UNIVERSITY OF BOLTON SCHOOL OF SPORT AND BIOMEDICAL SCIENCES. BEng (HONS)/MEng BIOMEDICAL ENGINEERING SEMESTER ONE EXAMINATIONS 2016/17

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1 UNIVERSITY OF BOLTON LH13 SCHOOL OF SPORT AND BIOMEDICAL SCIENCES BEng (HONS)/MEng BIOMEDICAL ENGINEERING SEMESTER ONE EXAMINATIONS 2016/17 BIOMEDICAL ENGINEERING MODELLING AND ANALYSIS MODULE NO: BME5001 Date: Wednesday 11 January 2017 Time: am noon INSTRUCTIONS TO CANDIDATES: Attempt any 5 of the 7 questions. Individual marks are shown within the question. This examination paper carries a total of 100 marks. This is an open book examination. Use of Microsoft Excel and Moodle is permitted, but please do NOT open any internet search engines or . Answers obtained using Excel must be written in answer booklets. Excel files must be submitted by transferral to an electronic medium (provided).

2 Page 2 of 5 Q1 The ordinary differential equation (ODE) describing the displacement Y(t) in mm at time t of a voice box simulator can be modelled approximately by the equation below: d 2 Y(t) dt 2 + B dy(t) dt + KY(t) = 16 mms -2 Given : d2 Y(t), dy(t) dt 2 dt and Y(t) all equal 0 at t = 0, B = 4 s -1 and K= s -1 use the method of Laplace transforms to derive an expression for Y(t) and sketch how Y(t) varies with time for the first 2 seconds. Q2 It can be shown that a simple four degree of freedom turning device subjected to torsional loads can be described by T = K where: T and are torque and rotation column vectors respectively and K is the stiffness matrix. Using, T = ( ) Nm and K = [ ]Nm / rad Calculate the displacement vector in degrees. Q3 Test data for the driving torque per angle relating to a small 50 W rotating pump is given in the table below: T(Nmm) Angle 0 π π π 2π 5π 1 7π 4π 3π 5π 11π (Rad) Use this information to generate specific coefficients for an approximate Fourier series and calculate the terms a 2 and b 3 in the series. Calculate the average torque and speed over this period. State why it is not possible to determine terms greater than the third harmonic for this data set.

3 Page 3 of 5 Q4 The pressure in a valve varies in relation to angular movement. The table and graph below φ2 show this variation. The work done by the system is given by the integral pφδ where p is the pressure in KPa, φ is the angle in radians and δ is the constant in mm 3. If δ is 2 x10 6 mm 3, calculate the work done in one cycle. Also, if it takes one minute for a cycle, what is the power rating of the valve? φ1 P (KPa) Table Q4 Angle (Degrees) Angle (Deg) Pressure (KPa)

4 Page 4 of 5 Q5 The stress σ, in MPa, at a point in a body can be described by the following matrix relative to the global co-ordinate system xyz. Using an appropriate technique determine the principal Eigen value (principal stress, Maximum Stress) at this point σ = [ ] MPa Determine also the associated Eigen vector for the maximum stress. Q6 Part of a valve regular operates at a frequency ω of 1.2 rad/s. If the equation of motion is given by: y +2αωny +ωn 2 y = 50Fe jωt with α = 0.15, ωn = 1.5 rad/s (where y is the displacement in mm) (i) Derive an expression for the relationship between F and y neglecting any transient terms. (10 marks) (ii) Calculate the lag between y and F when F is 0.25 N. (iii) Calculate also the steady state displacement y. (5 marks) (5 marks) [Total 20 marks]

5 Page 5 of 5 Q7 A treatment cream system is tested on two sets of patients A and B. Set A uses a treated cream and set B is tested with the untreated cream. The equipment measures the softness of the skin. The lower the value the better the system. The results are shown in table Q7 below. Table Q7 Set A Softness Factor Set B Softness Factor (i) Using this data test the hypothesis that the treatment has no change (H 0) to the one that there is a decrease (H 1). State in your answer the significant value of t and the probability associated with this value. (12 marks) (ii) Also estimate the decrease assuming a 99% confidence limit. (8 marks) [Total 20 marks] END OF QUESTIONS