直接用于轮胎设计的稳态滚动温度场及滚动阻力求解策略
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摘要
由粘性损耗引起的轮胎稳态滚动温度场(包括滚动阻力)是控制轮胎整体性能的关键因素之一,且轮胎滚动温度场是一个非常复杂的热力耦合问题,因此轮胎滚动温度场分析是轮胎学术界和工程界长期关注的一个具有挑战性的应用基础问题；尽管对此问题已进行了较长期的大量研究,并在近期由本课题组形成了较为完整的以“双向解耦”迭代算法为基础的求解策略(简称非直接策略),但该求解策略依赖于轮胎温度场的计算和表面温度场的测试,不可直接用于轮胎设计。本文以形成可靠有效的可直接用于轮胎设计的稳态滚动温度场及滚动阻力求解策略(简称直接策略)为目的,开展了一系列相关的工作。
提出了一个采用红外热像仪三方向测量滚动轮胎外表面温度场的方法,以及一个消除测试偏差的修正方法。该方法首先采用余弦四次方定律对测试结果进行了与辐射入射角α相关的修正。然后依据轮胎外表面任意点温度的同一性(即与观测方向无关)进行了与β(即表面点的入射方向与其法向的夹角)相关的进一步修正,并给出了一个轮胎外表面发射率与β的经验关系；进而形成了一个双角度(α和β)修正函数以及测试温度的修正公式。成功研制了一个滚动轮胎内表面和内腔温度场的KTWTS无线测试系统,并得到了有效的测试结果。依据ISO28580标准采用MTS滚动阻力试验机测量得到了轮胎稳态滚动阻力。上述滚动轮胎内外表面和内腔温度场以及轮胎滚动阻力的测试结果为本文求解策略的验证奠定了坚实的实验基础。
基于粘弹谱仪的轮胎胶料粘弹特性静应变相关性的实验研究,首次较充分地揭示了Payne效应与静应变的相关性。基于实验结果,本文提出了一个同时计及轮胎胶料复模量的动应变、温度和静应变相关性的修正的Kraus模型。该模型能较好地表征轮胎胶料复模量的动应变、温度和静应变相关性。
选取了RNG k-ε湍流模型,然后采用Fluent软件建立了相应的数值模型,从而求解得到了轮胎在不同运行速度下稳态滚动时内腔及外部空气的速度场和温度场,进而计算得到了轮胎内外表面上的对流换热系数分布。采用轮胎内表面的实测温度分布作为设定的壁面温度边界条件,计算得到的轮胎内腔温度分布与实测值十分吻合,这表明所采用的计算模型是有效可靠的,也即本文基于Fluent软件求解得到的轮胎内外表面对流换热系数是正确的。这意味着本文提出的Fluent求解策略可直接用于轮胎设计阶段的温度场及滚动阻力分析；这将轮胎滚动温度场和滚动阻力求解策略的研究提升到一个新的发展阶段。
将同时计及轮胎胶料复模量的动应变、温度和静应变相关性的修正的Kraus模型以及由Fluent求解策略确定的滚动轮胎热边界条件引入到非直接策略中,由此得到了可直接用于轮胎设计的稳态滚动温度场和滚动阻力的求解策略。两种策略得到的轮胎稳态温度场以及滚动阻力计算结果与相关实测结果的对比表明,本文提出的直接策略是可靠有效的,且显著提高了轮胎温度场及滚动阻力的计算精度(与非直接策略的计算结果比较)。还表明损耗模型对轮胎滚动阻力有显著影响,而热边界条件则对轮胎温度场有显著影响。基于直接策略,分析计算了不同工况下的轮胎稳态温度场和滚动阻力。结果表明,轮胎内部稳态温度随速度增大而升高,轮胎稳态滚动阻力则随速度增加而减小；还表明轮胎内部稳态温度随载荷增大而升高,轮胎稳态滚动阻力随载荷增大而增加。
The steady temperature field (as well as rolling resistance) due to the viscous dissipation in a rolling tire plays a key role in controlling the overall tire performance. However, the analysis of temperature field in a rolling tire is a very complex thermo-mechanical problem. Therefore obtaining the accurate temperature field in a rolling tire is a basic but challenging problem which attracts the long-term attention in the academic and engineering field of tire.Many researchers have studied on this problem for several decades and recently a relatively complete solving strategy (named non-direct strategy) based on the two-way iterative approach was established by our research group.However, this solving strategy depends on the calculation of tire temperature field and the test of surface temperature distribution, thereby it cannot be used for tire design directly. Aimed to establish a reliable and effective solving strategy (named direct strategy) of steady tire temperature field as well as rolling resistance which can be used for tire design directly, a series of studies are carried out in this dissertation.
With the aid of infrared thermal imager, a method to measure the outer surface temperature field in a rolling tire from three directions is presented. On this basis,a correction procedure for eliminating the measurement deviation is given. Firstly, the measurement deviation related to the radiative incident angle (a) of the surface point is corrected based on the cosine-fourth law. Then the measurement deviation related to the angle between the direction of incidence and the normal at the point (β) is corrected according to the identity of the temperature at an arbitrary surface point. And an empirical relationship between the surface emissivity and β is derived. Finally, the Dual-angle (α and β) correction function and the corresponding temperature correction formula are derived. The measured temperatures in different directions for the same tire surface tend to be the same after correction, thus the accurate outer surface temperature field is obtained. A wireless testing system (KTWTS) for the inner surface and the contained air temperature field is developed and necessary calibration is conducted. Then the tire inner surface and contained air temperature field at different speed is obtained by this system. Based on MTS rolling resistance testing machine, the tire steady rolling resistance is obtained according to the ISO28580standard. The above-mentioned test results of surface and contained air temperature field, as well as the tire rolling resistance, provide the solid foundation for the verification of the solving strategy proposed in this dissertation.
The experimental study on the prestrain dependence of the viscoelastic properties for tire rubbers, by means of Dynamic Mechanical Thermal Analyzer (DMTA), reveals the correlation of the Payne effect and prestrain relative fully for the first time. A modified Kraus model to characterize the dynamic strain, temperature and prestrain dependence of dynamic modulus for tire rubbers is presented based on the work of Wu Fuqi. The modified Kraus model is able to characterize the dynamic strain dependence, temperature dependence and prestrain dependence of dynamic modulus for tire rubbers accurately.
The RNG k-ε turbulence model is selected, and the corresponding numerical model is established by means of Fluent software. The velocity and temperature field of the contained air and the ambient air for a steady rolling tire at different speed are then obtained; furthermore the convective heat transfer coefficients on the inner and outer tire surface are calculated. The calculated temperature distribution of the tire contained air agree the test results well, provided the wall temperature boundary condition is set to be the test results of the inner tire surface temperature distribution. This indicates the adopted physical and numerical models are reliable and effective, and also demonstrates the obtained convective heat transfer coefficients on the inner and outer tire surface are correct. The presented solving strategy of the convective heat transfer coefficients based on Fluent software, can be applied to the tire design directly.
Taking into consideration the above new modified Kraus model and new thermal boundary conditions together, the direct solving strategy of steady temperature field as well as rolling resistance in a rolling tire for tire design is thus established based on the non-direct solving strategy. The comparisons between the calculated results of the surface temperature field and rolling resistance by two strategy and the corresponding test results, indicate the direct strategy is more reliable, effective and accurate. The comparisons also indicate different dynamic modulus models have a significant influence on the tire rolling resistance, while different thermal boundary conditions
have a significant influence on the tire temperature field. Finally, the steady tire temperature field and rolling resistance under different working conditions are calculated based on the direct solving strategy. The results indicate the steady tire temperatures increase, while the steady tire rolling resistance decreases with the increase of the tire speed. The results also indicate the steady tire temperatures increase, and the steady tire rolling resistance increase with the increase of the tire load.
提出了一个采用红外热像仪三方向测量滚动轮胎外表面温度场的方法,以及一个消除测试偏差的修正方法。该方法首先采用余弦四次方定律对测试结果进行了与辐射入射角α相关的修正。然后依据轮胎外表面任意点温度的同一性(即与观测方向无关)进行了与β(即表面点的入射方向与其法向的夹角)相关的进一步修正,并给出了一个轮胎外表面发射率与β的经验关系；进而形成了一个双角度(α和β)修正函数以及测试温度的修正公式。成功研制了一个滚动轮胎内表面和内腔温度场的KTWTS无线测试系统,并得到了有效的测试结果。依据ISO28580标准采用MTS滚动阻力试验机测量得到了轮胎稳态滚动阻力。上述滚动轮胎内外表面和内腔温度场以及轮胎滚动阻力的测试结果为本文求解策略的验证奠定了坚实的实验基础。
基于粘弹谱仪的轮胎胶料粘弹特性静应变相关性的实验研究,首次较充分地揭示了Payne效应与静应变的相关性。基于实验结果,本文提出了一个同时计及轮胎胶料复模量的动应变、温度和静应变相关性的修正的Kraus模型。该模型能较好地表征轮胎胶料复模量的动应变、温度和静应变相关性。
选取了RNG k-ε湍流模型,然后采用Fluent软件建立了相应的数值模型,从而求解得到了轮胎在不同运行速度下稳态滚动时内腔及外部空气的速度场和温度场,进而计算得到了轮胎内外表面上的对流换热系数分布。采用轮胎内表面的实测温度分布作为设定的壁面温度边界条件,计算得到的轮胎内腔温度分布与实测值十分吻合,这表明所采用的计算模型是有效可靠的,也即本文基于Fluent软件求解得到的轮胎内外表面对流换热系数是正确的。这意味着本文提出的Fluent求解策略可直接用于轮胎设计阶段的温度场及滚动阻力分析；这将轮胎滚动温度场和滚动阻力求解策略的研究提升到一个新的发展阶段。
将同时计及轮胎胶料复模量的动应变、温度和静应变相关性的修正的Kraus模型以及由Fluent求解策略确定的滚动轮胎热边界条件引入到非直接策略中,由此得到了可直接用于轮胎设计的稳态滚动温度场和滚动阻力的求解策略。两种策略得到的轮胎稳态温度场以及滚动阻力计算结果与相关实测结果的对比表明,本文提出的直接策略是可靠有效的,且显著提高了轮胎温度场及滚动阻力的计算精度(与非直接策略的计算结果比较)。还表明损耗模型对轮胎滚动阻力有显著影响,而热边界条件则对轮胎温度场有显著影响。基于直接策略,分析计算了不同工况下的轮胎稳态温度场和滚动阻力。结果表明,轮胎内部稳态温度随速度增大而升高,轮胎稳态滚动阻力则随速度增加而减小；还表明轮胎内部稳态温度随载荷增大而升高,轮胎稳态滚动阻力随载荷增大而增加。
The steady temperature field (as well as rolling resistance) due to the viscous dissipation in a rolling tire plays a key role in controlling the overall tire performance. However, the analysis of temperature field in a rolling tire is a very complex thermo-mechanical problem. Therefore obtaining the accurate temperature field in a rolling tire is a basic but challenging problem which attracts the long-term attention in the academic and engineering field of tire.Many researchers have studied on this problem for several decades and recently a relatively complete solving strategy (named non-direct strategy) based on the two-way iterative approach was established by our research group.However, this solving strategy depends on the calculation of tire temperature field and the test of surface temperature distribution, thereby it cannot be used for tire design directly. Aimed to establish a reliable and effective solving strategy (named direct strategy) of steady tire temperature field as well as rolling resistance which can be used for tire design directly, a series of studies are carried out in this dissertation.
With the aid of infrared thermal imager, a method to measure the outer surface temperature field in a rolling tire from three directions is presented. On this basis,a correction procedure for eliminating the measurement deviation is given. Firstly, the measurement deviation related to the radiative incident angle (a) of the surface point is corrected based on the cosine-fourth law. Then the measurement deviation related to the angle between the direction of incidence and the normal at the point (β) is corrected according to the identity of the temperature at an arbitrary surface point. And an empirical relationship between the surface emissivity and β is derived. Finally, the Dual-angle (α and β) correction function and the corresponding temperature correction formula are derived. The measured temperatures in different directions for the same tire surface tend to be the same after correction, thus the accurate outer surface temperature field is obtained. A wireless testing system (KTWTS) for the inner surface and the contained air temperature field is developed and necessary calibration is conducted. Then the tire inner surface and contained air temperature field at different speed is obtained by this system. Based on MTS rolling resistance testing machine, the tire steady rolling resistance is obtained according to the ISO28580standard. The above-mentioned test results of surface and contained air temperature field, as well as the tire rolling resistance, provide the solid foundation for the verification of the solving strategy proposed in this dissertation.
The experimental study on the prestrain dependence of the viscoelastic properties for tire rubbers, by means of Dynamic Mechanical Thermal Analyzer (DMTA), reveals the correlation of the Payne effect and prestrain relative fully for the first time. A modified Kraus model to characterize the dynamic strain, temperature and prestrain dependence of dynamic modulus for tire rubbers is presented based on the work of Wu Fuqi. The modified Kraus model is able to characterize the dynamic strain dependence, temperature dependence and prestrain dependence of dynamic modulus for tire rubbers accurately.
The RNG k-ε turbulence model is selected, and the corresponding numerical model is established by means of Fluent software. The velocity and temperature field of the contained air and the ambient air for a steady rolling tire at different speed are then obtained; furthermore the convective heat transfer coefficients on the inner and outer tire surface are calculated. The calculated temperature distribution of the tire contained air agree the test results well, provided the wall temperature boundary condition is set to be the test results of the inner tire surface temperature distribution. This indicates the adopted physical and numerical models are reliable and effective, and also demonstrates the obtained convective heat transfer coefficients on the inner and outer tire surface are correct. The presented solving strategy of the convective heat transfer coefficients based on Fluent software, can be applied to the tire design directly.
Taking into consideration the above new modified Kraus model and new thermal boundary conditions together, the direct solving strategy of steady temperature field as well as rolling resistance in a rolling tire for tire design is thus established based on the non-direct solving strategy. The comparisons between the calculated results of the surface temperature field and rolling resistance by two strategy and the corresponding test results, indicate the direct strategy is more reliable, effective and accurate. The comparisons also indicate different dynamic modulus models have a significant influence on the tire rolling resistance, while different thermal boundary conditions
have a significant influence on the tire temperature field. Finally, the steady tire temperature field and rolling resistance under different working conditions are calculated based on the direct solving strategy. The results indicate the steady tire temperatures increase, while the steady tire rolling resistance decreases with the increase of the tire speed. The results also indicate the steady tire temperatures increase, and the steady tire rolling resistance increase with the increase of the tire load.
引文
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