轮式阀微型压电泵的设计理论及试验研究
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摘要
微型压电泵的研究和发展已有三十多年的历史,随着新材料、新工艺的出现,压电泵的体积不断缩小、输出性能不断提高。近年来,部分微型压电泵已经开始产品化,并逐步地进入生物医药、精细化工、民用消费等各个领域,有着广泛的应用前景。然而,便携式微机电设备的蓬勃发展对微型压电泵产品提出了新的要求,特别是功耗、效率和寿命等。从国内外研究现状来看,微型压电泵的研究重心尚在结构的创新和输出性能的提升上,深入并系统地探讨微型压电泵工作原理、工作特性及其设计理论的研究并不多见。由于缺乏完善的理论指导,目前已形成产品的微型压电泵普遍功耗偏大,效率偏低。
本文结合国家高技术研究发展计划(863)项目“血糖检测与胰岛素注射微系统”(NO.2011AA040406)的技术要求,在微型化的前提下,通过对压电泵各部件及其系统工作原理和特性的分析,探明影响压电泵性能、功耗和效率的内在因素,为开发满足便携式微流体控制设备的微型压电泵产品提供理论与技术支撑。
压电振子是压电泵的动力元件,决定了压电泵的极限输出性能。而压电振子的驱动能力又由压电陶瓷决定,故压电陶瓷材料的选择十分重要。论文第二章通过比较各类压电陶瓷材料的电学特性和机械特性,决定选用兼有高耦合系数和高压电常数低功耗、大振幅的PZT5材料。有关圆形压电振子(以下简称压电振子)结构参数匹配和优化的理论计算方法已经比较成型,但由于计算过程涉及的参数过多,故实际应用困难。本文引入压电振子等效集中力的概念,将其直接与压电振子的输出力对应,并通过理论计算分别证明了压电振子中心点位移、等效集中力与驱动电压之间的线性关系,最终导出等效集中力与驱动电压的计算公式。利用压电振子中心点位移和等效集中力分别导出了压电泵极限流量及极限压力的表达式,并进一步得到了压电泵极限性能与电压的关系。在进行压电振子的优化设计时,其输出力和位移特性可作为压电振子驱动能力的直接评价标准。为了缩短压电振子的开发时间,降低开发成本,提出了一种可以很好地与理论计算结果相吻合的压电耦合有限元仿真方法,并通过试验测试对其准确性进行了评估,确定了该方法的可行性。
微阀是微型压电泵(以下简称压电泵)的关键流体控制元件,而微型被动截止阀在体积、成本和功耗等方面比其它形式的微阀更具优势。论文第三章通过比较常见微型被动截止阀的优缺点,最终选定轮式阀作为压电泵的微阀结构。首先对常用轮式阀的等效刚度进行了理论计算,并提出了可行的测量方法。随后对轮式阀的静态特性进行了分析,其中特别讨论了气液混合状态下轮式阀的临界开启压力和毛细作用引起的截止现象,毛细截止现象使压电泵具有完全截止能力,因而提高了压电泵的实用性。
由于阀座的存在,在交变压力的作用下,轮式阀阀片的运动状态在多数情况下为碰撞振动。试验发现,随着振动频率的增加,阀片与阀座的碰撞模式由滞留碰撞向非滞留碰撞转变。论文对该现象进行了理论分析,并明确了各碰撞模式发生的边界条件,推导了各碰撞模式下周期净流量和累计净流量的计算公式。研究表明,该公式反映的流量变化规律具有普遍性。
轮式阀工作时的能量损失大致可分为水头损失、碰撞损失和流量损失,其中水头损失与轮式阀及其安装结构有关,而碰撞损失与轮式阀的刚度、频率等因素相关。
论文第四章从吸程出流现象着手,通过理论和仿真分析证明了压电泵工作时除因泵腔容积变化引起的容积流外,压电振子对流体做功引起的惯性流对压电泵的输出流量亦有很大影响。在压电泵工作原理传统认识的基础上推导的流量计算公式,由于没有考虑这种影响,故计算结果与实际情况偏差较大。本文基于阀的过流特性提出了新的流量计算公式,计入了惯性流的影响,准确地表述了压电泵流量的变化趋势,与实验现象符合很好。
压电泵工作时,压电振子将电能转化为振动形式的机械能,而泵腔、阀等附属结构则将压电振子提供的机械能转化为流体流动的能量。若以电功率、机械功率及流动功率分别表述上述三种能量,则可认为在电功率不变的情况下,流动功率可作为评价压电泵工作效率的标准。流动功率可通过压电泵的压力-流量特性曲线直观地评价。同时,压力-流量的线性特征和变化规律表明压电泵的工作效率并不恒定,而与频率、负载及管路-系统特性有关。因此,除了最大程度地提高压电振子的机电转化效率、减小阀的工作损耗,还可以根据压力-流量特性和管路-系统特性调节压电泵的工作频率及驱动电压,使压电泵的工况点出现在压力-流量特性曲线的高效率点。
针对压电振子、被动截止阀和压电泵工作原理及特性的研究,为压电泵的设计提供了理论依据。论文第五章通过对压电泵驱动电压的试验研究,发现确如第二章所述,压电泵的输出流量和压力与驱动电压呈线性关系。而驱动波形的试验表明,与方波驱动相比,正弦波驱动时压电泵的工作效率更高。但考虑到方波驱动电路结构简单、效率高、易于微型化等优势,最终采用方波作为微型压电泵的驱动信号,并研制了微型、高效率的压电泵驱动电路。
根据轮式阀的工作特性及能量损耗因素,对轮式阀的刚度、阀片与阀孔的配合尺寸、预紧凸台的高度等结构参数进行了匹配,最终制成了包括驱动电路在内的,功耗仅为11mW的微型压电泵。其最大输出压力为30kPa,最大流量为25ml/min此外,第五章还对压电泵串联和并联时的输出特性进行了研究,并提出了压电泵串联和并联的选择依据和方法。
寿命测算是产品开发的重要环节,为了缩短压电泵产品的开发周期,根据压电泵产品的失效机理,论文第六章在实验室模拟环境下依据GB2689.1-81,应用定数截尾恒定应力加速寿命试验方法,对100台通过批量生产工艺制得的压电泵在加速应力水平下进行了3400小时的加速寿命试验,并采用GB2689.4-81规定的最好线性无偏估计法对试验数据进行了处理。结果表明,可靠度为0.95时,压电泵在正常应力水平下的寿命约为5800小时。
It has been over30years for research and development of micro-piezoelectric pump (take "micro-pump" for short) up to now. With the appearance of new materials and process, micro-pump dimensions have been reduced, and the output performances have been improved in the same time. Recently, some kinds of micro-pump have been produced as product, which goes to variance of application, e.g. biological medicine, fine chemicals, civil consumption and so on, with a bright future. However, new requirements are brought up with the rapid development of portal MEMS devices, especially the requirements of power consumption micro-pump, efficiency, lifetime, etc. Based on micro-pump research status home and aboard, the important point of study stays in the improvement for structure innovation and output performances. Systematical and deep study on the working principles, characteristics and design theory is rare. Because of lack of theoretical conduction, it's common to see high power consumption and low efficiency.
Combined with the technical specification of national high-tech research and development program (namely863program):MICRO SYSTEM OF BLOOD GLUCOSE DETECTION AND INSULIN INJECTION with the No.2011AA040406, in the premise of miniaturization, the internal factors for micro-pump performances, power consumption and efficiency are clarified through the analysis on all components, system working principles and characteristics of micro-pump, which are the theoretical and technical support for the development to satisfy the requirements of micro-pump products of portable micro fluid control devices.
Micro-pump, which determines the maximum output performance of micro-pump, is the driving element of the pump. And driving capacity is determined by the piezoelectric ceramics (PZT), which makes the choice for PZT very important. PZT5, with high coupling coefficient together with the piezoelectric constant of low power consumption, big amplitude, is chosen in the paper through the comparison of PZT electronic and mechanical characteristics in Chapter2. Regarding to the theoretical calculation methods of the round piezoelectric vibrator (take "piezo-vibrator" for short) structure parameter matching and optimization have been already mature, but too many parameters involved in the calculation makes the real application difficult. Piezo-vibrator equivalent fixate concept is introduced, which is corresponding with piezo-vibrator's output force directly. Through the theoretical calculation, the linear relationship among piezo-vibrator center point displacement, equivalent fixate and driving voltage is proved, and at last, the formula between equivalent fixate and driving voltage is educed. The expressions of maximum flow and maximum force of micro-pump are educed through piezo-vibrator center point displacement and equivalent fixates, and moreover, the relationship between limit performances and voltage are received. When it comes to the optimization for the piezo-vibrator, the output force and displacement characteristics can be the direct estimating index for the driving capacity. To reduce the development time for piezo-vibrator, and decrease the development cost in the same time, FEA simulation for electronic coupling which can well matched the theoretical calculation result is brought up. Furthermore, experiments are carried out to evaluate the veracity, and it turns out to be feasible.
The micro valve is the key control part in micro-pump. Micro passive cut-off valve has more advantages compared with other valves in dimension, cost and power consumption. Ultimately, wheel valve is chosen in the micro-pump as the micro valve through the advantages and disadvantages comparison of the common micro passive cut-off valve in Chapter3. Firstly, common wheel valve's equivalent rigidity is calculated in theory, and the feasible measurement methods are put forward. Then, statistic characteristics of wheel valve are analyzed, in particular, wheel valve critical working pressure and cut-off phenomena induced by capillarity, which is called capillarity cut-off phenomena are discussed. This phenomena guarantees complete cut-off capacity in micro-pump, which can increase micro-pump practicability.
Because of the existence of the valve sub-base, the motion status of wheel valve plate is vibro-impact in most instances. It turns out from the experiment that the impact mode of the valve sub-base and valve plate changes from retention collision to non-retention collision, which is analyzed in the paper in theory, and the boundary conditions of different impact modes are defined, periodic net flow and accumulated net flow expressions are educed in different impact modes. It indicates that the flow change rule shown in the expression is common through research.
During working, the energy loss of wheel valve can be divided into water head loss, collision loss and flow loss. Thereinto, water head loss is related with wheel valve and its mounting structure, and the collision loss is related with wheel valve rigidity, frequency, and so on.
It is found that there is cubage flow caused by pump chamber cubage change, and in addition, the inertia flow caused by the piezo-vibrator working on the fluid has big influence on the output flow, through theoretical and simulation analysis from Chapter4, starting from sucking outflow phenomena. The flow calculation formula educed from traditional micro-pump working principle has big deviation with the reality. Based on the valve overflow characteristics, new flow calculation formula is educed in this paper, and inertia flow is involved, so it expresses the micro-pump flow change tendency well and truly, which tallies with the experiment well.
The electrical energy is changed into mechanical energy in vibration form, which the pump chamber, valve and the accessory structure changes into the fluid's flow energy. Suppose electric power, mechanical power and flow power are used to express the three kinds of energy above, if the electric power has no change, flow power can be the criterion of the micro-pump working efficiency. The flow power can be estimated directly from the micro-pump pressure-flow characteristic curve. Meanwhile, the pressure-flow linear characteristic and change rule shows that the working frequency of micro-pump is not constant, but is related with the frequency, load and pipe-system characteristics. Therefore, except increase piezo-vibrator electromechanical transformation efficiency and decrease the valve working consumption into maximum extent, the micro-pump working frequency and driving voltage can be adjusted based on pressure-flow characteristics and pipe-system characteristics, to make the operating point appear in the maximum efficiency point of the pressure-flow characteristics'curve.
The research on piezo-vibrator, passive cut-off valve and micro-pump working principle and characteristics, has provided theoretical basis for high efficiency and low power consumption of the micro-pump. In Chapter5, experiments on micro-pump driving voltages are done, and the results are as stated in Chapter2, output flow and pressure have linear relationship with driving voltage. The driving waveform experiment indicates when it's sine wave the micro-pump is driven, it has higher working efficiency compared with square wave. However, since square wave drive electric circuit has the advantages of simple structure, high efficiency, easy to be miniaturized and so on, square wave is adopted as the driving signal of micro-pump finally, and miniaturized, low power consumption micro-pump driving circuit is developed.
Based on the factors of wheel valve working characteristics and energy consumption, the structure parameters like the rigidity of the wheel valve, the matching dimension between valve plate and valve hole, the height of the preload boss, are mated, in the end, micro-pump integrated with driving circuit, with the power consumption of11mW is made. The maximum output force is30kPa, and the maximum flow is25ml/min. Moreover, the output characteristics with the micro-pump in series and in parallel are studied in Chapter5, and the basis for the selection for in series and in parallel is introduced.
Lifetime test is an important part in product development, in order to shorten development time for micro-pump product, based on the failure mechanism of the micro-pump product,100micro-pumps manufactured in series production processes are tested in accelerated stress level for3400hours under accelerated life test with failure truncation constant-stress accelerated life test according to GB2689.1-81. The experimental data are analyzed with best linear unbiased estimation method regulated in GB2689.4-81. The result shows that the life time of the micro-pump under normal stress level is around5800hours with the reliability of0.95.
本文结合国家高技术研究发展计划(863)项目“血糖检测与胰岛素注射微系统”(NO.2011AA040406)的技术要求,在微型化的前提下,通过对压电泵各部件及其系统工作原理和特性的分析,探明影响压电泵性能、功耗和效率的内在因素,为开发满足便携式微流体控制设备的微型压电泵产品提供理论与技术支撑。
压电振子是压电泵的动力元件,决定了压电泵的极限输出性能。而压电振子的驱动能力又由压电陶瓷决定,故压电陶瓷材料的选择十分重要。论文第二章通过比较各类压电陶瓷材料的电学特性和机械特性,决定选用兼有高耦合系数和高压电常数低功耗、大振幅的PZT5材料。有关圆形压电振子(以下简称压电振子)结构参数匹配和优化的理论计算方法已经比较成型,但由于计算过程涉及的参数过多,故实际应用困难。本文引入压电振子等效集中力的概念,将其直接与压电振子的输出力对应,并通过理论计算分别证明了压电振子中心点位移、等效集中力与驱动电压之间的线性关系,最终导出等效集中力与驱动电压的计算公式。利用压电振子中心点位移和等效集中力分别导出了压电泵极限流量及极限压力的表达式,并进一步得到了压电泵极限性能与电压的关系。在进行压电振子的优化设计时,其输出力和位移特性可作为压电振子驱动能力的直接评价标准。为了缩短压电振子的开发时间,降低开发成本,提出了一种可以很好地与理论计算结果相吻合的压电耦合有限元仿真方法,并通过试验测试对其准确性进行了评估,确定了该方法的可行性。
微阀是微型压电泵(以下简称压电泵)的关键流体控制元件,而微型被动截止阀在体积、成本和功耗等方面比其它形式的微阀更具优势。论文第三章通过比较常见微型被动截止阀的优缺点,最终选定轮式阀作为压电泵的微阀结构。首先对常用轮式阀的等效刚度进行了理论计算,并提出了可行的测量方法。随后对轮式阀的静态特性进行了分析,其中特别讨论了气液混合状态下轮式阀的临界开启压力和毛细作用引起的截止现象,毛细截止现象使压电泵具有完全截止能力,因而提高了压电泵的实用性。
由于阀座的存在,在交变压力的作用下,轮式阀阀片的运动状态在多数情况下为碰撞振动。试验发现,随着振动频率的增加,阀片与阀座的碰撞模式由滞留碰撞向非滞留碰撞转变。论文对该现象进行了理论分析,并明确了各碰撞模式发生的边界条件,推导了各碰撞模式下周期净流量和累计净流量的计算公式。研究表明,该公式反映的流量变化规律具有普遍性。
轮式阀工作时的能量损失大致可分为水头损失、碰撞损失和流量损失,其中水头损失与轮式阀及其安装结构有关,而碰撞损失与轮式阀的刚度、频率等因素相关。
论文第四章从吸程出流现象着手,通过理论和仿真分析证明了压电泵工作时除因泵腔容积变化引起的容积流外,压电振子对流体做功引起的惯性流对压电泵的输出流量亦有很大影响。在压电泵工作原理传统认识的基础上推导的流量计算公式,由于没有考虑这种影响,故计算结果与实际情况偏差较大。本文基于阀的过流特性提出了新的流量计算公式,计入了惯性流的影响,准确地表述了压电泵流量的变化趋势,与实验现象符合很好。
压电泵工作时,压电振子将电能转化为振动形式的机械能,而泵腔、阀等附属结构则将压电振子提供的机械能转化为流体流动的能量。若以电功率、机械功率及流动功率分别表述上述三种能量,则可认为在电功率不变的情况下,流动功率可作为评价压电泵工作效率的标准。流动功率可通过压电泵的压力-流量特性曲线直观地评价。同时,压力-流量的线性特征和变化规律表明压电泵的工作效率并不恒定,而与频率、负载及管路-系统特性有关。因此,除了最大程度地提高压电振子的机电转化效率、减小阀的工作损耗,还可以根据压力-流量特性和管路-系统特性调节压电泵的工作频率及驱动电压,使压电泵的工况点出现在压力-流量特性曲线的高效率点。
针对压电振子、被动截止阀和压电泵工作原理及特性的研究,为压电泵的设计提供了理论依据。论文第五章通过对压电泵驱动电压的试验研究,发现确如第二章所述,压电泵的输出流量和压力与驱动电压呈线性关系。而驱动波形的试验表明,与方波驱动相比,正弦波驱动时压电泵的工作效率更高。但考虑到方波驱动电路结构简单、效率高、易于微型化等优势,最终采用方波作为微型压电泵的驱动信号,并研制了微型、高效率的压电泵驱动电路。
根据轮式阀的工作特性及能量损耗因素,对轮式阀的刚度、阀片与阀孔的配合尺寸、预紧凸台的高度等结构参数进行了匹配,最终制成了包括驱动电路在内的,功耗仅为11mW的微型压电泵。其最大输出压力为30kPa,最大流量为25ml/min此外,第五章还对压电泵串联和并联时的输出特性进行了研究,并提出了压电泵串联和并联的选择依据和方法。
寿命测算是产品开发的重要环节,为了缩短压电泵产品的开发周期,根据压电泵产品的失效机理,论文第六章在实验室模拟环境下依据GB2689.1-81,应用定数截尾恒定应力加速寿命试验方法,对100台通过批量生产工艺制得的压电泵在加速应力水平下进行了3400小时的加速寿命试验,并采用GB2689.4-81规定的最好线性无偏估计法对试验数据进行了处理。结果表明,可靠度为0.95时,压电泵在正常应力水平下的寿命约为5800小时。
It has been over30years for research and development of micro-piezoelectric pump (take "micro-pump" for short) up to now. With the appearance of new materials and process, micro-pump dimensions have been reduced, and the output performances have been improved in the same time. Recently, some kinds of micro-pump have been produced as product, which goes to variance of application, e.g. biological medicine, fine chemicals, civil consumption and so on, with a bright future. However, new requirements are brought up with the rapid development of portal MEMS devices, especially the requirements of power consumption micro-pump, efficiency, lifetime, etc. Based on micro-pump research status home and aboard, the important point of study stays in the improvement for structure innovation and output performances. Systematical and deep study on the working principles, characteristics and design theory is rare. Because of lack of theoretical conduction, it's common to see high power consumption and low efficiency.
Combined with the technical specification of national high-tech research and development program (namely863program):MICRO SYSTEM OF BLOOD GLUCOSE DETECTION AND INSULIN INJECTION with the No.2011AA040406, in the premise of miniaturization, the internal factors for micro-pump performances, power consumption and efficiency are clarified through the analysis on all components, system working principles and characteristics of micro-pump, which are the theoretical and technical support for the development to satisfy the requirements of micro-pump products of portable micro fluid control devices.
Micro-pump, which determines the maximum output performance of micro-pump, is the driving element of the pump. And driving capacity is determined by the piezoelectric ceramics (PZT), which makes the choice for PZT very important. PZT5, with high coupling coefficient together with the piezoelectric constant of low power consumption, big amplitude, is chosen in the paper through the comparison of PZT electronic and mechanical characteristics in Chapter2. Regarding to the theoretical calculation methods of the round piezoelectric vibrator (take "piezo-vibrator" for short) structure parameter matching and optimization have been already mature, but too many parameters involved in the calculation makes the real application difficult. Piezo-vibrator equivalent fixate concept is introduced, which is corresponding with piezo-vibrator's output force directly. Through the theoretical calculation, the linear relationship among piezo-vibrator center point displacement, equivalent fixate and driving voltage is proved, and at last, the formula between equivalent fixate and driving voltage is educed. The expressions of maximum flow and maximum force of micro-pump are educed through piezo-vibrator center point displacement and equivalent fixates, and moreover, the relationship between limit performances and voltage are received. When it comes to the optimization for the piezo-vibrator, the output force and displacement characteristics can be the direct estimating index for the driving capacity. To reduce the development time for piezo-vibrator, and decrease the development cost in the same time, FEA simulation for electronic coupling which can well matched the theoretical calculation result is brought up. Furthermore, experiments are carried out to evaluate the veracity, and it turns out to be feasible.
The micro valve is the key control part in micro-pump. Micro passive cut-off valve has more advantages compared with other valves in dimension, cost and power consumption. Ultimately, wheel valve is chosen in the micro-pump as the micro valve through the advantages and disadvantages comparison of the common micro passive cut-off valve in Chapter3. Firstly, common wheel valve's equivalent rigidity is calculated in theory, and the feasible measurement methods are put forward. Then, statistic characteristics of wheel valve are analyzed, in particular, wheel valve critical working pressure and cut-off phenomena induced by capillarity, which is called capillarity cut-off phenomena are discussed. This phenomena guarantees complete cut-off capacity in micro-pump, which can increase micro-pump practicability.
Because of the existence of the valve sub-base, the motion status of wheel valve plate is vibro-impact in most instances. It turns out from the experiment that the impact mode of the valve sub-base and valve plate changes from retention collision to non-retention collision, which is analyzed in the paper in theory, and the boundary conditions of different impact modes are defined, periodic net flow and accumulated net flow expressions are educed in different impact modes. It indicates that the flow change rule shown in the expression is common through research.
During working, the energy loss of wheel valve can be divided into water head loss, collision loss and flow loss. Thereinto, water head loss is related with wheel valve and its mounting structure, and the collision loss is related with wheel valve rigidity, frequency, and so on.
It is found that there is cubage flow caused by pump chamber cubage change, and in addition, the inertia flow caused by the piezo-vibrator working on the fluid has big influence on the output flow, through theoretical and simulation analysis from Chapter4, starting from sucking outflow phenomena. The flow calculation formula educed from traditional micro-pump working principle has big deviation with the reality. Based on the valve overflow characteristics, new flow calculation formula is educed in this paper, and inertia flow is involved, so it expresses the micro-pump flow change tendency well and truly, which tallies with the experiment well.
The electrical energy is changed into mechanical energy in vibration form, which the pump chamber, valve and the accessory structure changes into the fluid's flow energy. Suppose electric power, mechanical power and flow power are used to express the three kinds of energy above, if the electric power has no change, flow power can be the criterion of the micro-pump working efficiency. The flow power can be estimated directly from the micro-pump pressure-flow characteristic curve. Meanwhile, the pressure-flow linear characteristic and change rule shows that the working frequency of micro-pump is not constant, but is related with the frequency, load and pipe-system characteristics. Therefore, except increase piezo-vibrator electromechanical transformation efficiency and decrease the valve working consumption into maximum extent, the micro-pump working frequency and driving voltage can be adjusted based on pressure-flow characteristics and pipe-system characteristics, to make the operating point appear in the maximum efficiency point of the pressure-flow characteristics'curve.
The research on piezo-vibrator, passive cut-off valve and micro-pump working principle and characteristics, has provided theoretical basis for high efficiency and low power consumption of the micro-pump. In Chapter5, experiments on micro-pump driving voltages are done, and the results are as stated in Chapter2, output flow and pressure have linear relationship with driving voltage. The driving waveform experiment indicates when it's sine wave the micro-pump is driven, it has higher working efficiency compared with square wave. However, since square wave drive electric circuit has the advantages of simple structure, high efficiency, easy to be miniaturized and so on, square wave is adopted as the driving signal of micro-pump finally, and miniaturized, low power consumption micro-pump driving circuit is developed.
Based on the factors of wheel valve working characteristics and energy consumption, the structure parameters like the rigidity of the wheel valve, the matching dimension between valve plate and valve hole, the height of the preload boss, are mated, in the end, micro-pump integrated with driving circuit, with the power consumption of11mW is made. The maximum output force is30kPa, and the maximum flow is25ml/min. Moreover, the output characteristics with the micro-pump in series and in parallel are studied in Chapter5, and the basis for the selection for in series and in parallel is introduced.
Lifetime test is an important part in product development, in order to shorten development time for micro-pump product, based on the failure mechanism of the micro-pump product,100micro-pumps manufactured in series production processes are tested in accelerated stress level for3400hours under accelerated life test with failure truncation constant-stress accelerated life test according to GB2689.1-81. The experimental data are analyzed with best linear unbiased estimation method regulated in GB2689.4-81. The result shows that the life time of the micro-pump under normal stress level is around5800hours with the reliability of0.95.
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