車輛外文文獻翻譯-干式雙離合器變速器的離合器扭矩公式和校準(zhǔn)【中文5690字】【PDF+中文WORD】,中文5690字,PDF+中文WORD,車輛,外文,文獻,翻譯,干式雙,離合器,變速器,扭矩,公式,校準(zhǔn),中文,5690,PDF,WORD Mechanism and Machine Theory 46 (2011) 218–227 Contents lists available at ScienceDirect Mechanism and Machine Theory jour nal homepage : www. elsevier. com/ locate/mechmt Clutch torque formulation and calibration for dry dual clutch transmissions Yonggang Liu a,b, Datong Qin a, Hong Jiang c, Charles Liu c, Yi Zhang b,? a The State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, China b Department of Mechanical Engineering, University of Michigan-Dearborn, Dearborn, MI 48128, United States c Transmission & Driveline Research & Advanced Engineering, Ford Motor Company, Dearborn, MI 48128, United States a r t i c l e i n f o a b s t r a c t Article history: Received 2 March 2010 Received in revised form 15 September 2010 Accepted 21 September 2010 Available online 20 October 2010 Keywords: Dual clutch transmissions Clutch torque Calibration  This paper focuses on the clutch torque formulation and calibration for dry dual clutch transmissions (DCT). The correlation on the theoretical clutch torque and control parameters is established based on constant friction power and clutch actuator kinematics. An algorithm based on powertrain dynamics is proposed for the calculation of clutch torque during vehicle launch and shift operations. This algorithm uses wheel speed sensor data as input and is capable of determining the clutch torque while both clutches are slipping, thus provides a reliable correlation between clutch torque during real time operations and clutch actuator control variables. The accuracy of the proposed algorithm has been validated by torque measurement in prototype testing on prove ground. ? 2010 Elsevier Ltd. All rights reserved. 1. Introduction Dual clutch transmissions (DCT) feature drivability comparable to conventional automatic transmissions and fuel economy even better than manual transmissions. Due to these advantages, there is an on-going trend in the automotive industry to develop and market DCT vehicles that are fuel ef?cient but at no expenses of performance and drivability [1,2]. It can be predicted that vehicles equipped with dual clutch transmissions will have a signi?cant market share in the near future. The clutch torque control during launch and shifts is crucial for development of vehicles with DCT drive trains. Kinematically, gear shifting in a dual clutch transmission is similar to clutch-to-clutch shift in a conventional automatic transmission. Many valuable researches by both analytical and experimental means have been successfully conducted in transmission dynamics and control areas. Researchers at the Ford Research Laboratory [3,4] were among the ?rst to quantitatively analyze dynamic transients during transmission shifts by computer modeling and testing. The synchronization of the oncoming and off-going clutches had been achieved using hydraulic washout valves in automatic transmissions that have clutch-to-clutch shift patterns [5]. Systematic strategies that integrate engine control and clutch torque control had been developed for production vehicles for optimized vehicle launch and shift quality [6,7]. Researches and developments as those cited above have made possible the technology maturity of conventional automatic transmissions. Despite the similarity in clutch-to-clutch shift characteristics, a dual clutch transmission differs from a conventional automatic transmission in that the later has a torque converter between the engine output and transmission input. The presence of the torque converter cushions the powertrain dynamic transients and is therefore conducive for smoothness during vehicle launch and shifts. Without the cushion effect of torque converter, clutch torque control requires high precision to achieve launch and shift quality comparable to automatic transmissions. In a previous paper, the authors proposed a systematic model that analyzes the dynamic behavior of dual clutch transmissions and validated the model simulation based on prototype vehicle testing [8]. As a further study, the work presented in this paper is concentrated on the clutch torque formulation and calibration for dry dual clutch transmissions. Firstly, the theoretical or nominal clutch torque is correlated to the clutch design parameters based on the * Corresponding author. E-mail address: anding@umich.edu (Y. Zhang). 0094-114X/$ – see front matter ? 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechmachtheory.2010.09.005 3 Y. Liu et al. / Mechanism and Machine Theory 46 (2011) 218–227 assumption that the friction power is constant over the friction disk face. This formulation provides the basis for the design of clutch and its actuator. Secondly, an algorithm based on powertrain dynamics is established for the calculation of clutch torque in the launching clutch during launch and in both clutches during shift. This algorithm uses wheel speed sensor data as the input and is capable of accurately calculating the clutch torque while both clutches are slipping on a real time basis. The algorithm has several advantages: a) it enables the determination of clutch torque without using the friction coef?cient of the friction disk that varies as a function of temperature; b) it provides an effective way to calibrate the clutch torque against the design and control variables of the clutch and its actuator; c) it provides a reliable correlation between clutch torque and clutch control variable during real time operation for adaptive transmission control. Thirdly, the analytical formulation and algorithm for clutch torque calculation are validated against prove ground test data and laudable agreements are achieved between analytical and test data. 2. Analytical clutch torque formulation 2.1. Actuator kinematics and clutch torque The structure of one of the clutches and its actuator in a dry clutch DCT [9] is illustrated in Fig. 1. The other clutch and actuator assembly has similar design. Normally open clutch design is applied in DCT for safety considerations. As shown in the ?gure, the clutch actuator (or controller) consists of motor, spring, screw and roller. When the motor turns, the roller is displaced a distance x along the screw, creating the leverage for the generation of an axial force on the release bearing. This force is then magni?ed by the pressure plate level, resulting in the pressure force that clamps the friction disk. For a given clutch actuator design, the clutch torque is a function of motor rotation angle that is related to the roller displacement x by the screw parameter. In this paper, the concept of constant friction power (i.e. the conversion rate from kinetic energy to friction work during clutch slippage) is used for the formulation of the nominal clutch torque [10]. Based on this assumption, the energy conversion rate is expressed as follows: f ?p?v = Ct e1T where, f is the friction coef?cient of friction disk, p is the pressure, v is the relative velocity at a point, and Ct is the energy conversion rate per unitary area on the friction face. Based on this assumption, the pressure at any point over the disk face is expressed as, p = Ct f ?v = Ct = C f ?ω?r r  Ct e2T where ω is the angular velocity and r is the radius at the point. The quantity f ?ω is a constant over the disk face and is designated as C. Apparently, the pressure over the disk face varies reversely proportional to the radius. The maximum pressure pmax occurs at the Fig. 1. Sketch of dual clutch controller structure. 2 inner radius of the friction disk and the constant C can be expressed as C = dpmax, with d as the inner diameter of the friction disk. Plugging C back into Eq. (2), the pressure on the disk face is then expressed as, p = 1 2  pmax  d r : e3T The pressure force on the pressure plate can then be calculated as follows: F = 2π∫  D=2  p?r?dr = 2π∫ D=2 1 d?pmax  r?dr =  π?pmax?d?eD?dT  e4T d=2 d=2 2 r 2 where, D and d are the outer and inner diameters of the friction disk respectively. The clutch torque of one contact surface is calculated by the following, ， 2 2· TCL = 2π∫ D=2 f ?p?r2?dr = 2π? f ∫ D=2 1 d?pmax r2?dr = π?f ?pmax?d? D ?d d=2 d=2 2 r 8 e5T = = f F π?pmax?d?eD?dT D + d D + d ? ? 2 4 4 : The number of contact surfaces is two for each clutch, so the nominal clutch torque TCL is calculated by TCL = f ?F? D + d 2 : e6T 2.2. Correlation on clutch torque and control parameter The pressure force on the pressure plate is related to the force on the release bearing through the pressure plate lever. However, due to the deformation of the pressure plate lever that has a design similar to a diaphragm spring and the existence of backlashes, there exist non-linear characteristics between the clutch torque and the actuator control parameter. To account for this non- linearity, tests have been performed to measure the release bearing force (i.e. the engagement load). Based on test data, the release bearing force is correlated to the engagement travel as shown in Fig. 2. As shown in Fig. 2, there are substantial forces (denoted as F0) on the release bearing of both clutches when engagement travels are zero due to high rigidity for the pressure plate lever. Because of this, two separate functions must be used to correlate the release bearing force Fb with the roller displacement. The engagement load before release bearing travels is illustrated in Fig. 3. As shown in Fig. 3, the release bearing force Fb and the spring force Fs is related as follows before Fb reaches F0, xroller Fb = L?x  roller Fs e7T Fig. 2. Relationship between travel and load of bearing. 5 Y. Liu et al. / Mechanism and Machine Theory 46 (2011) 218–227 Fig. 3. Engagement load before release bearing travels. where, xroller indicates the position of the roller, L is the total effective length of lever, and Fs is the spring force with an initial value Fs0. The spring displacement is very small when Fb b F0 since release bearing displacement is near zero and the spring force remains almost constant, i.e., Fs = Fs0 if Fb b F0. At the threshold when Fb = F0, the displacement of roller xp can be solved from Eq. (7) as follows, F0 F xp = s0 + F0 L: e8T Fig. 4. Engagement load after release bearing travels. Table 1 Main parameters of clutch. Parameters Clutch 1 Clutch 2 Clutch outer diameter D1 = 232.5 mm D2 = 225 mm Clutch inner diameter d1 = 157 mm d2 = 157 mm Lever ratio iratio1 = 3.6 iratio2 = 4.2 Friction coef?cient f1 = 0.35 f2 = 0.35 Therefore, when xroller ≤ xp, the release bearing force is represented in terms of roller displacement by Eq. (7). After the bearing begins to travel, a separate function is required to correlate the release bearing force and the roller displacement since the spring compression is affected by the bearing travel. The engagement load after release bearing travels is illustrated in Fig. 4. As shown in Fig. 4, the amount of spring compression changed by the bearing travel is determined as follows, xb Δxs = L?x  roller xroller e9T where Δxs is the increment of spring length and xb is the engagement travel of bearing. Due to this increment, the spring force after bearing moving is expressed as follows: F = F ?k xroller s s0 L?xroller  xb e10T where k is the spring stiffness. The equilibrium of the actuator lever requires the following equation to be satis?ed Fsxroller = Fb eL?xroller T: e11T Combining Eqs. (10) and (11), the release bearing force Fb can be represented in term of the roller displacement as follows: 8 xroller F >  F 0 x ≤ x = L >< L?xroller s roller p Fs0 + F0 Fb = > ／ xroller ＼  xroller : F0 e12T L?x : > Fs0?k xb roller L?xroller xroller N xp = F s0 L + F0 2.3. Clutches torque and control parameter correlation As indicated in Eq. (6), the clutch torque is a function of the pressure force on the pressure plate, friction coef?cient and clutch dimensions. The main parameters of the two clutches used in the prototype are shown in Table 1. Fig. 5. Relationship between clutch torque and displacement of roller. Y. Liu et al. / Mechanism and Machine Theory 46 (2011) 218–227 227 Fig. 6. Dual clutch transmission dynamic model. According to Eq. (6), the nominal clutch torque in both clutch 1 and clutch 2 can be calculated as follows, r TCL1 = f1eFb1 iratio1TeD1 + d1T = 2 = 1000 = 0:35?e3:6Fb1Te232:5 + 157T = 2 = 1000 = 0:2454Fb1 TCL2 = f2eFb2 iratio2TeD2 + d2T = 2 = 1000 = 0:35?e4:2Fb2Te225 + 157T = 2 = 1000 = 0:2808Fb2  e13T where, Fb1 and Fb2 are the release bearing forces for clutch 1 and clutch 2 respectively. The spring constants are selected to be 150 N/mm for both actuators and the length of the actuator lever is L = 100 mm. The roller displacements at which release bearing begin to move are xp1 = 25 mm and xp2 = 30 mm respectively. The initial spring forces are determined by Eq. (8) as Fs1 = 1689 N and Fs2 = 1860 N. Before the release bearings start to move, the clutch torque and roller position can be expressed as following, 8 xroller1 xroller1 > TCL1 = 0:2454Fb1 = 0:2454 × L?x Fs = 414:48 × 100?x xrolle1 ≤ xp1 = 25 < roller1 xroller2 rolle1 : xroller2 e14T > TCL2 = 0:2808Fb2 = 0:2808 × L?x Fs = 522:29 × 100?x xrolle2 ≤ xp2 = 30 : rolle2 roller2 After the bearings start to move, the relationship between engagement travel xb and the bearing load Fb can be obtained from Fig. 2, which means that Fb is a function of xb, i.e., Fb = f(xb). When the engagement travel is smaller than 4 mm, it is accurate enough to ?t the function f(xb) by the following linear function Fb1 = 99:5xb1 + 563 xb1 ≤ 4mm: e15T Table 2 Main parameters of test vehicle. Parameters Value Vehicle mass M = 1400 kg Transmission gear ratios i1 = 3.917 i2 = 2.429 i3 = 1.436 i4 = 1.021 i5 = 0.848 i6 = 0.667 Final drive gear ratio ia1 = 3.762 ia2 = 4.158 Tire radius r = 0.2975 m Air resistance coef?cient Frontal area CD = 0.328 A = 2.12 m2 L?x So Eqs. (12) and (15) can be combined together (with β = xroller ) to correlate the clutch torque in clutch 1 as follows, roller 1 TCL1 = 0:2454 ×  1689 × 99:5β + 150 × 563β2! 1 1 = 1 99:5 + 150β2  41241β + 20724β2 99:5 + 150β2  1 1 xroller1 N xp1 = 25: e16T Similarly, the clutch torque in clutch 2 can be represented as a function of xroller2 as, 2 TCL2 = 0:2808 ×  1860 × 38:25β + 150 × 797β2! 2 2 = 2 38:25 + 150β2  19978β + 33570β2 38:25 + 150β2  2 2 xroller2 N xp2 = 30: e17T The clutch torques represented by Eqs. (16) and (17) can also be represented graphically by Fig. 5. 3. Algorithm for clutch torque calculation Eqs. (14), (16) and (17) provide the analytical calculation for the clutch torque in terms of roller position. However, this calculation must be calibrated for real world applications since the clutch friction coef?cient is temperature dependent. In this section, an algorithm based on powertrain dynamics is proposed for the accurate calculation of the clutch torque as described in the following. 3.1. DCT powertrain dynamics In a previous paper [8], the DCT powertrain dynamics during launch and shifts has been investigated in detail. The dynamic model for the dual clutch transmission used in the research is shown in Fig. 6. In this model, gear shafts are modeled as lumped masses and the four synchronizers are modeled as power switches. As indicated in Fig. 6, the mass moments of inertia of the lumped masses are denoted as following: engine output assembly including clutch input side (Ie), clutch 1 driven plate (I1), clutch 2 driven plate (I2), solid shaft (I3), hollow shaft (I4), transfer shaft 1 (I5), transfer shaft 2 (I6), output shaft (I7). In similar fashion, ωe, ω1, ω2, ω3, ω4, ω5, ω6, and ω7 denote the respective angular velocities. The wheel angular velocity is denoted by ωw. T1, T2 and To represent output torques of clutch 1, clutch 2 and output shaft respectively. The vehicle equivalent mass moment of inertia on the output shaft is denoted by I. The stiffness and damping coef?cient of the powertrain system are not considered since they do not affect the clutch torque calculations. 3.2. Calculation algorithm for clutch torque The calculation for cutch torque is based on the powertrain system dynamics. The equations of motion for vehicle launch and 1–2 upshift are presented in the following text. For other operation modes, similar equations can be derived according to the power ?ow path, as detailed in [8]. Fig. 7. Clutch torque comparison during launch. Fig. 8. Clutch torque comparison during 1–2 upshift. 3.2.1. Launch In the launch mode, the clutch torque in clutch 1 is gradually increased until it is fully engaged, while the clutch torque in clutch 2 is equal to zero. The torque of clutch 1 is directly used to drive the vehicle. The system of equations of motion is presented as follows. Te ?TCL1 = Ie?ω˙ e e18T TCL1?T1 = I1?ω˙ 1 e19T Ta 1 T1? i a1 i1 = Ieq?ω˙ 3 e20T Ta ?To = I7?ω˙ 7 e21T To?TLoad = I?ω˙ w e22T 1 where, i1 is ?rst gear ratio, ia1 is ?nal drive ratio which is shared by the 1st, 2nd, 5th and 6th gears. Te is the engine output torque. TCL1 is the clutch torque in clutch 1. Ta is the ?nal drive output torque. Ieq is the equivalent mass moment of inertia in the ?rst gear Fig. 9. Clutch torque comparison during operation in the 4th gear. for the lumped masses including the transfer shaft 1, assembly of the solid shaft and all other components rotating accordingly in the ?rst gear. ωw is the angular velocity of the wheel. The road load torque TLoad is expressed by the following equation: TLoad = ef ?W + RA + RGT?r e23T where, f is rolling resistance coef?cient, W is vehicle mass, r is tire radius, RA and RG are the air and grade resistances respectively. As can be seen from Eqs. (18)–(22), clutch torque TCL1 can be calculated using Eq. (18) or Eqs. (19)–(22) respectively. If the engine torque and engine speed can be measured accurately during vehicle launch torque TCL1 can then be directly found from Eq. (18). However, the engine torque and speed during transient operations are very hard to measure accurately resulting unacceptable inaccuracy for clutch torque calculation. On the other hand, the wheel speed of vehicle is more stable in comparison with engine speed and can be measured with high accuracy. Therefore, the clutch torque TCL1 can be calculated with high accuracy using Eqs. (19)–(22). In Eqs. (19)–(22), the angular velocities are related as follows: ω1 = ω3, ω7 = ωw and ω3 = ω7 ? ia1 ? i1. Thus the equations can be combined to present TCL1 in terms of ω?w as follows: ／I7 + I 1 ＼ ˙ TLoad TCL1 = ia 1 i1 + I1 + Ieqia1 i1 ωw  + ia1 i1 : e24T According to the above equation, the clutch torque TCL1 can be calculated during launch, and the accuracy only depends on the wheel acceleration that is the derivative of the wheel speed from the speed sensor. 3.2.2. Shifts The shift process is divided into two stages, which are torque phase and inertia phase. The system equations for a 1–2 shift are presented in the following, which can be easily extended to other shifts. Te ?TCL1?TCL2 = Ieω˙ e e25T Ta h 2 2 i a 1 TCL1?i1 + TCL2?i2? =i = eI3 + I1T?i1 + eI2