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譯文題目:Fe-thermal analysis of a ceramic clutch
有限元熱分析的陶瓷離合器
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Fe-thermal analysis of a ceramic clutch
1. Introduction
Abrasive dry running vehicle clutches are force closure couplings. Torque and speed transmission are ensured by the frictional force generated between two pressed surfaces. Reasons for the application of ceramic as a friction medium include good heat and wear resistance properties, which provide the opportunity to drive higher pressures, and a low density. Thus, an increasing power density is enabled with a parallel minimization of construction space.
Measurements with a first prototype of a clutch disk using ceramic facings were performed at Karlsruhe University in a laboratory specialized in passenger car drive system testing. In the course of analysis the finite element (FE) model was to be constructed with the knowledge of measurement data and measurement conditions. Calculations were intended to determine the temperature distribution of the clutch disk and its environment at each moment in time corresponding to measurements. It is essential to be familiar with the temperature range in order to examine the wear characteristics of the system. Thus, important information is derived from measurement data. In critical load cases, the highest expected temperatures must be forecast in space and time in order to protect measuring instruments close to the location of heat generation.
The goal of this study is to analyze and modify the clutch system to provide better operating conditions by improving the heat conduction and convection of the system or to increase the amount of the energy converted into frictional heat. Furthermore, it is desired to find better design solutions for more efficient clutch systems.
Calculations were performed by the Cosmos Design Star software. During model development, great care had to be taken for proper simplification of geometry, the selection of element sizes, and the correct adjustment of time steps due to the substantial hardware requirements for transient calculations. Changes in thermal parameters such as the surface heat convection coefficient and thermal load had to be taken into consideration on an on-going basis in terms of time and location. The two sides of the analyzed test clutch system can only be managed by two independent models linked by heat partition, according to the hypothesis that the contact temperature must be identical on both sides while there is proper contact between them and its value must be adjusted by iteration. Calculations revealed that the heat partition changed by cycle and it differed along the inner and outer contact rings. As a result of the different cooling characteristics between the ceramic and steel side, a heat ?ow is launched from the ceramic side to the steel side. This heat flow was also determined by iteration, its value also changes by cycle and differs along the inner and outer contact rings.
2. First prototype of a clutch using engineering ceramics as friction material
The examined clutch disk was developed according to the “specific ceramic” product development process established at the Institute for Product Development (IPEK) at the University of Karlsruhe. This development process already has the possibility for connection to a real transmission shaft; further, it has a cushion spring device for the facings allowing good start behavior. Abrasive clutches must comply with the following basic requirements:
l high torque transmission according to high friction coefficients,
l high comfort (no vibrations through self-induced chattering),
l homogeneous temperature distribution,
l low wear characteristic.
A critical element of the switch is the abrasive disk.With regard to the design utmost care must be taken to select the right material. A high and constant friction coefficient wear resistance and thermal resistance are desired characteristics. The clutch disk has instead of the generally applied ring-shaped abrasive inlet two rows of SSIC (as sintered) ceramic pellets. These pellets are placed on 6 separate segments. The segments are ?xed to the central hub by rivets. Each segment consists of 4 plates, 2 working as facing springs and 2 as carriers.
3. Measurements
Measurements were performed at the department of power train development of the Institute for Product Development (IPEK) at the Karlsruhe University (TH) Research University, where a category IV component test rig is used for tests of new frictional materials and examinations of new materials in real clutch disks. Real conditions are applied by the simulation of driving resistance (e.g. starting in the plane, starting at the hill). It is a component test rig leveled on the fourth position of the tribological testing environment.
In order to give an idea of dimensions: the equipment length is about 4-5m. The two electric motors and the axial force are controlled independently by computer; thereby many operational states can be realized. This enables the equipment to complete a myriad of tribological measurements all while properly modeling the operation of a clutch disk in a passenger car. It is also equipped with an automatic IT measurement system. Measurable quantities include the following:
l two heavy-duty electric motors (150 KW, Baumuller DS 160L-305),
l device suitable for exerting axial force,
l torque meter (Manner Sensortelemetrie MF100),
l axial force meter,
l steel disk in friction,
l replaceable head to affix the device to be tested,
l temperature along two different radii at 0.4mm below the abrasive surface of the steel disk (Omega HJMTSS-IM100U-150-2000,J-typeiro-constantan thermocouples),
l revolutions per minute for both sides (Polytene LSV 065).
The greatest challenge out of these is temperature measurement as we would like to know the temperature of the revolving steel disk. The two thermoelements placed in the steel disk forward data to the computer through a wireless blue tooth system and are placed 0.4mm below the abrasive surface of the steel disk on the two opposite arcs of the clutch disk.
3.2. Measurement process
Due to component analyses and cost reduction only one side of the clutch disk is mounted with ceramic facings. Thus, the clutch disk and its fitting will be referred to as the ceramic side, and the abrasive steel disk with its environment revolving together will be referred to as the steel side. In the course of measurements, data were collected at a sampling frequency of 100 and 1000HZ. Measurements were conducted according to the time curves.
The measurement starts by increasing the revolutions per minute of the steel side (the driving side) to a specific value (1500 rpm here). Then the ceramic side (the driven side), held at zero rpm, is pushed towards the steel disk and the axial force is applied until a designated value is reached (nominally 4200N here). Upon reaching the designated axial force the ceramic side is released and the two sides start to synchronize. A few seconds after synchronization, the axial load is discontinued and after some time both the steel and the ceramic sides—revolving at the same speed—are slowed down. This is deemed to be one measurement cycle. Ten cycles are completed in the course of a single measurement. During application of the axial force the ceramic side is held at zero rpm until the desired force is reached to ensure synchronization occurs at nearly the same time of each cycle. This is unfavorable from the viewpoint of both measurements and calculations. Measurements are usually conducted by changing only 3 parameters: the speed, the axial load and the inertia. The following figures are applied in various combinations:
l speed n: 700, 1100 and 1500 (rpm),
l axial force F: 4200, 6400 and 8400 (N) and
l inertia I: 1, 1.25 and 1.5 (kgm2).
Experimental measurements are launched with approx.10-15 min intervals, during which the system cools down to about 30-40 1C. This makes calculations difficult, as the exact temperature distribution of the system is not known at the commencement of the measurement. However, it can be assumed that a period of 10-15min is sufficient for a nearly homogeneous temperature distribution to be produced. The parameters for the following simulation have been chosen for an intermediate case with a speed n =1500 rpm, an axial force F = 4200 N and an inertia I = 1 kg m2.
4. Calculations of heat generation
The mechanical energy consumed during the friction of two bodies is transformed into heat. The generated heat can be calculated by the following simple formula: Q =μ·ν·F [W] .
where m is the the frictional coefficient; v is the sliding velocity; F is the force perpendicularly compressing the surfaces. And the heat flux density per surface unit is q=μ·ν·p [Wm2].
where p is the the pressure calculated as a ratio of the force and the contacting surface. As the ceramic tablets are placed at two different radii along the clutch disk, the heat generated must be calculated separately for each radii. Sliding can be divided into two sections. In the first section, the ceramic side is kept in a stationary position by braking, meanwhile the axial load is increased; therefore compression changes in the course of time while the speed difference between the two sides is constant. In the second section (at synchronization) the speed difference is equalized while the force value is constant, so velocity changes in time. On the basis thereof, the heat generated is
.
The nominal contact area is the aggregate of the contacting surfaces of the 24 and 18 ceramic tablets on the given ring. The diameter of ceramic tablets is:
.
Calculations were performed for the load case to be characterized by the following parameters:
.
Based on experimental measurements a constant friction coefficient of 0.4 was established.
.
The velocity can be calculated with the knowledge of the radius and the speed.
.
Surface pressure can be calculated as a ratio of the axial force and the contacting surface. This produces the same figure for each ceramic pellet, assuming an even load distribution.
.
Thus, the maximum values of the generated heat are
.
In the first section of sliding, the generated heat is rising due to the increase of the load force; in the second section, it is decreasing due to the equalization of the speed difference. It is necessary to know the time of each sliding section in order to be able to specify the generated heat time curve. These can be determined from measurement data series. Synchronization time can be easily determined from the speed of the ceramic side. Speed increase is linear. Force increase is non-linear. For the sake of simplicity, force increase was substituted by a straight line in calculations so that the area below the straight line is nearly identical with the area measured below the curve. Thus, the time difference between the two terminal points of the straight line is the time of the first sliding section.
The above-mentioned method was applied for each cycle and their average was specified. Based on these results, the following values were determined for sliding times:
.
Now the time curve of heat generation can be produced. The same curve was used in each cycle as there were no significant differences between parameters in each cycle. The generated heat-calculated this way-will appear as thermal load in the thermal model. It must be distributed appropriately between the contacting surfaces by taking into consideration heat partition. Heat partition requires the contact temperatures to be identical at both surfaces. Correct adjustment requires repeated iterations.
有限元熱分析的陶瓷離合器
1 引言
磨料空轉(zhuǎn)車輛離合器是力封閉聯(lián)軸器。扭矩和高速傳輸被壓緊表面之間產(chǎn)生的摩擦力所保證。應(yīng)用陶瓷是因?yàn)樗鳛槟Σ两橘|(zhì)具有好耐熱和耐磨損性能，提供了機(jī)會(huì)以驅(qū)動(dòng)更高的壓力，以及一個(gè)低的密度。因此，一個(gè)提功率密度啟用了一個(gè)平行的最小化建筑空間。
測(cè)量使用陶瓷飾面離合器盤的第一個(gè)原型在卡爾斯魯厄大學(xué)的一個(gè)實(shí)驗(yàn)室專門從事客車驅(qū)動(dòng)系統(tǒng)進(jìn)行了測(cè)試執(zhí)行。在分析過程中的有限元（FE）模型是將與測(cè)量數(shù)據(jù)和測(cè)量條件的知識(shí)所構(gòu)成。計(jì)算的目的是要確定在離合器盤上溫度的分布以及環(huán)境中的在每一時(shí)刻的及時(shí)測(cè)量目。至關(guān)重要的是熟悉的溫度范圍，為了檢驗(yàn)該系統(tǒng)的耐磨特性。因此，重要信息從測(cè)量數(shù)據(jù)中得出。在臨界負(fù)載的情況下，預(yù)計(jì)最高溫度必須在時(shí)間和空間上進(jìn)行預(yù)測(cè)，為保護(hù)接近發(fā)熱體的位置測(cè)量工具的。
本研究的目的是分析和修改該離合器系統(tǒng)通過改進(jìn)，以提供更好的工作條件熱傳導(dǎo)和系統(tǒng)或增加轉(zhuǎn)化成摩擦熱的能量的對(duì)流。此外，人們希望找到更有效的更好的離合器系統(tǒng)設(shè)計(jì)方案。
計(jì)算是由宇宙星空的設(shè)計(jì)的軟件進(jìn)行的。在模型開發(fā)階段，非常謹(jǐn)慎，必須采取幾何元素，選擇適當(dāng)?shù)暮?jiǎn)化尺寸，并且由于正確調(diào)整的時(shí)間步長(zhǎng)大量的硬件要求瞬態(tài)計(jì)算。熱物性參數(shù)的改變，如表面熱對(duì)流化系數(shù)和熱負(fù)荷，必須考慮到到在一個(gè)持續(xù)的基礎(chǔ)上在時(shí)間和地點(diǎn)方面。離合器系統(tǒng)的分析測(cè)試這兩方面，只能通過加熱隔板連接的兩個(gè)獨(dú)立的模型來(lái)管理，根據(jù)該假說認(rèn)為，接觸溫度必須是在兩個(gè)相同的雙方，同時(shí)他們要有適當(dāng)接觸，其價(jià)值需通過迭代來(lái)進(jìn)行調(diào)整。計(jì)算顯示，該熱分區(qū)按周期變化，它沿不同的內(nèi)，外接觸環(huán)。在不同的冷卻特性下，在陶瓷和鋼之間的結(jié)果是不同的 ，熱流從陶瓷側(cè)面向鋼側(cè)流動(dòng)。此熱流也通過迭代確定;它的價(jià)值也改變了周期和不同沿著所述內(nèi)和外接觸環(huán)。
2 采用工程陶瓷作為摩擦材料的第一個(gè)原型機(jī)
這款檢查過的離合器盤是根據(jù)“ 特定的陶瓷”產(chǎn)品而開發(fā)的，此材料的研發(fā)過程在流程在卡爾斯魯厄大學(xué)的Institute for Product Development (IPEK)雜志上發(fā)表過。此開發(fā)過程已經(jīng)具有的可能性，用于連接到一個(gè)真實(shí)的傳動(dòng)軸；甚至，它為面板有一個(gè)好的初始行為起到一個(gè)很好的緩沖作用。磨料配件必須符合以下基本要求：
1. 根據(jù)高摩擦系數(shù)高扭矩傳遞
2. 高舒適度（通過自感應(yīng)抖動(dòng)無(wú)共振）
3. 均勻的溫度分布
4. 低磨損特性
開關(guān)的一個(gè)關(guān)鍵因素是摩擦面.在設(shè)計(jì)極限方面，必須謹(jǐn)慎采取選擇合適的材料。高而恒定的摩擦系數(shù)，耐磨損和耐熱性是理想的特性。離合器圓盤能代替通常 應(yīng)用環(huán)形磨料入口兩排SSIC的（燒結(jié)）陶瓷顆粒。這些小球被放置在6個(gè)單獨(dú)的段位。該段由鉚釘固定到中心輪轂。每個(gè)段由4片組成，2個(gè)工作面對(duì)著彈簧和2個(gè)作為載體。
3 測(cè)量
3.1 測(cè)量設(shè)備
測(cè)量是在卡爾斯魯厄大學(xué)（TH）研究型大學(xué)的動(dòng)力傳動(dòng)系完成的，同時(shí)也是用于測(cè)試新的摩擦材料和新材料在實(shí)際離合器片中檢測(cè)的地方。真實(shí)情況是通過驅(qū)動(dòng)電阻的仿真應(yīng)用（例如，開始在平面上，開始于山）的試驗(yàn)裝置。這是一個(gè)組件試驗(yàn)臺(tái)夷為平地在摩擦測(cè)試環(huán)境的第四位。為了給維度的概念：設(shè)備長(zhǎng)度大約4-5m 。兩臺(tái)電動(dòng)機(jī)和軸向力是由計(jì)算機(jī)獨(dú)立控制;因此許多運(yùn)營(yíng)可實(shí)現(xiàn)的狀態(tài)。這使得設(shè)備來(lái)完成一個(gè)摩擦學(xué)測(cè)量無(wú)數(shù)，而所有正確建模在乘用車上的離合器盤的操作。它還配備用自動(dòng)的IT測(cè)量系統(tǒng)。可測(cè)量的量包括以下內(nèi)容：
1. 2個(gè)重型電機(jī)（150千瓦，Baume米勒DS160L-305）
2. 設(shè)備適用于施加軸向力
3. 扭力計(jì)（Sensortelemetrie MF100）
4. 軸力計(jì)
5. 鋼盤的摩擦
6. 可更換的頭部貼上設(shè)備進(jìn)行測(cè)試
7. 溫度沿兩個(gè)不同的半徑處為0.4mm以下的鋼盤（歐米茄HJMTSS-IM100U-磨料表面 150-2000，J鐵康銅熱電偶）
8. 每分鐘轉(zhuǎn)數(shù)為雙方（Polytec LSV065）。
這里最大的挑戰(zhàn)是這些我們想知道的旋轉(zhuǎn)鋼盤面上溫度的測(cè)量。兩個(gè)熱元件放置在鋼盤通過無(wú)線藍(lán)牙數(shù)據(jù)轉(zhuǎn)發(fā)給計(jì)算機(jī)系統(tǒng)和被放置為0.4mm以下的研磨面鋼盤上的兩個(gè)相對(duì)的圓弧的離合器盤。
3.2 測(cè)量過程
為了測(cè)量由組分分析和降低成本的一側(cè)離合器盤安裝用陶瓷襯片，由此，離合器磁盤及其配件將被稱為陶瓷側(cè)，而磨具鋼盤與它的環(huán)境一起旋轉(zhuǎn)會(huì)簡(jiǎn)稱為鋼側(cè)。在測(cè)量時(shí)，數(shù)據(jù)的過程中收集在100和1000Hz的采樣頻率。
在測(cè)量開始通過增加每轉(zhuǎn)鋼側(cè)（驅(qū)動(dòng)側(cè)）的分鐘為一個(gè)特定值（這里是1500轉(zhuǎn)）。然后在陶瓷側(cè)（驅(qū)動(dòng)側(cè)），在保持零轉(zhuǎn)速下被推向鋼盤和軸向力應(yīng)用，直到一個(gè)指定的值為止（名義上4200N在這里）。當(dāng)?shù)竭_(dá)所指定的軸向力的陶瓷側(cè)是釋放和雙方開始同步。幾秒鐘在同步之后，在軸向載荷終止和后一段時(shí)間都在鋼和陶瓷兩側(cè)繞轉(zhuǎn)在相同的速度會(huì)慢下來(lái)。這被視為一個(gè)測(cè)量周期。十個(gè)周期中的一個(gè)過程中完成單次測(cè)量。在應(yīng)用程序中的軸向力陶瓷側(cè)被保持在零轉(zhuǎn)速，直至所需的力達(dá)到以確保發(fā)生同步于幾乎每種相同的時(shí)間周期。這是不利的從兩者的觀點(diǎn)出發(fā)，測(cè)量目和計(jì)算。測(cè)量通常通過進(jìn)行僅改變3個(gè)參數(shù)：速度，軸向載荷和慣性。下面的數(shù)字是應(yīng)用于各種組合：
1.轉(zhuǎn)速n：700 ，1100和1500（RPM）
2.軸向力F： 4200 ，6400和8400（N）
3.慣量I：1 ，1.25和1.5（ kgm2為單位）
實(shí)驗(yàn)測(cè)量與約推出,10-15分鐘的時(shí)間間隔，在此期間，系統(tǒng)冷卻到約30-40攝氏度。這使得計(jì)算變得很困難，因?yàn)榇_切的該系統(tǒng)的溫度分布是不知道的開始測(cè)量。然而，可以假定經(jīng)過一段時(shí)間的10-15分鐘就足夠了一個(gè)幾乎均一要產(chǎn)生的溫度分布。下面的模擬已經(jīng)選擇了一個(gè)中間的情況下用轉(zhuǎn)速n=1500轉(zhuǎn)，一軸向力F=4200N和一個(gè)慣量I=1kgm2。
4 計(jì)算兩個(gè)摩擦過程中所消耗的機(jī)械能體被轉(zhuǎn)化成熱量
所產(chǎn)生的熱量可計(jì)算由下列簡(jiǎn)單的公式：Q =μ·ν·F [W]，其中μ為摩擦系數(shù)， v是滑動(dòng)速度， F是垂直壓縮表面上的力。和每單位表面的熱通量密度q=μ·ν·p [Wm2]，其中p是計(jì)算的力的比率的壓力和的接觸表面。作為陶瓷片被放置在兩個(gè)不同的半徑沿離合器盤，所產(chǎn)生的熱量必須分別計(jì)算每個(gè)半徑?；瑒?dòng)可分為兩部分。在第一部，所述陶瓷側(cè)被保持在一個(gè)固定的位置由制動(dòng)，同時(shí)在軸向負(fù)荷增大，因此在時(shí)間的過程中壓縮的變化，而速度雙方的差異是恒定的。在第二部分（在同步）的轉(zhuǎn)速差進(jìn)行均衡,而力值是恒定的，所以在時(shí)間的速度變化?；A(chǔ)物所產(chǎn)生的熱量是：
名義接觸面積是24的接觸表面的聚合和18陶瓷平板電腦在給定的半徑。陶瓷小塊的直徑是:
計(jì)算進(jìn)行了負(fù)荷情況的特點(diǎn)是以下參數(shù):
基于實(shí)驗(yàn)測(cè)量的恒定摩擦0.4系數(shù)成立。
速率可以通過速度和半徑的知識(shí)來(lái)計(jì)算：
表面壓力可以計(jì)算為軸向力的比率和接觸表面。這產(chǎn)生相同的數(shù)字的每個(gè)陶瓷顆粒，假設(shè)即使負(fù)載分布。
則有：
這樣的話，最大的集中熱值就是：
在滑動(dòng)的第一部分，所產(chǎn)生的熱上升，由于負(fù)載力的增加;在第二部分中，它是減小由于速度差的均衡。這是要知道各滑動(dòng)部分的時(shí)間，以可以指定所產(chǎn)生的熱量時(shí)間曲線。這些可以是從測(cè)量數(shù)據(jù)序列來(lái)確定。同步時(shí)間可以很容易地從陶瓷側(cè)的速度來(lái)決定。速度的提升是線性的。力的增加是非線性的。為了簡(jiǎn)單起見，力增加在被取代的由直線計(jì)算使下面的直線的面積近相同的曲線下測(cè)量的面積。因此，時(shí)間直線的兩個(gè)端點(diǎn)之間的差異是第一滑動(dòng)部的時(shí)間。
將上述方法應(yīng)用于每個(gè)周期和他們的平均被指定?；谶@些結(jié)果，下面的值被確定為滑動(dòng)時(shí)間：
應(yīng)力時(shí)間 s
同步時(shí)間 s
現(xiàn)在發(fā)熱的時(shí)間曲線可以產(chǎn)生。該相同的曲線被用在每一個(gè)周期，因?yàn)橛性诿恳粋€(gè)循環(huán)參數(shù)之間沒有顯著差異。所產(chǎn)生的熱量，計(jì)算出這種方式，會(huì)出現(xiàn)在熱模型的熱負(fù)荷。它必須分布的接觸表面通過考慮適當(dāng)?shù)刂g考慮熱分區(qū)。熱分區(qū)需要接觸的溫度是相同的兩個(gè)表面上。正確的調(diào)整需要反復(fù)迭代。