Find the first two natural frequencies and mode shapes for the torsion modes of the crankshaft.
Figure Q2 shows an idealisation of a crankshaft and flywheel for a five cylinder-in-line engine showing rotational stiffnesses and rotational inertias. The rotational stiffnesses represent the stiffnesses of the crank throws. They are all 16 x 105 Nm/rad. The rotational inertias represent the effective inertias of the pistons and con-rods referred to the crankshaft. These are all 1.8 kg m2. The rotational inertia of the flywheel is 35 kg m2. Find the first two natural frequencies and mode shapes for the torsion modes of the crankshaft. (Ignore the rigid body mode in which all inertias rotate equally at zero frequency. (
Department of Mechanical, Automotive and Manufacturing Engineering
Coursework Brief
Module Title
Power train and Engine Dynamics
Cohort (Sept/Jan)
Sept/Jan
Module Code
M21MAE
Coursework No. / Title
Coursework 2
Hand out date:
13/04/2015
Lecturer
Jonathan Saul
Due date:
01/05/2015
Estimated Time (hrs)
10 hrs
Coursework type:
Assignment
Extensions allowed:
If required please submit the appropriate forms to registry
% of Module Mark
50%
Submission arrangements:
This is an online submission. You must submit one document to the link on the Module Moodle page.
This is a calculation exercise, but does need to be word processed. Use the equation editor in Word to present your equations and calculations.
All assumptions must be stated throughout the document.
All calculations must be annotated so that the process can be followed.
Your work must include all graphs sketched and produced in excel.
This is an individual piece of work and therefore must be completed individually, and any student or groups of students seen to have copied, plagiarised, etc. will be subject to a plagiarism review panel.
Task and Quality Mark distribution:
Question 1
The firing order of a five-cylinder, in-line engine is 12345. Their physical order on the engine is 32451. The piston stroke is 80 mm and the length of each connecting rod is 180 mm. The pitch distances between the cylinder centres are 80 mm, 80 mm, 80 mm and 80 mm respectively. The reciprocating mass associated with the piston and con-rod is 1.2 kg for each cylinder.
(a) Show that the out-of-balance primary and secondary forces are zero
(2 marks)
(b) Evaluate the primary and secondary moments. Use an engine speed of 2400 rpm.
(8 marks)
Question 2
Figure Q2 shows an idealisation of a crankshaft and flywheel for a five cylinder-in-line engine showing rotational stiffnesses and rotational inertias. The rotational stiffnesses represent the stiffnesses of the crank throws. They are all 16 x 105 Nm/rad. The rotational inertias represent the effective inertias of the pistons and con-rods referred to the crankshaft. These are all 1.8 kg m2. The rotational inertia of the flywheel is 35 kg m2.
Find the first two natural frequencies and mode shapes for the torsion modes of the crankshaft. (Ignore the rigid body mode in which all inertias rotate equally at zero frequency.
(10 marks)
Flywheel
1.8 1.8 1.8 1.8 1.8 35
16 x 105 16 x 105 16 x 105 16 x 105 16 x 105
Figure Q2
Question 3
Under normal full-load conditions, the main engine harmonic of a car with a four-cylinder-in-line engine has an interior sound pressure with amplitude of 10.5 x 10-2 Pa at 3750 rpm at the driver’s ear position. The car has a so-called “active noise suppression system” installed. When switched on, the system controller causes the car’s audio loudspeakers to produce 10.5 x 10-2 Pa at the driver’s ears but at a phase of 160° relative to the main engine harmonic.
A graph of the frequency response curves for A, B and C weighting filters is shown in Figure Q3 for use in this question.
(a) What is the dB(A) level of the interior noise due to the main engine harmonic without the active noise suppression? (The reference pressure for dB sound levels is 20 micro-Pascals.)
(3 marks)
(b) What is the dB(A) level of the interior noise with the active suppression engaged?
(7 marks)
Figure Q3
The firing order of a five-cylinder, in-line engine is 12345. Their physical order on the engine is also 12345. The piston stroke is 80 mm and the length of each connecting rod is 180 mm. The pitch distances between the cylinder centres are 80 mm, 80 mm, 80 mm and 80 mm respectively. The reciprocating mass associated with the piston and conrod is 1.2 kg for each cylinder.
Determine the out-of-balance primary and secondary forces and primary and secondary couples for the engine. This will require you to draw vector diagrams to establish the net forces and net couples. Use an engine speed of 2400 rpm to evaluate the forces. Evaluate the moments of the primary and secondary forces first as moments about the vertical plane through the 3rd cylinder. Then repeat the calculations using a plane through the 1st cylinder. Hence show using vector diagrams that the sum of the moments is the same in both cases and hence that the net moments are couples.
Module Learning Outcomes Assessed:
4. Classify the main power train noise and vibration sources and transmission paths for a motor vehicle and relate vehicle interior noise to aspects of the design of engines and ancillaries through appropriate dynamic models.
5. Write test procedures, apply data analysis techniques and interpret results to understand specific NVH problems related to power train systems, and propose viable design modifications to solve them.
6. Describe and implement the use of Multi-Body systems analysis in engineering design analysis and simulate the kinematics and dynamic behaviour of engines and transmissions elements.
Employability Skills Covered:
Analysis and investigation; Written communication; time management
For group work, individual grades will be determined as follows (tick)
peer assessment
tutor assessment
log book
observed engagement
presentation/viva
individual elements
Academic Conduct Statement:
Mark allocation guidelines
0-39
40-49
50-59
60-69
70+
80+
Work mainly incomplete and /or weaknesses in most areas
Most elements completed; weaknesses outweigh strengths
Most elements are strong, minor weaknesses
Strengths in all elements
Most work exceeds the standard expected
All work substantially exceeds the standard expected
Feedback arrangement:
You will receive all feed back on Moodle 3 weeks post submission.
July 2014
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