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Applications of Advanced Analytical Methods for Mechanical Engineering

Apply advanced analytical knowledge and techniques in practical investigations using a range of mathematical methods in engineering problems.

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Added on  2023-05-28

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This assignment aims to apply advanced analytical knowledge and techniques in practical investigations for mechanical engineering problems. The investigations have been designed to develop understanding of, and ability to apply, a broad spectrum of advanced mathematical techniques in a range of engineering problems. The assignment includes 4 investigations related to mass-spring system, Newton's law of cooling, and toughness of stainless steel.

Applications of Advanced Analytical Methods for Mechanical Engineering

Apply advanced analytical knowledge and techniques in practical investigations using a range of mathematical methods in engineering problems.

   Added on 2023-05-28

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College of Engineering and Technology
1
Sensitivity: Internal
Programmes H300 Mechanical Engineering
H234 Mechanical and Manufacturing Engineering
H334 Motorsport Engineering
H335 Motorcycle Engineering
Module Title: ADVANCED APPLIED ANALYTICAL METHODS 2
Module Code 5ME526
Module Leader Dr Jilin Ye
Lecturers Dr Jiln Ye
Coursework no. 1
Title Applications of Advanced Analytical Methods
Weighting: 60%
Issue Date 1st October 2018
Submission Date By 16:00 on 13th December 2018
Applications of Advanced Analytical Methods for Mechanical Engineering_1
College of Engineering and Technology
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Sensitivity: Internal
Introduction
The aim of this assignment is to apply the advanced analytical knowledge and
techniques in practical investigations. The investigations have been designed to develop
your understanding of, and your ability to apply, a broad spectrum of advanced
mathematical techniques in a range of engineering problems.
Learning Outcomes
On successful completion of this assignment you should be able to:
1. Understand in depth an appropriate range of mathematical principles and
demonstrate the ability to select appropriate mathematical techniques for a
range of engineering problems.
2. Evaluate, analyse and model engineering situations using a range of advanced
mathematical methods.
3. Apply advanced mathematical process to resolve engineering problems.
Assignment brief:
You must complete the following 4 investigations and select suitable techniques to
analyse the data you have been given to answer the problems posed.
Your report should clearly demonstrate how you have selected and applied suitable
advanced analytical techniques to analyse the data and how your solutions address the
initial problems. You should clearly explain your methods, why they are suitable and
what the relevance is of your outcomes.
Applications of Advanced Analytical Methods for Mechanical Engineering_2
College of Engineering and Technology
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Sensitivity: Internal
Investigation 1: Mass-Spring System (25%)
This investigation uses the TecQuipment TM16 Range Universal Vibration Apparatus. The following
diagrams are taken from the TQ User Guide with permission (Figure 1 and Figure 2).
Figure 1. Force Againist Deflection
Figure 2. Setup for Mass-Spring Systems
Applications of Advanced Analytical Methods for Mechanical Engineering_3
College of Engineering and Technology
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Sensitivity: Internal
a) Determine the spring constant k
An experiment is conducted where masses are suspended from a spring and resulting
deflections recorded as shown in Table 1.
Mass
(kg)
Force
(N)
Depth gauge reading
(mm)
Mean reading
(mm)
Extension
(mm)
Loading Unloading
0.0 0 60 60 60 0
0.4 3.92 65 65 65 0
0.8 7.84 70 69 69.5 1
1.2 11.76 74 74 74 0
1.6 15.68 78 78 78 0
2.0 19.6 83 83 83 0
2.4 23.52 87 87 87 0
2.8 27.44 92 91 91.5 1
3.2 31.36 97 96 96.5 1
3.6 35.28 101 101 101 0
4.0 39.2 105 105 105 0
Coil diameter 44.6 mm
Wire diameter 3.1 mm
Number of coils 18
Table 1. Experimentally Measured Spring Deflections for Applied Masses
Complete/fill in the blank cells in the Table 1 with your calculation.
Extension = (gauge reading - gauge reading with no mass on the platform)
Plot a graph of extension(mm) against load (N) and determine the spring stiffness, k in N/m.
0
0.5
1
1.5
0 20 40 60
Extension
Force
Force Line Fit Plot
Extension
Predicted Extension
Applications of Advanced Analytical Methods for Mechanical Engineering_4
College of Engineering and Technology
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Sensitivity: Internal
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.129099
R Square 0.016667
Adjusted R Square -0.09259
Standard Error 0.488246
Observations 11
ANOVA
df SS MS F
Significance
F
Regression 1 0.036364 0.036364 0.152542 0.705201
Residual 9 2.145455 0.238384
Total 10 2.181818
Coefficients
Standard
Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept 0.181818 0.275408 0.660178 0.525673 -0.4412 0.804834 -0.4412 0.804834
Force 0.004638 0.011876 0.390567 0.705201 -0.02223 0.031503
-
0.02223 0.031503
So the spring constant is 4.638 N/m.
Applications of Advanced Analytical Methods for Mechanical Engineering_5
College of Engineering and Technology
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Sensitivity: Internal
b) Investigating the effect of mass on the time period of oscillation
Figure 3. Mass-Spring Oscillation Measurement
An experiment (Figure 3) is performed and the data is recorded in Table 2 below:
Mass
(kg)
Time for 20 oscilations (s)
3.d.p.
Period (s)
3.d.p.2

(s2)
0.8 6.840 0.342 0.117
1.2 7.400 0.37 0.137
1.6 7.925 0.39625 0.157
2.0 8.150 0.4075 0.166
2.4 8.480 0.424 0.179
2.8 8.905 0.44525 0.198
3.2 9.650 0.4825 0.233
3.6 9.980 0.499 0.249
4.0 10.220 0.511 0.2611
Coil diameter: 44.6 mm
Wire diameter: 3.1 mm
Number of coils: 18
Table 2. Measured Time for 20 Oscillations for Series of Added Masses
Applications of Advanced Analytical Methods for Mechanical Engineering_6

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