1 Introduction
2 Clutch Engagement Dynamics Analysis and Modeling
2.1 Clutch Engagement Dynamics Model
2.2 Friction Torque of Clutch Under Stick-slip Condition
3 Effect of Friction Coefficient Gradient on Judder Characteristic
4 Gradient Stability Analysis of Clutch Friction Coefficient
Variable | Implication | Value |
---|---|---|
\({J}_{1}(\mathrm{kg}\cdot {\mathrm{m}}^{2})\) | Equivalent moment of inertia of the crank connecting rod group of the first cylinder of the engine | 0.0182 |
\({J}_{2}(\mathrm{kg}\cdot {\mathrm{m}}^{2})\) | Equivalent moment of inertia of the crank connecting rod group of the second cylinder of the engine | 0.0182 |
\({J}_{3}(\mathrm{kg}\cdot {\mathrm{m}}^{2})\) | Equivalent moment of inertia of the crank connecting rod group of the third cylinder of the engine | 0.0182 |
\({J}_{4}(\mathrm{kg}\cdot {\mathrm{m}}^{2})\) | Equivalent moment of inertia of the crank connecting rod group of the fourth cylinder of the engine | 0.0182 |
\({J}_{5}(\mathrm{kg}\cdot {\mathrm{m}}^{2})\) | Inertia of flywheel and driving part of clutch | 0.5 |
\({J}_{6}(\mathrm{kg}\cdot {\mathrm{m}}^{2})\) | Equivalent moment of inertia of friction lining and wave plate | 0.015 |
\({J}_{7}(\mathrm{kg}\cdot {\mathrm{m}}^{2})\) | Equivalent rotational inertia of clutch driven disc hub | 0.04 |
\({J}_{8}(\mathrm{kg}\cdot {\mathrm{m}}^{2})\) | Equivalent rotational inertia of transmission | 0.02 |
\({J}_{9}(\mathrm{kg}\cdot {\mathrm{m}}^{2})\) | Equivalent moment of inertia of body and other driveline components | 4 |
\({c}_{1}(\mathrm{Nms}\cdot {\mathrm{rad}}^{-1})\) | The damping of the crank journal of the first cylinder of the engine | 0 |
\({c}_{2}(\mathrm{Nms}\cdot {\mathrm{rad}}^{-1})\) | The damping of the crank journal of the second cylinder of the engine | 0 |
\({c}_{3}(\mathrm{Nms}\cdot {\mathrm{rad}}^{-1})\) | The damping of the crank journal of the third cylinder of the engine | 0 |
\({c}_{4}(\mathrm{Nms}\cdot {\mathrm{rad}}^{-1})\) | The damping of the crank journal of the fourth cylinder of the engine | 0 |
\({c}_{5}(\mathrm{Nms}\cdot {\mathrm{rad}}^{-1})\) | Equivalent damping of flywheel and clutch driving part | 0 |
\({c}_{6}(\mathrm{Nms}\cdot {\mathrm{rad}}^{-1})\) | Friction lining damping | 0 |
\({c}_{7}(\mathrm{Nms}\cdot {\mathrm{rad}}^{-1})\) | Torsional damper damping | 0 |
\({c}_{8}(\mathrm{Nms}\cdot {\mathrm{rad}}^{-1})\) | Transmission equivalent damping | 0 |
\({c}_{9}(\mathrm{Nms}\cdot {\mathrm{rad}}^{-1})\) | Equivalent damping of body and other driveline components | 0 |
\({k}_{1}(\mathrm{Nm}\cdot {\mathrm{rad}}^{-1})\) | Equivalent torsional stiffness of the crank journal of the first cylinder of the engine | 20000 |
\({k}_{2}(\mathrm{Nm}\cdot {\mathrm{rad}}^{-1})\) | Equivalent torsional stiffness of the crank journal of the second cylinder of the engine | 20000 |
\({k}_{3}(\mathrm{Nm}\cdot {\mathrm{rad}}^{-1})\) | Equivalent torsional stiffness of the crank journal of the third cylinder of the engine | 20000 |
\({k}_{4}(\mathrm{Nm}\cdot {\mathrm{rad}}^{-1})\) | Equivalent torsional stiffness of the crank journal of the fourth cylinder of the engine | 20000 |
\({k}_{5}(\mathrm{Nm}\cdot {\mathrm{rad}}^{-1})\) | Spring equivalent stiffness of torsional damper | 2000 |
\({k}_{6}(\mathrm{Nm}\cdot {\mathrm{rad}}^{-1})\) | Equivalent torsional stiffness of transmission input shaft | 4000 |
\({k}_{7}(\mathrm{Nm}\cdot {\mathrm{rad}}^{-1})\) | Equivalent torsional stiffness of transmission output shaft | 6000 |
\({T}_{1}(\mathrm{N}\cdot \mathrm{m})\) | Engine excitation torque | 300 |
\({T}_{0}(\mathrm{N}\cdot \mathrm{m})\) | Road resistance torque | 100 |
\(F(\mathrm{N})\) | Clutch pressure | 4000 |
\({R}_{0}(\mathrm{m})\) | Outer radius of friction lining | 0.2 |
\({R}_{i}(\mathrm{m})\) | Inner radius of friction lining | 0.134 |
\({\mu }_{0}\) | Static friction coefficient | 0.3 |
μ′ | Real part | Imaginary part |
---|---|---|
− 0.01 | 0.0000 | ±1.6562i |
0.2144 | ±1.0688i | |
0.0001 | ±0.9246i | |
0.0210 | ±0.7424i | |
0.0329 | ±0.3220i | |
0.0041 | ±0.0983i | |
0.0678 | ±0.0319i | |
0.0038 | ±0.0046i | |
0.0000 | ±0.0000i | |
− 0.005 | 0.0002 | ±0.4772i |
0.0025 | ±0.3864i | |
0.4665 | ±0.32391i | |
0.0747 | ±0.5961i | |
0.3405 | ±0.7428i | |
0.1464 | ±0.1666i | |
0.0047 | ±0.0950i | |
0.1662 | ±0.9247i | |
0.0018 | ±0.0000i | |
0 | 0.0000 | ±1.3572i |
0.0000 | ±1.8790i | |
0.0000 | ±1.4684i | |
0.0000 | ±0.9248i | |
0.0000 | ±0.7433i | |
0.0000 | ±0.4408i | |
0.0000 | ±0.1948i | |
0.0000 | ±0 | |
0.0000 | ±0 | |
0.005 | -0.0012 | ±0.0000i |
-0.0025 | ±0.1971i | |
-0.0001 | ±0.1608i | |
-0.0210 | ±0.1055i | |
-0.0329 | ±0.0742i | |
-0.1464 | ±0.0387i | |
-0.4465 | ±0.0319i | |
0.0000 | ±0.0046i | |
0.0000 | ±0.0000i |
5 Simulation Analysis of Clutch Friction Coefficient Gradient
6 Bench Test of Judder Characteristics of Friction Lining
6.1 Experimental Equipment
6.2 Experimental Method
6.3 Test Program
6.4 Evaluation Basis
6.5 Test Result
7 Conclusions
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(1) There are two conditions of sticking and slipping in the clutch engagement process. By analyzing the dynamic models of the two conditions, the calculation model of the friction torque in the clutch engagement process is determined.
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(2) When the friction characteristic of the friction lining in the clutch has a negative gradient, the system loses stability and judder occurs; when the clutch friction characteristics have a zero gradient or a positive gradient, the system is in a stable state and the judder does not occur. Therefore, as far as possible, the friction gradient is chosen as a positive material to make the friction lining.
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(3) Through theoretical and simulation analysis, it is determined that when the self-excited vibration of the clutch friction lining is too large and the system damping is not enough to attenuate the judder signal, the system loses stability. With the improvement of the friction gradient characteristics of the clutch friction material, the friction coefficient gradient value is greater than − 0.005 s/m, which can effectively reduce the degree of system judder.
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(4) Based on the existing test standards and the viscous damping model of the single-DOF system, a clutch friction lining judder test bench and the corresponding damping test program are designed and developed. After a large number of tests, the experimental evaluation basis is established. Through the experimental analysis, it is concluded that the damping value set by the additional damper is 0.1 Nms. When the system damping caused by the self-excited vibration of the friction lining exceeds 0.1 Nms, the additional damper cannot completely suppress the judder signal, and the system produces judder behavior. When the system damping caused by the self-excited vibration of the friction lining does not exceed 0.1 Nms, the additional damper attenuates the judder signal and the system tends to be stable.