罗渊(1991-), 男, 重庆大学硕士研究生, 研究方向为汽车振动噪声控制, (E-mail)
为了高效精确地识别复杂结构刚体的惯性参数,基于频响函数质量线法,设计了惯性参数识别试验装置。采用多体动力学仿真分析了系统刚度与阻尼、噪声、激励点坐标误差、响应点坐标误差、激励角度误差以及传感器安装角度误差对惯性参数识别精度的影响规律。借助搭建试验装置,对已知惯性参数的样件进行识别,惯性参数误差都在5%以内。表明基于频响函数质量线法的试验装置可以高效精确地识别复杂结构刚体的惯性参数。
In order to identify the inertia parameters of complex structure rigid body with high efficiency and accuracy, an identification test device was built based on the FRF mass line method. The influence of system stiffness and damping, noise, coordinate error of excitation point and response point, angle error of hammer excitation and sensor installation on the identification accuracy were obtained by multibody dynamics simulation. A rigid body with known inertia parameters was identified by the proposed device and the error was within 5%. It shows that the test device based on the FRF mass line method can identify inertial parameters of complex structure rigid body efficiently and accurately.
复杂结构刚体的惯性参数识别是对其进行动力学分析和控制的前提和关键[
频域法[
针对上述问题,笔者在频响函数质量线法识别刚体惯性参数的基础上,提出了一种惯性参数识别装置。将待测刚体固定于该装置的托盘上,对托盘进行频率响应测试,利用频响函数质量线法,实现刚体惯性参数的精确与高效识别。
待测刚体固定于托盘上,在微小振动下刚体与托盘没有相对位移,忽略弹簧刚度和阻尼的影响,则振动模型可简化为如
刚体与托盘六自由度振动模型
Six DOF vibration model of rigid body and pallet
在
式中:
将式(1)写成矩阵形式
式中:
假设在
式中:
将式(6)写成
式中:
当rank(
假设对
式中:矩阵
则当有
式中:
则
式(13)两边同时乘以
式中
令
式中只有质量矩阵
当求得质量矩阵
由于托盘惯性参数
用式(17)可计算得到待测刚体所有惯性参数
式中:c, d分别代表
惯性参数识别装置由托盘和支架构成,托盘通过6根弹簧与支架连接,用于承载和固定待测刚体。在Adams动力学软件中建立仿真模型,如
多体动力学模型
Multi-body dynamic model
模型主要结构参数如
模型参数
Model parameters
托盘质量/kg | 托盘外接圆直径/mm | 托盘厚度/mm | 弹簧数量 | 单根弹簧刚度/(N·m-1) | 单根弹簧阻尼/N·(m·s-1)-1 | 待测刚体质量/kg |
14.3 | 350 | 20 | 6 | 1 000 | 0 | 18.6 |
惯性参数试验识别结果
Inertia parameter identification result
识别结果 | 质量/kg | 质心/mm | 转动惯量/(g·m2) | 惯性积/(g·m2) | ||||||||
理论值 | 18.600 | 8.000 | 11.500 | 80.000 | 241.300 | 194.200 | 90.400 | 1.700 | 11.800 | 17.000 | ||
试验识别值 | 18.500 | 8.200 | 11.100 | 79.600 | 244.200 | 201.000 | 88.100 | 1.800 | 12.200 | 16.400 | ||
试验误差/% | -0.248 | 2.500 | -3.470 | -0.500 | 1.200 | 2.980 | -2.200 | 4.700 | -3.700 | -3.500 | ||
仿真识别值 | 18.598 | 8.000 | 11.502 | 80.000 | 241.250 | 194.160 | 90.386 | 1.701 | 11.798 | 17.003 | ||
仿真误差/% | -0.010 | 0.000 | 0.017 | 0.000 | 0.020 | -0.019 | -0.015 | 0.028 | -0.021 | 0.017 |
本文惯性参数识别方法忽略了悬置弹簧的刚度和阻尼的影响,为了验证识别方法的正确性,需分析弹簧刚度与弹簧阻尼的变化对惯性参数识别精度的影响规律。
弹簧刚度对识别精度的影响
Influence of stiffness on identification precision
弹簧阻尼对识别精度的影响
Influence of damping on identification precision
频率响应函数测量过程中,无论是激励端还是响应端都会存在噪声,噪声的存在会影响惯性参数识别精度。在激励信号中分别加入一定信噪比的白噪声,惯性参数识别误差与激励噪声的关系如
噪声对识别精度的影响
Influence of noise on identification precision
激励点坐标构成式(14)中
响应点坐标误差对识别精度的影响
Influence of response point coordinate error on identification precision
激励点坐标误差对识别精度的影响
Influence of excitation point coordinate error on identification precision
激励角度与传感器安装角度分别影响
激励角度误差对识别精度的影响
Influence of Excitation angle error on identification precision
传感器安装角度误差对识别精度的影响
Influence of sensor installation angle error on identification precision
由
按照2.1所述搭建试验台,其中每根拉伸弹簧在其弹性主轴方向的刚度为1 000±5 N/m,阻尼很小,可忽略不计。
式(16)采用最小二乘法,需满足条件rank(
待测刚体为一个表面平整光滑的长方体钢块,长为210 mm,宽为100 mm,高为160 mm,中部有直径为80 mm的通孔。将其固定于托盘上,力锤敲击托盘上的激励点,三向加速度传感器拾取托盘表面振动加速度信号,输入到多通道分析仪,得到加速度频响函数。试验及其设备如
惯性参数识别试验
Experiment of inertia parameter identification
试验测得所有激励点响应点的加速度频响函数,由于数据太多,只选取1个激励点1个响应点的数据作为说明,加速度频响函数如
频响函数与相干函数
Frequency response function and coherence function
为了减小噪声等因素的影响,在计算频带内选取10组不同频率下的数据进行平均,再用平均后的数据导入笔者编译的惯性参数识别程序进行计算。惯性参数试验识别结果如
基于频率响应函数质量线的惯性参数识别方法,设计了一种复杂结构刚体惯性参数识别装置,通过仿真与试验分析,得到以下结论:
1) 在满足支撑条件下,系统刚度和阻尼应尽可能小;激励噪声、激励点坐标误差、响应点坐标误差、激励
角度误差与传感器安装角度误差对惯性参数识别精度均有不同程度的影响,其中激励角度误差的影响最为严重。
2) 试验结果表明样件的最大惯性参数识别误差为4.7%,满足工程应用要求,验证了基于质量线法惯性参数识别试验装置的准确性。
3) 笔者基于质量线法的惯性参数识别装置适用于识别一切具有刚体特性物体的惯性参数,不受对象外形及结构限制,识别过程简单,识别精度高,为刚体动力学分析,优化设计等提供理论参考。
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