DYNAMIC MODELLING AND SIMULATION OF A HEAVY VEHICLE TRAILING ARM AIR SUSPENSION Bohao Li, Arnold G. McLean - Faculty of Engineering, University of Wollongong, Australia

ABSTRACT This paper concentrates on the trailing arm air suspensions available on the rear tandem drive axles of some heavy prime movers. On such vehicles, the application of air suspension is believed to have a series of advantages including road friendly characteristics, better load sharing and self ride height adjustment. However, air suspensions are proved unstable under dynamic situations possessing inadequate support, harsh ride and chaotic response. In this paper, some individual components of the air suspension are modeled as well as the suspension vibration model and the pneumatic transmission line model. These models are then simulated using both SIMULINK and analytical techniques to find the causes for the adverse characteristics. From the simulation it is identified, the harsh ride is caused by insufficient flow in the transmission line whereas the chaotic response, at least to some extent, is found to be due to the haphazard design of the analogue feedback control system, especially the ride height control valve (HCV).

1. INTRODUCTION 1.1 Background Mechanical suspensions have dominated the area of heavy truck suspensions for many years and are still widely used on rigid trucks, especially construction trucks on which high stabilities are needed. This is because such suspensions have proven to be stable, reliable and relatively simple and robust in design. However, the air suspension has been substituting the traditional mechanical suspension (especially the leaf spring suspension) nowadays. In developed countries such as Europe countries, United States and Australia, air suspension has been the mainstay on long-haul prime movers. The idea of using air suspensions to replace mechanical suspensions was aroused by the naïve concept of inherently non-linear, better load-sharing and self leveling characteristics conceptually possible with air springs. The most significant feature of the air suspension is that it can provide constant natural frequency under different loads, which is much lower compared to that of the conventional suspension. Another minor advantage of air suspensions is that it is typically considerably lighter than mechanical suspension, which means the unsprung masses of vehicles, using air suspension, are typically much smaller than those using mechanical suspensions.

1.2 The Structure of a Typical Trailing Arm Air Suspension The typical structure of a trailing arm air suspension system is relatively simple. The axle is supported on two rigid (Neway) (see Figure 1) or flexible (Freightliner, Hendrickson) (see Figure 2) arms located under each side of the chassis rail. Each arm’s forward end is connected to the chassis rail by shackle having a large diameter rubber bush, and its rear end is connected to the bottom of the airbag. The axle is clamped to the link immediately forward of the airbag*. The shock absorber can be located either forward (Freightliner, Neway) or behind the airbag (Hendrickson), due to slightly different geometric details. The axle’s longitudinal motion is

limited by the trailing arms whereas its lateral motion is limited by a Panhard rod. This Panhard rod has one end connected to the differential housing and the other end connected to the inner side of one chassis rail. Another alternative design is to use the “V” type torsion bars to constrain both longitudinal and lateral motions. In this paper, the trailing arm will be treated as a rigid body for simplicity and the force transmitted through the Panhard rod to the chassis from the axle will be neglected.

1.3 Problem Definition Some unstable handling and rough ride characteristics have been experienced on those vehicles equipped with factory fitted air suspension system. For example, it is reported that when prime movers negotiate corners after a period of sustained high speed cruising, the air suspension may fail to respond. Air suspension failure not only makes the prime mover tend to roll over, but also cause the suspension components to prematurely fail. If one side of airbag fails, the loads on each side will be uneven. More seriously, more loads will compound on the failed side pedestal, shackle or torque rod, which will subsequently cause these components to fail. The outcome is devastating namely the whole suspension will lose constraint presenting adverse kinematical characteristics or loss of vehicle control. Due to the poor design of the pneumatic plumbing system and feedback control system, factory fitted air suspension systems often exhibit unstable or chaotic characteristics. The airbags are also slow to respond causing uneven loads between the leading and trailing axles. This further causes poor ride quality and serious road damage. Air suspension failure also causes the deviations in the universal joint drive angle. This is the main reason for transmission line vibrations [19]. Although air suspensions are often called “road friendly” suspensions, however, David Cebon pointed out that air suspensions are not actually “road friendly”, and they may cause even more serious road surface fatigue than mechanical suspensions due to poor and haphazard designs [1].

1.4 Current Methods of Improvement To improve the performance of air suspension systems, different aftermarket modifications have been adopted. However, the effects of some modifications have not been verified. The most common modification is using double action shock absorbers to replace the single action shock absorber. This is a simple way of increasing damping to dispel vibration quickly, although it will transmit extra force to both the chassis and the road surface. Another common modification is to use fast response, no delay, and minimum dead band height control valve to replace the original valve. For prime movers that use two individual HCVs to control each side of airbags, it is not unusual to observe that operators install just one fast response valve to replace the original two. Operators and drivers’ report indicate this is a relatively effective modification. However, such near standard systems remain far from optimal. ______________________________________________________________________ *In this paper the term airbag is used interchangeable with air spring or air bag. For this reason, the term airbag should not be confused with passenger vehicle airbags used for passenger protection during motor vehicle accidents.

One further modifications is to enlarge the diameter of the transmission line to increase airflow. On some prime movers, the original capillary sized transmission line has been replaced by much larger orifice sized transmission line of 50 mm diameter, which can increase the airflow significantly. To improve the feedback signal, Bill Haire of Haire Truck & Bus Repairs designed a unique mean ride height feedback linkage system to replace the ubiquitous rear axle feedback system [20]. This design ensures that the feedback signal represents the mean ride height of the leading and trailing axles rather than crudely the rear axle ride height. The Haire system also uses large or fast response 50 mm diameter transmission line with novel biased airflow orifices to generate inherent system damping.

1.5 Aims of This Paper The aim of this paper is to develop a series of dynamic models of a typical trailing arm air suspension including the vibration model and the pneumatic plumbing model involving both slow and fast response components. These models will then be used to investigate the system behaviour subjected to typical operation situations. SIMULINK is used to simulate the time response of these models under dynamic situations. This initial paper is aimed to find the adverse operation circumstances under which the trailing arm air suspension possesses dangerous behaviour and the possible causes for such responses. Therefore, some useful design recommendation result and some reasonable modifications can be applied to existing designs.

2. MODELLING OF RIDE HEIGHT FEEDBACK LINKAGE 2.1 Trailing Axle Ride Height Feedback Only The following part of analysis is based on the assumption that the Hendrickson height control valve is used, which is a rotation block type valve. (see Figure 3) On most new-built prime movers, the feedback link is directly connected to the trailing axle only, so the feedback signal is actually from the trailing axle exclusively. (see Figure 4) Hence when the leading axle hits a bump, no active port flow through the HCV occurs. Consequently only flow in the transmission line between the leading axle and the trailing axle occurs to achieve load sharing. After a small time delay determined by the vehicle road speed and bogie axle spacing, the trailing axle will hit the same bump, at which time the HCV will be actuated. This system response implies that the flow rate from the orifice port of the HCV can be expressed as:

r1    180( y cv − y a r ) a q v = K (θ v − θ db ) = K  − θ db  πrv      

(2-1)

Where: qv – Flow rate from the orifice port, m3/s K – Gain of the valve characteristics θv – Valve spindle angular displacement, degree θdb – Valve dead band angular displacement, degree ycv – Vertical displacement of the chassis at the valve, m yal – Vertical displacement of the feedback point on the trailing arm, m ya – Axle differential vertical displacement, m r1 – Radius from trailing arm connection point to centerline axle, m

ra – Radius from trailing arm connection point to feedback point, m rv – Radius of valve control arm, m

2.2 Mean Ride Height Feedback Some prime movers have been modified by replacing the original trailing axle feedback system with the innovative mean ride height feedback system. The arrangement of this mean ride height feedback system is depicted in the following schematic. (see Figure 5) The advantages of this mean ride height feedback system are obvious. Firstly, not only the trailing axle but also the leading axle will actuate the HCV instantly. Secondly, because the feedback link is connected to the near central point of the leading and trailing axles, the feedback signal always presents the mean height of the bogie rather than single axle. This mean height feedback minimizes the transient error signal generated by high frequency chassis vibrations, axles moving over bumps and chassis whip. On a mean ride height feedback system the HCV port flow rate can be expressed as:

q v = K (θ v − θ db ) =

K [( y cv −

ya ) − θ db ] 2 rv

(2-2)

An examination of equation (2-2) suggests the response of this feedback is equivalent to adding a gain with value of 0.5, on the unit feedback loop for the trailing axle feedback system (see Figure 6). This relatively low gain may be allayed by using a Hendrickson HCV which possesses favourable porting characteristics and internal details (Figure 3). It should be noted the mean height feedback linkage also occupies slightly more room, is slightly more complex, requires slightly greater maintenance and may be difficult to apply on vehicles with low ride height. Furthermore, the more complex linkage structure means it is slightly heavier than trailing axle ride height feedback system, and this, in turn, will have some very slight adverse effects on ride quality because the feedback linkage is additive to the vehicle’s unsprung mass.

3. SIMULATION OF THE SUSPENSION MODEL 3.1 Transient Response of the Suspension The diagram (see Figure 7) shows the model of the two-degree of freedom suspension model. It presents the suspension of one ‘corner’ of the whole vehicle. This model consists of springs, dampers and masses, and it will be used to develop the dynamic differential equations. The model notation is as follows:

Mu – The total unsprung mass, comprising of the axle, wheels, hubs, tyres and brake assembly mass, 800 kg assumed Ms – The proportion of the sprung mass supported by each air spring, 3200 kg assumed kt – Tyre spring stiffness, 0.81 MN/m under tyre pressure of 759 kPa (110 psi) kp – Airbags (air springs) spring stiffness, 125.6 kN/m assumed ct – Tyre damping coefficient, 0.003 Ns/m assumed cp – Shock absorber damping coefficient, 6013.62 N-s/m assumed, equivalent to 15% damping ratio x1 – Road signal input, m x2 – Axle displacement, m

x3 – Chassis displacement, m Fw – Road roughness input signal, m

3.1.1 Single Axle Suspension Vibration Model

According to the 2 DoF vibration model, the dynamic differential equation is:  d ( x 2 − x3 ) d ( x1 − x 2 ) d 2 x2  − + − − − = k ( x x ) C k ( x x ) C M  t 1  t p p u 2 2 3 dt dt dt 2  (3-1)   2 k ( x − x ) + C d ( x 2 − x 3 ) = M d x 3  p s 3 2  p 2  dt dt Hence the block diagram of the suspension system incorporating wheel unbalance can be developed using SIMULINK. (see Figure 8) The system response subject to excitation from passing over a 1 unit step, which is dimensionless, is shown in Figure 9. The forces transmitted to the chassis rail when Cp equals to 15% and 20% damping ratio are shown in Figure 10 and Figure 11, respectively. It can be seen that adoption of the shock absorber with larger damping coefficient do dissipate vibration energy rapidly, but it also transmits larger force to the chassis .

3.1.2 Grouped Axle Vibration Model The combination of two of the previous single axle models connected by a time delay block can be used to simulate tandem axles used on prime movers. The resulting block diagram is shown in Figure 12. The signal delay time is the time interval for the trailing drive wheel to be excited by a bump previously contacted by the leading drive wheel. If the wheelbase is 1295.4 mm, which is a standard value of Freightliner prime movers, the signal delay is 0.047s at a road speed of 100km/h. The response of the model subjected to a step input is shown in Figure 13. The dark trace represents the displacement of the chassis excited by leading axle while the light one represents the displacement of the chassis excited by trailing axle. The third trace is the input signal. It can be clearly seen that there is some time delay between two response curves although this time interval is very short at the speed of 100 km/h

3.2 Suspension Frequency Response The vibration model can also be expressed as shown in Figure 14. Substituting all parameters into this block diagram, the transfer function of the whole suspension can be achieved. Thus, the “bode” command in MATLAB can be used to get the system frequency response. (see Figure 15) It can be seen that there is a resonance occurring at 6 rad/s, which equals a frequency of 0.95 Hz. Two conclusions can be drawn: (1) If the system excitation source is wheel unbalance, adverse conditions will occur at a speed of 11.28 km/h; (2) If the excitation source is road undulations, road wavelengths of approximately 30 m will excite the vehicle when operating at 100km/h. Furthermore, in the high frequency range, the vibration amplitude decreases rapidly. This verifies that standard air suspensions have low frequency characteristics.

4. SIMULATION OF THE PNEUMATIC TRANSMISSION LINE CHARACTERISTICS 4.1 Transient Response of a Transmission Line Subjected to a Pressure Signal Input Anderson [3] provides the relationship between the supply pressure change and the terminal pressure change in a pneumatic transmission line with one end connected to an airbag. This system is shown in the schematic. (see Figure 16) The response of this system is given by:

p2 =

p1 2

*

1 + 4(V * / AL) E 2 1 V s s 1+ ( + ){E 2 + [1 + ]( ) 2 } * 2 AL β 1 + 2(V / AL) 12 β

(4-1)

Where: p1 – Supply pressure change, Pa p2 – Terminal (airbag) pressure change, Pa w12 – Weight flow rate from supply end to terminal end, kg/s V* - Effective volume = (1 + kp/k)V2, m3 kp – Airbag spring stiffness, 125.6 kN/m k – Connected mechanical spring stiffness. Here it is roughly the tyre spring stiffness, which is 0.81 MN/m V2 – Volume of airbag under set height, 0.01227 m3 if both the diameter and the set height of the airbag are assumed equalling to 250 mm A – Section area of transmission line, m2 L – Length of transmission line, 1.65 m 1

E2 – Equals 3200µ ( gRT / n) 2 L /(10 D) 2 P2 µ – Air viscosity, 1.81e-5 Pa.sec P2 – Pressure of airbag under 12.8t sprung mass, 639.5 kPa 1 2

β – Equals (ngRT ) / L s – Laplace operator If the transmission line is a capillary with inner diameter of 4.15mm, equation (4-1) can be rewritten as:

p2 =

1 p1 0.0566s + 0.200099 s + 1 2

(4-2)

Similarly, if the transmission line is an orifice tube with inner diameter of 50.8mm, equation (41) can be rewritten as:

p2 =

1 p1 0.000389s + 0.001375s + 1 2

(4-3)

The transient responses of these two different transmission line systems, to a step input pressure change, are presented in Figure 17 and Figure 18.

From an examination of the above figures, it can be concluded that the orifice transmission line does have a shorter rise time, but the pressure response exhibits high frequency oscillation because the damping ratio is extremely small. This finding is consistent with observed heavy vehicle behaviour in so far as vehicles fitted with simple orifice transmission lines exhibit high frequency oscillations and require the fitment of heavy-duty shock absorbers.

4.2 Frequency Response of Different Diameter Transmission Lines From equation (4-2) and (4-3), the Bode diagrams of the capillary transmission line system and the orifice transmission line system can be plotted using MATLAB. (see Figure 19 and Figure 20) It can be seen that the capillary resonance frequency occurs at about 4 rad/s, while the orifice resonance frequency occurs at about 50 rad/s.

4.3 Backflow in Capillary Transmission Line Systems One problem of the capillary transmission line is that when the airbag is compressed rapidly, there is insufficient flow through the transmission line causing extremely high pressure in the airbag, which may exceed the supply pressure of the reservoir. Thus, when the HCV valve opens, the air will flow from the airbag due to the pressure differential rather than flow into the airbag. This is an adverse situation, which will cause the airbag to deflate further. Thus, not only will the ride height deviate from the set value, but also the suspension components will be overloaded. Because the transmission line is a capillary, when compressed rapidly, there is insufficient airflow from it. This implies that when the airbag is subjected to rapid compressions, there is almost no gas mass transmitted out of the airbag through the capillary. On the other hand, should the compression process be sufficiently rapid to exceed 60 Hz the process can be assumed to be polytropic. The gas law for a polytropic process is given by: n

PsV2 = Ps ( A p hs ) n = Pb ( A p hb ) n

(4-4)

Where Ps – Static pressure of the airbag, 639.5 kPa assumed Pb – Pressure of airbag when back flow occurs, 828 kPa assumed which equals to the reservoir supply pressure hs – Airbag set height, 250 mm assumed hb – The height of the airbag when back flow occurs, mm Ap – Airbag effective area, 250 mm assumed n – Polytropic exponent, 1.4 in this case Thus, hb is given by hb = hs 1.4

Ps Pb

(4-5)

Substitution of all known variables into equation (4-5) yields hb equal to 207.04 mm, which corresponds to critical ∆h, where backflow differential between Ps and Pb occurs, is 42.96 mm

(i.e. 250 - 207.4 mm). This implies that when the compression displacement exceeds about 43 mm, the phenomena of back flow may occur in the transmission line.

5. CONCLUSION Some typical symptoms found on air suspensions include: Harsh ride dues to insufficient flow rate in the pneumatic transmission line. Chaotic response dues to poor design of the analogue ride height feedback system. By carefully modelling and simulation, some conclusions are listed below: To overcome the shortcomings of the capillary transmission line, it is simple to increase the diameter of the transmission line. This can not only increase the flow rate but also can reduce the restriction in the transmission line and reduce the delay time. However, the simple large diameter transmission line has another problem which is rapid fluctuation in the transient response. In practice, a compromise must be considered or preferably a large diameter biased orifice controlled transmission line should be utilized. The mean height feedback linkage does not possess the shortcomings of trailing axle feedback control. These shortcomings are generated by decreasing the amplitude of the feedback signal by half. For example, if the leading axle has a vertical displacement of 10cm while the trailing axle has no vertical motion, the vertical displacement of the feedback link is 5cm. This effect is equivalent to a gain of 0.5 relative to the unit feedback loop of the trailing axle feedback system. In some contrived situations this may cause steady state error. The mean height feedback linkage also occupies slightly more room, and it is slightly more complex and may be somewhat difficult to apply on vehicles with low ride height. Double action shock absorbers are effective to dissipate vibration energy rapidly, but will transmit larger forces to the chassis and road surface. The large dynamic forces may cause chassis component fatigue, tyre and road damage. Therefore, caution should be applied when substituting the original single action units with suitable double action shock absorbers. This work forms the basis of ongoing research into the dynamics of heavy vehicles at the University of Wollongong. Preparation is well advanced in regard publication of results of dynamic roll over simulations. Further work is in progress to accurately incorporate the effects of chaotic lever actions, biased flow orifice controlled transmission lines, vehicle speed dependent delay time, reservoir, air compressor and tyre compound hysteresis into the SIMULINK based dynamic simulation. This work should prove most significant for the safety and well being of the vital components in the overall heavy vehicle transport system

REFERENCES 1. HANDBOOK OF VEHICLE – ROAD INTERACTION – David Cebon (Swets & Zeitlinger B.V. – 1999 – ISBN 90-265-1554-5) 2. DIESEL EQUIPMENT II – Erich j. Schulz (McGraw Hill Book Co. – 1988 –ISBN 0-07055708-X (v.2)) 3. THE ANALYSIS AND DESIGN OF PNEUMATIC SYSTEMS – Blaine W. Andersen (John Wiley and Sons inc. – 1967) 4. MODERN CONTROL ENGINEERING 4th edition – Katsuhiko Ogata (Prentice Hall, Inc. – 2002 – ISBN 0-13-043245-8) 5. INTRODUCTION TO CONTROL SYSTEM ANALYSIS AND DESIGN 2nd edition – Francis J. Hale (Prentice Hall, Inc. – 1988 – ISBN 0-13-479767-1) 6. ENGINEERING VIBRATION – Daniel J. Inman (Prentice Hall, Inc. – 1994 – ISBN 0-13951773-1) 7. MODELING, ANALYSIS, AND CONTROL OF DYNAMIC SYSTEMS 2nd Edition – William J. Palm III (John Wiley & Sons, Inc. ISBN 0-471-07370-9)

8. MODELING AND SIMULATION OF DYNAMIC SYSTEM – Robert L. Woods, Kent L. Lawrence (Prentice Hall, Inc. – 1997 – ISBN 0-13-337379-7) 9. MASTERING SIMULINK® 2 – James B. Dabney, Thomas L. Harman (Prentice Hall, Inc. – 1998 – ISBN 0 –13-243767-8) 10. MATLAB (VERSION 5) USER’S GUIDE – STUDENT EDITION – Hanselman Littlefield, Duane C. Bruce (MathWorks, Inc and Prentice Hall – 195 – ISBN 0-1327-2550-9) 11. THE SHOCK ABSORBER HANDBOOK – John C. Dixon (Society of Automotive Engineers, Inc. – 1999 – ISBN 0-7680-0050-5) 12. ROAD VEHICLE SUSPENSION – Wolfgang Matschinsky (Professional Engineering Publishing Limited – 1998 – ISBN 1-86058-202-8) 13. FUNDAMENTALS OF VEHICLE DYNAMICS – Thomas D. Gillespie (Society of Automotive Engineers, Inc. – 1992 – ISBN 1-56091-199-9) 14. INVESTIGATION INTO THE SPECIFICATION OF HEAVY TRUCKS AND CONSEQUENT EFFECTS ON TRUCK DYNAMICS AND DRIVERS: FINAL REPORT – Peter F Sweatman and Scott McFarlane, report prepared for FORS by Roaduser International Pty Ltd 15. A STUDY OF DYNAMIC WHEEL FORCES IN AXLE GROUP SUSPENSION OF HEAVY VEHICLES – P. F. Sweatman, Published by Australian Road Research Board 16. CHARACTERISTICS OF FAST RESPONSE MEAN RIDE HEIGHT ANALOGUE CONTROLLED HEAVY VEHICLE AIR SPRING SUSPENSION SYSTEM – Dr Arnold McLean, J Lambert and W Haire Proceedings ATRF 2001 Hobart 17. PRIME MOVER AIR SUSPENSION RIDE HEIGHT CONTROL MALFUNCTION – Dr Arnold McLean Proceedings SAE Paper 99085 Melbourne 18. ACTIVE COMPUTER CONTROLLED AIR-SUSPENSION SYSTEMS FOR HEAVY PRIME MOVERS – A CONCEPTUAL EVALUATION – Dr Arnold McLean Proceedings ITSA 99 Adelaide 19. HENDRICKSON REFERENCE WHITE PAPER – REDUCING THE EFFECTS OF SUSPENSION-RELATED DRIVELINE VIBRATION (Published by Hendrickson International website, http://www.hendrickson.com/reference/white/04079801.htm) 20. BE THESIS – DYNAMIC CHARACTERISTICS OF HEAVY PRIME MOVERS – KENWORTH AIRGLIDE 100 BOGIE SUSPENSION – Rod Visman, UoW, 1999 21. BE THESIS – EVALUATION OF HEAVY PRIME MOVER BOGIE SUSPENSION MECHANIS – Gary Sawyer, UoW, 1998 22. STERLING ACTERRA – Cab and Chassis Vocational Reference Guide, Section 4 – Suspension (Published by Sterling Trucks, October 2000) 23. AirLiner Rear Suspension Specifications, available on Freightliner Trucks’ website, http://www.freightlinertrucks.com/components/

PRESENTING AUTHOR BIOGRAPHY Bohao Li – Mr Bohao Li was awarded the Bachelor of Engineering in Automobile Engineering from Shanghai University of Engineering Science, China in 2001. He was involved in the project of modelling and simulation of the heavy vehicle air suspension as a postgraduate student in the Faculty of Engineering, University of Wollongong, Australia under the supervision of the co author, graduating with a Master of Engineering Practice in Mechatronics with Distinction in 2002. The presenting author will continue this paramount work as a ME Honours candidate in 2003 with conversion to a PhD supervised by Dr Arnold McLean from 2004 onwards.

FIGURES

Figure 1: Neway Air Ride AD-200 air suspension

(From http://www.rvcalifornia.com)

Figure 2: Freightliner AirLiner 46 K air suspension

(From http://www.freightlinertrucks.com/components)

Figure 3: Hendrickson height control valve rotation block details

Figure 4: Trailing axle ride height feedback schematic

Figure 5: Mean ride height feedback schematic

Figure 6: The block diagrams for the trailing axle ride height feedback system (above) and mean ride height feedback system (below)

Figure 7: 2 DoF Suspension vibration model

Figure 8: Block diagram for a single axle suspension

Dark continuous line: vibration amplitude of the chassis Light continuous line: vibration amplitude of the axle Red line: the step input

Figure 9: System transient responses at 15% damping ratio

Figure 10: Force transmitted to the chassis at 15% damping ratio

Figure 11: Force transmitted to the chassis at 20% damping ratio

Figure 12: Block diagram for grouped axles

Dark continuous line: vibration amplitude of the chassis Light continuous line: vibration amplitude of the axle Red line: the step input

Figure 13: Transient response of grouped axles

Figure 14: Block diagram for the single axle suspension – Alternative expression

Figure 15: The Bode diagram of the vibration model

AIRBAG

AIR SUPPLY

TYRE STIFFNESS

TRANSMISSION LINE

Figure 16: The pneumatic transmission line system schematic

Figure 17: Pressure transient response of the capillary transmission line system

Figure 18: Pressure transient response of the orifice transmission line system

Figure 19: The Bode diagram of the capillary transmission line system

Figure 20: The Bode diagram of the orifice transmission line system