压电式高频疲劳试验机的设计理论与试验研究
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摘要
交变载荷作用下零部件的主要失效形式为疲劳破坏。目前，国内外预防疲劳破坏的主要有效手段是进行构件材料或者零部件的疲劳试验，测试其抗疲劳断裂性能，绘制S-N曲线，分析、计算其疲劳寿命。目前国内外已有的两大类疲劳试验机即电磁驱动型和电液伺服型，由于受系统阻抗与磁阻的限制，一般工作频率不大于200Hz，同时普遍存在振幅控制性差、共振稳定性不好、加载精度不高等问题，均不适用于对微小与硬脆材料零件、高频受力构件的疲劳检测。随着工业与科技的发展，工作在高频、小振幅受力工况下的微小、硬脆机械零部件的使用逐渐增多，这使得能够模仿小振幅、高速受载工况的、并具有较高检测效率的疲劳试验机的研发变得日益重要。
本文结合国家自然科学基金项目《压电驱动式高频疲劳试验机构设计理论与性能试验研究》，采用压电振子作为驱动元件，利用系统共振的方法，研制了适用于工作在高频、小振幅受力工况下的微小与硬脆零部件的压电式高频疲劳试验机（以下简称“压电疲劳机”），并进行了相关的设计理论、动力学分析、仿真、和样机实测的研究，内容如下：
1.基于弹性材料的板壳理论，建立了圆周固支条件下圆形双晶片压电振子的振动模型，求解了其一阶振动模态和所对应的固有频率；应用有限元软件对压电振子进行了模态分析；应用阻抗分析仪实测了压电振子的阻抗特性以获得其固有频率，比较了上述三个结果，验证了理论建模的合理性与求解的正确性。
2.应用集中质量法建立了压电疲劳机的动力学模型，并根据牛顿第二定律，建立了其机械系统的运动微分方程组，求解了其稳态响应；确定了板弹簧的参数设计原则，即在满足机械强度要求的前提下，它应具有很好的弹性和较小的刚度；由算例得知，426Hz和829Hz这两个频率为振型转换频率，它们的数值由机架的各个零部件参数（尺寸参数、位置参数）所决定。当工作频率低于426Hz时，压电疲劳机以主振型工作，当工作频率与这两个数值相等时，机架将产生较大的振动，而弹性加载器-试样系统则不受力或者只能受到较小的作用力。所以在选择弹性加载器质量、板弹簧刚度和试件刚度时，应尽量使主振型的工作频率偏离振型转换频率远些。
3.按一定的结构参数建立了压电疲劳机的实体模型与有限元模型，求解了各阶振动模态和所对应的固有频率，确定了第14阶振动模态为压电疲劳机工作的主振型，其所对应的工作频率为330.4Hz；通过改变压电疲劳机主要零部件的9个参数，研究了这些参数的变化对其主振型固有频率的影响、变化规律和原因，结果表明：压电振子金属基板厚度、板弹簧厚度、弹性加载器质量的增加以及金属基板直径的减小，都会引起主振型固频率显著地变大；设置输入165V、主振型工作频率为330.4Hz左右（330.0Hz至330.9Hz）的交变电压，对压电疲劳机进行了谐响应分析，验证了当其以主振型频率工作时，试件受载稳定，同时机架振幅不大。
4.试制了多种参数的零部件，装配了3台样机，改变样机主要零部件的9个参数，分别测试样机在六个不同驱动电压下施加在试件上的最大动载荷，分析这些参数的变化对施加在试件上的最大动载荷的影响、变化规律和原因。由实测结果可知，施加在试件上的最大动载荷，随着弹性加载器的质量增加而变大；随着驱动电压的增大而变大。可以通过调节上述两个参数，以满足按照疲劳试验载荷水平表，使压电疲劳机向试件施加不同载荷的要求。
5.以材料为HT100的试件为例，应用本文制成的样机对其进行循环特性为R=0.1的拉伸疲劳测试，工作频率为352.4Hz。绘制了HT100的S-N曲线，得到了其1.18×10~8循环周次的疲劳极限为23.049MPa；应用扫描电镜观察了疲劳断裂的HT100试件断口形貌,分析了裂纹源、裂纹扩展以及瞬断的微观情况。设计制成的样机满足对微小与硬脆构件进行疲劳试验所需的小幅和高频加载、共振稳定可靠、抗干扰能力强等要求。
6.设计制造了一台由矩形单晶片压电振子驱动，可提供微小载荷、高频率、高精度，适用于小尺度材料进行疲劳检测的压电式微小载荷疲劳试验机，并以蜻蜓翅翼为试样，对其施加给定循环特性R=0.1的33组交变应力，加载精度为0.01N，工作频率为207.4Hz。通过对试验过程中拍摄的图片和录制的视频分析了蜻蜓翅翼由于疲劳破坏所引起的一系列裂口产生、扩展的机理，其疲劳破坏裂口会首先出现在蜻蜓翅翼前缘脉或者后缘脉的附近部位，并随着循环载荷次数的增加而扩展。翅膜对裂口扩展几乎没有抵抗力；而翅脉则可以明显减缓甚至阻止裂口的扩展。设计制成的样机满足对小尺度材料进行疲劳试验所需的载荷小、加载精度高、工作稳定的要求。
The main failure mode of the parts under alternating load is fatigue failure. Currently,the main effective mean to prevent fatigue failure of materials or parts is carrying out fatiguetest on the subject, getting subject’s anti-fatigue fracture property, and getting the S-N curveto calculate its fatigue life. Now, there are two kinds of fatigue testing machine: fatiguetesting machine driven by electromagnetic and fatigue testing machine driven byelectro-hydraulic servo. Due to the restriction of system’s impedance and reluctance, theoperating frequency of them is lower than200Hz generally. Meanwhile because of badamplitude controlling ability and resonance stabilization, low loading accuracy, the abovetwo fatigue testing machine are not suitable to do high frequency fatigue test on small andhard and brittle specimen. With the development of industry and technology, the applicationof small, hard and brittle mechanical parts in the condition of high frequency, smallamplitude stress gradually increases, which makes it more and more important to develop afatigue testing machine to test materials or parts with small amplitude, high frequency load.
The paper is based on the National Natural Science Foundation Project named “Thestructure design and performance research of piezoelectric high frequency fatigue testingmachine”. By using piezoelectric vibrator as the driving source and the method of systemresonance, a piezoelectric high frequency fatigue testing machine to test materials or partswith small amplitude, high frequency load is developed. The corresponding research ondesign theory, dynamic analysis and simulation and prototype measurement is carried out,the main contents are as following:
1. Based on shell theory of the elastic material, the vibration mode of the circularpiezoelectric bimorph vibrator is established, and the first order vibration modal and thecorresponding natural frequency is solved; Applying the finite element software to do themodal analysis of piezoelectric vibrator; Applying impedance analyzer to measure theimpedance characteristics of the piezoelectric vibrator in order to obtain its natural frequency,comparing the above three results to verify the reasonable theoretical model and the reasonable solving process.
2. Applying the lumped-mass method, the4-dof dynamic model of the piezoelectrichigh frequency fatigue testing machine is established. According to Newton second law, thesystem’s differential equation group of mechanical motion is established in the paper, thesteady-state response is solved, and the designing principle of the plate spring’s parameter isdetermined: based on meeting the strength requirements, it should have good flexibility andsoftness; it is concluded that426Hz and829Hz are modal conversion frequencies. Whenoperating frequency is below426Hz, the fatigue testing machine works in the main vibrationmode; When the operating frequency is close to these two values, the rack of the fatiguetesting machine produces a greater vibration, and the force loading on the elastic loader andspecimens force is low.
3. According to the structural parameters in Table4.3, the solid model of piezoelectrichigh frequency fatigue testing machine and the finite element model of prototype is built,and the vibration modals and the corresponding natural frequencies are solved. The14thvibration mode is determined as the main vibration for the fatigue testing machine whoseworking frequency is330.4Hz; By changing the parameters of the nine main components offatigue testing machine, the impaction of these different parameters on its main modalnatural frequency、vibration mode is researched. The result shows that when the thickness ofpiezoelectric vibrator’s metal substrate, plate spring and the mass of loader increase，thenatural frequency of main vibration mode changes significantly; When the input voltage is165V, the main vibration work frequency is330.4Hz (330.0Hz to330.9Hz), the harmonicresponse analysis on the machine is carried out. It is verified that when the fatigue testingmachine works in frequency of main vibration modal, the load on specimen is stable, andamplitude of the frame of fatigue testing machine is little.
4. Components with different parameters are made in the paper, and four prototypes areassembled. By changing nine parameters of the main components of the prototype, themaximum dynamic load on the specimen when prototypes work in six different drivingvoltages is obtained with a series tests, and the influence of different parameters onmaximum dynamic load acting on the specimen is analyzed. The measured results show thatthe maximum dynamic load acting on the specimen becomes larger as the increasing of themass of the elastic loader and the driving voltage. By adjusting the mass of the elastic loaderand the driving voltage, the different requirements of load acting on specimen is meetcorroding the requirements of load table of fatigue testing.
5. Using the prototype to carry out the tensile fatigue test for HT100under the cyclecharacteristic of R=0.1and the working frequency of352.4Hz. The S-N curve of HT100isdrawn, and the fatigue limit (23.049Mpa) is get under the cycle times of1.18×10~8. The microstructure of the fatigue fracture of HT100is observed by scanning electronicmicroscope, the crack source and momentary interruption, as well as the crack propagationare analyzed.
6. A fatigue testing machine driven by the single rectangular crystal piezoelectric isdesigned and manufactured in this paper. The prototype could provide small, high frequencyand precision load, and carry out fatigue test for small scale materials. Using the prototype,33groups of alternating stress is loaded on dragonfly with the cyclic characteristics R=0.1,the loading precision of0.01N and the working frequency of207.4Hz. Based on thepictures and videos in the test, the appearance and expansion mechanism of dragonfly wingscleft caused by fatigue is analyzed in the paper. The fatigue cleft appears in the position ofpostal vein or front vein of dragonfly wings at first, and then it expands with the increasingof loading cycle times. Wing membrane almost can’t prevent the cleft extending, but the veincan significantly slow down or stop the extension of the cleft.
本文结合国家自然科学基金项目《压电驱动式高频疲劳试验机构设计理论与性能试验研究》，采用压电振子作为驱动元件，利用系统共振的方法，研制了适用于工作在高频、小振幅受力工况下的微小与硬脆零部件的压电式高频疲劳试验机（以下简称“压电疲劳机”），并进行了相关的设计理论、动力学分析、仿真、和样机实测的研究，内容如下：
1.基于弹性材料的板壳理论，建立了圆周固支条件下圆形双晶片压电振子的振动模型，求解了其一阶振动模态和所对应的固有频率；应用有限元软件对压电振子进行了模态分析；应用阻抗分析仪实测了压电振子的阻抗特性以获得其固有频率，比较了上述三个结果，验证了理论建模的合理性与求解的正确性。
2.应用集中质量法建立了压电疲劳机的动力学模型，并根据牛顿第二定律，建立了其机械系统的运动微分方程组，求解了其稳态响应；确定了板弹簧的参数设计原则，即在满足机械强度要求的前提下，它应具有很好的弹性和较小的刚度；由算例得知，426Hz和829Hz这两个频率为振型转换频率，它们的数值由机架的各个零部件参数（尺寸参数、位置参数）所决定。当工作频率低于426Hz时，压电疲劳机以主振型工作，当工作频率与这两个数值相等时，机架将产生较大的振动，而弹性加载器-试样系统则不受力或者只能受到较小的作用力。所以在选择弹性加载器质量、板弹簧刚度和试件刚度时，应尽量使主振型的工作频率偏离振型转换频率远些。
3.按一定的结构参数建立了压电疲劳机的实体模型与有限元模型，求解了各阶振动模态和所对应的固有频率，确定了第14阶振动模态为压电疲劳机工作的主振型，其所对应的工作频率为330.4Hz；通过改变压电疲劳机主要零部件的9个参数，研究了这些参数的变化对其主振型固有频率的影响、变化规律和原因，结果表明：压电振子金属基板厚度、板弹簧厚度、弹性加载器质量的增加以及金属基板直径的减小，都会引起主振型固频率显著地变大；设置输入165V、主振型工作频率为330.4Hz左右（330.0Hz至330.9Hz）的交变电压，对压电疲劳机进行了谐响应分析，验证了当其以主振型频率工作时，试件受载稳定，同时机架振幅不大。
4.试制了多种参数的零部件，装配了3台样机，改变样机主要零部件的9个参数，分别测试样机在六个不同驱动电压下施加在试件上的最大动载荷，分析这些参数的变化对施加在试件上的最大动载荷的影响、变化规律和原因。由实测结果可知，施加在试件上的最大动载荷，随着弹性加载器的质量增加而变大；随着驱动电压的增大而变大。可以通过调节上述两个参数，以满足按照疲劳试验载荷水平表，使压电疲劳机向试件施加不同载荷的要求。
5.以材料为HT100的试件为例，应用本文制成的样机对其进行循环特性为R=0.1的拉伸疲劳测试，工作频率为352.4Hz。绘制了HT100的S-N曲线，得到了其1.18×10~8循环周次的疲劳极限为23.049MPa；应用扫描电镜观察了疲劳断裂的HT100试件断口形貌,分析了裂纹源、裂纹扩展以及瞬断的微观情况。设计制成的样机满足对微小与硬脆构件进行疲劳试验所需的小幅和高频加载、共振稳定可靠、抗干扰能力强等要求。
6.设计制造了一台由矩形单晶片压电振子驱动，可提供微小载荷、高频率、高精度，适用于小尺度材料进行疲劳检测的压电式微小载荷疲劳试验机，并以蜻蜓翅翼为试样，对其施加给定循环特性R=0.1的33组交变应力，加载精度为0.01N，工作频率为207.4Hz。通过对试验过程中拍摄的图片和录制的视频分析了蜻蜓翅翼由于疲劳破坏所引起的一系列裂口产生、扩展的机理，其疲劳破坏裂口会首先出现在蜻蜓翅翼前缘脉或者后缘脉的附近部位，并随着循环载荷次数的增加而扩展。翅膜对裂口扩展几乎没有抵抗力；而翅脉则可以明显减缓甚至阻止裂口的扩展。设计制成的样机满足对小尺度材料进行疲劳试验所需的载荷小、加载精度高、工作稳定的要求。
The main failure mode of the parts under alternating load is fatigue failure. Currently,the main effective mean to prevent fatigue failure of materials or parts is carrying out fatiguetest on the subject, getting subject’s anti-fatigue fracture property, and getting the S-N curveto calculate its fatigue life. Now, there are two kinds of fatigue testing machine: fatiguetesting machine driven by electromagnetic and fatigue testing machine driven byelectro-hydraulic servo. Due to the restriction of system’s impedance and reluctance, theoperating frequency of them is lower than200Hz generally. Meanwhile because of badamplitude controlling ability and resonance stabilization, low loading accuracy, the abovetwo fatigue testing machine are not suitable to do high frequency fatigue test on small andhard and brittle specimen. With the development of industry and technology, the applicationof small, hard and brittle mechanical parts in the condition of high frequency, smallamplitude stress gradually increases, which makes it more and more important to develop afatigue testing machine to test materials or parts with small amplitude, high frequency load.
The paper is based on the National Natural Science Foundation Project named “Thestructure design and performance research of piezoelectric high frequency fatigue testingmachine”. By using piezoelectric vibrator as the driving source and the method of systemresonance, a piezoelectric high frequency fatigue testing machine to test materials or partswith small amplitude, high frequency load is developed. The corresponding research ondesign theory, dynamic analysis and simulation and prototype measurement is carried out,the main contents are as following:
1. Based on shell theory of the elastic material, the vibration mode of the circularpiezoelectric bimorph vibrator is established, and the first order vibration modal and thecorresponding natural frequency is solved; Applying the finite element software to do themodal analysis of piezoelectric vibrator; Applying impedance analyzer to measure theimpedance characteristics of the piezoelectric vibrator in order to obtain its natural frequency,comparing the above three results to verify the reasonable theoretical model and the reasonable solving process.
2. Applying the lumped-mass method, the4-dof dynamic model of the piezoelectrichigh frequency fatigue testing machine is established. According to Newton second law, thesystem’s differential equation group of mechanical motion is established in the paper, thesteady-state response is solved, and the designing principle of the plate spring’s parameter isdetermined: based on meeting the strength requirements, it should have good flexibility andsoftness; it is concluded that426Hz and829Hz are modal conversion frequencies. Whenoperating frequency is below426Hz, the fatigue testing machine works in the main vibrationmode; When the operating frequency is close to these two values, the rack of the fatiguetesting machine produces a greater vibration, and the force loading on the elastic loader andspecimens force is low.
3. According to the structural parameters in Table4.3, the solid model of piezoelectrichigh frequency fatigue testing machine and the finite element model of prototype is built,and the vibration modals and the corresponding natural frequencies are solved. The14thvibration mode is determined as the main vibration for the fatigue testing machine whoseworking frequency is330.4Hz; By changing the parameters of the nine main components offatigue testing machine, the impaction of these different parameters on its main modalnatural frequency、vibration mode is researched. The result shows that when the thickness ofpiezoelectric vibrator’s metal substrate, plate spring and the mass of loader increase，thenatural frequency of main vibration mode changes significantly; When the input voltage is165V, the main vibration work frequency is330.4Hz (330.0Hz to330.9Hz), the harmonicresponse analysis on the machine is carried out. It is verified that when the fatigue testingmachine works in frequency of main vibration modal, the load on specimen is stable, andamplitude of the frame of fatigue testing machine is little.
4. Components with different parameters are made in the paper, and four prototypes areassembled. By changing nine parameters of the main components of the prototype, themaximum dynamic load on the specimen when prototypes work in six different drivingvoltages is obtained with a series tests, and the influence of different parameters onmaximum dynamic load acting on the specimen is analyzed. The measured results show thatthe maximum dynamic load acting on the specimen becomes larger as the increasing of themass of the elastic loader and the driving voltage. By adjusting the mass of the elastic loaderand the driving voltage, the different requirements of load acting on specimen is meetcorroding the requirements of load table of fatigue testing.
5. Using the prototype to carry out the tensile fatigue test for HT100under the cyclecharacteristic of R=0.1and the working frequency of352.4Hz. The S-N curve of HT100isdrawn, and the fatigue limit (23.049Mpa) is get under the cycle times of1.18×10~8. The microstructure of the fatigue fracture of HT100is observed by scanning electronicmicroscope, the crack source and momentary interruption, as well as the crack propagationare analyzed.
6. A fatigue testing machine driven by the single rectangular crystal piezoelectric isdesigned and manufactured in this paper. The prototype could provide small, high frequencyand precision load, and carry out fatigue test for small scale materials. Using the prototype,33groups of alternating stress is loaded on dragonfly with the cyclic characteristics R=0.1,the loading precision of0.01N and the working frequency of207.4Hz. Based on thepictures and videos in the test, the appearance and expansion mechanism of dragonfly wingscleft caused by fatigue is analyzed in the paper. The fatigue cleft appears in the position ofpostal vein or front vein of dragonfly wings at first, and then it expands with the increasingof loading cycle times. Wing membrane almost can’t prevent the cleft extending, but the veincan significantly slow down or stop the extension of the cleft.
引文
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