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CAE Software of Twin-Tubes Shock Absorber Outer-Characteristic
Changcheng Zhou, Jie Meng
School of Traffic and Vehicle Engineering
Shandong University of Technology
Zibo 255049, China greatwall@sdut.edu.cn Abstract
The pathway throttle and local throttle loss of oil flow in telescopic shock absorber were analyzed, and the pathway loss coefficient and equivalent length of piston holes were studied. According to the thickness and the pre-deformation of throttle slice, and the throttle holes area, the velocity points of valve opening were researched and the analytic formulas of shock absorber velocity when valve opening were given. With the velocity points of valve opening, the model of shock absorber outer characteristic was established by piecewise linear math function. Based on this, the CAE software for shock absorber outer characteristic was developed. A practical example of simulation of shock absorber outer characteristic was given with this CAE software, and the performance test was conducted to verify the CAE software. The results show that the
CAE software is reliable, and the values simulated is close to that tested.

1. Introduction
The shock absorber of automobile is one of the most important components of suspension system, and plays a vital role in the driving process of vehicles[1,2].
The characteristic of shock absorber influences driving smoothness and ride comfortableness of vehicles[3].
The shock absorber used most commonly on automobile is telescopic shock absorber[4].
The characteristic simulation has the significance for the design of shock absorber. With the characteristic simulation, the flaws of design could be found and modified in time, so the design and develop could speed up, while also the test costs could be reduced. However, at present, both in domestic and abroad, the characteristic of shock absorber is simulated mostly with ready-made simulation

_____________________________

978-1-4244-3701-6/09/$25.00 ©2009 IEEE

Yuanyi Liu
School of Mechanical Engineering
Shandong University of Technology
Zibo 255049, China liuyy@sdut.edu.cn software[5]. Utilizing this method, most of necessary parameters used in the modeling of characteristic are obtained through the experiment tests, therefore, it is hard to establish the accurate simulation model, and the simulation results is also not reliable. Though some scholars had built the model of characteristic with math function, due to the inaccurate analysis of the shock absorber damping component, and the imprecise computation of throttle slice deformation and opening size of the throttle valve with the Mechanical Design
Handbook that provides only the maximum deformation proximately formula. Thus, it is difficult to build the accuracy model, and the CAE software developed is unreliable.
In this paper, by the analysis to the pathway throttle loss coefficient and local throttle loss coefficient of piston holes, with the analytic formula of throttle slice deformation, according to the velocity points at which the valve opening, the model of shock absorber outer characteristic was established by the piecewise linear function. The CAE software of shock absorber outer characteristic was developed, the simulation example was given with the CAE software, and the performance test was conducted for to verify the CAE software. 2. Analysis of damping element
When the characteristic of shock absorber is analyzed, the throttle holes, piston hole and piston slot should be taken into account, meanwhile the local throttle loss must also be considered. The analysis on the structure, the throttle pressure and the flux of the throttle valves are as follows.

2.1. Throttle holes
Throttle slice of rebound valve is composed of superposition slices with small gaps and not, and the

rectangular cross-sections of these gaps form the throttle hole area. The types of throttle holes are determined by the ratio of throttle hole’s length and hydraulic diameter l / DHA . For single throttle hole, its area is A0i= G l A , circumference is lC 2(G  l A ) and hydraulic diameter is d HA 4 A0 i / lC . So the relation between throttle pressure and flux can be expressed as follows[6] 2 p0
.
(1)
QA0 H A0

U

Where, H is the flow coefficient of throttle orifice which is decided by the type of orifice; p0 is the throttle pressure of throttle hole, A0 is the total area of the throttle holes which can be obtained by the thickness of slice with holes h1, width of throttle hole lA and number nA, that is A0 h1l A n A .

2.2. Deformation of throttle slice
Normally, the velocity of shock absorber is quite slow, and the throttle pressure is low, thus the deformation of throttle slice could be regard as minor deflection bending deformation. According to the calculation method of the bending deformation coefficient[7], the deformation at valve mouth radius can be expressed as pf f rk Grk 3
(2)
h
Where, Grk is the deformation coefficient of throttle slice at valve mouth radius; h is the thickness of throttle slice; pf is the pressure on throttle slice.
The opening size of throttle valve is determined by the total deformation f rk and pre-deformation f rk 0 of throttle slices at valve mouth radius, that is[8]
G rk f rk  f rk 0
(3)

2.3. Throttle slot

2.4. Piston slot

pH

3
SG rk p f
.
6 Pt ln(rb / rk )

(4)

12QH Pt LH
.
3
S DhG H (1  1.5e 2 )

(5)

Where Dh is the inner diameter of cylinder, Pt is the dynamic viscosity of oil; QH is the flux of piston slot; e is eccentricity of piston, generally 0  e  1 , LH is the length of piston slot.
2.3.1. Pathway throttle Loss. Let piston orifice is smooth orifice, then the critical Reynolds number is
Rec=2300. So, the critical velocity of piston orifice is vc
(6)
vc Q R e c /d h
Where, Q is the kinematics viscosity of oil.
So, the critical velocity of shock absorber is vc Ah d hQ R e c
(7)
Vc
2
2
Sh

( Dh  d g )

Where, Sh is the annular area between piston
2
2 cylinder and piston rod, and S h S ( Dh  d g ) / 4 ; d g is the diameter of piston rod; Ah is the total area of
2
piston orifice, and Ah nhS d h / 4 .
While velocity of shock absorber VVc, the flow regime of fluid is turbulent flow, and the pathway throttle loss coefficient is as

ª 4S hV º
0.3164 «
(9)
»
¬ nhS d hQ ¼
Where, Re is Reynolds number.
Therefore, the pathway throttle-loss coefficient has relation to flowing velocity of oil. Thus, while analyzing the characteristic of shock absorber, it should be in accordance with the velocity of the shock absorber and the flow state of oil in piston hole, furthermore, with different pathway throttle-loss coefficient formulas.

Oh

When the moving velocity of shock absorber is greater than first valve opening velocity, the deformation of throttle slice at valve-mouth radius position is greater than the pre-deformation of throttle slice at this position, and the annular throttle slot formed between throttle slice upper surface and piston lower surface. So the relation between flux of throttle slot and throttle pressure is as[6]
Qf

The piston slot size has relation to the fit tolerance of piston and inner diameter of cylinder. The minimum fit clearance is G H min , and the maximum fit clearance is G H max . Thus the average fit clearance is G H =
( G H min  G H max )/2. So the throttle pressure of piston slot can be expressed as[6]


0.3164 R e 0.25

2.3.2. Local throttle loss. When oil flows through the piston hole into the cavity of the rebound valve, there are three local throttle loss, that is, respectively,

expand ] h1 , suddenly reduce ] h 2 and change direction
] h3 .
Total local throttle loss is computed with superposition principle, and then converted it into the pathway throttle loss. Therefore, the length of piston hole converted is
(10)
Le (] h1  ] h 2  ] h3 )Oh / d h
Where, ] h1 is the local throttle loss of suddenly shrinkage as oil flows from rebound chamber to piston orifices; ] h 2 is the local throttle loss of suddenly expansion when oil flows from piston orifice to rebound valve cavity; ] h 3 is the local throttle loss of direction change when oil passes through piston orifice.
It is known that, establishing the model of outer characteristic of shock absorber, the local damping loss should be converted into the equivalent length of piston hole, based on the number and the diameter of piston hole, and the velocity points.

3. Math model of outer characteristic
3.1. Velocity point of valve opening firstly
The velocity point of valve opening first is determined by the thickness of throttle slice, predeformation of slice and orifice area. An example of rebound valve is given to illustrate the procedure, the oil flow paths before the rebound valve opening firstly is shown as in the Figure 1.

-Piston hole

Q0 k1

A0H 2 p f k1 / U .

(12)

Piston holes and orifices are the series, that is
Q0 k 1 Qhk1 , so the throttle pressure of piston holes can be expressed as
128Pt Lhe Q0 k 1 phk1 .
(13)
S nh d h4
Throttle orifice and piston holes are in parallel with piston slot, therefore, the throttle pressure of piston circle slot is equal to the sum of throttle pressure of piston holes and throttle orifices, i.e. pHk1 phk1  p f k 1 .
So, the flux of piston circle throttle-slot is expressed such as
3
S DhG H (1  1.5e2 ) pHk1
.
(14)
QHk1
12Pt LH
According to the continuity theorem of oil, the flux of throttle orifices, piston holes and piston circle slot should satisfy the relation equation, i.e.
Q0 k1  QHk 1 VK 1 Sh . Thus, the velocity at which the rebound throttle-valve opening could be obtained, it is such as
3
2
A0H 2 p f k1 S DhG H (1  1.5e )( phk1  p f k1 )
(15)
VK 1 f

Sh
U
12 S h Pt LH

3.2. Velocity point of valve opening maximally
While rebound valve opening secondly, the throttle slice would touch the limit gasket and lower of shield ring as a result of deformation, so, the maximum opening size of valve is G max . It is constant and equal to the value of throttle slot, the oil paths after rebound valve opening secondly as Figure 2.

Piston slot-Piston orifice

-Piston hole
Piston slot

- Piston orifice

Figure 1 Oil paths before the rebound valve opening.
Throttle slot

Defining pre-deformation of throttle slice at valve mouth radius is f rk 0 , when the deformation is equal to the pre-deformation, the rebound valve opens first.
According to the formula of the slice deformation, the pressure on slice at this time is p fk 1 h3 f rk 0 / Grk .
(11)
When the valve opens first, the pressure on slice is equal to the throttle pressure of orifice, i.e. p f k1 p0 k1 .
The flux of orifice can be expressed as

Figure 3 Oil paths after rebound valve opening maximally.

After the throttle rebound valve being at the maximum opening size, the total deformations of throttle slice is f rk 2 G max  f rk 0 . So, the pressure on throttle slice is p fk 2

(G max  f rk 0 )h3 / Grk . For the

throttle orifice is parallel with the throttle slot of

rebound valve, so, p0 k 2 orifice is Q0 k 2

p fk 2 , the flux of throttle

A0H 2 p fk 2 / U .

Thus, the flux of

throttle slot of rebound valve is
3
SG max p fk 2
.
(16)
Qf k 2
6Pt ln(rb / rk )
Throttle orifice is parallel to throttle slot of rebound valve, and then series to piston hole, so
Qhk 2 Q fk 2  Q0 k 2 .Therefore, the throttle pressure of piston holes is
128Pt Lhe (Q fk 2  Q0 k 2 )

.
(17)
S nh d h4
So, the flux of through piston circle slot is
3
S DhG H (1  1.5e 2 )( phk 2  p0 k 2 )
.
(18)
QHk 2
12Pt LH
According to the continuity theorem of oil, when the rebound valve reaches the maximum opening size, the velocity of shock absorber is
Vk 2 f (QHk 2  Q fk 2  Q0 k 2 ) / S h .
(19)
phk 2

3.3. Piecewise characteristic linear

function

model

opening and maximum opening size. Vk1 y is the velocity at which the compression valve opens firstly,
Vk 2 y is the velocity at which the valve opens maximally. 4. CAE software and simulation example
Based on the math model of outer characteristic of shock absorber, the CAE software could be developed by the tools software, i.e. VC++.

4.1. Input windows of parameters
4.1.1. Input windows of structure parameters of shock absorber. In this input window, the structure and valves parameters of shock absorber, the oil parameters, and the slice material are inputted, such as, the inner diameter of inner tube, the diameter of piston rod, throttle area, throttle-slices thickness and their numbers, the oil density and its viscosity. They are shown, respectively, in Table 1, Table 2 and Table 3.
Table 1 Input parameters of structure

of

3.3.1. Rebound process (V>0). The outer characteristic of shock absorber in rebound process can be expressed by the following piecewise linear function[9,10] ­( p f 1  ph1 ) S h , 0  V d Vk1 f
°
Fd ®( p f 2  ph 2 ) S h , Vk1  V d Vk 2 f .
(20)
°
¯( p f 3  ph3 ) S h , V ! Vk 2 f
Where, p f 1 , p f 2 , p f 3 ; ph1 , ph 2 and ph 3 are the

throttle pressure of throttle slot of rebound valve and piston hole, when rebound valve is on three kinds of conditions that are before opening, after opening and maximum opening size.
3.2.2. Compression process (V…...

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...compliment them which will make the client smile therefore raise their self-esteem. A care assistant can help to give clients a sense of approval by regularly asking the clients of they wanted to do something, for example walking or gardening, this will help to make the clients feel loved and cared for by others. Also if clients have received a new haircut or new clothes then the care assistant should complement them and praise them for how they look. Lastly a care assistant should find out different things about the clients that they are caring for as a way to get to know them better and be able to talk about their interests more with them. Kitchen staff and the chef can show a positive attitude to clients by smiling at them and saying hello whenever they see them, this will give clients a positive feeling towards the kitchen staff and chef. Privacy Being undisturbed by others in situation that can cause embarrassment to a person. A care manager has the job and responsibility of keeping all client’s personal information and details safe and secure away from anyone that does not have authority of access. They should also make sure that they are respectful towards clients, for example knocking before entering their rooms gives the client their own sense of privacy in their own room. A care assistant can show privacy towards their clients by not discussing their personal information to anyone during work unless necessary and not outside of work. They should also give......

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...Hello World This is just a sample essay.   Contrary to popular belief, Lorem Ipsum is not simply random text. It has roots in a piece of classical Latin literature from 45 BC, making it over 2000 years old. Richard McClintock, a Latin professor at Hampden-Sydney College in Virginia, looked up one of the more obscure Latin words, consectetur, from a Lorem Ipsum passage, and going through the cites of the word in classical literature, discovered the undoubtable source. Lorem Ipsum comes from sections 1.10.32 and 1.10.33 of "de Finibus Bonorum et Malorum" (The Extremes of Good and Evil) by Cicero, written in 45 BC. This book is a treatise on the theory of ethics, very popular during the Renaissance. The first line of Lorem Ipsum, "Lorem ipsum dolor sit amet..", comes from a line in section 1.10.32. The standard chunk of Lorem Ipsum used since the 1500s is reproduced below for those interested. Sections 1.10.32 and 1.10.33 from "de Finibus Bonorum et Malorum" by Cicero are also reproduced in their exact original form, accompanied by English versions from the 1914 translation by H. Rackham. There are many variations of passages of Lorem Ipsum available, but the majority have suffered alteration in some form, by injected humour, or randomised words which don't look even slightly believable. If you are going to use a passage of Lorem Ipsum, you need to be sure there isn't anything embarrassing hidden in the middle of text. All the Lorem Ipsum generators on the Internet tend to......

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...“Do not impose on others what you do not wish for yourself.” – Confucius Applying the Golden Rule - refusing to engage in intentional and avoidable harm - promoting the overall welfare of host country citizens - avoiding violation of host country norms Scenario: Company X in host country allows unsafe practices such as workers climbing high-rise structures without proper harnesses and safety lines or operation of loud machinery without hearing protection (ear plugs). By home country’s safety regulations, these practices are deemed unsafe and clearly violate the golden rule. Switching roles with the workers, you would not want to put your life on the line every time you climb structures to do your job. Or you would not want your hearing to be impaired after years of operating loud machinery without hearing protection. Therefore, there is a clear violation of the Golden Rule. Another scenario will be in the case of exploitation or slave labour. Goodin’s 5 conditions: 1) Imbalance of power between the exploited and the dominant 2) Exploited party needs the resources provided by dominant party to protect his vital interest 3) Dominant party exercises discretionary control over this vital resource 4) Only access to this resource is through the exploitive relationship 5) Resources provided by the exploited are used without adequate compensation By the Golden Rule, it is safe to assume that no one would want to be exploited or be enslaved and be stripped of......

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...A "Hello, World!" program is a computer program that outputs "Hello, World!" (or some variant thereof) on a display device. Because it is typically one of the simplest programs possible in most programming languages, it is by tradition often used to illustrate to beginners the most basic syntax of a programming language. It is also used to verify that a language or system is operating correctly. Purpose This section does not cite any references or sources. Please help improve this section by adding citations to reliable sources. Unsourced material may be challenged and removed. (April 2015) A "Hello, world!" program has become the traditional first program that many people learn. In general, it is simple enough so that people who have no experience with computer programming can easily understand it, especially with the guidance of a teacher or a written guide. Using this simple program as a basis, computer science principles or elements of a specific programming language can be explained to novice programmers. Experienced programmers learning new languages can also gain a lot of information about a given language's syntax and structure from a "Hello, world!" program. In addition, "Hello, world!" can be a useful sanity test to make sure that a language's compiler, development environment, and run-time environment are correctly installed. Configuring a complete programming toolchain from scratch to the point where even trivial programs can be compiled and run can......

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...Chapter Three Summary: Ender woke up to a father who was disappointed and Ender could tell he was. But before Ender headed to school an International fleet officer came to the house to have a talk with Ender. Colonial Graff came to inform that Ender nearly beat a kid too death, but wanted him to also inform them that Ender passed and was eligible to enter battle school. Ender was shocked at what has just happened because of the whole monitor incident. Enders parents were very angry with Colonial Graff for just not wanting Ender to needing him after what he has done. Colonial Graff told them it was part of the last test and that he has passed. He said that Ender didn’t just beat him, but he needed to so he can protect him self from harm. So Ender went with him because he felt that it was what he was born for. Reflection: This made me feel angry with Colonial Graff because not only did he convince Ender, but also he lied to him about what his family thinks of him. I think the outcome would have been different if Ender just stayed with his family and moved on too his abnormal life. If I were to predict what will happen next I would say Ender is going to the battle school were he will learn to become the next commander. Question/Answer: Would Colonial Graff really let Ender stay home instead of going to battle school? I believe that he wouldn’t because he said that he would even tell him......

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