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Department of Mechanical Engineering 2016 – 2017

Experimental Reporting Skills

Case Study: Safety of a Fairground Ride

Andrew Hari Widjaja (ahw16)

Group 4B

27th October 2016

Table of Contents

1. Abstract iii

2. Nomenclature and Abbreviations iv

3. Introduction 1

4. Materials and Methods 2

4.1 Force Before Hole is Drilled 2

4.2 Test Specimen 2

4.3 Tensile Testing Machine 3

4.4 Strain Gauge 4

4.5 Equipment Errors 5

5. Results 6

6. Discussion 7

7. Bibliography 8

8. Appendices 9

8.1 Appendix A. Calculation of Safety Factor of rod before drilled 9

8.2 Appendix B. Measurement of Young’s Modulus of Mild Steel 11

8.3 Appendix C. Calculation of Young’s Modulus of Aluminium 12

8.3 Appendix D. Derivation of SCF formula 13

8.4 Appendix E. Calculation of Safety Factor of rod after drilled 13

  1. Abstract

Fairgrounds contain different modes of transport for people who want to experience a sensation of risk and danger. In this case, a fairground ride is set to be loaded with 500 kg mass, which rotates on a horizontal track at a maximum speed of 30 rpm. This experiment aims to test the fairground Safety Factor (SF) when a hole is drilled through its connecting rod for additional lighting. Two different setups were used to calculate the SF: before (setup 1) and after (setup 2) a 25 mm diameter hole was drilled through a connecting rod of the fairground ride. Tensile Testing Machine (TTM) and extensometer were used to record the extension with varying forces while strain gauge was used to measure the strain at the point of attachment. From these data, stress-strain graphs were plotted and were then used to calculate the SF for both scenarios. The fairground SF decreased significantly from around 10 where hole has not been drilled to around 3 where hole has been drilled. It was concluded that SF of 3 is insufficient as many assumptions have been made in calculations and properties which led to overestimation on the SF. Two of the assumptions made were: connecting rod and lights are weightless, and engineering stress was used instead of true stress. It is concluded that it is not safe to drill a hole through the rod.

 

2. Nomenclature and Abbreviations

A Cross – sectional Area (m2)

E Young’s Modulus (Pa)

Fc Centripetal Force (N)

m Mass (kg)

r Radius (m)

Vmax Maximum Voltage (V)

Vnom Nominal Voltage (V)

Strain

Stress (Pa)

f Fatigue Strength (Pa)

max Maximum Stress (Pa)

nom Nominal Stress (Pa)

UTS Ultimate Tensile Stress (Pa)

y Yield Stress (Pa)

Angular Velocity

LYS Lower Yield Stress

SF Safety Factor

SCF Stress Concentration Factor

UTS Ultimate Tensile Stress

3. Introduction

A 25 mm diameter hole is planned to be drilled through the connecting rod of the fairground to attach flashing lights to the fairground ride (Figure 1). This experiment aims to make a safety assessment whether the proposed modification is safe to be carried out or not. Unfortunately, it is not possible to non-destructively test the whole system. Hence, a laboratory test was devised. The test was executed by measuring the properties and dimensions of a test piece which was made from the same material as the connecting rod used in the fairground ride. This report also includes calculations for Safety Factor (SF). SF is defined as a ratio between material stress (yield or fatigue) and maximum stress.

Figure 1. Proposed modification to the fairground ride. Modification hole is highlighted by the dotted circle.

4. Materials and Methods

4.1 Force Before Hole is Drilled

Since the car is only held by the rod and is rotating in a horizontal track, the only force acting is Centripetal Force (Fc). Maximum angular is used to get maximum possible force. nom can then be calculated with equation (2).

(1)

(2)

4.2 Test Specimen

Figure 2. Test specimen

The test specimen used was made of mild steel and had a gauge length of 50 mm. The ends of the test specimen are made bigger than the gauge length part so that the machine will have a better grip of it. The diameter, which was measured with Vernier Caliper, was (7.95  0.75%) mm.

4.3 Tensile Testing Machine

Figure 3. Tensile Testing Machine

The test specimen was pulled with varying forces up to a maximum (breaking point) while the data of load and its extension was being recorded to a computer at a 0.1 second interval. From these data, stress and strain can be calculated and plotted. Young’s modulus () can then be calculated by working out the gradient of the elastic part of the graph (linear region). In this experiment, Young’s modulus was only used for validation as no calculation requires Young’s modulus. To calculate SF, equation (5) was used. Fatigue Strength can be estimated to be two-thirds of the Ultimate Tensile Strength.

(3)

(4)

(5)

(6)

4.4 Strain Gauge

Figure 4. Extensometer & Strain Gauge (Front) Figure 5. Extensometer & Strain Gauge (Back)

Strain gauge is a device to measure the strain of an object at the point of attachment. It is made of very small gold foil. When the foil is stretched, electrical resistance changes. This was recorded and logged to a computer. The data was later processed to obtain Stress Concentration Factor (SCF) which was used to calculate maximum stress after hole was drilled. SCF is the quotient of the maximum stress and applied stress. In this experiment, aluminium can be used instead of mild steel because it is only dependent on geometry only.

(7)

The data will also be used to calculate the Young’s Modulus of Aluminium. As stated previously, Young’s Modulus was not required in the calculation but it was used as a checkpoint if something goes wrong.

(8)

Where BV = 2.5 and GF = 2.1  5%

To calculate the SF after the hole was drilled, equation (6) was used again. However, max has increased, so it had to recalculated with equation (9) before substituting it back to equation (6).

(9)

4.5 Equipment Errors

1. Load Cell : 1%

2. Extensometer : 1%

3. Micrometer : 0.005 mm

4. Vernier Caliper : 0.005 mm

5. Ruler : 0.5 mm

6. Strain Gauge : 5%5. Results

Maximum force experienced by the rod occurs when the rod is spinning at maximum speed. Thus maximum force can be calculated with equation (1). Graph 1 is the result of Tensile Testing Machine. This graph can be used to obtain UTS  and LYS. From the graph, UTS  and LYS  are (4.88102  2.5%) and (3.21102  2.5%) MPa respectively. Equation (6) can then be used to calculate yield and fatigue Safety Factors of the rod before hole was drilled. SFyield = (9.76  2.5%)  and SFfatigue = (9.89  2.5%) (Appendix A). Young’s Modulus can also be determined with Graph 1 for the elastic region which is the linear region by calculating the gradient, to give (26  1%) GPa. This result is compared with the data obtained from extensometer where the value of Young’s Modulus is equal to (220  1%) GPa (Appendix B).

The results of 2nd experiment which used strain gauges were used to calculate Young’s Modulus of aluminium and SF of supporting rod after hole was drilled. From calculation, Young’s Modulus of aluminium is 73 GPa (Appendix B) while SF after drilling the hole was (2.82  12.5%) and (2.86  12.5%) for yield and fatigue SF respectively (Appendix D).

6. Discussion

The Young’s Modulus of mild steel was significantly different when different machine was used. When extensometer was used, it was found that Young’s Modulus is around (220  1%) GPa, however this value was much smaller when Tensile Testing Machine was used, around (26  1%) GPa. This was mostly caused by the different in region which the machine is recording the extension. In Tensile Testing Machine, test specimen has gripping sections which are bigger than the part in the middle. When it was pulled, extension did not only occur in the gauge length region, gripping section was also extended but was not accounted for (as 50 mm was used as the gauge length). On the other hand, extensometer clamped the gauge length region only and thus, giving a much more reliable result.

The Safety Factors before the 25 mm diameter hole was drilled was (9.76  2.5%) and (9.89  2.5%). This value might seem to be excessive, however it is important to remember that fairground equipment is not regularly maintained. Hence, this is compensated by using more materials to increase the SF in order for the equipment to be as safe as possible even it means the cost increased.

After the hole was drilled, its SF decreases drastically to (2.82  12.5%) and (2.86  12.5%). The minimum SF is these industries are normally two. These values are still above two which means it is still safe. However, in the calculation, only the mass of car was used. It was assumed that the connecting rod and flashing lights were weightless which is not possible. Secondly, the system has run for a number years, there must be some wear and tear in the system. Thus, if these points were accounted for, the SF might decrease even further. So, drilling a hole in the rod is not advised unless further modifications are made to the system to support the weights and increase the SF.

Another important point is that all the stress calculations that has been made in this report were made with the assumptions that cross-sectional area does not change when specimen is extended, which is not true. Engineering stress is defined as the applied load divided by the original cross – sectional area of a material while true stress is the applied load divided by the cross – sectional area of the specimen at a given time. If this was taken into account, SF might decrease even more.

In conclusion, it might be better to search for an alternative to attach flashing lights to the system. There are a number of solutions instead of drilling a hole that might cause safety of passengers to be compromised. For example, the lights can be stuck to the rod without drilling a hole.

7. Bibliography

• Borrowick, J. N., n.d. How to Write a Lab Report. New Jersey: Prentice Hall.

Forrest, P., 1962. Fatigue of Metals. Oxford: Pergamon Press.

• Imperial College London, n.d. Blackboard. [Online]

Available at: https://bb.imperial.ac.uk/webapps/blackboard/execute/content/file?cmd=view&content_id=_991758_1&course_id=_9028_1&framesetWrapped=true

[Accessed 28 10 2016].

• Kirkup, L., 1994. Experimental Methods: An Introduction to the Analysis and Presentation of Data. Australia: John Wiley and Sons.

• Packer, R. C. B. B. L. D. &. W. I., 2007. A review of the design review process for the fairground rides. Surrey(Epsom): Tech. Rep., Atkins Limited for the Health and Safety Executive.

• R. Packer, B. C. D. L. I. W., 2007. A review of the design review process for fairground rides, s.l.: Atkins Limited.

8. Appendices

8.1 Appendix A. Calculation of Safety Factor of rod before drilled

Figure 1. Proposed modification to the fairground ride. Modification hole is highlighted by the dotted circle.

Centripetal force formula was used to calculate the force experience by the rod.

(1)

Nominal stress calculation

(2)

Uncertainties calculation for UTS  and LYS.

(4)

F has an uncertainty 1% because load cell was used and A has an uncertainty of 0.75% which was the result of recording the diameter of test specimen three times with micrometer.

1st reading : 7.88 mm

2nd reading : 8.00 mm

3rd reading : 7.96 mm

The range of readings is 0.12 mm. So, the uncertainty is 0.06 mm. This is then converted to percentage to give 0.75%. The area of a circle is r2, which means the uncertainty of the area is 1.5%. Hence, uncertainty of  is 1.75%.

From graph 1, UTS  and LYS  are (4.88102  2.50%) and (3.21102  2.50%) MPa.

Calculation of SF uses equation (6).

(6)

8.2 Appendix B. Measurement of Young’s Modulus of Mild Steel

Graph 2. Stress - Strain Graph for mild steel test specimen with Extensometer

The linear regression line equation for this graph:

(10)

If equation 10 is compared to a general straight line equation, which is , the gradient can be known. In this case, the gradient is (220725  1%) MPa or (220  1%) GPa.

8.3 Appendix C. Calculation of Young’s Modulus of Aluminium

Measurements of aluminum plate:

• Width: mm

• Thickness: mm

Table 1. Strain Gauges results

Force (N)

4483

4488

4484

4485

Gauge Number

V1 (mV)

V2 (mV)

V3 (mV)

Vavg (mV)

1

0.340

0.342

0.346

0.343

2

0.325

0.331

0.326

0.327

3

0.183

0.180

0.183

0.182

4

0.103

0.105

0.105

0.104

5

0.087

0.090

0.090

0.089

6

0.083

0.087

0.084

0.085

7

0.096

0.099

0.099

0.098

8

0.099

0.096

0.095

0.099

9

0.104

0.106

0.104

0.105

Gauge number 1&2 are considered as Vmax while 6-9 are Vnom.

Calculation of Aluminium’s Young’s Modulus uses equation (8)

(8)

Where BV= 2.5 and GF 2.1  5%

8.3 Appendix D. Derivation of SCF formula

By definition, SCF is the ratio between maximum stress and the stress applied to an object.

(7)

8.4 Appendix E. Calculation of Safety Factor of rod after drilled

See Appendix C to see the derivation for equation (7)

(7)

By using equation 9, maximum stress can be calculated.

(9)

Calculation of SF uses equation (6).

(6)

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