10 divided by 8, which is 1.25. Gear A rotates at 150 RPM, so Gear B is 150 RPM divided by 1.25, which gives us 120 RPM. Gear A has a torque of 20 Newton meters, so Gear B is 1.25 multiplied by 20 Newton meters, which is 25 Newton meters. This gear rotates in the opposite direction to Gear A; it will rotate slower because it is larger, but it has more torque.
If Gear C has 20 teeth, then the ratio is 20 divided by 10, which is 2. The RPM will be the same as B, which is 120 RPM, because these two gears are compound and share the same shaft. The torque is also going to be the same as B, so it’s 25 Newton meters. This gear also rotates in the opposite direction to Gear A; it will rotate slower than Gear A because of the size of Gear B, and it will also have less torque than Gear A, again because of Gear B.
If Gear D has 8 teeth, then the ratio is 8 divided by 20, which is 0.4. The RPM is 120 RPM from Gear C divided by 0.4, which is 300 RPM. The torque is 0.4 multiplied by 25 Newton meters from Gear C, which equals 10 Newton meters. So this gear rotates in the same direction as Gear A; it rotates faster but with less torque.
So we need to consider the application of the gearbox, how many gears are connected, and what torque and speed we require.
That’s it for this video! To continue learning about mechanical and automotive engineering, check out one of the videos on screen now, and I’ll catch you there for the next lesson. Don’t forget to follow us on Facebook, Twitter, Instagram, LinkedIn, as well as TheEngineeringMindset.com.
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This version maintains the essential information while improving clarity and readability.
Gear – A rotating machine part having cut teeth or cogs, which mesh with another toothed part to transmit torque. – In mechanical engineering, gears are used to change the speed and torque of a motor.
Train – A series of gears or other mechanical components that transmit motion and force from one part of a machine to another. – The gear train in the transmission system allows the car to switch between different speeds efficiently.
RPM – Revolutions per minute, a unit of rotational speed or the number of turns in one minute. – The motor operates at a maximum of 3000 RPM, which is suitable for high-speed applications.
Torque – A measure of the force that can cause an object to rotate about an axis. – Increasing the torque in an engine can improve the vehicle’s acceleration performance.
Ratio – The quantitative relation between two amounts, showing the number of times one value contains or is contained within the other. – The gear ratio determines the relationship between the input speed and the output speed in a gearbox.
Mechanical – Relating to machines or the principles of mechanics. – Mechanical systems often require regular maintenance to ensure optimal performance.
Engineering – The application of scientific and mathematical principles to design and build structures, machines, and systems. – Engineering students must understand the fundamentals of physics to solve complex problems.
Friction – The resistance that one surface or object encounters when moving over another. – Reducing friction in mechanical components can lead to increased efficiency and longevity.
Efficiency – The ratio of useful work performed by a machine or in a process to the total energy expended or heat taken in. – Improving the efficiency of an engine can significantly reduce fuel consumption.
Dynamics – The branch of mechanics concerned with the motion of bodies under the action of forces. – Understanding the dynamics of a system is crucial for predicting how it will respond to external forces.
