Belt Drive Laboratory Exercise

Belt Drive Laboratory Exercise An investigation into the relationship between tensions in a slipping pulley and comparison of experimental and theoretical results 1. Summary The transmission of power across machines and systems in industry is vitally important and belt drives can provide this in a cheap but efficient form. In this experiment, a flat belt was attached around a pulley at four separate contact angles and the tensions both before and after the pulley were recorded as the mass was changed to investigate the belt tension ratio and efficiency of the pulley, and how this compared to theoretical results. The experimental and predicted results were found to be very similar, confirming the expectation that an increase in contact angle would cause an increase in belt tension ratio. Also, a peak efficiency of 67.95% was measured which was significantly lower than the average modern day efficiency of 95%.   2. List of Symbols Symbol Meaning  µ coefficient of friction between belt and pulley ÃŽÂ ± half vee belt angle ÃŽÂ ² angle of contact between belt and pulley T ­1 tension after pulley T2 tension before pulley mm millimetres N newtons V volts A amps g grams à Ã¢â‚¬ ° rotational speed rpm revs per minute ÃŽÂ · efficiency POUT output power PIN input power T torque Nm newton metres 3. Introduction Belt drives are a cost effective, easy to use devices designed for power transmission between machines or shafts. The origins of traction devices can be traced back as far as the Babylonians and Assyrians with flat belts, made of leather, becoming the main source of power transmission in factories during the industrial revolution. Although flat belts are still used today, the introduction of vee belts by John Gates in 1917 revolutionised short distance power transmission, being able to generate more power than a flat belt for a pulley of certain diameter. Modern belt drives are able to transmit power at an efficiency of 90-98%, averaging 95% [1]. Vee belts provided the opportunity for continuously variable transmission with their ability to work on pulleys of variable diameters, a useful advantage over other forms of transmission. However, the main disadvantage is the slip between belt and pulley which can limit the efficiency of the drive; the factors contributing to this are the belt profile, the friction and the amount of torque. This report investigates the relationship between the tensions in a stationary flat belt pulley and subsequently the torque and efficiency, comparing the experimental results with expected values calculated using the theory outlined below. 4. Theory Given the coefficient of friction  µ, vee belt angle 2ÃŽÂ ± and angle of contact ÃŽÂ ² (rad), the relationship between higher tension and lower tension in a slipping pulley, known as the belt tension ratio, is given by the following equation: [2] (equation 1) Given for a flat belt ÃŽÂ ± = 90 ° and knowing sin (90 °) = 1, this equation can be rewritten: (equation 2) It is this theoretical equation which the experimental results will be compared against in order to analyse the relationship between the belt tension ratio and coefficient of friction. 5. Method 5.1 Apparatus Belt drive system set up as shown above in figure 1, with the central pulley of radius 50mm and a load cell measuring with an uncertainty of  ­Ã‚ ­Ãƒâ€šÃ‚ ±0.005N. DC electric motor to provide initial rotational movement of the central pulley, measuring voltage (V) with an uncertainty of  ±0.05V and current (I) with an uncertainty of  ±0.005A. Masses, 100g each, to vary the load applied at the free end of the string Hand held optical tachometer capable of measuring rotational speed (à Ã¢â‚¬ °) of the pulley with an accuracy of  ±0.5rpm. 5.2 Procedure The free end of the string was placed accordingly to ensure the angle of contact, ÃŽÂ ², between the belt and pulley was à Ã¢â€š ¬/2. The motor supply voltage was set to 10V and it was made sure that the pulley was rotating in the correct direction by checking T2 > T1. The spring balance was zeroed before the minimum load, 100g, was placed on the free end of the string and a measurement for T1 recorded off the spring balance. 100g masses were then added individually until a maximum mass was applied and the value on the spring balance after the addition of each mass was recorded. These masses were then removed, the angle of contact changed, and the experiment then repeated for angles of à Ã¢â€š ¬, 3à Ã¢â€š ¬/2 and 2à Ã¢â€š ¬. The maximum mass was achieved when the motor was close to stalling but the voltage value still read 10V. When performing the experiment at the 3à Ã¢â€š ¬/2 angle of contact, values for current and pulley rotational speed were also measured after the addition of each 100g mass. The current (I) was measured by the digital multimeter while the rotational speed of the pulley (à Ã¢â‚¬ °) was measured using the hand held optical tachometer. 6. Results The tension after the pulley (T1) and the mass added to the free end of the string were recorded and collected in a table, which can be found in Appendix A. The values for the mass were converted from kg to N to give the corresponding tensions (T2). A graph of T2 against T1 (figure 2) was then drawn for all four angles of contact ÃŽÂ ². This experimental value was calculated from figure 3 to be 0.3269. Using this value and equation 1 for all four angles, a theoretical plot of the belt tension ratio was able to be produced and compared with the experimental results achieved at the four points, shown through figure 4. 7. Discussion It was expected that as the angle of contact increased, the value of T1 would decrease and therefore the value of the belt tension ratio would increase. It can clearly be seen from the experimental data points produced in figure 4 that the results from this experiment were as expected. Also from figure 4, an analysis of the experimental data points and the theoretical line of best fit shows a clear correlation between the two calculations, confirming the theory discussed during section 3 of the report. The slight differences found between these two forms of data, particularly at ÃŽÂ ²=3à Ã¢â€š ¬/2 where the largest error is found, can be accredited to systematic errors due to the measurements from the load cell. Observing figure 6, the motor efficiency shows a generally increasing trend though the curve begins to flatten out as T2 reaches 9.810N. This shows the relationship between torque and efficiency not to be linear but instead parabolic, demonstrating the idea of a peak efficiency at each contact angle. By differentiating the equation of the line of best fit we can calculate that the maximum efficiency is achieved at a torque of 1.627 Nm with this efficiency being 67.95%. This efficiency is significantly smaller than the modern day average of 95% stated in the introduction; this difference in values can be attributed to various factors affecting the calculations. Firstly, it was assumed that the motor driving the pulley was 100% efficient; in reality this would not be the case as there would be energy lost internally through friction, cooling systems and core losses. Secondly, this experiment was conducted using a constantly slipping flat belt as opposed to a more commonly used form of transmission such as a vee belt, where higher efficiencies would be anticipated. 8. Conclusion To conclude, the experiment outlined in this report was useful in demonstrating the relationship between tensions in a slipping pulley, successfully validating the theory from section 3 that belt tension ratio is related to angle of contact; as ÃŽÂ ² tends towards 2à Ã¢â€š ¬, the belt tension ratio tends towards a maximum due to an increased area of contact and consequently larger friction. In the experiment, a maximum efficiency of 67.95% was calculated at a torque of 1.627 Nm. The graph of efficiency against torque analysed in section 5 demonstrates a need to find the optimum torque of a system in order to achieve maximum efficiency from it. The findings from this experiment are statistically insignificant as the nature of the pulley does not correspond to common industry types. However, the experiment was useful in showing the basic relationships between angles of contact, belt tension ratio and efficiency found in belt drives and the effect slipping can have on the output of these systems. Appendix A Raw Data à Ã¢â€š ¬/2 à Ã¢â€š ¬ 3à Ã¢â€š ¬/2 2à Ã¢â€š ¬ Weight (kg) T2 (N) T1 (N) Current (A) Speed (revs/min) T1(N) T1(N) T1 (N) 1.0 9.810 5.80 3.8 1218 3.40 1.70 0.9 8.829 5.20 3.5 1239 3.05 1.50 1.15 0.8 7.848 4.60 3.2 1256 2.70 1.35 1.00 0.7 6.867 4.00 2.9 1280 2.40 1.15 0.90 0.6 5.886 3.45 2.6 1308 2.05 0.95 0.75 0.5 4.905 2.85 2.3 1340 1.70 0.80 0.60 0.4 3.924 2.25 2.0 1370 1.35 0.60 0.45 0.3 2.943 1.65 1.7 1399 1.00 0.40 0.35 0.2 1.962 1.15 1.3 1429 0.65 0.25 0.25 0.1 0.981 0.5 1.0 1470 0.30 0.10 0.10 [1] Carlisle Power Transmission products, Inc., Energy loss and belt efficiency, [Online]. Available: http://www.clark-transmission.com/images/pdf/carlisle/energy_loss_and_belt_efficiency.pdf. [Accessed 9 February 2016]. [2] J. Darling, ME 10010 Solid mechanics 2 Belt Drive Labratory Exercise, University of Bath, 2016. [3] University of Geulph, Department of Physics, What is torque?, [Online]. Available: https://www.physics.uoguelph.ca/tutorials/torque/Q.torque.intro.html. [Accessed 16 February 2016]. [1] PIX Transmissions Limited, Belts Brief history and types, [Online]. Available: http://www.pixtrans.com/blog/belts%E2%80%93brief-history-and-types.html. [Accessed 9 February 2016]. [2] Groschopp, Efficiency and losses in electric motors, 24 March 2015. [Online]. Available: http://www.groschopp.com/efficiency-and-losses-in-electric-motors/. [Accessed 10 February 2016]. [3] Habatec, Introduction to the power transmission flat belt drive, 2011. [Online]. Available: http://www.habatec.net/HNet/HabaTEC.nsf/vwWebContent/FF5800BDAD1854E0C12571CA0028442B?OpenDocument. [Accessed 10 Feb 2016]. [4] IHS Engineering360, Flat belt pulleys, [Online]. Available: http://www.globalspec.com/learnmore/motion_controls/power_transmission/flat_belt_pulleys. [Accessed 15 February 2016]. [5] J. Darling, ME 10010 Solid mechanics 2 Belt Drive Labratory Exercise, University of Bath, 2016. [6] V. R. Chennu, Belt drives types, advantages, disadvantages, 31 October 2015. [Online]. Available: http://me-mechanicalengineering.com/belt-drives-types-advantages-disadvantages/. [Accessed 15 February 2016].

Fundamentals of Local Area Networks

1. A family wishes to connect several devices to share an internet connection and a Bluetooth wireless printer. They have three personal computers. One is in the same room as the printer. The other two are together in another room. In addition, they want to utilize the network for an internet-enabled television and a VoIP phone. †¢Describe what network device or devices you would recommend they purchase and explain why. My recommendations for this family are to subscribe to a cable internet or DSL service provider. They will need a modem which acts as the gateway for their network.I would have then purchase a wireless Concurrent dual band 802. 11n router and wiring that connect the modem to the router. This would allow them to connect all of their devices over a wireless network and would enable them to send print jobs to the printer through the Bluetooth connection; they will be able to connect their internet-enabled TV thru the wireless network. I would recommend them to purch ase a VoIP phone that can be connected into their computer or router. I feel that this would be the simplest solution for this family. Describe the media utilized. The type of media that will be utilized is wireless 802. 11 for the network and 802. 15. 3 for the Bluetooth printer (Kay, 2006). 2. An enterprise level company wishes to set up a network to support several hundred business users as well as manufacturing equipment in a new building. Describe what network device or devices you would recommend they purchase and explain why. My recommendations would be they purchase: Network switch this is a network appliance used for routing information from one computer to another similar.Routers act as a network gateway, and are often used between an organization's local network and the Internet this would give them a good firewall. Bridges help to direct the traffic over the network. Cat 6 cabling will be used to connect each work station. Fiber-optic cabling will be used to connect hubs to each other. Servers they will manage the access service in the network. †¢Make a list describing different common types of server applications. File serving allows users to share information over the network.The main purpose of a file server is to reduce the amount of storage programs, applications, and files take up on a client’s workstation. A file server can also house database table information (White, 2011). Mail serving is a computer that keeps a record of each email that goes in and out of the network (White, 2011). Print serving usually a computer that is connected to one or more printers that other client workstations can connect to, that accepts print jobs and sends them to the appropriate printer or assigns the print jobs the appropriate priority (White, 2011).Video/media serving this allows for streaming of videos on demand, and for the storage, and recall, of digital media, including pictures, music, and videos (White, 2011). Monitoring and Distributed P rocessing can s be utilized to monitor network resources and health, but when workstations are idle, the processor’s power can be put to good use by applying that power to other processes, thus by increasing overall efficiency (White, 2011). †¢Show which of these applications would you combine together on a single server and which you would use separate servers for.Explain your choices of which to combine and which to leave separate. The applications I would combine are the mail serving, file serving, video/media serving because combining these file will save a lot of storage space. This is the setup we have at my job and it works well. 3. For the network that you have chosen to characterize, identify all network devices utilized and explain the purpose of each in the network. The following devices make up my network a cable modem, this act as the gateway to the internet.A wireless router this device connects all the computers and printer to my network, allowing them to communicate and access the internet. Through the wireless access to the network, they will also have access to the print server, which is housed on the main computer, and thus the printer. References: Kay, R. (2006). UWB, Bluetooth and IEEE 802. 15. 3 Retrieved from: http://www. computerworld. com/s/article/110298/UWB_Bluetooth_and_IEEE_802. 15. 3 White, C. (2011). Data Communications and Computer Networks. (6th ed. ).Cengage Learning. Unit 5 Assignment Rubric Project Requirements|Possible Points|Earned Points| A family wishes to connect several devices to share an internet connection and a bluetooth wireless printer. They have three personal computers. One is in the same room as the printer. The other two are together in another room. In addition, they want to utilize the network for an internet-enabled television and a VoIP phone. Describe what network device or devices you would recommend they purchase and explain why. Also describe the media utilized.Note, you are not required t o detail the topology utilized, but thinking about this will help you to choose and justify your device choices. |15|| An enterprise level company wishes to set up a network to support several hundred business users as well as manufacturing equipment in a new building. Describe what network device or devices you would recommend they purchase and explain why. Note, you are not required to detail the media or topology utilized, but thinking about these will help you to choose and justify your device choices. 15|| Make a list describing different common types of server applications. Show which of these applications you would combine together on a single server and which you would use separate servers for. Explain your choices of which to combine and which to leave separate. |10|| For the network that you have chosen to characterize, identify all network devices utilized and explain the purpose of each in the network. |15|| Total (Sum of all points)|55|| Point deducted for spelling, gra mmar and/or APA errors|| Adjusted Total points|||

Similarities Between Ancient Greece And China Essay

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Chronicle of a Death Untold by Gabriel García Márquez

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