带附加气室空气弹簧动力学特性研究
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摘要
以空气弹簧为弹性元件的空气悬架系统表现出了诸多的优越性,如果在此基础上再增加一附加气室组成带附加气室空气弹簧系统,还可以进一步提高悬架系统的减振性能。不仅对公路车辆,对于作业环境、行驶路况更为复杂的农用车辆、工程车辆、林用车辆等非公路车辆来说,应用带附加气室空气悬架可有效地提高它们对不同路况、不同作业环境的适应能力。
本文以Firestone公司生产的1T15M-2膜式空气弹簧为弹性元件,通过管路和节流孔接入附加气室建立了带附加气室空气弹簧系统。结合目前国内外相关的研究结论,利用理论分析与实验相结合的方法对带附加气室空气弹簧系统的动力学特性进行了系统地研究,对此系统动力学特性的影响因素和影响规律进行了详细地分析,分析了带附加气室空气悬架的设计方案。所完成的工作及取得的结论归纳如下：
1.基于刚体动力学、热力学及空气动力学理论建立了带附加气室空气弹簧系统的非线性动力学理论模型,在Matlab／Simulink环境下建立了系统振动仿真模型,仿真分析了不同节流孔开度和不同附加气室容积下系统簧上质量位移阶跃响应特性和位移幅频响应特性。仿真结果表明,附加气室能够显著降低系统固有频率,合理设置节流孔开度可以有效衰减振动。
2.通过空气弹簧静特性实验建立了空气弹簧静刚度、空气弹簧内压及有效面积随弹簧拉伸、压缩变形时与弹簧高度之间的变化关系。基于系统非线性模型创建了带附加气室空气弹簧系统动刚度理论模型。建立了系统动刚度实验测试系统,结合实验对系统动刚度理论模型进行了验证并分析了系统动刚度的影响因素。研究结果表明,空气弹簧初始气压的增加、振动频率的升高和振幅的增大均会增大系统动刚度；随节流孔开度的增大,系统动刚度由最大值逐渐减小到最小值；附加气室容积的增大也有利于降低系统的动刚度,但当附加气室容积超过弹簧容积2～3倍以后,附加气室容积的变化对系统动刚度的影响不再明显。动刚度理论计算结果与实验结果比较吻合,验证了动刚度理论模型的正确性。
3.为了简化模型,有利于对悬架系统的分析和控制,利用小偏差线性化的方法在小振幅的条件下对带附加气室空气弹簧系统的数学模型进行了线性化处理,分别获得了系统的动刚度线性化模型和系统线性运动微分方程,由线性微分方程得出了簧上质量位移传递函数。
4.基于复刚度建立了带附加气室空气弹簧系统的等效刚度、等效阻尼比以及固有频率的理论计算模型；构建了等效力学模型特性参数的实验测试系统,实验研究了节流孔开度、附加气室容积、簧上质量等因素对等效力学特性参数的影响关系,并对等效力学参数模型进行了验证。研究结果表明,附加气室容积为主气室容积2倍时,节流孔由小变大过程中,可以使系统等效刚度降低60%左右,系统固有频率降低0.45Hz,系统等效阻尼比呈现先增大后减小的趋势。附加气室容积的增大使得系统等效刚度和固有频率降低,但当附加气室容积大于主气室容积2～3倍后,附加气室容积的增大对系统的等效刚度和固有频率影响便不再明显。当节流孔完全打开时,增大附加气室容积只略微增大系统等效阻尼比,当节流孔开度处在最大阻尼状态时,增大附加气室容积可明显增大系统的等效阻尼比。在保持空气弹簧静态工作高度不变的前提下,增加簧上质量会增大弹簧等效刚度,但簧上质量的变化对弹簧的等效阻尼比和固有频率影响不大。比较理论计算结果和实验结果表明,系统等效刚度、等效阻尼比和固有频率的计算模型在一定范围内保持了较高的精度。
5.构建了带附加气室空气弹簧振动响应特性实验系统,实验研究了节流孔直径、附加气室容积以及激振频率对振动系统的位移传递率、最大动载荷以及簧上质量响应加速度的影响。实验结果表明,节流孔直径由小到大的变化过程中,系统在共振频率点的位移传递率、最大动载荷和响应加速度均方根值的变化规律基本相同,三者均首先迅速降低,在节流孔直径d=6mm左右,降低到最小值,之后随节流孔继续增大,各指标又开始缓慢回升。改变附加气室容积对系统的位移传递率、动载荷及响应加速度也具有显著的影响,在附加气室容积小于主气室容积2倍的范围之内时,附加气室容积的增大能够显著降低系统在共振频率点的位移传递率、加速度均方根值以及最大动载荷,但当附加气室容积超过主气室容积2倍时,附加气室容积的增大对以上三个指标的影响不再明显。
6.提出并分析了带附加气室被动空气悬架和半主动空气悬架的设计方案。建立了刚度、阻尼可调半主动空气悬架1／4车辆振动模型,基于振动模型在Matlab／Simuink环境下建立了车辆平顺性仿真模型,通过在不同路面和不同车速下仿真,比较分析了带附加气室刚度、阻尼可调半主动空气悬架与传统无附加气室被动空气悬架的平顺性性能指标。研究结果表明,通过适当调节节流孔开度和减振器阻尼系数,带附加气室刚度、阻尼可调半主动空气悬架在大多路况下能够降低车身加速度均方根值30%以上,在保证有效降低车身加速度的前提下,对动载荷的改善并不明显.
通过本课题的研究,可以进一步完善带附加气室空气悬架动力学理论体系,为带附加气室空气悬架系统的设计和控制提供理论依据和技术支持,对促进带附加气室空气弹簧系统在车辆减振系统中的应用,改善车辆悬架系统的减振性能具有重要的理论意义和实用价值。
Although the suspensions with air springs as their elastic elements have many advantages, the performance of suspension would be further improved if an auxiliary chamber is appended to air spring. Not only for the road vehicles, but for the off-road vehicles such as agriculture vehicles, construction vehicles, forestry vehicles, the application of air suspension to them would help to improve their adapting ability to running road condition and working environment.
Based on 1T15M-2 type diaphragm air spring produced by Firestone company, the air spring with auxiliary chamber system was established through a tube and a orifice. According to related studies at home and abroad in present, the dynamic characteristics of air spring with auxiliary chamber system was systematically researched using the methods of theoretical analysis combining with experiments, and influential factors and influential laws on the system's dynamic characteristics have been analyzed in detailed, and design schemes of air suspension with auxiliary chamber system were presented. The completed work and achieved results are generalized as follows:
1. The non-linear dynamics theoretical model of air spring with auxiliary chamber was established based on rigid dynamics, thermodynamics and fluid dynamics. Simulation model of system was established under Matlab/Simulink environment. Displacement step respond characteristics and amplitude frequency characteristics of the system were simulating analyzed. The results showed that, natural frequency of the system would be reduced under the function of auxiliary chamber, and vibration of the system would be greatly attenuated by properly adjusting the open size of orifice.
2. Relation between static stiffness of air spring and air spring deformation and relation between effective area of air spring and air spring deformation were established according to the static characteristics experiments. The dynamic stiffness theoretical model of system was established, and the experimental system for dynamic stiffness of system was established. The dynamic stiffness theoretical model was verified to be correct by experiments, and the influential factors on dynamic stiffness were analyzed. The results showed that, dynamic stiffness of system increases with the increasing of air spring pressure, vibration frequency and vibration amplitude, and dynamic stiffness of system drops from the maximum to minimum with the increasing of orifice diameter. Increasing volume of auxiliary chamber is help to decrease dynamic stiffness of system, but when the volume of auxiliary is more 2-3 times than that of air spring, changing volume of auxiliary chamber has little affect on dynamic stiffness. The results of dynamic stiffness theoretical model and the results of experiments are close on the whole, which proved that dynamic stiffness theoretical model are correct.
3. In order to simply the model and help to analyze and control suspension, the mathematical model of air spring with auxiliary chamber system was linearized with small deviation linear method under the condition of little amplitude. The linear dynamic stiffness model of system and linear kinematics difference equation were obtained, and transfer function of sprung mass displacement was reduced from linear difference equation.
4. Effective stiffness calculating model, effective damp ratio calculating model and natural frequency calculating model of air spring with auxiliary chamber system were established based on complex stiffness. Test system for mechanical parameters of effective model was established, and the influential laws of orifice open, auxiliary chamber volume, sprung mass on the mechanical parameters of effective model, at the same time the effective mechanical parameters calculating models were verified by test. The study results showed that, when the volume of auxiliary chamber was 2 times that of air spring, with the increasing of orifice open, effective stiffness of system could be decreased by 60%, and natural frequency could be decrease by 0.45Hz, and effective damp ratio was increased first, then decreased. By increasing volume of auxiliary chamber can decrease effective stiffness and natural frequency, but when the volume of auxiliary chamber was more than 2-3 times that of air spring, increasing volume of auxiliary chamber has little effect on effective stiffness and natural frequency of system. When orifice open widely, by increasing the volume of auxiliary chamber only increased damp ratio of system a little, while orifice open at the condition of maximum damp, by increasing volume of auxiliary chamber could obviously increased effective damp ratio of system. Keeping the static operational high of air spring unchanged, effective stiffness would increase with the increasing of sprung mass, but the change of sprung mass has little effect on effective damp ratio and natural frequency of system. Comparing calculation results of model with test results showed that the calculation model of effective stiffness, effective damp ration and natural frequency keep a high accuracy within a certain limit range.
5. Experimental system for vibration response characteristic of air spring with auxiliary chamber was established, Effect of orifice diameter, volume of auxiliary chamber and excitation frequency on displacement transmissibility, maximum dynamic load and response acceleration was studied by experiments. Experiments showed that, during the course of increasing orifice open from close to wide, the change laws of displacement transmissibility, maximum dynamic load and response acceleration of system were about the same, they all fell rapidly at first, they fell to the minimum value when orifice diameter increase to about 6mm, and then they all increased slowly with the continue increase of orifice diameter. Change of auxiliary chamber volume also has obvious effect on displacement transmissibility, maximum dynamic load and response acceleration of system. By increasing volume of auxiliary chamber could depress the tree indexes mentioned above, but when the volume of auxiliary chamber was more than 2 times that of air spring, increase of auxiliary chamber has little effect on the tree indexes.
6. Design schemes of passive air suspension with auxiliary chamber and semi-active air suspension with auxiliary were presented and analyzed. A quarter-vehicle vibration model with adjustable stiffness and adjustable damp suspension was established, and the simulation model for vehicle ride was established under Matlab/Simulink environment based on the vibration model. Ride performance indexes of passive air suspension and semi-active suspension with adjustable stiffness and adjustable damp were compared and analyzed through simulation of vehicle running on different pavements with different velocity. The results showed that, acceleration root mean square vehicle body with semi-active suspension increased more than 30% on the most pavements. But the dynamic load of tire has little improvement under the precondition of effectively decreasing acceleration of vehicle body.
Through the research in this project, the dynamics theory system of air spring with auxiliary chamber will be further improved, which will provide a theoretical basis and technical support for design and control of air suspension with auxiliary chamber. And this research is of important theoretical significance and practical value to promote the application of air spring with auxiliary chamber system to vehicle and to improve the performance of vehicle suspension system.
本文以Firestone公司生产的1T15M-2膜式空气弹簧为弹性元件,通过管路和节流孔接入附加气室建立了带附加气室空气弹簧系统。结合目前国内外相关的研究结论,利用理论分析与实验相结合的方法对带附加气室空气弹簧系统的动力学特性进行了系统地研究,对此系统动力学特性的影响因素和影响规律进行了详细地分析,分析了带附加气室空气悬架的设计方案。所完成的工作及取得的结论归纳如下：
1.基于刚体动力学、热力学及空气动力学理论建立了带附加气室空气弹簧系统的非线性动力学理论模型,在Matlab／Simulink环境下建立了系统振动仿真模型,仿真分析了不同节流孔开度和不同附加气室容积下系统簧上质量位移阶跃响应特性和位移幅频响应特性。仿真结果表明,附加气室能够显著降低系统固有频率,合理设置节流孔开度可以有效衰减振动。
2.通过空气弹簧静特性实验建立了空气弹簧静刚度、空气弹簧内压及有效面积随弹簧拉伸、压缩变形时与弹簧高度之间的变化关系。基于系统非线性模型创建了带附加气室空气弹簧系统动刚度理论模型。建立了系统动刚度实验测试系统,结合实验对系统动刚度理论模型进行了验证并分析了系统动刚度的影响因素。研究结果表明,空气弹簧初始气压的增加、振动频率的升高和振幅的增大均会增大系统动刚度；随节流孔开度的增大,系统动刚度由最大值逐渐减小到最小值；附加气室容积的增大也有利于降低系统的动刚度,但当附加气室容积超过弹簧容积2～3倍以后,附加气室容积的变化对系统动刚度的影响不再明显。动刚度理论计算结果与实验结果比较吻合,验证了动刚度理论模型的正确性。
3.为了简化模型,有利于对悬架系统的分析和控制,利用小偏差线性化的方法在小振幅的条件下对带附加气室空气弹簧系统的数学模型进行了线性化处理,分别获得了系统的动刚度线性化模型和系统线性运动微分方程,由线性微分方程得出了簧上质量位移传递函数。
4.基于复刚度建立了带附加气室空气弹簧系统的等效刚度、等效阻尼比以及固有频率的理论计算模型；构建了等效力学模型特性参数的实验测试系统,实验研究了节流孔开度、附加气室容积、簧上质量等因素对等效力学特性参数的影响关系,并对等效力学参数模型进行了验证。研究结果表明,附加气室容积为主气室容积2倍时,节流孔由小变大过程中,可以使系统等效刚度降低60%左右,系统固有频率降低0.45Hz,系统等效阻尼比呈现先增大后减小的趋势。附加气室容积的增大使得系统等效刚度和固有频率降低,但当附加气室容积大于主气室容积2～3倍后,附加气室容积的增大对系统的等效刚度和固有频率影响便不再明显。当节流孔完全打开时,增大附加气室容积只略微增大系统等效阻尼比,当节流孔开度处在最大阻尼状态时,增大附加气室容积可明显增大系统的等效阻尼比。在保持空气弹簧静态工作高度不变的前提下,增加簧上质量会增大弹簧等效刚度,但簧上质量的变化对弹簧的等效阻尼比和固有频率影响不大。比较理论计算结果和实验结果表明,系统等效刚度、等效阻尼比和固有频率的计算模型在一定范围内保持了较高的精度。
5.构建了带附加气室空气弹簧振动响应特性实验系统,实验研究了节流孔直径、附加气室容积以及激振频率对振动系统的位移传递率、最大动载荷以及簧上质量响应加速度的影响。实验结果表明,节流孔直径由小到大的变化过程中,系统在共振频率点的位移传递率、最大动载荷和响应加速度均方根值的变化规律基本相同,三者均首先迅速降低,在节流孔直径d=6mm左右,降低到最小值,之后随节流孔继续增大,各指标又开始缓慢回升。改变附加气室容积对系统的位移传递率、动载荷及响应加速度也具有显著的影响,在附加气室容积小于主气室容积2倍的范围之内时,附加气室容积的增大能够显著降低系统在共振频率点的位移传递率、加速度均方根值以及最大动载荷,但当附加气室容积超过主气室容积2倍时,附加气室容积的增大对以上三个指标的影响不再明显。
6.提出并分析了带附加气室被动空气悬架和半主动空气悬架的设计方案。建立了刚度、阻尼可调半主动空气悬架1／4车辆振动模型,基于振动模型在Matlab／Simuink环境下建立了车辆平顺性仿真模型,通过在不同路面和不同车速下仿真,比较分析了带附加气室刚度、阻尼可调半主动空气悬架与传统无附加气室被动空气悬架的平顺性性能指标。研究结果表明,通过适当调节节流孔开度和减振器阻尼系数,带附加气室刚度、阻尼可调半主动空气悬架在大多路况下能够降低车身加速度均方根值30%以上,在保证有效降低车身加速度的前提下,对动载荷的改善并不明显.
通过本课题的研究,可以进一步完善带附加气室空气悬架动力学理论体系,为带附加气室空气悬架系统的设计和控制提供理论依据和技术支持,对促进带附加气室空气弹簧系统在车辆减振系统中的应用,改善车辆悬架系统的减振性能具有重要的理论意义和实用价值。
Although the suspensions with air springs as their elastic elements have many advantages, the performance of suspension would be further improved if an auxiliary chamber is appended to air spring. Not only for the road vehicles, but for the off-road vehicles such as agriculture vehicles, construction vehicles, forestry vehicles, the application of air suspension to them would help to improve their adapting ability to running road condition and working environment.
Based on 1T15M-2 type diaphragm air spring produced by Firestone company, the air spring with auxiliary chamber system was established through a tube and a orifice. According to related studies at home and abroad in present, the dynamic characteristics of air spring with auxiliary chamber system was systematically researched using the methods of theoretical analysis combining with experiments, and influential factors and influential laws on the system's dynamic characteristics have been analyzed in detailed, and design schemes of air suspension with auxiliary chamber system were presented. The completed work and achieved results are generalized as follows:
1. The non-linear dynamics theoretical model of air spring with auxiliary chamber was established based on rigid dynamics, thermodynamics and fluid dynamics. Simulation model of system was established under Matlab/Simulink environment. Displacement step respond characteristics and amplitude frequency characteristics of the system were simulating analyzed. The results showed that, natural frequency of the system would be reduced under the function of auxiliary chamber, and vibration of the system would be greatly attenuated by properly adjusting the open size of orifice.
2. Relation between static stiffness of air spring and air spring deformation and relation between effective area of air spring and air spring deformation were established according to the static characteristics experiments. The dynamic stiffness theoretical model of system was established, and the experimental system for dynamic stiffness of system was established. The dynamic stiffness theoretical model was verified to be correct by experiments, and the influential factors on dynamic stiffness were analyzed. The results showed that, dynamic stiffness of system increases with the increasing of air spring pressure, vibration frequency and vibration amplitude, and dynamic stiffness of system drops from the maximum to minimum with the increasing of orifice diameter. Increasing volume of auxiliary chamber is help to decrease dynamic stiffness of system, but when the volume of auxiliary is more 2-3 times than that of air spring, changing volume of auxiliary chamber has little affect on dynamic stiffness. The results of dynamic stiffness theoretical model and the results of experiments are close on the whole, which proved that dynamic stiffness theoretical model are correct.
3. In order to simply the model and help to analyze and control suspension, the mathematical model of air spring with auxiliary chamber system was linearized with small deviation linear method under the condition of little amplitude. The linear dynamic stiffness model of system and linear kinematics difference equation were obtained, and transfer function of sprung mass displacement was reduced from linear difference equation.
4. Effective stiffness calculating model, effective damp ratio calculating model and natural frequency calculating model of air spring with auxiliary chamber system were established based on complex stiffness. Test system for mechanical parameters of effective model was established, and the influential laws of orifice open, auxiliary chamber volume, sprung mass on the mechanical parameters of effective model, at the same time the effective mechanical parameters calculating models were verified by test. The study results showed that, when the volume of auxiliary chamber was 2 times that of air spring, with the increasing of orifice open, effective stiffness of system could be decreased by 60%, and natural frequency could be decrease by 0.45Hz, and effective damp ratio was increased first, then decreased. By increasing volume of auxiliary chamber can decrease effective stiffness and natural frequency, but when the volume of auxiliary chamber was more than 2-3 times that of air spring, increasing volume of auxiliary chamber has little effect on effective stiffness and natural frequency of system. When orifice open widely, by increasing the volume of auxiliary chamber only increased damp ratio of system a little, while orifice open at the condition of maximum damp, by increasing volume of auxiliary chamber could obviously increased effective damp ratio of system. Keeping the static operational high of air spring unchanged, effective stiffness would increase with the increasing of sprung mass, but the change of sprung mass has little effect on effective damp ratio and natural frequency of system. Comparing calculation results of model with test results showed that the calculation model of effective stiffness, effective damp ration and natural frequency keep a high accuracy within a certain limit range.
5. Experimental system for vibration response characteristic of air spring with auxiliary chamber was established, Effect of orifice diameter, volume of auxiliary chamber and excitation frequency on displacement transmissibility, maximum dynamic load and response acceleration was studied by experiments. Experiments showed that, during the course of increasing orifice open from close to wide, the change laws of displacement transmissibility, maximum dynamic load and response acceleration of system were about the same, they all fell rapidly at first, they fell to the minimum value when orifice diameter increase to about 6mm, and then they all increased slowly with the continue increase of orifice diameter. Change of auxiliary chamber volume also has obvious effect on displacement transmissibility, maximum dynamic load and response acceleration of system. By increasing volume of auxiliary chamber could depress the tree indexes mentioned above, but when the volume of auxiliary chamber was more than 2 times that of air spring, increase of auxiliary chamber has little effect on the tree indexes.
6. Design schemes of passive air suspension with auxiliary chamber and semi-active air suspension with auxiliary were presented and analyzed. A quarter-vehicle vibration model with adjustable stiffness and adjustable damp suspension was established, and the simulation model for vehicle ride was established under Matlab/Simulink environment based on the vibration model. Ride performance indexes of passive air suspension and semi-active suspension with adjustable stiffness and adjustable damp were compared and analyzed through simulation of vehicle running on different pavements with different velocity. The results showed that, acceleration root mean square vehicle body with semi-active suspension increased more than 30% on the most pavements. But the dynamic load of tire has little improvement under the precondition of effectively decreasing acceleration of vehicle body.
Through the research in this project, the dynamics theory system of air spring with auxiliary chamber will be further improved, which will provide a theoretical basis and technical support for design and control of air suspension with auxiliary chamber. And this research is of important theoretical significance and practical value to promote the application of air spring with auxiliary chamber system to vehicle and to improve the performance of vehicle suspension system.
引文
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