英語翻譯 : 汽車減振器參數化模型的發展和實驗驗證 作者： KIRK SHAWN RHOADES 摘 要 這篇論文描述了汽車減振器的一個參數化模型的實現過程。研究的目標是創造一個可以準確地預測阻尼力的減振器模型來作為 學生型方程式賽車 團隊的一個設計工具。這項關于單筒充氣減振器研究適合于 學生型方程式賽車 的應用。 這個模型考慮到了減振器中每一個單獨的流通路徑，并且建立了對每一個流通路徑的流通阻力模型。閥片組的撓度由一個力平衡方程計算出并且與流通阻 力相關。這些方程產生一個可以用牛頓的迭代方法求解的非線性方程組。 這個模型的目標是創建準確的力 -速度和力 -位移關系并用于檢驗。應用一個震動測力計使模型與真實的減振器數據聯系起來以驗證準確性。通過一個有效的模型，組件包括常通孔、活塞孔、壓縮和復原閥片是不同的以獲得減振器阻尼力效果的了解。 一、減振器功能特性 1.減振器的構造 要理解減振器的工作過程第一步是要弄清楚減振器的各個組成部件是如何相互作用產生阻尼力的。下面本文將對減振器的組成和功用做一個簡單的介紹。減振器的參數特性通常由力 -速度和力 -位移曲線給出。關于這些圖形的更詳細的描述將在這一部分給出。 有許多類型的汽車懸架減振器，其作用通常是用來緩和沖擊。這其實是一個誤稱，因為減振器實際上并不能緩和沖擊，這是懸架彈簧的作用。眾所周知，一個彈簧振子系統在沒有能量耗散時會做永久的簡諧振動，其中彈簧與振子的勢能與動能分別地相互轉化。在這篇論文的目的中，減振器的術語將會被使用。減振器的功能就是消除系統動能并將其轉化為內能。 減振器的構造有許多類型：雙筒減振器，單筒帶或不帶蓄能器的減振器，甚至中間有一個桿的減振器類型。在這篇論文的目的中，單筒的 不帶蓄能器的減振器將被用于實驗。 不同類型的減振器的另一個主要區別時其外部適應性的特征。有的減振器裝配后仍可以被調節。汽車通常使用不可調節的減振器。相反地，在賽車中使用的減振器通常有一定程度的可調節性。既然這項研究的焦點是幫助賽車懸架設計，這種單筒減振器具有可調性。 圖 1 單筒減振器的組成 圖 1 顯示了單筒減振器的主要組成元件，外部可調減振器。這種減振器包含一個在充滿油液的圓筒中運動的活塞總成。減振器的外罩包含了所有的內部元件。一個裝配完全的減振器被分為 三個壓力腔：氣室、復原腔和壓縮腔。氣室與壓縮腔通過一個浮動活塞分開。這個浮動活塞將氣室中的氣體與液體分隔開來，在壓縮腔與復原腔室中，典型的液體是油液。減振器中應用最多的氣體是氮氣，因為其不與油液發生反應。它對溫度相對地不敏感并且不含水蒸氣。 壓縮腔是位于浮動活塞與連桿活塞之間的那一部分體積。復原腔是有活塞桿的那一部分體積。壓縮腔與復原腔完全地被油液充滿，在這里應用的是典型的是5W 重的油液。 活塞與活塞桿相連，活塞桿通過一個用來保持油液的密封裝置。桿密封裝置同時阻止灰塵和其他污染物進入復原腔影響內部油液的 流動。活塞在其外罩上也有一個密封裝置位于其外徑和內徑之間。這個密封裝置將壓縮腔與復原腔分隔開來。 圖 1 所示的球型支座是用來將減振器安裝在車體上。在未對減振器施加彎曲應力時，它們允許一定的裝配誤差。在賽車的應用上，減振器的活塞桿一般連接在車橋上，而套筒的另一面一般連接在車架上以減少不定質量的變化幅度。 2.減振器的一般工作過程 減振器有兩個典型的工作行程：壓縮行程與復原行程。這兩個行程每一個都將被單獨試驗。圖 2 所示的是壓縮行程模型。 圖 2 壓縮行程流通圖 在壓縮行程中，液體有壓縮腔流入復原腔。由于油液具 有很強的不可壓縮性，活塞桿進入復原腔，復原腔和壓縮腔中油液和活塞桿的體積之和必然增大。為了適應這種體積增大，浮動活塞在氣室中壓縮氮氣，氣體壓縮的體積與活塞桿進入的體積相同。單筒減振器同時具有壓縮氣室以保持一個提升的油液壓力的優點，這可以幫助阻止油液空穴的形成。模型分析顯示活塞一英寸的位移只引起氣室壓力四到十 磅 /平方英寸 的改變，根據氣室初始壓力而不同。這個小的壓力改變意味著一個幾乎相同的壓力施加在壓縮腔力的液壓油液上。氣室中的壓力用 Pg 表示。 氣室中的壓力顯示出一個氣體彈簧效果。力等于活塞桿的面積與 Pg 的乘積 ，這個力一直作用在活塞桿上。氣體彈簧效果是與活塞速度無關的，但與位移十分相關，并與加速度有微弱的關聯。在壓縮行程中氣體彈簧力是不斷增大的。 壓縮行程中總的流量是三個流通路徑的綜合。這些流量與壓力腔之間的壓力差有關。復原腔中的壓力用 Pr 表示，壓縮腔中的壓力用 Pc 表示。在壓縮行程中，Pc 大于 Pr，這個壓力差使油液由壓縮腔進入復原腔，并產生阻尼力。流通路徑和各腔壓力在圖 2 中顯示并在下面解釋。 第一條流通路徑是常通孔。常通孔流通路徑開始于壓縮腔活塞桿的終點處，結束于復原腔活塞一面的活塞桿處。常通孔的尺寸是可以通過圖 2 所示的活塞桿中的可動針閥調節的。針閥可以通過圖 1 所示的常通孔調節器旋入或旋出。常通孔可以被調節成全開以減少阻尼至全閉增大阻尼。改變針閥的幾何形狀或尺寸也可以改變常通孔的流量。常通孔在低速減振中起首要作用因為這個孔常開，與活塞速度無關。 第二條流通路徑是活塞孔流通路徑。活塞孔流通路徑通過活塞上的固定直徑孔，再通過變形后允許流通的薄閥片組。活塞孔流通路徑由壓縮閥片或閥片組控制。為了簡化，在圖 2 中至顯示了一個閥片，壓縮閥中的液流通過復原閥片中的一個孔。復原閥中的孔取消了在活塞中開一個流通路徑的必要，并且這是一個 允許閥流通的簡單的方式，降低了活塞制造的復雜性。 提高速度可以降低復原腔的壓力和增大油液流通速度。不同的壓力引起不同的閥片變形。壓縮閥片，位于復原腔，根據活塞的速度限制液流的流通面積。速度增大，閥片變形增大，從而液流流通面積增大。 Pv 被定義為在活塞孔通道內部的壓力。 第三條流通路徑是在活塞與套筒內壁之間密封裝置的泄露。泄露流通至少在重要性上不如前兩種流通路徑，但是很難將其完全消除。長時間的使用會使密封裝置退化，增大泄露流通量，并且降低減振器的阻尼力。這種活塞套筒密封裝置應該定期更換以使泄露流通量與其它流通方 式比起來不會過多。 復原行程流通圖 圖 3 所示的是復原行程工作過程。在復原行程中，活塞桿在充滿油液的套筒中被撤回，從而引起油液從復原腔流入壓縮腔。壓縮腔和復原腔中油液和活塞桿的體積之和因為活塞桿的撤出而減小，氣室中的氣體擴張。 復原行程的液流是從復原腔流入壓縮腔。前面討論的所有的閥，常通孔和泄露孔仍然存在，只是方向與原來相反。 常通孔現在開始于活塞桿上空的入口處，結束于活塞桿在壓縮腔的終點處。所有的由常通孔引起的低速阻尼屬性都可以有壓縮行程移植到復原行程。 活塞孔流通路徑在概念上與壓縮行程一致，只不過具體的流通孔是不同的。復原行程的壓力關系是 PrPvPc。閥內液流通過壓縮閥片上適當的孔并引起壓縮腔內復原閥片的變形。如前所述，復原速度的增大將會導致閥片變形和液流面積的增大。 泄露流量與前所述具有同樣的重要性并且通過活塞和外套筒間相同的軸對稱的缺口。只有方向復原行程與壓縮行程是相反的。 通過測試復原行程與壓縮行程，可以看到減振器的物理工作過程是復雜的。減振器具有不同的位移，速度和加速度。方程還與壓力，閥片變形，油液流量等因素有關。這些都將成為建立減振器工作模 型的基礎。 3.減振器的工作特性 既然在任何汽車或賽車中的減振器活塞速度一直處于不斷變化的狀態，這就很難定義和解釋減振器的工作情況。為了評估減振器的工作狀況，在減振器測力計上測試成為一種規范。這項研究中使用的減振器測力計是一個 Roehrig 2VS。這種減振器測力計是施加一個按正弦規律變化的位移。位移的振幅和頻率是給定的。位移的一階導數和二階導數分別是速度和加速度。 圖 4 全過程力 -速度特性 圖 5 與 F-V 圖相應的 減振器活塞位移 -時間關系 圖 6 與 F-V 圖相應的減振器活塞速度 -時間關系 使減振器工作過程參數化的最初方法是輸出力 -速度關系。圖 4 至 6 顯示了基本的 F-V 圖像與相應的運動曲線。 圖 4 顯示了全過程的力 -速度曲線，包括壓縮行程和復原行程。這有時候被稱作連續的速度輸出特性（ CVP）。對力和速度給出常規的注釋是重要的。壓縮行程中速度是負的，而復原行程中，減振器度增大，速度是正的。在一些實例中，速度方向的定義可能是相反的。習慣上使用的是 Roehrig 測試測力計，在這篇報告中將會始終使用到它。 習慣上使用的力是減振器 產生的力。復原力是負的，壓縮力為正。有一段速度接近于零的區域，那里的情況并不真實。這是由于減振器的滯后效果造成的。圖 4 中所示的滯后作用是當速度增大和速度降低時的力的差異。也就是說，當減振器加速和減速時其產生不同力是不同的。滯后作用這個詞語通常用來指這種效果，在本文中將會一直使用這個概念表示在 F-V 圖像上力的差異。然而，這種效果并不是傳統的科學文獻中定義的滯后性。這種現象的原因將會在文獻回顧部分給出解釋。 圖 4-6 上還有標記有 1-4 的點。這些是減振器運動中的關鍵點。點 1 是循環的開始。減振器充分延伸，并且開始速 度為零。從點 1 至點 2 減振器速率不斷增大，進行的是壓縮行程。在點 2，達到最大負向速度。這通常對應于壓縮行程中力的峰值。此時位移為零，這意味著全行程的一半已被壓入減振器。從點 2 至點3，速率開始下降。點 3 標志著壓縮行程的結束。這時的位移達到負的最大值，這意味著減振器被充分壓縮，速度降至零。過了點 3，復原行程立即開始，伴隨著速度的不斷增大。在點 4，復原行程的力達到峰值，位移再次變為零，所以減振器擴張至復原行程的一半。循環而后從點 4 回到點 1，隨著活塞速率的降低，復原行程繼續進行。在點 1，減振器回到完全張開狀態，速度減 為零。 所有的圖形通常排除了氣體彈簧力。因此，這個力在速度為零時其值也為零。 其它的有時被用到的表征減振器工作狀態的圖像是力 -位移圖像。圖 7 顯示了典型的 F-D 曲線。這個曲線是減振器參數化后所有的機械設備被用來測量和測繪力 -位移曲線的結果。 圖 7 全過程力 -位移特性 F-D 圖像使用慣用的力符號，壓縮時為正，復原時為負。在壓縮行程和復原行程中力都不是關于 y 軸對稱的。在 F-V 圖像中同樣的滯后作用是產生這種不對稱性的原因。 為了獲得進一步理解，可以用一個假想的理想彈簧，理想阻尼器，正弦運動來解釋滯后性。一個理想 線性彈簧在 F-D 圖像中產生的剛度 K 是一條傾斜直線。在 F-V 圖像中是一個橢圓（見附錄 A）。一個理想的線性阻尼器在 F-V 圖像中會產生一條傾斜的剛度直線，在 F-D 圖像中是一個橢圓。在一個實際減振器的 F-V圖像中滯后作用導致減振器產生像彈簧的力。 二、文獻回顧 進行文獻回顧有兩個主要目的：第一個目的是通過研究減振器功能的參數化模型的發展過程，對單獨的內部元件和內部液流在過去如何被參數化獲得一個更好的理解。 文獻回顧第二個目標是對發生在 F-V 圖像中的滯后作用獲得一個深刻的理解。理解產生這種現象的原因和如何使之最小化在 減振器設計中具有起決定作用的重要性。所有這些概念將會在引用文獻中被找到。 三、減振器規格 這項研究中所使用的減振器是 Tanne 賽車產品中的一個 Tanner 外部可調減振器 Gen 2。它是一個充氣的單筒構造，里面有一個浮動活塞將氣室和油腔分割開來。 Tanner Gen 2 的最初用途是四分之一微型車競賽中，但是它的尺寸，價格和可用的阻尼力范圍使其也可以應用在 學生型方程式賽車 中。 Tanner Gen 2質量輕，價格相對便宜，并且可以通過內部調節取得理想的阻尼力。圖 8 顯示了一個 Tanner Gen 2 減振器的三維模型 。 圖 8 Tanner Gen 2 減振器 減振器伸張到最長時距球型支座的中心是 10.33 英尺。減振器行程大約是 3英尺。減振器外罩和端蓋是由鋁制成，而鍍鉻的桿是由拋光的鋼制成。端蓋上面有螺紋可以拆除從而使得拆裝容易。 活塞和閥片的設計用來控制活塞孔液流，允許這部分制造時成本比其他賽車低得多。活塞是由機械鋁制成的，并且具有 6 個液流孔。活塞如圖 9 所示。 圖 9 Tanner Gen 2 鋁質活塞 活塞液流孔具有 0.038 英寸的直徑，用來將活塞裝配到活塞桿上的孔直徑是 0.25 英寸 。位于圓筒的外徑上的溝槽是用來裝配活塞與圓筒之間橡膠密封裝置的。這種活塞設計比起 Ohlins 和 brand 牌的減振器復雜性要小很多，并且這種簡單的設計生產起來要便宜許多。 根據所需的減振器水平不同，可用的活塞的孔徑從 0.14 英寸（軟減振器）到 0.038 英寸（硬減振器）。在沒有任何閥片時， 6 個孔在壓縮和復原行程都允許液流通過。 Tanner 賽車產品的一套閥片組的一個單獨閥片也可以使用。如圖 10 所示 . 圖 10 Tanner Racing G2 的一套碳纖維閥片組 Tanner 賽車上的一套閥片組包含碳纖 維閥片。這些閥片擁有與鋼幾乎相同的彈性模量和泊松比，但是它們的質量要輕得多。閥片有孔的位置與活塞上可以用來在壓縮行程與復原行程中開通一條液流通路的孔是一致的。例如，如果兩孔閥片被用在活塞壓縮面而三孔閥片被用在活塞復原面，只要沒有公用孔，復原行程中將會存在兩個單獨的液流通路而壓縮行程中將會存在三條單獨的液流通路。閥片的排列可以為 Tanner Gen 2 減振器創造無窮的可能。另外也可以利用不同厚度或不同材質的閥片來得到想要的阻尼特性。 用來調節常通孔的有螺紋的針閥可以旋轉 3.75 圈。標記 0 圈的位置等效于一個全閉 的常通孔。調節器旋轉的圈數越大，常通孔開度越大。這是一個很實際的考慮，因為全閉活塞是容易辨認的。 減振器油液用的是 Tanner Tuned 振動油。這種油液的屬性是未知的，所以典型的 5W 油將被用在模型上，其密度和粘度最為重要。 英語原文 DEVELOPMENT AND EXPERIMENTAL VERIFICATION OF A PARAMETRIC MODEL OF AN AUTOMOTIVE DAMPER A Thesis by KIRK SHAWN RHOADES ABSTRACT This thesis describes the implementation of a parametric model of an automotive damper. The goal of this research was to create a damper model to predict accurately damping forces to be used as a design tool for the Formula SAE racecar team. This study pertains to monotube gas charged dampers appropriate to Formula SAE racecar applications. The model accounts for each individual flow path in the damper, and employs a flow resistance model for each flow path. The deflection of the shim stack was calculated from a force balance and linked to the flow resistance. These equations yield a system of nonlinear equations that was solved using Newtons iterative method. The goal of this model was to create accurately force vs. velocity and force vs. displacement plots for examination. A shock dynamometer was used to correlate the model to real damper data for verification of accuracy. With a working model, components including the bleed orifice, piston orifice, and compression and rebound shims which were varied to gain an understanding of effects on the damping force. FUNCTIONAL DAMPER CHARACTERISTICS The first step in understanding the operation of a damper is to understand how he components interact to create the damper force. A brief discussion of damper components and functionality is given in this section. The characteristics of damper are usually presented graphically in Force vs. Velocity and Force vs. Displacement graphs. A detailed description of these graphs is contained in this section. GENERAL CONFIGURATION OF DAMPER There are many types of automotive suspension dampers, which are commonly referred to as shock absorbers. This is a misnomer because the damper does not actually absorb the shock. That is the function of the suspension springs. As is well known, a spring/mass system without energy dissipation exhibits perpetual harmonic motion with he spring and the mass exchanging potential and kinetic energy, respectively. For the purpose of this paper, the term damper will be used. The function of the damper is to remove the kinetic energy from the system and to convert it into thermal energy. There are numerous configurations of dampers: twin tube, monotube with or without reservoir, and even a rod through damper type. For the purpose of this thesis, a monotube damper without a separate reservoir will be examined. Another major distinction in damper types is the feature of external adjustability, .e. if the damping can be adjusted after the damper is assembled. Automotive applications generally use a nonadjustable damper. In contrast, many dampers for racing applications have some degree of adjustability. Since the main focus of this research is to aid in racecar suspension design, the monotube damper chosen has adjustable damping. Figure 1 displays the major components of a monotube style, externally adjustable damper. The damper is comprised of a piston assembly that moves inside a fluid filled cylinder. The outer housing of the damper contains all internal components. A fully assembled damper is partitioned into three pressure chambers: gas, rebound and compression. The gas chamber is separated from the compression chamber by a floating piston. This floating piston separates the gas in the gas chamber from the fluid, typically oil, in the compression and rebound chambers. The gas used for most damper applications is dry nitrogen because it does not react with oil. It is relatively insensitive to temperature and contains no water vapor. The compression chamber is the volume between the floating gas piston and the piston attached to the rod. The rebound chamber is the volume on the rod side of the piston. The compression and rebound chambers are completely filled with oil, typically 5W weight oil designed for this application. The piston is connected to the piston rod which exits the housing through a rod seal that retains the oil. The rod seal also prevents dirt and other contaminates from entering the rebound chamber and affecting internal flow of oil. The piston also has a seal between its outer diameter and the inner diameter of the outer housing. This seal separates the compression and rebound chambers. The spherical bearings shown in Figure 1 are for mounting the damper to the vehicle. They allow for some degree of misalignment in mounting without imposing bending loads on the damper. For racing applications, the piston rod of the damper is usually mounted to the wheel suspension, while the cylinder side is connected to the frame of the vehicle in order to minimize the unsprung weight. GENERAL OPERATION OF DAMPER There are two modes of operation in a damper: compression and rebound. Each of these modes will be examined individually. The compression operation mode is shown in Figure 2. During the compression stroke, fluid flows from the compression chamber into the rebound chamber. Since the oil is effectively incompressible, as the piston rod enters the rebound chamber the sum of the volumes of the oil and the rod in the rebound and compression chambers must increase. To accommodate this volume increase, the gas piston compresses the nitrogen in the gas chamber to decrease the gas volume by an amount equal to the volume of the inserted rod. Monotube dampers also have the advantage of pressurizing the gas chamber to maintain an elevated pressure on the oil, which helps prevent oil cavitation. Model analysis has shown only a four to ten psi change in the gas chamber pressure for one inch of piston rod displacement, depending on initial gas pressure value. This small pressure change means an almost uniform pressure exerted on the hydraulic oil in the compression chamber. The pressure in the gas chamber is denoted Pg. A gas spring effect is also present due the pressure in the gas chamber. A force equal to the area of the rod times the gas pressure, Pg, will be on the rod at all times. Gas spring effect is independent of piston velocity, but strongly dependant on displacement and very weakly dependant on acceleration. The gas spring force increases during the compression stroke. Total flow during compression is comprised of flow through three flow paths. These flows are related to the pressure differences in the pressure chambers. Pressure in the rebound chamber is denoted as Pr and pressure in the compression chamber is denoted Pc. During compression Pc is greater than Pr; this pressure difference drives the flow from the compression chamber to the rebound chamber and generates the damping force. Flow paths and chamber pressures are shown in Figure 2 and explained below. The first path is the flow through the bleed orifice. The bleed orifice flow path begins at the end of the piston rod in the compression chamber and ends out of the side of the piston rod in the rebound chamber. The bleed orifice size can be adjusted by moving the needle valve inside the piston rod in Figure 2. The needle valve is adjusted in or out using the bleed adjustment shown in Figure 1. The bleed flow orifice can be adjusted from fully open for less damping to fully closed for increased damping. Modifications to the geometry of the needle value or size of the bleed orifice can change the bleed orifice flow also. The bleed orifice dominates the low speed damping because this orifice is always open, regardless of piston velocity. The second flow path is the valve orifice flow path. Valve orifice flow travels through constant diameter holes in the piston and past thin washer-like shims that deflect to allow flow. Valve flow is controlled by the compression shim or shims. For simplicity, only one shim is shown in Figure 2. The flow into the compression valve travels through a hole in the rebound shim. This hole in the rebound shim eliminates the need to machine a flow path in the piston and is a simple way of allowing valve flow and decreasing complexity of piston manufacture. Increased velocity decreases the pressure in the rebound chamber and increases the flow rate. The pressure differential also triggers shim. The compression shim, located in the rebound chamber, limits the area for flow depending on the velocity of the piston. With increased velocity, shim deflection increases and valve flow area increases. Pv is defined as pressure inside the exit of the orifice in the piston. The third flow path is the leakage flow around the piston-cylinder wall seal. Leakage flow is at least an order of magnitude less then other two flows, but is difficult to eliminate completely. With prolonged usage the seal may degrade, increase the leakage flow, and lessen the damping force from the damper. The piston cylinder seal should be replaced periodically so that the leakage flow does not become significant in comparison to the other flow paths. Rebound operation is shown in Figure 3. During the rebound stroke, the piston rod is being withdrawn from the fluid filled cylinder, causing flow from the rebound to the compression chamber. The combined volume of oil plus the rod in the compression and rebound chambers is now decreasing due to the removal of the rod, and the gas in the gas chamber expands. The flow in rebound is from the rebound chamber to the compression chamber. All the valve, bleed, and leakage flow paths discussed previously still exist, only their directions have reversed. The bleed orifice flow now begins at the side inlet hole in the piston rod, and exits out the end of the piston rod into the compression chamber. All the properties of low speed damping dominated by the bleed are retained in the transition from compression to rebound. The valve orifice flow path is conceptually the same as for compression, only the specific orifice is different. During rebound the pressure relationships arePrPvPc . The valve flow now travels through the appropriate hole in the compression shim and initiates the deflection of the rebound shim in the compression chamber. As before, an increase in rebound velocity will result in increased shim deflection and valve flow area. The leakage flow is of the same magnitude and travels through the same axisymmetric gap between the piston seal and the outer cylinder. Only the direction in rebound is opposite of that in compression. After examination of the rebound and compression stroke, it can be seen that physical operation of the damper is complex. Dampers are displacement, velocity and acceleration dependant. The equations relating pressures, shims deflections, flows, etc. will be the basis for modeling the behavior of a damper. CHARACTERIZATION OF DAMPER OPERATION Since the position and velocity of a damper in any automotive or racing application is in constant state of change, it is hard to define and interpret damper performance. To evaluate the performance of a damper, testing on a damper dynamometer has become the norm. The damper dynamometer used in this research is a Roehrig 2VS. This damper dynamometer imposes a sinusoidal input for displacement. The displacement is defined by specifying the amplitude and the frequency. The first and second derivatives of the displacement are the velocity and acceleration, respectively. The primary means used to characterize damper performance is the Force vs. Velocity (FV) plot. Figures 4 through 6 show the basic FV plot and the corresponding motion profiles. Figure 4 shows a Force vs. Velocity plot for a full cycle, compression and rebound strokes. This is sometimes referred to as a Continuous Velocity Plot (CVP). It is important to note the sign conventions for force and velocity. Compression results in negative velocities, while rebound, increasing length, results in positive velocities. In some instances 1, the velocity definitions may be opposite. The convention shown here is used by the Roehrig