液力變矩器的減振性能分析

液力變矩器的減振性能分析

Analysis of Torsional Damper in Torque Converter

張祖金1, a

采埃孚(中國)投資有限公司

aZujin.Zhang@zf.com

ZHANGZujin1, a

1ZF(China)InvestmentCo.,Ltd.

aZujin.Zhang@zf.com

[摘要]分析車輛動力總成的扭轉(zhuǎn)振動特性，有助于改善車輛的舒適性和經(jīng)濟(jì)性。本文著重介紹自動變速箱的扭振減振性能，通過理論假設(shè)，簡化典型的橫置前驅(qū)得機(jī)械模型，并建立相應(yīng)的數(shù)學(xué)模型?；诖藬?shù)學(xué)模型，通過MATLAB計(jì)算仿真，比較評估相同扭振減振器不同參數(shù)的對系統(tǒng)減振特性的影響，以及介紹在不同減振器下差速器的速度響應(yīng)的區(qū)別。

Abstract[]Recognizing torsional vibration of the powertrain in vehicle is the main topic with regard to the comfort, and furthermore to fuel economy. This paper is analyzing the torsional damping performance of automatic transmission, mainly simplifying the mechanical model of typical front - transversal powertrain and building up the mathematical model; at the end evaluate the system characteristics affected by different damping rates of same type damper via MATLAB calculation, in addition introduce the differential reaction of different damper types.

關(guān)鍵詞：自動變速箱液力變矩器扭振減振器NVHMATLAB

文章編號：1006-8244(2015)03-003-10

中圖分類號：U463.22+1.1

Key words: automatic transmissiontorque convertertorsional dampingNVHMATLAB

1　前言

當(dāng)前市場上對于乘用車駕駛舒適性的要求顯著提高，與此相反的是越來越高的發(fā)動機(jī)動力要求和不斷要求降低成本的變速箱。在自動變速箱中，扭轉(zhuǎn)振動引起的變速箱噪音和振動需通過集成在液力變矩器中的扭振減振器來減少甚至消除，因此需要選擇合適的減振器。然而，實(shí)際應(yīng)用中減振器的選擇很大程度上取決于成本，并且需要匹配各種工況。所以對低扭矩的發(fā)動機(jī)、緊湊的布置空間和低成本控制的應(yīng)用，此時可以選擇基礎(chǔ)的單級減振器。

本文所討論的變速箱是應(yīng)用于橫置前驅(qū)的動力總成，此系統(tǒng)因布置空間有限也對發(fā)動機(jī)的尺寸有所限制。自動變速箱中由液力變矩器取代了手動變速箱中的離合器，但液力變矩器中也包含鎖止離合器和扭振減振系統(tǒng)。通過液力變矩器的液力耦合實(shí)現(xiàn)車輛起步后，合適的扭振減振器能夠?qū)崿F(xiàn)在較低的發(fā)動機(jī)轉(zhuǎn)速下閉合鎖止離合器, 因此可以滿足舒適性要求的同時還能降低油耗。扭振減振器的選擇需要在開發(fā)前期進(jìn)行篩選評估。

1　Introduction

Comfort driving requirements in the passenger car are increasing significantly every year from market, in contrast to higher excitation of engine and lower cost of transmission. Transmission noise caused by torsional vibration shall be substantially reduced or even eliminated by the torsional damper of torque converter, so the correct rate of advanced damper shall be selected. However, the selection of damper type is often dependent on the cost, and the rate needs to be balanced for all operating conditions. The standard damper system will be applied when the powertrain comes to low torque engine, compact configuration space and low cost of transmission.

本文所討論的扭轉(zhuǎn)減振器的分析主要關(guān)注于以下兩個方面，第一點(diǎn)是通過MATLAB計(jì)算，比較評估相同扭振減振器不同參數(shù)的對系統(tǒng)減振特性的影響，第二點(diǎn)是介紹在不同減振器下差速器的速度響應(yīng)的區(qū)別。因此，首先討論裝配自動變速箱的動力總成的架構(gòu)，從而建立了系統(tǒng)的數(shù)學(xué)模型，并在最后進(jìn)行上文所提到兩點(diǎn)進(jìn)行展開討論。

2　扭振減振器的結(jié)構(gòu)分類

扭振減振器的功能主要是阻斷發(fā)動機(jī)的扭振激勵傳到自動變速箱, 因此扭振減振器在動力總成的位置應(yīng)位于發(fā)動機(jī)和變速箱的輸入渦輪之間。理想狀態(tài)下所有的扭振激勵都被消除，但實(shí)際中總有一部分扭振激勵會傳遞到自動變速箱。這就要求扭振減振器之后傳遞動力到自動變速箱輸入軸的零件應(yīng)具有較小的轉(zhuǎn)動慣量，以減小侵入自動變速箱的扭振強(qiáng)度。這就是需要選擇合適的扭振減振結(jié)構(gòu)形式的原因。與此同時，還有另外許多因素需要被考慮進(jìn)去，例如動力傳遞的遲滯，結(jié)構(gòu)布置空間等等。發(fā)展至今，扭振減振器的在液力變矩器里面結(jié)構(gòu)形式種類已經(jīng)能夠滿足各種應(yīng)用的匹配要求，例如有限的軸向布置空間，最好的減振性能，低成本等需求。下圖1中形象的介紹了不同的扭振減振器的結(jié)構(gòu)形式：無減振(OD)，單級扭振減振器(TD)，渦輪扭振減振器(TTD)，雙級扭振減振器(TWD)，以及目前最先進(jìn)的離心鐘擺式扭振減振器(DAT)。相較于傳統(tǒng)的減振器, 裝配了先進(jìn)的扭振減振器如TWD和DAT的液力變矩器，其鎖止離合器可以允許在極低的發(fā)動機(jī)轉(zhuǎn)速下實(shí)現(xiàn)鎖止并保證良好的減振性能。這一特點(diǎn)可以極大的降低整車的油耗，提高經(jīng)濟(jì)性。

單級扭振減振器是個較為傳統(tǒng)的結(jié)構(gòu)形式，常常用于緊湊型車?yán)?。下表一是同樣單級扭振減振器但不同的減振參數(shù)的例子。

3　內(nèi)燃機(jī)的扭振激勵

考慮整個動力總成的扭振激勵是非常復(fù)雜的，其激勵源也是多方面的，但內(nèi)燃機(jī)的扭振激勵在扭振分析中是動力總成中的主要扭振激勵源。如大家所知, 當(dāng)某個氣缸內(nèi)的混合氣體被壓縮后再點(diǎn)燃，會生成一個作用于活塞頂部的燃燒膨脹氣體的壓力PG，此壓力推動活塞下行并帶動曲軸旋轉(zhuǎn)，并在一個切向力TG作用下產(chǎn)生某個角加速度，但又馬上被下一氣缸的壓縮沖程所阻礙，如此就導(dǎo)致了扭轉(zhuǎn)的速度和扭矩波動。不斷波動的速度和扭矩隨時間變化并產(chǎn)生了周期性的扭振激勵。本文只討論由內(nèi)燃機(jī)多缸周期性工作所產(chǎn)生的激勵。

The transmission in this paper is designed for the front - transversal powertrain which normally requires compact design of transmission as well as limited size of engine. Automatic transmission is normally equipped with hydrodynamic torque converter, which integrates a lock-up clutch and a torsional damper system. Torsional damper with adequate rate allows the lock-up clutch close at an early stage with low engine speed after vehicle launching by hydrodynamic power transmitting, so that it will contribute to not only comfort but also fuel economy. An appropriate rate of torsional damper needs to be pre-evaluated at the beginning of design.

Analysis of torsional damper in this paper mainly focus on two aspects, first is to evaluate the system characteristics affected by different damping rates of same type damper via MATLAB calculation, second is to introduce the differential reaction of different damper types. So firstly introduce the features of the powertrain with AT, then build up the mathematical model for the system, and at the end come to the two aspects mentioned above.

2　Configurations of torsional dampers

The function of torsional damper system is to isolate the torsional vibration from engine to transmission, so the damper shall locate among engine, turbine of TC and transmission. Ideally all the torsional vibration will be eliminated, but there is always still certain vibration that will intrude into transmission. In this case, the final part of TC transmitting power to transmission shall have less inertia in order to minimize the intensity of vibration. This is the reason for choosing proper configuration of torsional damper. In the meantime, some other factor shall be taken into consideration, like hysteresis of power transmitting, limitation of space. Nowadays torsional damper configurations inside of TC have been developed to be adaptable for all kinds of application requirements, such as limited axial space, best damping performance, low cost and so on. In Fig. 1 the different configurations are illustrated: no damper (OD), torsional damper (TD), turbine torsional damper (TTD),twin damper (TWD), and the most advanced centrifugal pendulum torsional damper (DAT). Compared to conventional converters, the lock-up clutch of a torque converter equipped with the advanced torsional damper like TWD or DAT can be applied at an extremely low engine speed. This feature can significantly reduce fuel consumption.

OD

TD

TTD

TWD

DAT

表1　兩種TD減振器的減振參數(shù)

由某個氣缸燃燒膨脹氣體驅(qū)動生成的曲軸扭矩Tc是一個關(guān)于曲軸轉(zhuǎn)角的周期性函數(shù)。又由于任何周期性函數(shù)都可以近似的以傅里葉展開式來表達(dá)，因此曲軸扭矩Tc可以表示為i個正弦函數(shù)之和，如下表達(dá)式1所示。

(1)

其中，T0是個平均值，Nm；Ti是第i階諧波扭矩的幅值，Nm；ω是曲軸的角速度，rad/s；φi是第i階諧

A TD damper is a conventional damper which is normally used in the compact car. In Table 1 are the damping characteristics of two TD dampers as example.

3　Torsional vibration excitation of internal combustion engine

The torsional vibration excitation in whole powertrain is very complex, and the excitation sources are so multifaceted, but the excitation of the internal combustion engine is always the main torsional vibration excitation source of driveline. As well known, each time there is a booming gas pressure PGwhen the compressed gas mixture is ignited in one cylinder, then the piston will push the crankshaft to rotate by a tangential pressure TGwith an angular acceleration, but it is immediately retarded by the compression stroke in the next cyl-波扭矩的相位角，rad。

表達(dá)式1只是關(guān)于某個氣缸的的扭矩的周期變化，但是對多缸的發(fā)動機(jī)，例如4缸發(fā)動機(jī)，需要考慮其各缸的工作順序及點(diǎn)火間隔。其4個氣缸按照某一順序依次點(diǎn)火(如1-3-4-2)，且各缸之間的點(diǎn)火間隔φ固定為180°。據(jù)此，整合各缸所產(chǎn)生的扭矩即為曲軸總的輸出扭矩T，而此扭矩T也包含各階i(0.5, 1, 1.5, 2, 2.5, 3…)諧波扭矩。根據(jù)點(diǎn)火順序，各缸的第i階諧波扭矩之間會有一個相位角i*φ。每階的扭矩都是一個扭矩矢量，可以歸納并圖示為下圖2。

圖2各階扭矩向量

Fig.2Torque vector at different excitation order i

如圖所示，把不同的階數(shù)歸類，根據(jù)相同的相位角可以分成三組，每組對應(yīng)個矢量圖。且由上圖各矢量的對比可知，其中一組階數(shù)(i= 2, 4, 6…)的各扭矩矢量具有相同的相位角，也就是說這些扭矩矢量在同樣一個方向疊加，增強(qiáng)至最大。因此，4缸發(fā)動機(jī)主激勵階數(shù)為第2階。 在此，在扭矩T的傅里葉展開式中，只考慮主要激勵階數(shù)(i=2，4，6)的諧波扭矩。此時，相位角為0，且圓頻率ω為2πn/60。 據(jù)此分析結(jié)果，并代入表達(dá)式1中，發(fā)動機(jī)扭振激勵T可以表示為表達(dá)式2，可應(yīng)用于強(qiáng)迫振動分析。

T(t)=T2sin(πn/15)t+T4sin(2πn/15)t+T6sin(πn/5)t

(2)

其中，n發(fā)動機(jī)轉(zhuǎn)速，r/min；t為時間，s。

4　動力總成的扭振振動分析

為了對動力總成進(jìn)行仿真分析，需要對整個系統(tǒng)進(jìn)行質(zhì)量彈性系統(tǒng)分析，并據(jù)此建立相應(yīng)的數(shù)學(xué)模型。實(shí)際上，動力總成是個非常復(fù)雜的連續(xù)多質(zhì)量彈性阻尼系統(tǒng)，很難用數(shù)學(xué)模型來模擬。因此，需要對系統(tǒng)進(jìn)行一些假設(shè)以簡化系統(tǒng)：

a. 在輸入軸及輸出軸之間的旋轉(zhuǎn)件，假定其為集中質(zhì)量，且為絕對剛性無彈性。

b. 對連接旋轉(zhuǎn)件的軸，假定其為無質(zhì)量，只作為彈性元件進(jìn)行工作，且其剛度為線性的。

inder, resulting in speed fluctuations. Because of that, the excitation mainly comes from. In this paper, only this excitation will be taken into consideration for simulation.

The torque Tcof crankshaft generated by the explosion pressure of one cylinder is a periodic function of the crank angle. Any periodic function can be approximately expressed by Fourier expansion, so the function of Tcis a sum of numerous harmonic functions, see Eq.1 as below.

(1)

In which, T0 is average value, Nm; Ti is the amplitude of harmonic torque at i order, Nm; ω is the angular speed of crankshaft, rad/s; φi is the phase angle of harmonic torque at i order, rad.

Eq.1 can only express the torque generated by one cylinder, but there are 4 cylinders of one engine. 4 cylinders are ignited referring to defined sequence (such as 1-3-4-2) and equal ignition interval φ of 180°between every cylinder. In this case, the torques generated by each cylinder will be integrated as the result of torque of crankshaft T, and this torque T consists of different harmonic torque at every excitation order i (0.5, 1, 1.5, 2, 2.5, 3…). The harmonic torque of certain excitation order i will have a delay with the phase angle i *φ between adjacent cylinder according to ignition sequence. The torque of every order is a vector, can be illustrated as Fig.2.

It is shown from Fig.2 that there are mainly 3 kinds of vector diagram for 3 group of excitation orders, and it is also easily found that the vector of one group of excitation orders (i = 2, 4, 6…) have same phase angle, which means these torque vectors are strengthened together in same direction to maximum. So the main excitation order for 4 cylinders engine is 2ndorder. In this paper, the main excitation orders (i = 2, 4, 6) will be taken into consideration. In this case, the phase angle is 0, and ω is equal to 2πn/60. Based on the analysis and combined with Eq.1, the torsional vibration excitation of engine T can be expressed as Eq.2, which is used for forced vibration analysis.

c. 假定無阻尼，且無內(nèi)部激勵。

因此，此系統(tǒng)可認(rèn)為是離散集中質(zhì)量的彈性減振多自由度系統(tǒng)，此簡化系統(tǒng)用于仿真模擬計(jì)算，主要關(guān)注于系統(tǒng)的固有特性分析等。

4.1動力總成的質(zhì)量彈性系統(tǒng)

車輛的動力總成應(yīng)進(jìn)行系統(tǒng)的減振分析及設(shè)計(jì)，以減少甚至隔絕扭振激勵。整個系統(tǒng)可以抽象的描述為一條扭轉(zhuǎn)質(zhì)量和扭轉(zhuǎn)彈簧連接的動力總成鏈。液力變矩器中的扭振減振器也是動力總成中的一部分，因此需要將扭振減振器列在此簡化的動力總成鏈上，以便于分析扭振減振參數(shù)對動力總成的振動解耦的作用。本文著重討論動力總成中的變速箱，所以發(fā)動機(jī)模型會更為概括簡化。另外，自動變速箱都有4至9個檔位，而每個檔位的轉(zhuǎn)動慣量和對應(yīng)的輸入輸出軸的剛度都可能不相同。在此這里只考慮在某個2檔的情況下的動力總成。因此，基于假設(shè)和其他邊界定義，結(jié)合實(shí)際的動力總成，可將系統(tǒng)簡化為如下圖3所示的結(jié)構(gòu)。此系統(tǒng)主要包括了發(fā)動機(jī)，液力變矩器，變速箱，驅(qū)動半軸，車輪和車身其它部分。如圖3所示可知，轉(zhuǎn)速由發(fā)動機(jī)通過變速箱以一定速比變換后傳遞至驅(qū)動半軸，然后傳至車輪。

T(t)=T2sin(πn/15)t+T4sin(2πn/15)t+T6sin(πn/5)t

(2)

In which, n engine speed, r/min; t is time, s.

4　Torsional vibration analysis of the powertrain

In order to analyze the powertrain system by simulation, it is necessary to build up the mathematical model based on the mass-elastic system of whole powertrain. Actually the real powertrain system is a very sophisticated continuous mass-elastic-damping system, so it is difficult to simulate by mathematical method. Here are some hypotheses in order to simplify the system:

a. Lumped mass for the rotating parts between input shaft and output shaft, which is absolute stiff without elastic

b. No mass for the shafts, which only work by elastic function. And the stiffness of elastic parts are linear

c. No damping will be considered, and no internal excitation

圖32檔時動力總成的質(zhì)量彈性系統(tǒng)簡化模型

Fig.3Mass-elastic model of powertrain in 2ndgear at drive condition

此動力總成中的所有的質(zhì)量元件及彈性元件都列在下表2中。

4.2動力總成系統(tǒng)的數(shù)學(xué)模型

由實(shí)踐經(jīng)驗(yàn)可知，降低連接發(fā)動機(jī)和變速箱的液力變矩器的傳動元件的剛度，可以有效地消除部分扭轉(zhuǎn)激勵進(jìn)入變速箱。這就是在動力總成結(jié)構(gòu)中，扭振減振器在離合器或在自動變速箱的液力變矩器中是個必不可少的元件。為了優(yōu)化系統(tǒng)的扭轉(zhuǎn)特性，需要了解動力總成系統(tǒng)的主振型和固有頻率。各個檔位都有各自的振動數(shù)學(xué)模型，這里將討論上文所建立的2檔時的動力總成系統(tǒng)。

基于圖3所示的動力總成系統(tǒng)簡化模型，系統(tǒng)的數(shù)學(xué)模型可以表達(dá)為:

Therefore, here we assume the system is a discretely distributed lumped mass - elastic - damping system with multi-degree of freedom, which is common used for the simulation of a vibration system without too much unstable factor, so that the simulation can focus on the nature behavior of the system.

4.1Mass-Elastic system of powertrain

The powertrain of a vehicle shall be systematically damped towards torsional vibration. The whole system could be abstracted and described as a chain of torsional masses and torsion springs. Torsional vibration damper in TC is a part of the pow-

表2　2檔時系統(tǒng)中所有質(zhì)量元件的轉(zhuǎn)動慣量和彈性元件的扭轉(zhuǎn)剛度

(3)

為了能夠?qū)κ?用MATLAB進(jìn)行計(jì)算，將使用剛度矩陣法進(jìn)行仿真計(jì)算。剛度矩陣法的構(gòu)建方法主要定義扭轉(zhuǎn)剛度Kxy為：當(dāng)轉(zhuǎn)動慣量y的角位移為1弧度，且其余所有的轉(zhuǎn)動慣量的角位移為0時，需要作用在轉(zhuǎn)動慣量x上的扭矩。基于此原則，并根據(jù)如圖3所示的2檔時動力總成系統(tǒng)簡化模型，可構(gòu)建系統(tǒng)的扭轉(zhuǎn)剛度矩陣K為矩陣1。此剛度矩陣包含兩個較為特別的地方，其一為扭轉(zhuǎn)剛度5和6都是存在速比轉(zhuǎn)換，另外一點(diǎn)為從差速器傳遞動力到左右半軸時分成左右兩部分，最終得到如下矩陣。

ertrain, so it shall be considered into the system in order to understand what the decoupling function in powertrain would be with certain dynamic parameters of the torsional damper. In this paper, the analysis is mainly for the transmission, so the engine will not be considered into each cylinder. In addition, normally an automatic transmission has several gears, so the mass and elastic of each gear shall be different. Here we only consider 2ndgear situation. Therefore, the mass-elastic system of this powertrain can be simplified to the model shown in Fig. 3. The system mainly includes engine, torque converter, transmission, drive shafts, wheels and vehicle body. In Fig.3, speed transferring with certain ratio from gearsets to drive shafts, and futher to wheels.

矩陣1，系統(tǒng)扭轉(zhuǎn)剛度矩陣K

轉(zhuǎn)動慣量矩陣 J可以直接根據(jù)系統(tǒng)模型建立如下矩陣2:

矩陣2，系統(tǒng)轉(zhuǎn)動慣量矩陣J

此兩個矩陣中的所有轉(zhuǎn)動慣量和扭轉(zhuǎn)剛度都已羅列在表2中。

4.3相同類型不同減振參數(shù)下固有頻率和主振型

為了研究動力總成系統(tǒng)的扭轉(zhuǎn)振動特性，很重要的一點(diǎn)是要了解系統(tǒng)的固有頻率和主振型。當(dāng)系統(tǒng)不受外力影響，沒有阻尼消減振動時，此時系統(tǒng)在初始激勵作用下以固有頻率進(jìn)行自由振動。因此，系統(tǒng)的自由振動方程可以表示為如下式4。

(4)

這里將對配有單級減振器的系統(tǒng)進(jìn)行計(jì)算，比較同種類型的減振器不同減振參數(shù)對系統(tǒng)的固有頻率和主振型的影響。根據(jù)表2，在MATLAB創(chuàng)建扭振剛度矩陣K和轉(zhuǎn)動慣量矩陣J。 由于對比相同類型不同減振參數(shù)的計(jì)算，各需要創(chuàng)建想應(yīng)得剛度和慣量矩陣。根據(jù)創(chuàng)建的矩陣，按照MATLAB矩陣運(yùn)算的方法，計(jì)算系統(tǒng)的固有頻率和主振型。不同的剛度矩陣中，由表1可知，扭振減振器B相較于扭振減振器A具有較低的剛度。據(jù)經(jīng)驗(yàn)可知，系統(tǒng)發(fā)生共振的風(fēng)險基本上發(fā)生在第2和第3階固有頻率。因此，這里主要比較第2和第3階固有頻率下扭振振動振型。具體的對比圖形見下圖4。圖4中，x軸式轉(zhuǎn)動慣量的序號，而y軸是正則化的振型。

如圖4所示，較低的扭振減振器剛度可以降低系統(tǒng)的固有頻率并改變系統(tǒng)的振型。但這并不意味著扭振減振器的剛度越低越好，因?yàn)檩^低的扭振減振器剛度在同樣的扭矩容量的情況下需要更長的減振行程，且扭振剛度越低則意味著更大的扭矩傳遞遲滯，最后合適扭振減振器剛度需要通過系統(tǒng)結(jié)合發(fā)動機(jī)周期激勵進(jìn)行仿真計(jì)算并通過整車及臺架試驗(yàn)評估。

4.4 不同類型的扭振減振器的減振性能

4.4.1在發(fā)動機(jī)激勵下的動力總成振動方程

運(yùn)用扭轉(zhuǎn)振動方程對動力總成系統(tǒng)進(jìn)行振動仿真主要是避免動力總成系統(tǒng)發(fā)生共振。而在動力總成系統(tǒng)中發(fā)生共振的情況大概有兩種：第一種是當(dāng)在某一發(fā)動機(jī)轉(zhuǎn)速下發(fā)動機(jī)的主激勵頻率與動力總成系統(tǒng)的某階固有頻率接近；第二種是在某階系統(tǒng)的固有頻率對應(yīng)的振型中發(fā)動機(jī)的振幅不為0。

(a) 2階振型比較

(b) 3階振型比較

All the masses and elastic parts are listed in the following Table 2.

4.2Mathematical model of the system

It has been leant in the practical application that certain portion of the torsional vibration can be diminished effectively by reducing the torsional stiffness between the engine and the gearbox. This is why the torsional damper in the clutch disc or here in the torque converter is always an essential element in the powertrain. In order to optimize vibrational behavior, the vibration forms and natural frequencies of the entire powertrain have to be known. Every gear ratio results in a different vibrational model since there are strong influences on the adjacent components. The model here is going to analyze the 2ndgear.

一般而言，發(fā)動機(jī)激勵的系統(tǒng)響應(yīng)的振動方程都是隨發(fā)動機(jī)轉(zhuǎn)速變化的函數(shù)。但表達(dá)式2中的發(fā)動機(jī)激勵函數(shù)是關(guān)于時間的函數(shù)。因此，為了更好的仿真計(jì)算，這里需要建立系統(tǒng)的頻率響應(yīng)函數(shù)，具體見表達(dá)式5到10。

首先，定義扭矩向量T和角位移向量θ為：

(5)

(6)

然后將式5和式6代入式3中，可得：

(7)

這里定義H(ω) 為：

Based on the model shown in Fig.3, the mathematical model of the system can be express as:

(3)

In order to calculate the Eq.3 by MATLAB, the stiffness matrix method will be utilized. It is defined that the torsional stiffness Kxyis: the torque applied on the inertia x when the angle of inertia y is 1 rad and the angle of all other inertias are 0. Based on the Fig.3, the torsional stiffness matrix Kcan be built as matrix 1. This matrix contains two special definitions, one is that torsional stiffness 5 and 6 are transferred with ratios, another one is that the power transferring line is divided into two lines from differential to right and left drive shafts.

Matrix 1, Stiffness matrixKof system based on the system model

(8)

由式8[1]和圓頻率ω=2πn/60，可得：

(9)

最后，根據(jù)式7和式9，可得系統(tǒng)的頻率響應(yīng)函數(shù)為：

(10)

基于此頻率響應(yīng)函數(shù)，可以根據(jù)發(fā)動機(jī)激勵計(jì)算系統(tǒng)的響應(yīng)。

4.4.2不同類型的扭振減振器下的速度響應(yīng)的例子

為了更直觀的對比不同類型的扭振減振器的減振性能，這里將舉例說明相同系統(tǒng)不同類型的扭振減振器的區(qū)別，如下圖5所示的差速器速度響應(yīng)的在不同類型扭振減振器下的區(qū)別。本例中將展示以下幾種類型的扭振減振形式OD，TD，TTD和TWD，但沒有DAT。

Inertias matrix Jcan be easily built up based on the Table 2 as matrix 2:

Matrix 2, Inertias matrix J

For the values of all stiffness and inertias can be found in the table 2.

4.3Natural frequencies and vibration forms at different damping rate

(a) 無減振時的差速器速度波動

(b) TD減振時的差速器速度波動

(c) TTD減振時的差速器速度波動

(d) TWD減振時的差速器速度波動

(e) 差速器速度波動的對比

圖5清晰地顯示了扭振減振器可以降低系統(tǒng)的固有頻率，特別是可以將2階固有頻率降低到發(fā)動機(jī)非常用的轉(zhuǎn)速區(qū)間，因此動力總成可以快速通過2階固有頻率的共振區(qū)間。由圖可知，其中TWD減振器的減振性能最好，在系統(tǒng)的工作區(qū)域幾乎可以消除明顯的扭振影響。當(dāng)然無減振的情況下是最壞的工況，很容易由于振動產(chǎn)生噪聲甚至導(dǎo)致整個動力總成的損壞。

To study the torsional vibration behavior of powertrain system, it is very important to know the torsional vibration forms and natural frequencies of the entire powertrain. The natural frequency only can be calculated when the system is vibrating freely without excitation and damping. So the torsional vibration formula can be expressed as Eq.4.

(4)

5　結(jié)論

上文概述了相同類型的扭振減振器不同減振參數(shù)，以及不同類型的扭振減振器對動力總成扭轉(zhuǎn)振動系統(tǒng)的影響。在開發(fā)階段對動力總成系統(tǒng)進(jìn)行扭轉(zhuǎn)振動系統(tǒng)仿真計(jì)算分析是一個有效的系統(tǒng)設(shè)計(jì)方法。而在樣件開發(fā)階段，可以進(jìn)一步對系統(tǒng)進(jìn)行標(biāo)定試驗(yàn)，根據(jù)要求調(diào)整減振參數(shù)。如此，可以根據(jù)客戶需求設(shè)計(jì)合適的扭轉(zhuǎn)振動性能。

參考文獻(xiàn)

[1]吳天行，華宏星： 機(jī)械振動， 清華出版社，第60頁

Here it is going to compare two TD dampers integrated into system for analysis, and these two dampers are in different TC with different damping date. Insert the matrix Kand Jinto MATLAB, and start to utilize MATLAB to calculate Eq.4 with two damper characteristics as well as corresponding inertias. Damper B is less stiff comparing to damper A as indicated in table 2. It is quite well known that high risk of resonance normally occur 2ndand 3rdnatural frequency. Here are the comparisons of the torsional vibration forms between two dampers at 2nd, 3rdnatural frequency. The details can be found in the Fig. 4. In the Fig. 4, x-axis is the number of the masses, and the y-axis is the regularized offset.

Figure 4 illustrate that the torsional damper with less stiffness will reduce the natural frequency of the system and change the torsional vibration form of the system. But this doesn’t mean that a torsional damper with lower stiffness is better, because the lower stiffness will require more angular stroke of damper with same torque capacity, and lower stiffness means bigger hysteresis, at the end the suitable rate of damper shall be verified by the system simulation with engine excitation.

4.4Damping performance of different dampers in the system

4.4.1Mathematical model of powertrain system with engine excitation

The purpose of the torsional vibration simulation is to avoid the resonance in powertrain. There are two conditions when the powertrain generate the resonance: first is that the excitation frequency of main order at certain engine working speed comes close to one natural frequency of system; second is that the torsional vibration form at this natural frequency shows the amplitude of engine is not 0.

Normally, it is necessary to see the response of the system changing as a function of the engine speed. But the excitation of engine described in the Eq.2 is as a function of time. So here it is necessary to build up the frequency-response-function for the system as shown in Eq.5-10.

First, set the torsional torque vector T and stable response angle vector θ are:

(5)

(6)

Then put Eq.5 and Eq.6 into Eq.3, so:

(7)

Here define as the matrix H(ω):

(8)

Based on Eq.8 [1] and theω was defined before as2πn/60, so:

(9)

At the end, based on the Eq.7 and Eq.9, the frequency-response-function is:

(10)

Based Eq.10, it is possible to calculate the response when the input of engine excitation is defined.

4.4.2Speed fluctuation response examples of different damper types

Here is going to introduce one example about the comparison of speed fluctuation of differential as shown in Fig.5 when different dampers are applied in the system, in order to see the damping performance of each kind of damper. The configuration types of OD, TD, TTD, TWD will be

shown in this example, but not for the DAT damper.

Figure 5 illustrate very clear that dampers can decrease the natural frequencies of system, especially move the 2ndnatural frequency to the not-normal working speed, so that the powertrain can skip very fast away resonance of 2ndnatural frequency. The best damping performance is the TWD damper, which can almost eliminate the torsional vibration out of working zone. And the worst is no damper situation, this will easily result in heavy noise or even damage in the powertrain.

5　Conclusion

It has been shown that the different respond affected by different torsional damping characteristics and different dampers’ configurations in the powertrain. Simulation calculation is an effective way for pre-evaluation of torsional damper performance in the development phase. In the prototype phase, the torsional damper can be fine-tuned after calibration. This guarantees optimum torsional damping characteristics for the OEM according customer specific requirements.

References

[1]Wu Tainxing & Hua Hongxing: Mechanical vibration, published by Qinghua university, Page 60 & Hua Hongxing: Mechanical vibration, published by Qinghua university, Page 60