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附 錄
Research on Self-Adaptive Shift Schedule in Automated Mechanical Transmission of Heavy-Duty Commercial Vehicle
In our country, commercial vehicles include heavy-duty commercial vehicles, middle-duty commercial vehicles, light-duty commercial vehicles and mini commercial vehicles. Heavy-duty commercial vehicles market in china has been growing up rapidly in these years. With the increase of the fuel price, heavier emissions regulations, continued pressure on operating costs, increasing traffic congestion, and a shortage of skilled drivers, these changes will take place in the engine , the exhaust gas treatment system, and the transmission on vehicles, especially middle-duty and heavy-duty commercial vehicles.At the aspect of the transmission, we look at automated Mechanical transmission (AMT) attentively, which is low produce cost, high efficient, can shift and operate clutches automatically. Till now, the vehicle factories in our country have no ability to manufacture the automatic gearbox. In recent years, many manufacturers have been trying to seek automatic products, which suit our country situation and can be developed independently. In respect that we have many Mechanical transmission plants, for its high efficiency, low cost, and easier manufacture, AMT is considered to be the right product, which is the most suitable for us and has greatest potential in the development of industry.A new technology for AMT is non-clutch operation, and this technology bases on customary AMT. In the process of gear-shifting torque,the clutch does not separate from the engine and we need to adjust the running speed and the torque of the engine only. Eaton Company already uses this new technology in one transmission. If we put the new technology in commercial vehicles, there will be great meaning in automatic transmission of the commercial vehicles.Shift schedule decides the time to shift and it is the soul of the automatic transmission. When the AMT is working, by comparing the states of the vehicle with the optimal shift schedule, the AMT decides the optimal shift time and achieves the shift automatically. This will lessen the tiredness of the driver and improve the safety. Consequently, how to establish the best shift schedule is a crucial research aspect of AMT.The shift schedule of the automatic transmission comes from 1-parameter、2-parameter to 3-parameter operation. In recent years, more and more researchers pay attention to intelligent control theory, and they want put this theory in shift schedule to make the shift.Combined with the national 863 project, Research and Development of AMT, this paper aims at the shift schedule of the AMT in heavy-duty commercial vehicles. According as the characteristic of the engine and the parameter of the vehicle, this paper established the traditional shift schedule and the self-adaptive shift schedule and according to this regulation simulates actual situation of the vehicle. When the AMT is working, by comparing the states of the vehicle with the optimal shift schedule, the AMT decides the optimal shift time and achieves the shift automatically. This will lessen the tiredness of the driver and improve the safety. The outcome shows these regulations are feasible. This paper has researched on these aspects as follows:1.At first the development history and the present conditions of automatic transmission are introduced in detail. At the same time, this paper analyses the makeup, the principium and the technique of AMT. At last the excellence and principium of the technique (non-clutch operated AMT) are discussed.2.Research on shift schedule of automatic transmissionThis paper analyses the characteristics of some kinds of shift schedules. Shift schedule is realized by electronic shift system.3.The establishment of the shift scheduleShift schedule is the basic part of automatic transmission. In this paper, dynamic capability and fuel consumption are considered. According as torque and fuel consumption characteristics of the engine, 2-parameter traditional shift schedule for the commercial vehicle is obtained. This regulation can be used in electronic control unit (TCU) directly and there are certain significance and actual value.Then this paper designs the self-adaptive shift schedule.4.Modeling of gear-shift regulation and vehicleFor qualitatively researching on the effectiveness of the shift schedule control system designed, and proceeding the simplification to the very complicated vehicle system, and putting forward the some assumption conditions of the simplification. At the same time keeps its general dynamic characteristics. And according to the construction parameter and technique data of one commercial vehicle, making use of the language of MATLAB with the tool of SIMULINK, for engine, transmission, shift schedule, whole vehicle dynamic model to proceed to set up models in SIMULINK.5.The simulation of shift schedule and the analysisFor the sake of verifying the rationality and possibilities of the shift schedule, this paper makes use of the models above. On the whole vehicle model this paper set up the simulation to test the regulation in some simulative situation. By the simulation analysis, the simulation result indicates that the simulation model and the shift schedule designed in the article are reasonable.In conclusion, this paper studied the shift schedule of the automated mechanical transmission systematically on the basis of former research. In the paper, only the above work is completed because of limited time and the difficulty of AMT system. Further research should be continued in order to improve the properties of the AMT system and vehicle in the future.
Shifting performance is defined as the extent of swiftness and softness during the procedure of non-power shifting and to extend the life of the power train. The index is comfort of passenger, time duration and shock, nine factors maybe influence the shifting performance, and two experimental methods can be used to investigate the nature of this performance: one is collecting real-time data during road experiment and analyzing them, the other is the simulation of the operation conditions of the vehicle.
The core of the AMT system is the control strategy, the principle of the clutch engagement, shifting procedure, the choice of control method and the CAN communication between TCU and ECU can influence the shifting performance.
Shifting schedule is the schedule of auto shifting time between two shifts with controlling parameters. It includes economical and dynamical shifting schedule. At present, shifting schedule of two controlling parameters (vehicle speed and opening on throttle) is mainly used. If shifting schedule is not good, shifting will not happen at right time and the working condition of engine will be severe. It will make the sound of engine abnormally and stability badly through the whole shifting procession. Sometimes even flame out Schedule of clutch engagement is determined by releasing journey of clutch, opening of throttle, shifting, vehicle speed and loading. The main
Controlling goals are engaging quantity and engaging speed. The engaging control of clutch is mainly referred to the control of engaging speed. It is divided into three stages: fast, slow, fast. Shifting quality is directly influenced by the second stage. If engaging harder, it will make shifting concussion, even flame out; if engaging more slowly, it will make the friction time longer and reduce its longevity. The main controlling parameters are difference between initiative and passive and torques on both sides. When torques being approximately equal, it is proved by experiments that it can guarantee shifting time and not make concussion through the procession of engagement at the time of difference of rotating speed below some value. Meanwhile, the abrasion of clutch is not severe.
Shifting procedure is the procedure through working harmoniously among engine, clutch and transmission. Their cooperation will affect shifting time heavily. In order to decrease the shifting time, the time that is spent on the friction of the clutch should be decreased first. If we intend to increase the time of non-load stage, which helps to minimize the difference of the rotary speed between the driving disc and the driven disc. If we intend to shorten the time of the non-load stage, engage the clutch immediately after the gear change. The clutch can engage in a satisfying period if the new method of controlling the engaging speed of the clutch is realizable. And the time that is spent on synchronizing the gears should also be shortened. It can be realized in the following two ways. The first is to decrease the difference of the driving gear and the driven gear. The second is to increase the shifting force. If realizing the union control between ECU and TCU by CAN bus, AMT has the best control and the best shifting performance by use of communication strategy between TCU and ECU.
Influence on shifting performance by hardware
The elements in hardware system are the basis of proper functions of AMT. Executors, sensors, electronic components, hydraulic systems have influences on shifting performance, the choice of hardware parameters is of vital important to improvement of shifting performance.
With the development of the theory and technology of vehicle, the technical increasingly mature of microprocessor and the extensive application of electronic technique on the car, people have no limit at satisfying the automotive means of transportation only, facing gradually from the request of the car power, economy and easily manipulating, flexibility, safety, an d the intelligent type of car becomes the focus in the vision of people increasingly. Company’s publicity slogan of" person, car, life"," make people the center" etc. On the side exhibit the expectation of people to the automotive individuation, humanity.
In the development direction of the car intelligence, the intelligence of the automatic gearbox has important effect. But the intelligence of the automatic gearbox embodies at the establishment of the shift regulation. For the fashion, for satisfying people to the new automotive request, for competitive advantage of the car type, at present, each big factory in world worked very much in shift regulation of new car type. Among those, the most arresting is AL4 automatic gearbox developed by PEUGEOT/CITROEN and RENAULT in that there unexpectedly are the 10 kinds of so many shift regulations. In the big system of person— car — road, the good and bad of the car control, reflect primarily in the coordination of the vehicle and environment (road), the coordination of the vehicle and person. And so, the electronic automatic control system can save various regulations to provide the driver to choose to use, not only having the economic regulation, motive (call to sport the type again) regulation, but also still having the general (usual) regulation, environment temperature and regulation with the outsider condition variety etc. Namely, the point of shifting can be freely enacted for every kind of regulation. In the intelligence direction of the shift regulation, everyone has made much work up to now, parts of the results has been applied on the car. But the work that developing this intelligent shift regulation still is hard, this is mainly because of:
1. The intelligence degree of the current intelligent gearbox needs to be increased, and it expresses at that accurate degree to identify environment is not high and to identify the driver’s driving can't give satisfaction.
2. The intelligence function is still not perfect. The intelligent automatically shift system is an open system; it must be continuously perfect and plentiful on the current foundation. Only this way, it can adapt to the driving request of the different drivers, reducing the driver’s labor strength, increasing the performance of the whole vehicle.
Conventional design method which used in the structure parameters' design of automobile gear box and synchronizer is a time-wasting job and hard work, and it is difficult to get idea design parameters and no good to the enhancement of products qualities. The optimum design of automobile gearbox and synchronizer which take the advantage of computers seeking the best structure parameters within constrains is a perfect and high-quality design method. The main target of this article is to set up a optimum mathematical model of structure parameters of the truck's gearbox and synchronizer, the auth or use a optimum method based on K-T equation to improve the design level of automobile gearbox and synchronizer. Gear box is a important part of transmission, so the optimization of automobile gearbox is very important because the transmission is a main part of automobile. According to the design request and character sofa sort of truck, the optimum mathematical model of truck's gearbox is analyzed and set up in this article to decrease its weight and volume when the strength, stiffness, and lifetime of parts are permitted. And we can receive a satisfaction result through optimizing it's parameter for instance.
重型商用車電控機(jī)械式自動變速器換擋規(guī)律的研究
機(jī)械式自動變速器AMT(Automated Mechanical Transmission),是在原有齒輪式機(jī)械變速器的基礎(chǔ)上加裝電腦控制系統(tǒng),對供油調(diào)節(jié)裝置、離合器、變速箱的控制采用了電機(jī)驅(qū)動或液壓驅(qū)動的執(zhí)行機(jī)構(gòu),實現(xiàn)起步、選擋、換擋的自動化控制,使汽車成為自動變速的汽車。本文結(jié)合“十一五”國家863計劃現(xiàn)代交通技術(shù)領(lǐng)域“汽車開發(fā)先進(jìn)技術(shù)”重點項目課題“重型商用車的機(jī)械自動變速器(AMT)開發(fā)”項目,針對重型商用車AMT的換擋規(guī)律進(jìn)行相關(guān)研究。通過重型商用車AMT的結(jié)構(gòu)與工作特點的分析,結(jié)合發(fā)動機(jī)特性與重型商用車的使用要求,對換擋規(guī)律進(jìn)行深入分析與研究,設(shè)計了兩參數(shù)組合型換擋規(guī)律;在此基礎(chǔ)上,為最大限度地降低油耗,使發(fā)動機(jī)工作在最經(jīng)濟(jì)工作區(qū),提出了基于功率與車速的兩參數(shù)控制的自適應(yīng)換擋規(guī)律;MATLAB/SIMULINK工具建立起重型商用車的整車動力學(xué)模型,對重型商用車的兩參數(shù)組合型換擋規(guī)律與自適應(yīng)換擋規(guī)律分別進(jìn)行了仿真分析與研究,驗證了所提出方案的有效性和可行性。本文的研究成果對于開發(fā)重型商用車AMT系統(tǒng)具有重要價值和現(xiàn)意義。
車輛自動變速器通常分為液力機(jī)械式自動變速器（簡稱AT）、電控機(jī)械式自動變速器（簡稱AMT）和機(jī)械式無級變速器（簡稱CVT）。AMT以其傳動效率高、成本低和易于制造等優(yōu)點成為一種具有極具發(fā)展?jié)摿Φ淖詣幼兯倨?。AMT 換檔品質(zhì)的研究則是AMT技術(shù)體系研究中關(guān)鍵的一環(huán)，換檔品質(zhì)的好壞真接影響到AMT產(chǎn)業(yè)化進(jìn)程及在市場上的競爭能力。
AMT有很好的市場前景，但由于AMT 的換檔過程必需切斷動力，所以其換檔品質(zhì)較AT和CVT要差一些。只有提高AMT的換檔品質(zhì)，使之接近或超過AT、CVT的換檔品質(zhì)，方能在市場上形成競爭力。所以對AMT換檔品質(zhì)的研究就成為AMT 技術(shù)體系研究中關(guān)鍵的一環(huán)。
AMT發(fā)展分為三個階段：半自動的SAMT階段、全自動階段和智能階段。AMT 結(jié)構(gòu)分為硬件和軟件兩部分，硬件系統(tǒng)包括被控對象、執(zhí)行機(jī)構(gòu)、傳感器、TCU等；軟件系統(tǒng)由實現(xiàn)控制策略的軟件組成。
自動變速器(AT)的換檔性能的優(yōu)劣對整車性能有很大的影響。自動變速器換檔品質(zhì)問題研究是自動變速箱研究領(lǐng)域中的一個重要研究課題。換檔品質(zhì)的控制通過電液系統(tǒng)來完成?？刂破鞲鶕?jù)實時的油門開度、車速等信號，發(fā)出操縱指令控制換檔結(jié)合元件的油壓變化規(guī)律，實現(xiàn)平穩(wěn)換檔。本文對自動變速器的換檔品質(zhì)控制系統(tǒng)、換檔過程結(jié)合元件油壓變化規(guī)律進(jìn)行了較深入的分析和研究。
文中首先對換檔品質(zhì)的現(xiàn)有評價方法和指標(biāo)進(jìn)行了分析和總結(jié)，并對現(xiàn)有AT換檔品質(zhì)的控制方式進(jìn)行了較為全面的介紹和分析。
提出了一種自動變速器換檔過程分析的等效力學(xué)模型和發(fā)動機(jī)一變矩器動力學(xué)簡化模型，以適應(yīng)車輛起步、換檔實時控制研究的需要。應(yīng)用所建立的數(shù)學(xué)模型，對自動變速器的換檔過程進(jìn)行了詳細(xì)的分析。
制定了適當(dāng)?shù)膿Q檔過渡過程結(jié)合元件的油壓變化規(guī)律，可改變自動變速器的換檔品質(zhì)。對AG4自動變速箱的油壓控制給出了具體的計算方法。可改善自動變速器的換檔品以AG4自動變速箱2H檔到3H檔為例進(jìn)行了模擬仿真，仿真的結(jié)果對所建立的簡化模型和提出的期望油壓規(guī)律進(jìn)行了驗證。
詳細(xì)分析了AG4液壓操縱系統(tǒng)的供油調(diào)壓和換檔品質(zhì)控制工作原理。并對換檔品質(zhì)控制的框圖設(shè)計做了初步的探討。利用自動變速器電液控制試驗臺對AG4自動變速箱的控制系統(tǒng)和液壓系統(tǒng)進(jìn)行了測試。通過試驗驗證了本文所建立的數(shù)學(xué)模型及其分析結(jié)論。
電控機(jī)械式自動變速器(Automated Mechanical Transmission, AMT)是一種新型的自動變速系統(tǒng)，其通過對手動固定軸式變速器和干式摩擦離合器的自動化改造從而實現(xiàn)了選檔、換檔以及離合器和油門的自動操縱。AMT技術(shù)適合我國國情，有著廣泛的市場和發(fā)展前途。換檔規(guī)律是電控機(jī)械式自動變速器的靈魂，它是判斷換檔時機(jī)的依據(jù)。在應(yīng)用中，通過將采集的車輛行駛狀態(tài)與換檔規(guī)律相對比，從而判斷是否達(dá)到最佳的換檔點并自動執(zhí)行換檔操作，這樣大大減輕了駕駛員的疲勞，提高行駛安全，同時使整車具有較好的動力性及燃油經(jīng)濟(jì)性。本論文選擇電控機(jī)械式自動變速器換檔規(guī)律這一關(guān)鍵性問題作為研究對象，研究目的是為AMT制定最佳的換檔規(guī)律以提高車輛的動力性和燃油經(jīng)濟(jì)性。通過對影響車輛動力性和燃油經(jīng)濟(jì)性的因素進(jìn)行分析，本論文推導(dǎo)了最佳動力性和最佳燃油經(jīng)濟(jì)性換檔規(guī)律的制定方法。為解決質(zhì)量影響問題，提出了一種變結(jié)構(gòu)的最佳換檔系統(tǒng)，豐富了換檔規(guī)律理論。鑒于計算機(jī)仿真技術(shù)與實車測試相比可以節(jié)省大量的人力物力，本論文在進(jìn)行換檔規(guī)律的設(shè)計中，采用MATLAB/Simulate仿真工具箱建立了最佳換檔規(guī)律的仿真模型，利用此仿真模型對制定的最佳動力性和最佳燃油經(jīng)濟(jì)性換檔規(guī)律進(jìn)行仿真，仿真結(jié)果表明本論文所建立的換檔規(guī)律是合理的。
換檔品質(zhì)是指在保證動力傳動系統(tǒng)壽命的前提下，能夠迅速、平穩(wěn)換檔的程度，其評價的指標(biāo)主要是舒適性，量化指標(biāo)包括換檔時間和沖擊度。換檔品質(zhì)的影響因素包括軟、硬件兩方面九大因素，并且可用兩種實驗方法對換檔品質(zhì)進(jìn)行研究，一種是整車道路實驗實時采集數(shù)據(jù)進(jìn)行分析；第二種方法就是通過做模擬整車工況的臺架實驗。
AMT的控制策略是AMT控制的全部控制思想，控制策略里換檔規(guī)律、離合器結(jié)合規(guī)律、換檔時序、控制方法的選擇、以及近來比較熱門的通過CAN總線實現(xiàn)的TCU和ECU通訊策略都對檔品質(zhì)有影響，控制策略制訂得是否合理，將直接決定AMT 的換檔品質(zhì)。
換檔規(guī)律是指兩排檔間自動換檔時刻隨控制參數(shù)變化的規(guī)律，包括經(jīng)濟(jì)性和動力性換檔規(guī)律。目前汽車上多用兩控制參數(shù)（車速和油門開度）的換檔規(guī)律。換檔規(guī)律沒做好，就會使汽車在不該換檔的時候換檔，該換檔的時候不換檔，使發(fā)動機(jī)工況嚴(yán)重不好，造成整個換檔過程中發(fā)動機(jī)聲音的異常和平順性的不良，有時還可能使發(fā)動機(jī)熄火。離合器結(jié)合規(guī)律受離合器釋放行程、油門開度、發(fā)動機(jī)轉(zhuǎn)速、檔位和車速、載荷等素影響，主要控制目標(biāo)是結(jié)合量和結(jié)合速度。而離合器接合控制主要指接合速度的控制，大體上分快、慢、快三個階段。其中直接影響換檔品質(zhì)的是第二階段，如果接合過快將造成換檔沖擊，甚至熄火；若過慢將使離合器滑磨時間過長，有損其壽命?？刂频膮?shù)主要是離合器主從動片轉(zhuǎn)速差及兩邊扭矩值,實驗表明在扭矩值大致相同，轉(zhuǎn)速差小于一定值時接合離合器既能保證換檔時間又不會產(chǎn)生沖擊，離合器磨損也不太嚴(yán)重。
換檔時序是發(fā)動機(jī)、離合器、變速器三者協(xié)調(diào)動作的時序 ,它們的配合情況對換檔時間有很大的影響。減小換擋時間最重要的是盡可能地縮小離合器滑摩時間。如果延長空載階段時間，將減小離合器主從動盤轉(zhuǎn)速差。有利于縮短滑摩時間。如果盡可能縮短空載時間，掛上新?lián)鹾罅⒓唇雍想x合器，如果離合器接合速度控制的新方法可行，也可以在較短的時間內(nèi)完成離合器的接合。其次是減小齒輪同步時間，這可以通過兩種方式實現(xiàn)：1.減小齒輪間轉(zhuǎn)速差；2.增大換擋力。
運用TCU和ECU通訊策略，通過CAN總線實現(xiàn)發(fā)動機(jī)和變速器之間的聯(lián)合控制，AMT能夠達(dá)到最優(yōu)控制，獲得最理想的換檔品質(zhì)。
硬件系統(tǒng)元器件性能對換檔品質(zhì)的影響：
硬件系統(tǒng)元器件實現(xiàn)AMT功能的基礎(chǔ)，硬件系統(tǒng)里執(zhí)行機(jī)構(gòu)、傳感器、電子元器件、液壓系統(tǒng)等都對換檔品質(zhì)有影響，硬件參數(shù)的選擇對AMT換檔品質(zhì)的提高是至關(guān)重要的。
伴隨汽車?yán)碚摷夹g(shù)的發(fā)展，微處理器的技術(shù)的日益成熟和電子技術(shù)在汽車上的廣泛應(yīng)用，人們已經(jīng)不再只局限于滿足汽車的代步功能，對汽車動力性、經(jīng)濟(jì)性的要求逐步向易操縱性、機(jī)動性、安全性轉(zhuǎn)移，智能型汽車日益成為人們目光中的焦點。商家的“人、車、生活”,“以人為本”等宣傳口號也側(cè)面體現(xiàn)了人們對汽車的個性化、人性化的期望。
在汽車智能化的發(fā)展方向上，自動變速器的智能化占有重要一席。而自動變速器的智能化又集中體現(xiàn)在換擋規(guī)律的制定上。為順應(yīng)潮流，為滿足人們對汽車的新要求，加強(qiáng)各自車型的競爭優(yōu)勢，目前，世界各大廠商在新車型的換擋規(guī)律上大做文章，最引人注意的是標(biāo)致—雪鐵龍集團(tuán)和雷諾公司開發(fā)的AL4 自動變速器竟內(nèi)置了10 種換擋規(guī)律之多。在人—車—路的大系統(tǒng)中，汽車控制的優(yōu)劣，主要反映在車輛與環(huán)境（路）的協(xié)調(diào)、車輛與人的協(xié)調(diào)，故電子自動控制系統(tǒng)可存儲多種規(guī)律供駕駛員選用，不僅有經(jīng)濟(jì)性規(guī)律、動力性（又稱運動型）規(guī)律，而且還有一般（日常）規(guī)律、環(huán)境溫度以及隨外界條件變化的規(guī)律等。 即換擋點可以自由設(shè)定為各種規(guī)律。在換擋規(guī)律智能化的方向上，各方面至今已作了不少的工作，其中部分成果已開始在汽車上應(yīng)用。但是開發(fā)此項智能換擋規(guī)律的工作依然艱巨，這主要因為：
1.現(xiàn)有的智能變速器的智能程度有待提高，它表現(xiàn)在對環(huán)境的識別判斷的準(zhǔn)確度不高，對駕駛員的意圖識別不能令人滿意。
2.智能功能還不完善。智能自動變速系統(tǒng)是開放的系統(tǒng)，它應(yīng)在現(xiàn)有的基礎(chǔ)上不斷完善、豐富，只有這樣才能適應(yīng)不同駕駛員的駕駛要求，減少駕駛員的
勞動強(qiáng)度，提高汽車的整體性能。適應(yīng)駕駛員個性的換擋規(guī)律是研究項目中的重要一項，為了使汽車能夠在選換擋時體現(xiàn)不同駕駛員的風(fēng)格特點，適應(yīng)不同駕駛員的對加速的不同要求，前人工作的基礎(chǔ)上對適應(yīng)駕駛員風(fēng)格的換擋規(guī)律作了較為深入的研究，對駕駛員的駕駛意圖、風(fēng)格特點提出了新的識別策略，并系統(tǒng)地提出了換擋智能調(diào)整控制的解決方案。
傳統(tǒng)設(shè)計方法設(shè)計汽車變速器與同步器結(jié)構(gòu)參數(shù)是一項非常費時和艱苦的工作，而且難以求得較理想的設(shè)計參數(shù)，不利于產(chǎn)品性能的提高。變速器與同步器的優(yōu)化設(shè)計則可利用計算機(jī)在約束域內(nèi)按預(yù)定目標(biāo)高速有效地優(yōu)選出最佳的結(jié)構(gòu)參數(shù)，是一種理想的高質(zhì)量的設(shè)計方法。研究的主要目標(biāo)是建立一個載貨汽車變速器與同步器結(jié)構(gòu)參數(shù)的優(yōu)化設(shè)計數(shù)學(xué)模型，采用基于K-T(Kuhn-Tucker)方程解的方法進(jìn)行優(yōu)化計算，以期提高汽車變速器與同步器的設(shè)計水平。汽車傳動系是汽車的主要組成部分，變速器又是傳動系的重要部件，因此汽車變速器的優(yōu)化設(shè)計十分重要。以輕型載貨汽車為例，根據(jù)汽車變速器的設(shè)計要求與特點，在保證零件的強(qiáng)度、剛度、使用壽命等條件下，以減少重量和體積作為追求目標(biāo)，分析建立了載貨汽車變速器優(yōu)化設(shè)計的數(shù)學(xué)模型，并通過實例對其進(jìn)行了參數(shù)優(yōu)化，獲得了滿意的設(shè)計效果。
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