Development of a Mechanical System to Dynamically Calibrate Pressure Sensors
using a Vibrating Liquid Column
Mugisha Macbeth Ruhweza
Sustainable Energy Engineering, masters level 2017
Luleå University of Technology
Department of Engineering Sciences and Mathematics
Development of a Mechanical System to Dynamically Calibrate Pressure Sensors using
a Vibrating Liquid Column
Mugisha Ruhweza Macbeth
mugruh-1@student.ltu.se
Department of Engineering Sciences and Mathematics
February 23rd ,2017
Preface
This thesis is the final step on my five-year journey of studying the Master Programme in Sustainable Energy Engineering, specializing in Wind and Hydro Power at the Lulea University of Technology. During my period at the University, I had the opportunity to learn extensive knowledge about renewable energy sources and acquired experience of working in project format. Using the necessary methods and tools to develop smart energy solutions, the current energy situation can change in a positive direction.
With immense gratitude, I would like to acknowledge the support and help of my Professor Michel Cervantes at the Lulea University of Technology. He has also been my examiner and consistently allowed this project to be my work but guided and advised me whenever he thought I needed it.
I would also like to thank Arash Soltani Dehkharqani, a Ph.D. student at the Lulea University of Technology.
He was always available whenever I had a question regarding my master thesis.
I would like to take this opportunity and thank all the professors who ever taught me at the University and thanks to those who never taught me but were able to help me whenever I needed it. Thank all my classmates and friends for being patient with me and making me grow as an engineer but also as an individual.
Finally, I would like to express my very profound gratitude to my family and to my partner for providing me with unfailing support and continuous encouragement throughout the process of doing my master thesis.
Lulea, 23rd February 2017 Mugisha Macbeth Ruhweza
Abstract
This report describes a simple mechanical system developed for producing dynamic pressures of up to 50 kP a from zero-to-peak and over the frequency range 0-58 Hz. The system is constructed for dynamic calibration of pressure sensors and consists of an open tube, 30 cm in height, mounted vertically on the support plate.
The support plate is connected to the vibration exciter which is driven by a piston, a connecting rod, disc and axle, and an electric motor. The pressure sensor to be calibrated is mounted vertically at the bottom of the open tube so that the diaphragm of the sensor is in contact with the working liquid in the tube.
When the system is started, the motion of the piston provides a sinusoidal movement to the open tube and calibration is achieved.
The different parts of the system are designed using NX Siemens. MatLab is used to determine the results and graphs from the equations derived. The analysis shows that the displacement, velocity, and acceleration of the system are highly affected by the distance between the disc centre and the disc pin, and the rotational speed of the system. The length of the connecting rod does not affect the displacement and barely affects the velocity and acceleration of the system. The total force, torque, and power of the system is utilized to select the electric motor and the frequency inverter
Key Words: Dynamic calibration; working liquid; pressure sensor; liquid column.
Sammanfattning
Denna rapport beskriver ett enkelt mekaniskt system som utvecklas f¨or att producera dynamiska tryck upp till 50 kP a fr˚an noll-till-topp och ¨over frekvensomr˚adet 0-58 Hz. Systemet ¨ar konstruerat f¨or dynamisk kalibrering av trycksensorer och best˚ar av ett ¨oppet r¨or 30 cm h¨ojd monteras vertikalt p˚a st¨odplattan.
St¨odplattan ¨ar ansluten till vibrationsexcite dvs, den yttre cylindern som drivs av en kolv , en vevstake, skiva och axel och en elmotor. Trycksensorn som skall kalibreras ¨ar monterad vertikalt vid botten av det
¨
oppna r¨oret s˚a att membranet hos sensorn ¨ar i kontakt med arbetsv¨atskan i r¨oret. N¨ar systemet startas, ger r¨orelsen hos kolven som ger vibrationer till det ¨oppna r¨oret och kalibrering uppn˚as.
De olika delarna av systemet ¨ar utformade med hj¨alp av NX Siemens. MatLab anv¨ands f¨or att best¨amma resultaten och diagram h¨arledda fr¨an ekvationerna. Analysen visar att den f¨orskjutning, hastighet och acceleration av systemet ¨ar i h¨og grad p˚averkade av avst˚andet mellan skivans centrum och skivtappen, och rotationshastigheten hos systemet. L¨angdn av vevstaken p˚averkar inte f¨orskjutningen och p˚averkar knappt hastigheten och accelerationen hos systemet. Den totala kraften, vridmomentet och kraften i systemet anv¨andes f¨or att v¨alja de andra komponenterna i systemet dvs, den elektriska motorn och
frekvensomvandlaren.
Nyckelord: Dynamisk kalibrering ; arbetsv¨atska ; Trycksensor; v¨atskepelare.
Contents
Preface i
Abstract ii
Sammanfattning iii
List of Figures v
List of Tables vi
1 Introduction 1
1.1 Background . . . 1
1.2 Aim and Objective . . . 2
1.3 Assumptions and Limitations . . . 2
1.4 Literature Review . . . 3
2 Nomenclature 5 3 Pressure Amplitude 7 3.0.1 Displacement . . . 7
3.0.2 Velocity . . . 11
3.0.3 Acceleration . . . 14
3.0.4 Natural Frequency of the Liquid Column . . . 16
4 Design and Description of the System 18 4.1 Open Tube . . . 19
4.2 Plate support . . . 21
4.3 Piston . . . 23
4.3.1 Piston Cylinder . . . 26
4.3.2 LBBR50 and LUHR50 Design Specifications . . . 27
4.4 Connecting rod . . . 28
4.4.1 Drawn cup needle roller bearings . . . 29
4.4.2 HK0306 T N . . . 29
4.4.3 Moving parts . . . 30
4.5 Disc and axle . . . 31
4.6 The vertical support . . . 31
4.7 The horizontal support . . . 32
4.8 Torque and Power . . . 33
4.9 Electric motor . . . 34
4.10 Frequency inverter . . . 35
4.11 Axle coupling . . . 36
4.12 Y-Bearing Plummer Block . . . 37
4.13 Pressure sensor . . . 37
5 Experiment 39
6 Conclusion 42
7 Recommendation 43
References 45
A Equations for Displacement 46
B Equations for Velocity 49
C Tube design with dimensions 50
D Plate support design with dimensions 51
E Piston designs with dimensions 52
F Connecting rod design 55
G Disc and Axle 56
H Vertical support 57
I Horizontal support 57
J Electric motor design specifications 58
K Design specification of the frequency inverter 62
L Design specifications of the Linear ball bearings 64
M Design specifications of the Linear bearings unit 66
N Design specifications of the needle bearings 67
O Design specifications of the Y-bearing block 69
P Design specifications of the pressure sensor 70
List of Figures
1 Piston with top and bottom dead centre . . . 7
2 Displacement theory of the system . . . 8
3 Triangles . . . 9
4 Displacement with varying values of the distance between the disc centre and the disc pin . . 10
5 Displacement of the system with varying values of the length of the connecting rod . . . 10
6 Displacement of the system with varying values of the rotational speed . . . 11
7 Velocity with varying values of the distance between the disc centre and the disc pin . . . 12
8 Velocity of the system with varying values of the length of the connecting rod . . . 12
9 Velocity of the system with varying values of the rotational speed . . . 13
10 Acceleration of the system with varying values the distance between the disc centre and the disc pin . . . 14
11 Acceleration of the system with varying values of the length of the connecting rod . . . 15
12 Acceleration of the system with varying values of the rotational speed . . . 15
13 System Overview . . . 18
14 Node and antinode of sound waves . . . 19
15 Open Tube design . . . 20
16 Open Tube cross sectional view . . . 20
17 The plate support . . . 22
18 The cross section view of the plate support . . . 22
19 The design of the piston outer cylinder . . . 23
20 The cross sectional view of the piston outer design . . . 24
21 The piston design . . . 24
22 The cross sectional view of the piston . . . 25
23 The piston pin . . . 25
24 LBBR50 linear ball bearings . . . 27
25 LUHR50 bearing unit . . . 27
26 Connecting rod . . . 29
27 Drawn cup needle bearing . . . 30
28 Disc ,disc pin and disc axle . . . 31
29 Vertical support of the system . . . 32
30 Horizontal support of the system . . . 32
31 Electric motor . . . 34
32 Sketch with dimensions of the motor . . . 35
33 Frequency Inverter . . . 36
34 Axle Coupling . . . 36
35 Y-bearing plummer block . . . 37
36 Piezoelectric Pressure transducer . . . 37
37 Mechanical system . . . 38
38 Frequency spectrum of acceleration . . . 39
39 Frequency spectrum of pressure at various speed . . . 41
40 Triangles . . . 46
41 Open Tube design with dimensions . . . 50
42 Open Tube cross sectional design with dimensions . . . 50
43 Plate support design with dimensions . . . 51
44 The cross section of the plate support . . . 51
45 The the design of the piston outer cylinder . . . 52
46 The the cross sectional design of the piston outer cylinder . . . 52
47 The cross sectional view of the piston . . . 53
48 The design of the piston . . . 53
49 The piston pin 2D . . . 54
50 Connecting rod . . . 55 51 Disc ,disc pin and disc axle . . . 56 52 Vertical support of the system . . . 57
List of Tables
1 List of symbols . . . 5
2 List of symbols . . . 6
3 Optimum Operating parameters of the system . . . 17
4 Total mass . . . 33
5 Force, Torque and Power . . . 34
6 Acceleration and frequencies obtained during the experiment . . . 40
7 Difference between experimental pressure amplitude and theoretical pressure amplitude . . . 41
1 Introduction
The need for dynamic pressure calibration has increased.The demand for precise measurements has increased in both industrial and research applications. In hydropower turbines such as Francis and Kaplan, pressure measurements are performed to acquire better perception regarding flow behavior. Determination of the dy- namic sensitivity of pressure sensors, which are utilized to measure the pressure is needed. Static calibration is not sufficient for this purpose, and so another method is required. The two principal methods used during the last decades are; Oscillating Pressure Calibration and Step Pressure Generators.
Different pressure fluctuations are exerted on the Kaplan turbine runner blade with different amplitudes and frequencies. However, to get accurate pressure fluctuation measurements on the runner blade, the pressure sensor response should be fast and precise. This thesis will develop a mechanical system to calibrate pressure sensors dynamically using a vibrating liquid column. Experiments will be carried out on the system in the laboratory with a piezoelectric pressure sensors using the same conditions. The results obtained from both the pressure sensors during dynamic calibration will be analyzed.
There are many different dynamic pressure calibration systems used to calibrate pressure sensors, and the commonly used are listed below; [28, 29, 30].
• The Galton whistle which has a tube sharp at one edge and closed at the other end with a movable piston. Air is blown over the tube to excite the organ pipe resonance. The piston position is used to control the resonant frequency of the system. Both the reference pressure sensor and the pressure under test are mounted on the piston.
• Small shock tubes are used to provide rise time and frequency response characteristics for pressure sensors. However, it is difficult to determine the pressure level in step response method because the system is not usually made for pressure sensitivity during dynamic calibrations.
• Sinusoidal vibration of liquid column mounted vertically on the exciter of an electrodynamic shaker is also used to calibrate pressure sensors dynamically
However, most of these dynamic pressure calibration systems do not meet all the required pressure amplitudes and frequency range required for a specific application, thus developing a mechanical system in this project.
1.1 Background
The missile and space vehicle programs brought the need for precise measurements of rapidly changing pressures. The need for high precision and response measurement has created the need to improve calibration techniques. The frequency response concept established in the electronic and servo fields in the early days was later on developed to measure dynamic pressure for electronic components in the system.
This method evolved both the experimental and analytical methods of calibrating dynamic pressure sensors.
The calibration method has improved over the years due to the development of transform methods such as Fourier and Laplace [7].
In 1971 the National Bureau of Standard Instrumentation Applications Sections developed a method for generating sinusoidally varying pressure amplitude over a frequency range of a few Hertz to about 1 kHz [1]. Many experiments were carried out over the years for development of a dynamic pressure source and calibration methods using liquid as a working medium for the pressure source [2].
A technique commonly used in wind engineering and studying airfoils is to measure dynamic pressures of the tap connected to a remote pressure sensor via a length of seal tubing system. The pressure disturbances lead to distortion caused by a combination of factors such as resonance at the organ pipe and viscous damping [8]. Bergh and Tijdeman [9] developed a critical theoretical model to solve the distortion problem. The model based on a small amplitude assumption that represents the tubing system as a linear time-invariant system. The system can then be described using characteristic transfer functions giving amplitude and phase distortion of sine wave input. Historically distortion was corrected by introducing restrictions to the tubing system in particular locations to flatten the resonant peaks to produce better amplitudes and phase response as linear as possible. Today this is typically done digitally using inverse transfer functions.
1.2 Aim and Objective
The purpose of this project is to build a mechanical system to provide the necessary vibration to the pressure source. The aim of the thesis is to design and construct a system that is capable of operating at the frequency range 0-300 Hz and pressure amplitude of 90 kP a. A step-by-step approach is used to solve the thesis problem. Firstly, several questions listed below were formulated to define and determine the necessary parameters;
• How much acceleration does the system have?
• How much is the displacement?
• How long is the connecting rod?
• What is the optimum value of the distance between the disc centre and the disc pin?
• What is the total mass of the moving parts?
• How much force is exerted on the connecting rod?
The equations to determine the different relevant parameters of the system were derived and the optimum values of these parameters, for example, the acceleration and the distance between the disc centre and the disc pin were determined using MatLab program. A suitable electric motor, bearings, bearing blocks and the frequency inverter for the system were selected based on the determined optimum parameter values of the system. The process also involved visiting experts at Momentum Lulea, SKF Lulea, and Ahlsell Lulea to inquire about the price of the different components and gather more information about the components.
1.3 Assumptions and Limitations
• Acceleration is limited to 300 m/s2 maximum.
• The tube is assumed to be infinitely stiff.
• No-slip Condition
• System considered having a single degree of freedom
1.4 Literature Review
Paul S Lederer et al. (1976) carried out an experiment to develop a new dynamic pressure source for calibration of pressure sensors. A pressure source with a liquid-filled cylindrical vessel, 11 cm in height was mounted upright on the armature of the vibrating exciter driven by an amplified sinusoidal varying voltage.
The pressure source was used to produce sinusoidal pressure amplitude of up to 34 kP a zero-to-peak at the frequency range of 50 Hz to 2 kHz. The pressure sensor mounted near the bottom of the tube, and its diaphragm was in contact with the working liquid in the tube. A small section of the tube was filled with small steel balls to damp the motion of the working fluid. The steel balls were able to extend the useful frequency range to higher frequencies than for an undamped pressure sensor. Over a frequency range of up to 20% of the resonance frequency of the liquid-column pressure sensor combination, the dynamic pressure source was able to provide absolute calibration results to within 5% of the right pressure supplied. [2]
In an experiment for Development of Dynamic Calibration Methods for Pogo Pressure Transducers, Carol F. Vezzetti et al. (1976) suggested vibrating the dynamic pressure source vertically. Two pressure source methods were used to measure oscillatory pressure generated in the propulsion system of the space shuttle.
Rotation of mercury-filled tube in a vertical plane at frequencies below 5 Hz generated sinusoidal pressures of up to 48 kP a peak-to-peak. Vibrating the same mercury filled tube sinusoidally in the vertical plane extended the frequency range from 5 Hz to 100 Hz at the pressure of up to 140 kP a peak-to-peak. Although mercury was recommended for calibrations of pressure sensors at frequencies of 20 Hz, it’s toxicity limits the use due to safety reasons. [11]
They experimented on different pressure sources. A windmill pressure source was designed and constructed with a displacement capability of 1.3 cm peak-to-peak, acceleration of 200 m/s2 and frequency at 30 Hz.
The windmill rotates about the vertical plane in the earth’s gravitational field so that the liquid column experiences a sinusoidally varying pressure. This rotation occurs at constant angular velocity where by the pressure sensor being calibrated experiences pressure from two components; a sinusoidally varying component produced by the interaction of the tube and the mass of the fluid and the earth’s gravitational field. [11]
They obtained results from the windmill and observed that they were consistent with that from the same closed-tube column when a vibrating exciter instead was used. They did not demonstrate this but made a suggestion that the time-varying acceleration field seen by the liquid column for the configurations was equivalent when acceleration varied from 10 m/s2 to −10 m/s2. The pressure produced by the liquid column using the Windmill source subjected to boundary conditions was equivalent to those generated by the vibration exciter. [11]
They were also able to carry out different tests in which a long vertical column was driven up and down through various displacements using the eccentric and connecting rod. The experiment was purposely intended to increase the range of displacement of the system over that of a vibrating exciter. The displacement achieved was ranging from 5.1 cm to 11.4 cm peak-to-peak. However, the pressure sensor mounted at the bottom of the liquid column tube produced much noise during operation which resulted in an incorrect output sinusoidal signal. When they disconnected the drive and tried moving the system manually, they were able to obtain clean output sinusoidal signal. Analysis indicated that a considerable refinement of the mechanical drive reduced the noise level even with a shorter liquid column. No further work was carried out, and no recommendations about this pressure source suggested further studies. [11]
Other pressure sources were also investigated to produce pressure suitable to calibrate a pressure sensor dynamically using a closed-tube column by Carol F. Vezzetti et al. in 1976. A dual centrifuge pressure source used subsequently; it was determined that the presence of electrical noise, especially at frequencies of few hertz militate against using this form of the dynamic pressure source. They also investigated a double-acting piston in a closed-tube liquid column mounted on a vibrating exciter. Limited tests were carried out, but no satisfactory waveform obtained because some mechanical problems degraded the pressure waveform. [2]
John S Hilten et al. in 1972 had conducted an experiment to determine empirically the excellent system to calibrate dynamic pressure sensors. The work included tests of three different makes of pressure sensors having different ranges, diaphragm sizes, and natural frequencies. Calibrators also using a liquid column of different heights, diameters, and working fluids tested. The sinusoidal pressure calibrating system was found to be a simple, accurate device and optimum for dynamic pressure sensor calibrations. Both static and dynamic calibration data were obtained with values from 5 Hz to 2 kHz with pressure levels of up to 134 kP a peak-to-peak. The dynamic sinusoidal pressure calibrating system was more than capable to calibrate these values dynamically. [1]
They also tried to carry out experiments with very high values of acceleration of up to 580 m/s2
peak-to-peak. They found out that very high acceleration generated an equivalent pressure amplitude of about 131 kP a from the pressure sensor under test, but this also created vibration problems to the system causing reduced waveform thus poor results. They measured this wave distortion with a commercial distortion meter at 400 m/s2 and obtained 0.6% wave distortion of the system. They decided to avoid high acceleration at least above 300 m/s2 during calibration. They also observed from the three pressure sensors under test, that the sensor with the lowest sensitivity, i.e.,.1.8 mV /psi was affected by the electrical noise by lowering the accuracy of output measurements at a moderate acceleration of about 20 m/s2. [1]
They also attempted to improve the output response obtained from the pressure sensor during calibrations.
They did this by increasing the damping from 0.001 to 0.6. The damping created flat frequency response of about 4% to approximately 80% of the natural frequency. This was done by increasing the surface area of the working liquid and increasing the viscosity of the working liquid. The surface area increased due to the increase of the tube dimensions, and the viscosity increased using other working liquids with better viscosity property than water. In this case, they used SAE 140 weight oil and by cooling it to an appropriate temperature, they obtained better damping that improved the output response of the system. [1]
Leonardo Bertini et al. in 2015 carried out an experiment to design and optimize a compact high-frequency electrodynamic shaker. The Shaker was engineered for test bench to investigate vibrational dynamics of centrifugal compressor bladed wheels at the frequency range of 1 Hz to 10 kHz. High rotational speed bladed wheels like a turbine, and compressors are examples of mechanical structures that experience vibrations with high frequency. The high-frequency excitation occurs at the rotational speed regimes of the machines when blades of the turbine interact with the flow from stator vanes. Three different types of stingers are used in the experiment i.e. beam stinger, wire stinger, and ball stinger. The effects of the stingers during dynamic calibration were monitored, and the ball stinger with spherical slot support was found to be the most effective, and also the more convenient regarding mounting time and reliability. [25]
2 Nomenclature
Table 1: List of symbols
Symbol Description Unit
a Acceleration ms2
B Bulk modulus of water P a
fn Natural frequency of the liquid column Hz
Ftotal Total force exerted on the connecting rod N
h Liquid column height in the tube m
hc Tube base height m
HI Thickness of the connecting rod m
hp Piston height m
hT Tube height m
hpc Height of the outer cylinder m
hplate Plate height m
LI Length of the I-section of the connecting rod m
Lpp Length of the piston pin m
MB Total mass of lower and upper part of the rod kg
MC Mass of tube base kg
MI Mass of I-section of the rod kg
Mp Mass of the piston kg
MT Mass of the tube kg
MW Mass of the working liquid kg
MCR Total mass of connecting rod kg
Table 2: List of symbols
Symbol Description Unit
Mnb Total mass of the drawn cup needle bearings kg
MT Mass of the tube kg
Mpc Mass of the outer cyliner kg
Mpp Mass of the piston pin kg
MT Mass of the tube kg
Mneedle Total mass of the bearing used on the rod kg
Mpiston Piston total mass kg
Mplate Total mass of the plate kg
Mtotal Total mass of the moving parts kg
Mtube Total mass of the open tube kg
ρw Density of water mkg3
ρS Density of structural steel mkg3
RB Outer radius of the upper and lower part of the connecting rod m
Rc Outer radius of the tube base m
RT Outer radius of the tube m
r Distance between the disc centre and the disc pin m
rB Inner radius of the upper and lower part of the connecting rod m
rpc Inner radius of the outer cyliner m
rpc Radius of the piston pin m
rT Inner radius of open tube m
WI Width of the I-section of the connecting rod m
The tables 1 and 2 show the list of the symbols used in this project and their respective description.
3 Pressure Amplitude
The sinusoidal-pressure source consists of a rigid cylindrical tube closed at the bottom and open at the top.
The tube is mounted vertically on the plate attached to the outer cylinder. The pressure sensor is mounted at the bottom of the tube. The diaphragm of the pressure sensor has a vertical orientation to minimize the effect of vibration on the sensor response. The pressure amplitude of the system depends on the combination of factors; acceleration, the density of the working liquid, the height of the liquid column.
3.0.1 Displacement
The connecting rod starts to rotate from the top dead centre to the bottom dead centre. The disc axle will rotate at 180◦ and the piston will move one stroke i.e. 2 x r. The increase in the length of the connecting rod will increase the angle θ and the angle will get closer to 90◦ but never reaches 90◦ [10].
Figure 1: Showing the top dead centre and the bottom dead centre
Figure 2: Showing the unit of the system with disc and connecting rod The piston displacement is determined using equation 1
S = (L + r) − x (1)
The cosine rule is used to derive the equation of the distance from the disc center to the top end of the connecting rod as shown in the figure 2
Figure 3: Showing triangles CBD and ABD From triangle CBD
x = r · cosθ +p
L2− r2· sin2θ (2)
Where the negative value of x is ignored. Putting equation 2 in equation 1 gives equation of the displacement of the system as shown in equation 3.
S = (L + r) − (r · cosθ +p
L2− r2· sin2θ) (3)
The angle in degrees is converted into radians with respect to time
S = (L + r) − (r · cos(ωt) +p
L2− r2· sin2(ωt)) (4)
[See details of equations in Appendix A].
The length of the connecting rod and the distance between the disc centre and the disc pin are determined by trying different values of the parameters in equation 4 using Matlab. In Matlab using equation 4, the effect of the connecting rod length, the distance between the disc centre and the disc pin, and the rotational speed, on the displacement of the system is analyzed. This is done by keeping the other two variables constant while one variable is varied. The results obtained are graphed in figure 4, 5 and 6.
Figure 4: Showing displacement of the system with varying values of the distance between the disc centre and the disc pin
Figure 5: Showing displacement of the system with varying values of the length of the connecting rod
Figure 6: Showing displacement of the system with varying values of the rotational speed
At the top dead centre, the displacement of the system is zero. The displacement of the system as shown in the figures starts to increase when the piston moves from top dead centre towards the bottom dead centre.
When the piston reaches half the stroke, the displacement of the piston becomes 0.0015 meters from the blue colored sine wave in figure 4 and 0.0015 meters in both figure 5 and 6. The maximum displacement of the system from zero-to-peak is achieved when the piston moves to bottom dead centre at 180◦i.e. when the piston has moved one stroke. After the bottom dead centre towards the top dead centre the displacement of the system starts to decrease from peak-to-zero i.e. the sine wave slope shown on figure 4 ,5 and 6. This is because the piston is moving back to the top dead centre where displacement is zero.
In figure 4 the distance between the disc centre and the disc pin is varying. The increase in this distance affects the system by increasing the displacement. Varying values of the connecting rod length has no effect on the displacement of the system; this is evident in figure 5. In figure 6 the values of the rotational speed of the system are varying and does not affect the displacement of the system. However, when the rotational speed of the system is increased the sine graph creates a left phase shift. Because when the rotational speed of the system increases; it takes less time for the piston to complete two strokes i.e. one periodic cycle.
3.0.2 Velocity
The average velocity of the system can be determined by 2nL, and n is the rotational speed of the motor, but this does not account for the speed of the system at different disc angles i.e. the instantaneous velocity.
The average speed is limited because loading on the bearings is proportional to the instantaneous piston speed. Since bearing technology has considerably improved over the years, the average velocity of systems using the piston mechanism has also increased. In 1970 the average velocity of slow moving systems and large systems was about 6.5 m/s, today the average piston velocity is about 8.5-9 m/s [10]. The instantaneous piston velocity is also directly linked to the power produced by the system. The higher the piston velocity, the greater the power. The piston velocity with respect to time determined by taking the first derivative of equation 4 is given in equation 5. [See details of equations in Appendix B].
v = r · ω · sin(ωt) + r2· ω · sin(2 · ωt)
2 · L (5)
Equation 5 is used in MatLab and the effect of the distance between the disc centre and disc pin, the connecting rod length and the rotational speed of the system on the velocity is analyzed and graphed as shown in figure 7 , 8 and 9.
Figure 7: Showing the velocity of the system with varying values of the distance between the disc centre and the disc pin
Figure 8: Showing velocity of the system with varying values of the length of the connecting rod
Figure 9: Showing velocity of the system with varying values of the rotational speed
In figures 7 ,8 and 9 the velocity at both the top dead centre and bottom dead centre is zero. The maximum speed from zero-to-peak of the system is reached before 90◦ after top dead centre. Then the velocity of the system starts to decrease as the piston moves towards the bottom dead centre. After the bottom dead centre, the speed of the system begins to increase again but in the reverse direction leading to negative values on the graph. The maximum velocity from zero-to-peak of the system is again obtained before 270◦ after bottom dead centre. Then the velocity decreases again until it reaches zero at top dead centre.
Varying distance between the disc centre and the disc pin affects the speed of the system as shown in figure 7. The increase in this distance increases the amplitude of the sine graph thus increasing the velocity of the system. In figure 8 the varying values of the connecting rod length affects the speed of the system slightly.
The increase in connecting rod length decreases the velocity of the system slightly. The effect of varying rotational speed on the velocity of the system is illustrated in figure 9. The increase in rotational speed increases the velocity of the system and at the same time making the sine graph to have a left phase shift.
This is because the maximum velocity point moves closer to 90◦and the graph starts to form a simple sine graph, but it never reaches 90◦. The increase in rotational speed decreases the time it takes for the system to complete two strokes thus the left phase shift in figure 9.
3.0.3 Acceleration
The equation to determine the acceleration of the system is derived by differentiating velocity equation 5 as given below.
v = ds
dt = r · ω · sin(ωt) + r2· ω · sin(2 · ωt)
2 · L (6)
a = dv
dt = r · ω2· cos(ωt) +r2· ω2· cos(2 · ωt)
L (7)
Using equation 7 in MatLab , the effect of the distance between the disc centre and the disc pin, the connecting rod length and the rotational speed on the acceleration of the system is graphed in figure 10 ,11 and figure 12.
Figure 10: Showing acceleration of the system with varying values of the distance between the disc centre and the disc pin
Figure 11: Showing acceleration of the system with varying values of the length of the connecting rod
Figure 12: Showing acceleration of the system with varying values of the rotational speed
The maximum acceleration of the system is obtained at the top dead centre as shown in figures 10 ,11 and figure 12. After the top dead centre, the acceleration of the system starts to decrease until when the system reaches its maximum velocity where the acceleration is zero. Deceleration starts to occur after the system has obtained its maximum velocity and is moving towards the bottom dead centre. The system at the bottom dead centre begins to accelerate again towards the maximum speed point after bottom dead centre, after the maximum velocity point i.e. before 270◦ the system starts to decelerate towards the top dead centre and the process occurs continuously when the system is operating
The effect of varying distance between the disc centre and the disc pin on the acceleration of the system is shown in figure 10. The increase in this distance increases the acceleration of the system. In figure 11 the effect of varying connecting rod length on the acceleration is illustrated. The increase in the connecting rod length decreases the acceleration of the system. However, when the connecting rod length is reduced to less than 10 mm, the black colored sine graph shows a ’bump’. This bump is because when the system is decelerating towards the bottom dead centre and reaches the bottom dead centre it stops and changes direction to start accelerating back to the maximum velocity point after bottom dead centre and before 270◦ and then decelerates back to the top dead centre.
Varying rotational speed affects the acceleration vigorously compared to velocity and displacement. An increase in rotational speed increases the acceleration of the system and causes the sine graph to shift to the left as shown in figure 12. The left phase shift is because the time it takes for the system to complete one period is less as the rotational speed increases.
The pressure amplitude of the system is determined using the density of the working liquid, the acceleration of the system and the height of the liquid column. When the system is at rest, the static pressure acting on the pressure sensor diaphragm is (g · h · ρ) and when the tube is vibrated sinusoidally in a vertical direction the pressure seen by the sensor will increase. The pressure amplitude is also theoretically limited because acceleration level sufficiently high to reduce the liquid pressure to zero is never achieved, but the values near the vapor pressure of the liquid can be attained. Operating at higher values of acceleration would result in sine wave distortion in the tube thus the output of the pressure sensor will be affected [11]. The pressure amplitude generated by the liquid column onto the sensor is determined using equation 8
PA= ρw· a · h (8)
There is a variety of working liquids like tetranitromethane, mercury and petroleum oils used in the calibration of dynamic pressure sensors. In this project, water was chosen as the working liquid because it has relatively high bulk modulus and it permits inter-comparison between experimental results [2].
3.0.4 Natural Frequency of the Liquid Column
The theoretical natural frequency value of a liquid column can be obtained because stationary waves are set up in the column at resonance. The velocity of propagation of these waves is the speed of sound in the medium. Waves at several harmonically related frequencies may exist, but only the lowest frequency is of interest. The system is considered as a single degree of freedom with natural frequency equal to that of the lowest harmonic of the column resonance [1].
The speed of sound through a medium depends on the stiffness and density of the medium i.e. the speed of sound travels faster if the medium is stiff. This is because the molecules of the medium have strong intermolecular forces with other molecules surrounding it and any disturbance is transmitted faster along the medium. The denser the medium, the slower the speed of sound through the medium because the medium has more inertia and therefore more sluggish to changes in oscillations.
The speed of sound through a medium is determined using equation 9
Vs= s
B
ρw (9)
The bulk modulus measures the stiffness of the medium i.e. how much pressure is required to compress the medium. The natural frequency of the liquid is directly proportional to the square root of the
velocity of sound in the liquid and inversely proportional to the height of the liquid column as given in equation 10
fn= 0.25 · 1
h· Vs (10)
Equation 9 in equation 10 gives equation 11
fn= 0.25 · 1 h·
s B ρw
(11)
Absorbed gasses by the working liquid in the tube can affect the value of the natural frequency. The working liquid used should always be carefully evacuated for fifteen minutes before calibration. This will remove most of the absorbed gasses and gas bubbles.
The optimum operating values determined for the system are all summarized in table 3
Table 3: Optimum Operating parameters of the system
Quantity Value
Length of the Connecting rod 150 mm
Distance between the disc centre and the disc pin 1.5 mm
Rotational speed 3480 rpm
Displacement 3 mm
Average Velocity 0.55 ms
Average Acceleration 200 ms2
Pressure amplitude 50 kPa
Natural frequency 1.5 kHz
Table 3 Showing the optimum parameters of the system
The value of the distance between the disc centre and the disc pin for the system is determined 1.5 mm.
This value is chosen with the aim of keeping the rotational speed as large as possible and not exceeding the maximum acceleration of 300 m/s2. High acceleration values above 300 m/s2 are difficult to control during calibration. The high values of acceleration also tend to over range the pressure sensor and very low values of acceleration below 20 m/s2 are affected by the electrical noise produced by the sensor during calibration, this lowers the degree of accuracy of the response signal. The value of the displacement of the system is limited, displacement values lower than 1.5 mm will decrease the vibrational force required for the system during calibrations and higher values of displacement will increase the acceleration exponentially.
The connecting rod length is usually kept between 3 to 4.5 times the rotating disc radius. Shorter connecting rod length increases obliquity, and this leads to side thrust force on the piston cylinder whereas longer connecting rod length increases the height of the system. In this project, the length of the connecting rod is chosen to be approximate 6 times the rotating disc radius to increase the height of the system. The connecting rod is 150 mm long with thickness of 7 mm. The rotational speed and density of the working liquid are known values and are used to determine the displacement of the system [4, 5].
4 Design and Description of the System
This section describes the detailed design of the units of the system and the overall view of the system is shown in in figure 13.
Figure 13: Showing the overview of the system where by
• A = Electric motor
• B = Frequency inverter
• C = Motor axel
• D = Axel coupling
• E = Disc axel
• F = Bearing blocks
• G = Horizontal support
• H = Ground support
• I = Disc
• J = Connecting rod
• K = Bearing unit
• L = Plate support
• M = Open tube
• N =Vertical support
4.1 Open Tube
The design of the open tube is straightforward and suitable for use in both a mechanical system and an electrodynamic shaker. The open tube is designed with an open top and a circular base, and the pressure sensor is mounted vertically at the bottom of the tube. The open tube is made of structural steel to protect against corrosive liquids and has an outside diameter of 30 mm and the inner diameter of 26 mm. The diaphragm of the pressure sensor mounted at the bottom of the tube is in contact with the working liquid.
The tube has fewer liquid connections to limit leaks.
The pressure amplitude in an open tube column depends on the acceleration of the system, height of the liquid column and the density of the working liquid. The increase in one or combination of these parameters will result in an increased pressure amplitude. Limitations imposed on the parameters such as resonance frequency and maximum available displacement are considered and taken into account when designing the open tube column.
Sound waves traveling in the tube are reflected back when they reach the closed bottom end of the tube, and if the wavelength is right, the reflected wave will combine with the original wave to form a standing wave in the tube filled with working liquid during calibration. In the open tube, a node and antinode are created. Maximum vibration in the tube occurs at the antinode; this is because at the closed end of the tube small amount of sound wave energy is transmitted while towards the open end or away from the closed end more sound energy is transmitted. Thus the maximum pressure amplitude in the tube occurs at regions with antinodes [23].This is illustrated in figure 14.
Figure 14: Showing node and antinode of sound waves
In an open-tube, the upper surface of the working liquid is unconstrained and therefore becomes the locus of a pressure node. At the lower end of the tube, the velocity of the working liquid is constrained to be zero, but the pressure amplitude is at maximum. The result is that pressure amplitude is proportional to distance from the node at the open end. When the tube has closed ends at both sides, the upper surface of the working liquid is constrained to zero velocity, and maximum pressure amplitude occurs at both ends of the tube [12]. For the detailed design of the tube, [See details of the open tube design in Appendix D].
Figure 15: Showing the design of the open tube
Figure 16: Showing the cross sectional view of the open tube
The total mass of the open tube column is determined by summing the mass of the working liquid, the mass of the tube column and the mass of the circular thin tube base. The primary working liquid used in this system is water and the mass of water in the open tube column is determined using equation 12.
Mass of the working liquid i.e. water is determined using equation 12
Mw= ρw· π · r2T· h (12)
The mass of the open tube is determined using equation 13
MT= ρS· π · (R2T− r2T) · hT (13)
The mass of the circular tube base is determined using equation 14
MC= ρS· π · [R2C− R2T] · hC (14)
Total mass of the open tube is given by equation 15
Mtube= Mw+ MT+ MC (15)
4.2 Plate support
The plate is used to mount the pressure sensor with flush installation method. Precision mounting of pressure sensors is important for calibration because the sensing crystals of most of the pressure sensors are located at the top of the diaphragm. Loading on the side of the diaphragm will create distortions in the response signal. Avoiding loading on the side of the diaphragm is important to prevent stresses and strains on the diaphragm of the pressure sensor. Flush installation of the pressure sensor in a plate or a wall is good because it minimizes turbulence and prevents an increase in a chamber volume. [26] [See details of the design of the plate support in Appendix E].
The mass of the plate support is determined using equation 16
Mplate= ρS· π · R2C· hplate (16)
Figure 17: Showing the plate support
Figure 18: Showing the cross section view of the plate support
4.3 Piston
The change in load over time in a piston requires good static and dynamic characteristics of the piston, like high structural strength, low wear, and seizure resistance. Due to this fact, the strength property of the piston is a deciding factor for the load capacity of the piston. Material with high conductivity is of an advantage because it promotes uniform distribution of temperature throughout the piston. Low temperature leads to greater loading capability and also improve other parameters of the piston like the hammering limitation.
Aluminium-silicon alloy is widely used as piston material due to their significant combined properties like high thermal conductivity, easy to cast and forge. However, in this project, the wear resistance of the aluminum-silicon alloy is not sufficient to meet the required load exerted by the linear bearings on the piston cylinder walls [13]. Structural steel is used instead to improve the wear resistance and match the hardness of the linear bearings on the cylinder walls to avoid deformation of the piston during operation which would lead to rough motion and friction.
The piston of the system has a long outside cylinder with smooth cylinder walls that moves through the linear bearing cylinder. The piston has different parts like the piston head and the piston pin where the connecting rod is connected. The linear bearing cylinder wall consists of SKF linear bearings to minimize the contact area between the outer cylinder and the linear bearing cylinder, and this also reduces friction.
The tolerance of the outer cylinder is considered and taken into account when designing the piston of the system. The outer cylinder has an outer diameter of 50 mm and height of 100 mm. The piston has an outer diameter of 40 mm and height of 30 mm. The diameter of the piston pin is 3 mm with length of 20 mm.
The total mass of the piston unit is determined by summing the mass of the outer cylinder, the piston, and the piston pin. [See details of the design of the piston unit in Appendix F].
Figure 19: Showing the design of the piston outer cylinder
Figure 20: Showing the cross sectional view of the piston outer cylinder
Figure 21: Showing the piston design
Figure 22: Showing the cross sectional view of the piston
Figure 23: Showing the design of the piston pin
The mass of the piston outer cylinder is determined using equation 17
MPC = ρS· π · (R2C− r2PC) · hPC (17)
The mass of the piston is determined using equation 18
MP= ρS· π · r2PC· hP (18)
The mass of the piston pin support is determined using equation 19
MPP= ρS· π · r2PP· LPP (19)
The total mass of the piston is determined using equation 20
Mpiston= MPC+ MP+ MPP (20)
4.3.1 Piston Cylinder
The piston cylinder is made up of SKF linear ball bearings LBBR50 and bearing unit LUHR50 as shown in both figure 24 and 25. The LBBR is a patented SKF linear ball bearing that is combined of a plastic cage with hardened steel raceway segments to guide the ball sets.The bearings conform to dimension series 1 according to ISO 10285. The LBBR raceway segments have been designed entirely to utilize the entire length of the load to increase the capacity of the bearings and extend bearing service life. The plastic cage has been redesigned to provide optimum performance. All ball recirculations are designed to offer no resistance to the cage on the running-in and runout of the recirculation.The outside diameter tolerance of the linear ball bearings is such that no additional axial fixation is required [14].
The redesigned cage also accommodates larger balls to provide increased load capacity and service life.
The unsealed bearings are fitted with non-contacting shields to protect the bearing from large contaminant particles. The LBBR linear ball bearings do not need to be secured axially in the housing provided the housing bore is sized correctly. The cost-effective linear bearing unit IS extremely compact and can accommodate loads exceeding 5 kN . LUHR50 consist of a housing of extruded aluminum and the compact LBBR50 linear bearing with similar dimensions. The bearings are lubricated with grease to increase efficiency and prevent metallic contact this will reduce friction [14].
4.3.2 LBBR50 and LUHR50 Design Specifications
• Maximum rotational speed = 30000 rpm
• Inner diameter = 50 mm
• Height = 70 mm
• LUHR50 housing width = 103 mm
• Tolerance = +31 µm and −8 µm
Figure 24: Showing LBBR linear ball bearings
4.4 Connecting rod
The connecting rod is a component of the system and acts as a link member between the piston and the rotating disc. The connecting rod converts the reciprocating motion of the piston to oscillatory motion of itself and then converts this energy into rotary motion by transmitting the thrust force of the piston to the disc [3]. The main parts of the connecting rod are:
• The lower end which connects the connecting rod to the disc through a disc pin.
• The middle rod usually of I-section.
• The upper end which connects the connecting rod to the piston through a piston pin.
The connecting rod primarily undergoes tensile and compression loading under the system cyclic process.
The forces acting on the connecting rod are; force due to maximum piston force, force created by the inertia of the connecting rod and the reciprocating mass, and forces due to friction on the piston pin [4, 5]. For functionality, the connecting rod has the highest possible rigidity at the lowest weight. Connecting rods are made from various materials like steel, aluminum, and titanium. Connecting rods made of steel are widely used; this is because they have high strength and long fatigue life [6].
The force on the connecting rod will be maximum when the disc and the connecting rod are at 90◦ with each other. However, at this position the piston acceleration is zero thus for practical purposes the force on the connecting rod is taken to be equal to the maximum inertial force on the piston due to the tube and the pressure sensor [21]. The maximum inertial force acting on the connecting rod occurs at the top dead centre where (Θ = 0) [22]. From figure 2 The total mass of the connecting rod is determined by equation 24. [See details of the design of the connecting rod in Appendix G].
The mass of the I-section part of the connecting rod is determined using equation 21;
MI= ρS· LI· WI· HI (21)
Mass of the upper and lower part of the connecting rod is determined using equation 22;
MB = 2 · ρS· (R2B− r2B) · HI (22)
The total mass of the connecting rod is determined by summing the mass of the lower and upper part, and the mass of the I-section as given by equation 23.
MCR= MI+ MB (23)
Figure 26: Showing the connecting rod of the system
4.4.1 Drawn cup needle roller bearings
Drawn cup needle roller bearings are bearings that have a deep drawn, thin-walled outer ring with either open ends or a closed end. These bearings are characterized by a very low sectional height and high load carrying capacity. They are used when the bore housing is not used as a raceway and cage assembly but in a very compact environment and economical bearing arrangement. These bearings have a recommended maximum operating temperature of 140◦ C unless otherwise stated in the design specifications. The seal, cage material, and the greases used to reduce friction limits the maximum operating temperature of the bearings. The housing bore design is simple and does not require shoulders or snap rings in locating the axially of the bearing. So the bearings are mounted using an interference fit in the housing bore. [27].
The needle bearings are made of hardened steel and of the same size. Both the upper and lower end of the connecting rod has HK0306 T N needle roller bearings.
4.4.2 HK0306 T N
• Maximum force = 1.23 kN
• Maximum rotational speed = 24000 rpm
• Outer diameter = 6.5 mm
• Inner diameter = 3 mm
• Tolerance high = +24 µm
• Tolerance low = +6µm
• M = 0.001 g
Total mass of both the upper and lower end bearings is given by equation 24
Mneedle= 2 · Mnb (24)
Figure 27: Showing the drawn cup needle bearing
4.4.3 Moving parts
The moving parts of the system are; the open tube, the outer cylinder with the piston , the piston pin, the needle bearings on both ends of the connecting rod, the pressure sensor, and the connecting rod. The total mass the moving parts is determined by summing the mass for all the moving parts given by equation 25
Mtotal= Msensor+ MCR+ Mpiston+ Mtube+ Mneedle+ Mplate (25)
The total inertial force exerted on the connecting rod is determined by equation 26
Ftotal= Mtotal· acceleration (26)
4.5 Disc and axle
The disc is a rotating mechanism that is used to store rotational energy, and the energy is transferred to the disc by applying torque on it, this increases the rotational speed hence stores the energy. The disc stores the energy when the piston is at top dead centre and releases the energy when the piston is at bottom dead centre. The piston and the connecting rod are offsets of the disc axle and want to push the disc axle from side to side at each piston stroke. The energy stored in the disc is used to damp this process and reduces the system’s vibration, thus balancing the system.
The tolerance of the needle roller bearings used on the lower end of the connecting rod inner diameter is considered and taken into account to design the disc and the disc pin of the system. The disc is made of structural steel with the outer diameter of 24 mm. The disc pin on the disc has a diameter of 3 mm and disc pin length of 10 mm. The disc axle is 60 mm long with a diameter of 14 mm. [See details of the design of the disc and axle in Appendix H].
Figure 28: Showing the disc , disc pin and the axle of the system
4.6 The vertical support
The vertical support is made of steel, and it holds the piston cylinder in place. The support is 300 mm long and 200 mm wide with thickness of 20 mm. The vertical support consists of bolt holes at the bottom used to attach it firmly to the horizontal support of the system. [See details of the design of the vertical support in Appendix I].
Figure 29: Showing the vertical support of the system
4.7 The horizontal support
The horizontal support is made of steel and holds the electric motor, the bearing blocks and the vertical support of the system in place. The horizontal support is 400 mm long and 200 mm wide with thickness of 40 mm. [See details of the design of the horizontal support in Appendix J].
Figure 30: Showing the horizontal support of the system
4.8 Torque and Power
The system’s torque is the turning effort that acts about the disc axle axis of rotation. It is equivalent to the product of the total thrust force exerted on the connecting rod and perpendicular to the distance between the disc centre and the disc pin. When the disc axle moves 180◦ from top dead centre to bottom dead centre, the effective distance between the disc centre and the disc pin increases from zero to maximum before reaching 90◦ and then decreases to zero again at the bottom dead centre. Both at top dead centre and bottom dead centre the torque of the system is zero because there is no turning moment thus no power is transmitted. This states that the torque of the system is continuously changing, but some of the torque cancels out when overcoming compression resistance and expansion losses. The torque determined for the system is the average torque throughout the system cycle [16].
T orque = Ftotal· r (27)
The power of the system increases with piston speed, and the power is determined using equation 28
P ower = T orque · 2 · π · n
60 (28)
The total mass of the moving parts, exerted force on the connecting rod, the torque and power of the system are all summarized in table 4 and table 5
Table 4: Total mass
Quantity Mass (Kg)
Mtube 0.569
Mpiston 0.8411
MCR 0.066
Mneedle 0.002
Mplate 0.31
Msensor 0.0046
Mtotal 1.79
Table 4 Showing the total mass of the moving parts of the system
The total force exerted on the connecting rod of the system is determined by equation 26. The torque of the system by equation 27, and finally the power of the system is determined by equation 28 and the values obtained are shown in table 5 below;
Table 5: Force, Torque and Power
Quantity Values Unit
Total force 358 N
Torque 0.54 Nm
Power 197 W
Table 5 Showing the values of force, torque and power
4.9 Electric motor
The electric motor suitable for the system is selected using the determined values of torque, power, and rotational speed. The WEG electric motor chosen for the system is the W 22 three phase motor type built using a high-quality iron to ensure maximum durability and high performance in dynamic conditions. The cooling system is redesigned to provide air flow to the motor frame which keeps the operational temperatures low and assures reliability and extended lifetime. The aerodynamic concept of the fan cover increases sufficient airflow, minimizing losses due to the recirculation of air between the fan and the fan cover.
Energy consumption accounts for 90% of total operational costs throughout the lifetime of the motor, the remaining 10% is included in the cost of acquisition, installation, and maintenance. This leads to energy efficiency which is a primary objective of the new design. The W 22 range also exceeds the required European efficiency requirements giving energy savings and reduced payback time [17].
Figure 31: Showing the three phase W22 electric motor
The specifications of the electric motor are listed below;
• Standard frame (71)
• Induction motor
• Two poles
• Frequency = 60 Hz
• Rotational speed = 3410 rpm
• Power = 0.55 kW
• Efficiency class (1E3)
• Voltage = 220 /380 V
• Current = 2.16/ 1.25 A
• Full load torque = 1.54 N m
• Weigth = 8 kg
Figure 32: Showing the sketch and dimension of the electric motor
4.10 Frequency inverter
The induction three phase electric motor has electric magnets on either side in the stator and the rotor. The poles of the stator fields are driven by the mains frequency and rotates in a circle after the poles of the rotor field i.e. the rotor starts to spin. The motor always rotates a little bit slower than the magnetic poles in the stator; this is to sustain the current in the rotor windings and thus keeping the rotor magnet. It is hard to control the power, torque and rotational speed of the electric mo- tor. An inverter is used in this project to monitor and increase the rotational speed of the electric motor [18].
Figure 33: Showing the type of the frequency inverter used on the motor
• Type IN L BEV I
• Three phase
• Power = 0.75 kW
• Voltage = 200 /240 V
4.11 Axle coupling
Flexible couplings are used to connect two axles mechanically to transmit power from the electric motor to the rotating disc. They compensate for the axle misalignment in a torsionally rigid way. Misalignment can be angular, parallel or skew. It is important to use the axle coupling because the misalignment could affect the velocity and acceleration of the driven axle [20]. The motor and disc axle both have 14 mm in diameter.
Figure 34: Showing the axle coupling
4.12 Y-Bearing Plummer Block
The Y-bearing plummer block is used to support both the axel of the motor and that of the disc. The bearing has a housing made of composite material to enable it to operate reliably in challenging environments for extended periods without maintenance [19].
Figure 35: Showing the Y-bearing plummer block
4.13 Pressure sensor
The piezoelectric pressure sensor in the project uses the effect of piezoelectric on the material to measure the input and output signal of the system. When the crystal is distorted by the exerted pressure force by the working liquid, an electric charge is produced and is measured by an electrometer. The piezoelectric pressure sensor is used to measure dynamic pressure changes and can not be used to measure static pressure changes because it is a transient device [7]. The piezoelectric pressure sensor is preferred in the project because the pressure sensor is small and light in weight, the sensor is not complicated to install, the sensor has a wide dynamic temperature and frequency range , and the sensor has ultra low noise.
The purpose of a pressure sensor is to convert pressure input signal from the working liquid to an electrical output signal that is recorded on the computer [7]. The pressure sensor produces a positive going output voltage for increasing pressure input. The high natural frequency of the pressure sensor gives a wide usable frequency range. The pressure sensor has fast response time i.e. 1µsec and non-resonant response to rapid step response functions.
Figure 36: Showing the piezoelectric pressure sensor
Figure 37: Showing the developed mechanical system
5 Experiment
Experiments were carried out on the built mechanical system shown in figure 37 to see if the system is working according to the design. The sampling frequency used is 1000 Hz and four similar trials using the same conditions were carried out in the laboratory. The different trials at five different speeds for 5 Hz, 10 Hz, 15 Hz, 20 Hz, and 25 Hz were carried out to investigate if the output signal obtained from the pressure sensor during the experiments are similar. Looking at figures 38 and 39 in the frequency domain, it shows that there are five dominant frequencies corresponding to the five different speeds. The amplitude of the five fundamental frequency signals increase with speed as shown in figures 38 and 39 .The most dominant frequency in the frequency domain figures 38 and 39 is red colored with the highest amplitude.
Fast Fourier Transform method is applied on the signals got from the experiments to check if the five different frequencies manually set on the mechanical system are obtained by the pressure sensor used or not.
The calibration sensitivity factor for both the acceleration and pressure is quantified in terms of millivolts per g of acceleration and millivolts per kilo pascals respectively where g is the equivalent of the acceleration due to the Earth’s gravity. The pressure sensor sensitivity is calibrated through the useful frequency range of the device and at higher frequencies, the frequency response decreases because the calibrated sensitivity factor has decreased. It is possible to convert pressure and acceleration in volts to kilo pascals and meters per second squared respectively knowing the calibration sensitivity factor of 14.5 milliV olt/kP a for pressure and 104.3 milliV olt/g for acceleration.
Figure 38: Shows frequency spectrum of acceleration
The value of acceleration and corresponding frequencies obtained from figure 38 at the five different system test frequencies during the experiments are represented in table 6. The theoretical acceleration values also represented in table 6 are determined using equation 29. These values are determined using the system test frequencies set on the system manually to compare with the accelerometer acceleration from figure 38.
Acceleration = r · ω2 (29)
Table 6: Acceleration and frequencies obtained during the experiment System test
frequency (Hz)
Experimental frequency
(Hz)
Accelerometer acceleration
(m/s2)
Theoretical acceleration from equation 29
(m/s2)
5 5.2 1.3 1.5
10 10.5 4.9 5.9
15 15.8 11.9 13.3
20 21.1 20.6 23.7
25 26.4 31.7 37
Table 6 Shows the acceleration obtained from the accelerometer during the experiment and acceleration obtained theoretically using equation 29
According to table 6 the actual mechanical system during the experiment seem to vibrate faster compared to the system test frequency. This can be due to decreased weight of the moving parts on the mechanical system during the experiment caused by less working liquid in the column and light material used to construct the liquid column.The accelerometer acceleration increases with increase in frequency but increase in frequency beyond 25 Hz during the experiment leads to increase in acceleration which creates unwanted vigorous vibrations on the mechanical system.
Figure 39: Shows the frequency spectrum of pressure at various speed
The pressure amplitude and corresponding frequencies from figure 39 are obtained and represented in table 7. In order to compare the experimental pressure amplitudes to theoretical pressure amplitudes , the experimental pressure amplitude obtained at 5 Hz is used as a reference point to determine the height of the liquid column. The theoretical acceleration values determined from equation 29, the density of the working liquid and the liquid column height is used in equation 30 to determine the theoretical pressure amplitude for all the five different system test frequencies.
Pressure = ρ · acceleration · height (30)
Table 7: Difference between experimental pressure amplitude and theoretical pressure amplitude System test
frequency (Hz)
Experimental frequency
(Hz)
Experimental pressure amplitude
(kP a)
Theoretical pressure amplitude from
equation 30 (kP a)
Difference between experimental and theoretical pressure
amplitudes (%)
5 5.2 0.18 0.18 0
10 10.5 0.73 0.71 2
15 15.8 1.69 1.59 10
20 21.1 2.89 2.84 5
25 26.4 4.54 4.44 10
Table 7 Shows the difference between experimental pressure amplitude and theoretical pressure amplitude
