Understanding Designs of Mechanical Systems By Ezra Thompson and John Mativo

As shown, mechanical advantage is critical for energy conservation and efficiency. Introduction

Have you ever wondered how to interest students in learning mechanical principles? If yes, then this article is for you. Mativo and Stienecker (2007) and Mativo (2009) encourage the learning of engineering to be both fun and educational. Why mechanical systems? Learning mechanical principles takes students beyond the hands-on experience into higher-order learning. Haik and Shahin (2011) discuss the engineering design processes, which include essential transferable skills. Mechanical systems, such as transportation systems, have such transferable skills as they are applied everywhere in daily routines for personal and industrial purposes. This article examines mechanical systems based on science, technology, engineering, and mathematics (STEM) standards based on the Georgia state engineering and technology program. This approach provides a model that integrates different subject areas toward a solution. The interdisciplinary approach is hoped to stimulate critical-thinking skills through hands-on activities. A history and description of mechanical power transmission theory is given, followed by design problem scenarios in which two practical examples are given to interest and engage high school students in mechanical design systems. A related class activity is provided at the end of the article for teachers to use with students.

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All drawings are made by the authors and equations are mathematical representation of physical behavior.

Mechanical Power Transmission Theory

The development of power transmission stretches back to the Babylonian and Egyptian era in the 1500s BC. They used belts and pulleys to transmit power between shafts (Scott 2000). Transmission devices have been used primarily to gain mechanical advantages (MA) for accomplishing difficult tasks. Power transmission development continued and was used to grind wheat and grains, lift water and materials with capstan, and as a windlass, combined with ropes and pulleys, later in the second century BC to third century AD. Around 200 AD the Europeans began using wind mills, pneumatics, flat belts, spiral gears, linked chains and antifriction bearings. In the eighteenth century metal gears replaced wooden gears, ropes, and belts. Steam engines began to provide water for pumping water. By the turn of the nineteenth century, alternative energy saw high pressure water and air replacing human and animal power sources. In the 20th century internal combustion engines and electric motor became the main prime movers for industry (Scott 2000), with electricity remaining the primary source of energy. Figures 1(a) and (b) represent simple machines of a lever and a pulley with a mechanical advantage of one (where, MA= Load ÷ Effort = 1) . Today, simple machines are used within more complex power transmission configuration systems or integrated systems. Power transmission systems follow the principle of energy conservation that energy cannot be created nor destroyed. It can be transformed into different forms.

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Lever Effort

Load

Fulcrum

Figure 1 a: Simple machines - Lever

Learning Standards

The activities described below are based on principles on STEM standards for engineering and technology programs in Georgia (downloaded 8/15/2010). The relevant standards are: • ENGR-STEM3 – Students will design technological problem solutions using scientific investigation, analysis and interpretation of data, innovation, invention, and fabrication while considering economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability constraints. • ENGR-STEM4 – Students will apply principles of science, technology, engineering, mathematics, interpersonal communication, and teamwork to the solution of technological problems. • ENGR-STEM5 – Students will select and demonstrate techniques, skills, tools, and understanding related to energy and power, bio-related, communication, transportation, manufacturing, and construction technologies.

Recommended Sequence of Activities

Effort

Load

Figure 1b: Simple machines - Pulley

Design Problem Scenario

A manufacturer would like to design an automated system similar to the one shown in figure above, to raise 2.5Kg loads, 200cm up unto a conveyor belt, within a time of 30 seconds. The design will include a controlled basic electric circuit as prime mover. The power transmission system should gain MA as work is done on a container holding the load at the opposite end. The designer must analytically determine and select the most effective of the availed two power transmission system examples described above.

Design Objective

The purpose of this design concept is for students to apply principles in science, technology, engineering, and mathematics (STEM). Students will primarily focus on the electrical (see Figure 2) and mechanical (see Figures 3 and 5) systems by examining: • the transmission of energy • explaining different patterns of motion of objects (e.g. acceleration, and inertia)

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1. Research: Find out about the variety of applications of raising loads using automated systems. Look at examples like elevators, cranes, car lifts, and robotics machines. Historic development of lifting loads from the human arm to use of automated machines. 2. Apply analytical tools to design and to show how two systems can be used for power transmission to raise maximum load 2 Kg through a height of 20 cm. The prime mover will be a mini-motor (rated @ 12Volts/0.14Amps). 3. Construct model automated systems using available materials, tools, and other resources. 4. Test automated lift systems to determine which power transmission system will be more efficient to lift loads. 5. Discuss the differences between systems actual operation.

Example of Basic Electric Circuit Design

An electrical circuit is represented in Figure 2 on page 3. It consists of a source (12 Volts DC), control device (singlepole switch), conductors (22 gauge wires), and a load (motor). These components are arranged in series with only one path for current to flow. The design of electrical circuits is based on Ohm’s Law and derived power formulas (Buban, Schmitt, and Carter, 1999). Example: If the 12 V source delivers 0.14Amp to the motor its maximum power, P (in watts, W) can be calculated, P = current, I x voltage, V = 0.14A x 12 V = 1.68 W.

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d

Control Device

Source

Load

M

Conductor

Figure 2: Basic Electric Motor Circuit.

Practical Example of Power Transmission #1

In this example Figure 3 shows a power transmission system that is made up of a belt and pulley to be driven by a motor/ gearbox. The load will be raised as the pinion (driver pulley) drives the driven pulley. With a gear ratio of 100:1 the pinion output rotation will be 125 rev/min. A second pulley (Radius - 20 mm pulley), connected to the driven pulley axle to raise the load, is also connected to the shaft of the motor. The motor shaft rotates at a velocity of 125 rev/min. A 40 mm diameter pulley will be connected to the same shaft with Wheel #2. If a rope tied to the load will be fixed at the other end to the pulley, what are the torque, power and current specifications of the motor that can be used for raising the 2Kg load through a distance of 200 cm? What will be the acceleration of the load as it is raised upward? Driven Pulley

Motor/Gearbox Ratio 100:1

F

Figure 4: Force applied perpendicular to the axis pulley. Rotation: The distance 200cm or (2 m) that the load is raised will be equivalent to the number of revolutions times πD , (where d = 40 mm, is the diameter of the pulley that is on the shaft being driven). Thus, 2m = 2π(0.02m)  (# of revs.) and # of revs = 2m . = 16 2π (.02) Since it must take a time of 30s to raise the load, then rev 16 rev = = 0.53 . s 30s Dia. = 10mm of pinion is connected to motor/gearbox output shaft, has a ratio of 1:4 with the driven wheel. Therefore, it has a rev 4(.53) = = 2.1 . s 1 Power can now be determined at the motor shaft. The gearbox ratio of 100:1 from the motor to the pinion will be factored into this calculation. Pshaft =

Torque (N – m)  Rev (RPM) 9549

(9549 is constant like 5252 for power calculations in footpound and horsepower). Pshaft = (0.4905 (N – m)  (2.1 rev  60 min  100)/ (9549  s  1) = 0.65W If voltage applied to motor will be 12 volts then current, 0.65W I= 0.054 A . 12V

Practical Example of Power Transmission #2 2.5 Kg Load

Figure 3: Force applied perpendicular to the axis pulley. The calculation of torque can be done when a load is acting at a distance from the center of a pulley as shown in figure 4. Pulley’s Torque, T = Force, F  Distance, d = (mass  gravity)  distance Therefore, m T - (2.5 Kg  9.81 s2 )  (0.02 m) = 0.4905 N - m. 3

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Figure 5 is an example of a moveable class 2 pulley with a mechanical advantage of 2. Pulley C is connected to the motor/gearbox as prime mover with a similar gear ratio of 100:1. ∑ F = ma: 24.525 – 2T = 2.5 a

(Pulley free body diagram equation to find acceleration, (a) of load moving up 200 cm. s - ut +

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1 2 1 at = 2m = 0 + a(302) 2 2

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m Therefore, a = 0.0044 s2 Thus, 24.525 – 2T = 2.5 (0.0044) , yields T = 12.26 N (this is the tension in the rope that will create the torque on pulley A), connected to the output drive shaft of motor/gearbox. Therefore, T = (12.26 N)  (0.02 m) = 0.245 N – m

Pulley B Pulley A Driver C

2.5 Kg Load Figure 1. Practical Example of a Class 2 Pulley Power Transmission System.

Rotation: The length of rope that will turn around pulley C is twice the distance 200cm or (2 m) that the load will be raised , (where d = 40 mm, is the diameter of the pulley that is on the shaft being driven. Thus, 4m - 2π(0.02m)  (# of revs) and # of revs = 4m - 32 . 2π (.02) Since it must take a time of 30s to raise the load, then, rev = 32 rev = 1.06 s 30s . Power can now be determined at the motor shaft. The gearbox ratio of 100:1 from the motor to the pinion will be factored into this calculation. Torque (N – m)  Rev (RPM) Pshaft 9549 (9549 is constant like 5252 for power calculations in footpound and horsepower). Pshaft = (0.4905 (N – m)  (1.06 rev  60 min  100)/ (9549  s  1) = 0.164W

Typical Motor (M) Specs: Voltage Range: 6V-12V. Nominal Voltage: 12V. RPM: 12,500 max.

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Sample Class Activity Objective: To demonstrate the influence of mass on mechanical advantage of mechanical power transmission system. Supplies: Motor/gear combination unit 100:1, 6 V DC, pulleys dia. 40 mm & dia. 10 mm , drive belt, chainsprocket system 40 teeth & 20 teeth, weights 0.5 Kg to 2.5 Kg, and work area (1m x 1m). Specifications may vary with what is available in your laboratory. In the absence of supplies in your laboratory, you may use those described earlier in the paper. Procedure: 1. Secure the motor unit at the table so that its shaft is hanging over table to allow pulley/belt/load operations. 2. Once item number 1 above is achieved, the pulley should hang perpendicular to the horizontal radius of the motor. Attach various masses from 50 kg to 200 kg for experimentation. 3. Record your results of how long it takes to raise each load through the distance for which load is raised. 4. Calculate the power at shaft to raise applied load. 5. Repeat steps 1–4 for another system. Questions to explore with class: • What difference does the hands-on activity make in reinforcing the theory related to mechanical principles of the paper? • What are the differences in MA created by the different system set up? • How can other systems in real life situation such as a crane lift mechanism be analyzed? Conclusion The article provides historical background, theory, and practical examples of how mechanical systems are applied. As shown, mechanical advantage is critical for energy conservation and efficiency. The interdisciplinary components of STEM shows the links of how engineering discipline mathematical and scientific principles contribute to finding solutions to common problems. The class activity will provide students fun and interesting ways of learning. The design examples show that practical example #2 requires less power to raise the same load of 2.5 Kg through a distance of 200 cm. In example #1 the torque produced at the motor is a direct result of the load being raised. In

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example #2 the power transmission has a better mechanical advantage, which reduces the torque on the prime mover. Please note that assumptions of a weightless and frictionless power transmission system were made to simplify computations. It is worth stating that your computation and experimentations variance will be partially caused by this assumption. Other causes of the variance or error may include human error and instrument calibration. A class activity was given for your exploration.

References

Buban P., Schmitt M., and Carter C., (1999). Electricity and electronics technology. Glencoe/McGraw-Hill, NY. Scott T. E., (2000). Power transmission: Mechanical, hydraulic, pneumatic, and electrical. Ohio University Columbus Ohio. Georgia Performance Standards. Retrieved from: http://www.bufordcityschools.org/ BHS/teachers/andrewsmalley/documents/ EngineeringandTechnologyGeorgiaPerformance StandardsENGINEERINGAPPLICATIONS.pdf. Haik, Y. & Shahin, T. M. (2011). Engineering design process. Cengage Learning. Stamford, CT. Mativo, J. M. (2009). Engineering design: The mechatronics approach and cognitive experience. American Society for Engineering Education. Retrieved from http://soa.asse. org/paper/conference/paper-view.cfm?id=10043. Mativo. J. M. & Stienecker, A. (2007). Innovative exposure to engineering basics through mechatronic summer honors program for high school students. American Society for Engineering Education. Retrieved from http://soa.asee. org/paper/conference/paper-view?id=3984.

Ezra Thompson is a doctoral degree students at the University of Georgia in Athens, GA. He can be reached via email at [email protected]. John Mativo, Ed.D. is a professor in the Workforce Education Department/Faculty of Engineering at the University of Georgia in Athens, GA. He can be reached via email at [email protected]. This is a refereed article.

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