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 哈尔滨工业大学学报  2019, Vol. 51 Issue (7): 192-200  DOI: 10.11918/j.issn.0367-6234.201807145 0

引用本文

ZHANG Zhigang, YU Xiaoxia, PENG Yuanping, HOU Yabin, OU Xin. Synchronization mechanism modeling and structural effect factors analysis of synchronizer[J]. Journal of Harbin Institute of Technology, 2019, 51(7): 192-200. DOI: 10.11918/j.issn.0367-6234.201807145.

文章历史

1. 重庆理工大学 汽车零部件制造及检测技术教育部重点实验室，重庆 400054;
2. 重庆青山工业技术中心，重庆 402761

Synchronization mechanism modeling and structural effect factors analysis of synchronizer
ZHANG Zhigang1, YU Xiaoxia1, PENG Yuanping1, HOU Yabin2, OU Xin2
1. Key Laboratory of Manufacture and Test Techniques for Automobile Parts, Ministry of Education, Chongqing University of Technology, Chongqing 400054;
2. Chongqing Qingshan Industrial Technology Center, Chongqing 402761, China
Abstract: Four mathematical models of oil film pressure, contact force of asperity, axial force of synchronizer ring and cone torque are established by means of average Reynolds equation and asperity friction principle. The coupling number of oil film thickness and speed difference of synchronization is solved by using 4-Runge-Kutta method. The changing rule of oil film thickness, speed difference, viscous torque, asperity friction torque and total torque are analyzed. After verification of the mathematical model of synchronization, the effects of structure factors such as the width of synchronizer ring, radius of synchronizer ring, cone angle and thickness of friction material of synchronizer are studied by the model. The results show that the increase of the width of synchronous ring results in increasing viscous torque and asperity friction torque, decreasing the decline rate of oil film thickness, the response of asperity friction torque is delayed and the synchronization time is increased. With the increase of the radius of synchronous ring, the viscous torque and asperity friction torque increase, the oil film thickness descends and the synchronization time is shortened. When the friction angle increases, the viscous torque increases, the asperity friction torque decreases, the speed difference descends slowly and the synchronization time prolongs. With the increase of friction material thickness, the asperity friction torque and the changing rate of oil film thickness increase correspondingly, but the minimum oil film thickness and the synchronization time decrease.
Keywords: synchronizer     synchronization mechanism     numerical calculation     test verification     effect factors

1 同步器摩擦模型 1.1 同步器简介

 图 1 同步器摩擦阶段划分 Fig. 1 Division of synchronizer friction phase

1.2 油膜压力模型

1) 油膜在摩擦副表面上无相对滑动.

2) 与剪切力相比，油膜所受体积力可忽略不计.

3) 由于同步环和摩擦锥环之间轴向间隙小，故假设油膜压力沿油膜厚度无变化.

4) 油膜径向压力梯度为零.

5) 润滑油为牛顿流体，遵循牛顿粘性定理.

6) 由于同步时间较短，且变速器润滑油粘温曲线较为稳定，故假定同步过程中润滑油粘度不变.

 图 2 油膜挤压模型坐标系 Fig. 2 Oil film extrusion model coordinate system

 $\frac{\partial }{{\partial x}}\left( {\frac{{{h^3}\partial p}}{{\partial x}}} \right) = 6\eta \left( {{u_2} - {u_1}} \right)\frac{{\partial h}}{{\partial x}} + 12\eta \left( {{w_1} - {w_2}} \right).$ (1)

 $\frac{\mathrm{d}}{\mathrm{d} x}\left(\frac{h^{3} \mathrm{d} p}{\mathrm{d} x}\right)=12 \eta \frac{\mathrm{d} h}{\mathrm{d} t},$ (2)

 $\frac{{\rm{d}}}{{{\rm{d}}x}}\left( {{\mathit{\Phi }_x}\left( {{h^3} + 12\mathit{\Phi }d} \right)\frac{{{\rm{d}}p}}{{{\rm{d}}x}}} \right) = 12\eta \frac{{{\rm{d}}h}}{{{\rm{d}}t}},$ (3)

 $\left\{ {\begin{array}{*{20}{c}} {{\mathit{\Phi }_x} = 1 - C{{\rm{e}}^{ - rH}},}&{\gamma \le 1;}\\ {{\mathit{\Phi }_x} = 1 + C{{\rm{e}}^{ - rH}},}&{\gamma > 1.} \end{array}} \right.$ (4)

 $\sigma = \sqrt {\sigma _1^2 + \sigma _2^2} ,$ (5)

 $p = \frac{{6\eta {x^2}}}{K}\frac{{{\rm{d}}h}}{{{\rm{d}}t}} + \frac{{{C_1}}}{K}x + {C_2}.$ (6)

 $\left\{ \begin{array}{l} p\left( {x = 0} \right) = 0,\\ p\left( {x = b} \right) = 0. \end{array} \right.$ (7)

 $p = \frac{{6\eta }}{K}\left( {bx - {x^2}} \right)\frac{{{\rm{d}}h}}{{{\rm{d}}t}}.$ (8)

 $h = \frac{{{h_{{\rm{oil}}}}}}{2}\left[ {1 + {\rm{erf}}\left( {\frac{{{h_{{\rm{oil}}}}}}{{\sqrt 2 \sigma }}} \right)} \right] + \frac{\sigma }{{\sqrt {2\pi } }}\exp \left( { - \frac{{h_{{\rm{oil}}}^2}}{{2{\sigma ^2}}}} \right).$ (9)

 $\operatorname{erf}(x)=\frac{2}{\sqrt{\pi}} \int_{0}^{x} \mathrm{e}^{-\eta^{2}} \mathrm{d} \eta$ (10)

 $\frac{\mathrm{d} h}{\mathrm{d} t}=\left\{\frac{1}{2}\left[1+\operatorname{erf}\left(\frac{h_{\mathrm{oil}}}{\sqrt{2} \sigma}\right)\right]\right\} \frac{\mathrm{d} h_{\mathrm{oil}}}{\mathrm{d} t}.$ (11)

$g\left( {{h_{{\rm{ oil }}}}} \right) = \frac{1}{2}\left[ {1 + {\mathop{\rm erf}\nolimits} \left( {\frac{{{h_{{\rm{ oil }}}}}}{{\sqrt 2 \sigma }}} \right)} \right]$, 则式(8)可化为

 $p_{\text { oil }}=\frac{6 \eta}{K}\left(b x-x^{2}\right) g\left(h_{\text { oil }}\right) \frac{\mathrm{d} h_{\text { oil }}}{\mathrm{d} t}$ (12)

 图 3 初始油膜压力分布 Fig. 3 Initial pressure distribution of oil film

1.3 微凸体接触力模型

 ${p_c}\left( H \right) = \frac{{16\sqrt 2 }}{{15}}{\rm{ \mathsf{ π} }}{\left( {\lambda \beta \sigma } \right)^2}E'\sqrt {\frac{\sigma }{\beta }} A{F_{\frac{s}{2}}}\left( H \right).$ (13)

 $\frac{1}{{E'}} = \frac{1}{2}\left[ {\frac{{1 - \upsilon _1^2}}{{{E_1}}} + \frac{{1 - \upsilon _2^2}}{{{E_2}}}} \right]$ (14)
 ${F_n}\left( u \right) = \int_u^\infty {{{\left( {s - u} \right)}^n}{\varphi ^ * }\left( s \right){\rm{d}}s}$ (15)

 ${\varphi ^ * }\left( s \right) = \frac{1}{{\sqrt {2{\rm{ \mathsf{ π} }}} }}{{\rm{e}}^{ - \frac{1}{2}{s^2}}}.$ (16)

 $\left\{ \begin{array}{l} {p_c}\left( H \right) = {\left( {\lambda \beta \sigma } \right)^2}E' \times 1.1104 \times {10^{ - 5}}{\left( {4.0 - H} \right)^{6.084}},\\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;H < 4.0;\\ {p_c}\left( H \right) = 0,\;\;\;\;\;H \ge 4.0. \end{array} \right.$ (17)

1.4 同步环轴向力模型

 ${F_{{\rm{total}}}} = \left( {1 - B} \right){F_{{\rm{oil}}}} + B{F_c}$ (18)

 $\begin{array}{l} B = \frac{{{{\rm{ \mathsf{ π} }}^2}{{\left( {\lambda \beta \sigma } \right)}^2}}}{2}\left\{ {\left( {1 + {H^2}} \right)\left[ {1 - {\rm{erf}}\left( {\frac{H}{{\sqrt 2 }}} \right)} \right] - } \right.\\ \;\;\;\;\;\;\left. {\frac{{\sqrt 2 }}{{\sqrt {\rm{ \mathsf{ π} }} }}H\exp \left( {\frac{{{H^2}}}{2}} \right)} \right\} \end{array}$ (19)

 ${F_{{\rm{oil}}}} = {\rm{ \mathsf{ π} }}{b^3}\eta \left( {2r + b\sin \alpha } \right)\frac{{g\left( {{h_{{\rm{oil}}}}} \right)}}{K}\frac{{{\rm{d}}{h_{{\rm{oil}}}}}}{{{\rm{d}}t}}.$ (20)
 $\left\{ {\begin{array}{*{20}{c}} \begin{array}{l} {F_c} = \left( {2r + b\sin \alpha } \right){\rm{ \mathsf{ π} }}b{p_c},\\ {F_c} = 0, \end{array}&\begin{array}{l} H < 4.0;\\ H \ge 4.0. \end{array} \end{array}} \right.$ (21)

 $\left\{ \begin{array}{l} \frac{{{\rm{d}}{h_{{\rm{oil}}}}}}{{{\rm{d}}t}} = \frac{{\left[ {{F_{{\rm{sleeve}}}}\sin \alpha - B{\rm{ \mathsf{ π} }}b{p_c}\left( {2r + b\sin \alpha } \right)} \right]K}}{{\left( {1 - B} \right)\eta {\rm{ \mathsf{ π} }}{b^3}g\left( {{h_{{\rm{oil}}}}} \right)\left( {2r + b\sin \alpha } \right)}},\\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;H < 4.0;\\ \frac{{{\rm{d}}{h_{{\rm{oil}}}}}}{{{\rm{d}}t}} = \frac{{{F_{{\rm{sleeve}}}}\sin \alpha K}}{{\left( {1 - B} \right)\eta {\rm{ \mathsf{ π} }}{b^3}g\left( {{h_{{\rm{oil}}}}} \right)\left( {2r + b\sin \alpha } \right)}},\\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;H \ge 4.0. \end{array} \right.$ (22)

1.5 同步力矩计算模型

 $T = \left( {1 - B} \right){T_{{\rm{oil}}}} + B{T_c}.$ (23)

 ${T_{{\rm{oil}}}} = \left( {{\varphi _f} + {\varphi _{fs}}} \right)\frac{{\pi \eta \omega }}{{2h}}\left[ {{{\left( {r + b\sin \alpha } \right)}^4} - {r^4}} \right].$ (24)
 $\left\{ \begin{array}{l} {T_c} = \left( {2{r^2} + 2rb\sin \alpha + 0.5{b^2}{{\sin }^2}\alpha } \right){\rm{ \mathsf{ π} }}b{f_c}{p_c},H < 4.0;\\ {T_c} = 0,\;\;\;\;\;H \ge 4.0. \end{array} \right.$ (25)

 ${f_c} = 0.12 + 0.002\log \left( \omega \right).$ (26)

 $T = I\frac{{{\rm{d}}{\omega _i}}}{{{\rm{d}}t}}.$ (27)

 $\begin{array}{l} \frac{{{\rm{d}}{\omega _i}}}{{{\rm{d}}t}} = \frac{{{\rm{ \mathsf{ π} }}\eta \omega }}{{2hI}}\left( {{\varphi _f} + {\varphi _{fs}}} \right)\left( {1 - B} \right)\left[ {{{\left( {r + b\sin \alpha } \right)}^4} - {r^4}} \right] + \\ \;\;\;\;\;\;\;\;\;\frac{B}{I}\left( {2{r^2} + 2rb\sin \alpha + 0.5{b^2}{{\sin }^2}\alpha } \right){\rm{ \mathsf{ π} }}b{f_c}{p_c}. \end{array}$ (28)

2 数值仿真与试验验证 2.1 数值求解初始值

2.2 数值求解方法

2.3 模型验证 2.3.1 台架原理

 图 4 同步器单体试验台 Fig. 4 Single synchronizer test rig

2.3.2 试验与仿真对比

 图 5 试验与仿真结果对比 Fig. 5 Comparison results of experiment and simulation

3 同步器结构参数对同步过程的影响

 图 6 同步过程相关参数定义 Fig. 6 Definition of synchronization parameters

3.1 同步环宽度

 图 7 同步环宽度对同步过程的影响 Fig. 7 Effect of synchronizer ring width to synchronization

3.2 同步环半径

 图 8 同步环半径对同步过程的影响 Fig. 8 Effect of synchronizer ring radius to synchronization

3.3 摩擦锥角

 图 9 摩擦锥角对同步过程的影响 Fig. 9 Effect of cone angle to synchronization

3.4 摩擦材料厚度

 图 10 摩擦材料厚度对同步过程的影响 Fig. 10 Effect of thickness of friction material to synchronization

4 结论

1) 同步环宽度变化对最小油膜厚度影响较小，对同步力矩影响较大.同步环宽度减小，油膜厚度下降速率加快，粘性转矩和粗糙接触转矩减小，粗糙接触转矩响应迅速，同步时间缩短.

2) 最小油膜厚度和转速差下降速率与同步环半径大小无关. 2种同步环半径下同步过程中的粘性转矩和粗糙接触转矩大小和响应快慢不同.随着同步环半径增加，粘性转矩和粗糙接触转矩增大，油膜厚度下降速率加快，同步时间缩短.

3) 粘性转矩和粗糙接触转矩大小与同步环摩擦锥角相关性较大.同步环摩擦锥角增大，粘性转矩增大，粗糙接触转矩减小，转速差下降速率变缓，同步时间增加.

4) 摩擦副材料对粘性转矩和粗糙接触转矩大小影响较小，对油膜厚度下降速率和粗糙接触转矩响应快慢影响较大.摩擦副材料厚度减小，粗糙接触转矩相应延迟，油膜厚度下降速率减缓，同步时间延长.

 [1] TSENG C Y, YU C H. Advanced shifting control of synchronizer mechanisms for clutchless automatic manual transmission in an electric vehicle[J]. Mechanism & Machine Theory, 2015, 84: 37. [2] LU T, LI H, ZHANG J, et al. Supervisor control strategy of synchronizer for wet DCT based on online estimation of clutch drag torque[J]. Mechanical Systems & Signal Processing, 2016, 66: 840. [3] WALKER P D, ZHANG N. Engagement and control of synchroniser mechanisms in dual clutch transmissions[J]. Mechanical Systems & Signal Processing, 2012, 26(1): 322. [4] LIN S, CHANG S, LI B. Gearshift control system development for direct-drive automated manual transmission based on a novel electromagnetic actuator[J]. Mechatronics, 2014, 24(8): 1214. DOI:10.1016/j.mechatronics.2014.09.008 [5] PENTA A, GAIDHANI R, SATHIASEELAN S K, et al. Improvement in shift quality in a multi speed gearbox of an electric vehicle through synchronizer location optimization[C]// WCXTM 17: SAE World Congress Experience. 2017: 2 [6] 陈震, 钟再敏, 章桐. 基于ADAMS的同步器结合过程仿真分析[J]. 汽车工程, 2011, 33(4): 340. CHEN Zhen, ZHONG Zaimin, ZHANG Tong. Simulation analysis on the synchronizing process of synchronizer based on ADAMS[J]. Automotive Engineering, 2011, 33(4): 340. [7] 余晓霞, 张志刚, 苏洪. 基于AMESim同步器换挡性能仿真与优化[J]. 机械传动, 2018, 42(3): 60. YU Xiaoxia, ZHANG Zhigang, SU Hong. Simulation and optimization of synchronizer shift performance based on AMESim[J]. Mechanical Transmission, 2018, 42(3): 60. [8] 戴丰, 鲁统利, 张建武. 基于分形理论的同步器接触磨损模型[J]. 汽车技术, 2009(5): 15. DAI Feng, LU Tongli, ZHANG Jianwu. A model for synchronizer contact wear based on fractal theory[J]. Automotive Technology, 2009(5): 15. DOI:10.3969/j.issn.1000-3703.2009.05.004 [9] 徐万里, 赵巍, 张学明, 等. 变速箱同步器失效过程与失效机理分析[J]. 机械工程学报, 2014, 50(14): 69. XU Wanli, ZHAO Wei, ZHANG Xueming, et al. Analysis on failure process and failure mechanism of transmission synchronizer[J]. Mechanical Engineering Journal, 2014, 50(14): 69. [10] HÄGGSTRÖM D, NYMAN P, SELLGREN U, et al. Predicting friction in synchronizer systems[J]. Tribology International, 2016, 97: 89. DOI:10.1016/j.triboint.2015.12.038 [11] BROWN G, WALKER G M, FRIEND C, et al. Understanding MTF additive effects on synchroniser friction[J]. Sae International Journal of Fuels & Lubricants, 2012, 5(1): 447. [12] 吴荣华.同步器换档特性分析与优化设计[D].重庆: 重庆大学, 2012: 5 WU Ronghua.Analysis and optimal design for synchromesh behaviour[D]. Chongqing: Chongqing University, 2012: 5 [13] PASTOR BEDMAR A. Synchronization processes and synchronizer mechanisms in manual transmissions[J]. International Journal of Advanced Research in Computer Engineering & Technology, 2012, 1(3): 2. [14] DOWSON D. A generalized Reynolds equation for fluid-film lubrication[J]. International Journal of Mechanical Sciences, 1962, 4(2): 159. DOI:10.1016/S0020-7403(62)80038-1 [15] PATIR N, CHENG H S. An average flow model for determining effects of three-dimensional roughness on partial hydrodynamic lubrication[J]. Journal of Tribology, 1978, 100(1): 12. [16] PATIR N, CHENG H S. Application of average flow model to lubrication between rough sliding surfaces[J]. Journal of Tribology, 1979, 101(2): 220. [17] GREENWOOD J A, TRIPP J H. The contact of two nominally flat rough surfaces[J]. ARCHIVE Proceedings of the Institution of Mechanical Engineers 1847-1982 (vols 1-196), 1970, 185(1970): 625. [18] GREENWOOD J A, WILLIAMSON J B P. Contact of nominally flat surfaces[J]. Proceedings of the Royal Society of London, 1966, 295(1442): 300. DOI:10.1098/rspa.1966.0242