CN110728056A - Maximum current simulation test method for charging and discharging of lithium ion battery - Google Patents
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Abstract
本发明提出的一种锂离子电池充放电的最大电流仿真测试方法,包括建立与待测试电芯相符合的电芯电化学‑热耦合模型,以预设的放电电流对电芯电化学‑热耦合模型进行充放电;预设多个电荷节点,采集充放电过程中各电荷节点对应的充放电开始时刻电压值、充放电结束时刻电压值和最大充放电电流值;然后各电荷节点对应的充放电DCR值。本发明通过电芯电化学‑热耦合模型的建立,实现了通过模型仿真对锂离子电池充放电过程中最大电流的测试。通过本方法可以快速计算出电池在不同温度、不同SOC范围的最大充放电电流值,避开了实验不断尝试的过程,大幅降低实验数量级规模,保证了测试精度,并缩短了测试周期。
The present invention provides a maximum current simulation test method for charging and discharging lithium ion batteries, which includes establishing a cell electrochemical-thermal coupling model consistent with the cell to be tested, and using a preset discharge current to measure the electrochemical-thermal power of the cell The coupling model is used to charge and discharge; multiple charge nodes are preset, and the voltage value at the start of charge and discharge, the voltage value at the end of charge and discharge, and the maximum charge and discharge current value corresponding to each charge node during the charge and discharge process are collected; Discharge DCR value. The invention realizes the test of the maximum current in the charging and discharging process of the lithium ion battery through model simulation through the establishment of the electrochemical-thermal coupling model of the battery cell. This method can quickly calculate the maximum charge and discharge current values of the battery at different temperatures and different SOC ranges, avoid the process of continuous experimentation, greatly reduce the scale of the experiment, ensure the test accuracy, and shorten the test cycle.
Description
技术领域technical field
本发明涉及锂离子电池测试技术领域,尤其涉及一种锂离子电池充放电的最大电流仿真测试方法。The invention relates to the technical field of lithium ion battery testing, in particular to a maximum current simulation testing method for charging and discharging lithium ion batteries.
背景技术Background technique
一线整车企业对动力锂离子电池能量密度要求较高,一般要求整车具有500 公里以上续航里程。First-tier vehicle companies have higher requirements on the energy density of power lithium-ion batteries, and generally require the vehicle to have a cruising range of more than 500 kilometers.
因此,国外一线整车企业都要求使用正极材料为NCM811的三元动力锂离子电池,同时,对锂离子电池的功率map能力要求严格,需要对锂离子电池建立电化学-热耦合模型,在产品研发前预估电池不同SOC不同温度条件最大脉冲充放电上限电流和DCR。Therefore, foreign first-tier vehicle companies all require the use of ternary power lithium-ion batteries with NCM811 cathode material. At the same time, the power map capability of lithium-ion batteries is strictly required. It is necessary to establish an electrochemical-thermal coupling model for lithium-ion batteries. Before research and development, the maximum pulse charge and discharge upper limit current and DCR of the battery under different SOC and different temperature conditions were estimated.
现有技术中采用的测试方法,周期长,难以保证测试效率和生产效率。The testing method adopted in the prior art has a long period, and it is difficult to ensure testing efficiency and production efficiency.
发明内容SUMMARY OF THE INVENTION
基于背景技术存在的技术问题,本发明提出了一种锂离子电池充放电的最大电流仿真测试方法。Based on the technical problems existing in the background art, the present invention proposes a maximum current simulation test method for charging and discharging a lithium ion battery.
本发明提出的一种锂离子电池充放电的最大电流仿真测试方法,电池放电测试包括:The present invention proposes a maximum current simulation test method for charging and discharging lithium ion batteries. The battery discharge test includes:
S1、建立与待测试电芯相符合的电芯电化学-热耦合模型,将电芯电化学- 热耦合模型的温度设置为预设的第一测试温度,并将电芯电化学-热耦合模型调整到预设的充电上限值;S1. Establish a cell electrochemical-thermal coupling model consistent with the cell to be tested, set the temperature of the cell electrochemical-thermal coupling model to a preset first test temperature, and set the cell electrochemical-thermal coupling model The model is adjusted to the preset charging upper limit value;
S2、设置放电截止电压,并以预设的放电电流对电芯电化学-热耦合模型进行放电;S2, set the discharge cut-off voltage, and discharge the electrochemical-thermal coupling model of the battery cell with a preset discharge current;
S3、预设多个电荷节点,采集放电过程中各电荷节点对应的放电开始时刻电压值、放电结束时刻电压值和最大放电电流值;S3, preset a plurality of charge nodes, and collect the voltage value at the start of discharge, the voltage value at the end of discharge, and the maximum discharge current value corresponding to each charge node during the discharge process;
S4、根据放电开始时刻电压值、放电结束时刻电压值和最大放电电流值计算各电荷节点对应的放电DCR值;S4. Calculate the discharge DCR value corresponding to each charge node according to the voltage value at the start of discharge, the voltage value at the end of discharge and the maximum discharge current value;
电池充电测试包括:Battery charging tests include:
S5、建立与待测试电芯相符合的电芯电化学-热耦合模型,将电芯电化学- 热耦合模型的温度设置为预设的第二测试温度,并将电芯电化学-热耦合模型调整到预设的放电下限值;S5. Establish a cell electrochemical-thermal coupling model that is consistent with the cell to be tested, set the temperature of the cell electrochemical-thermal coupling model to a preset second test temperature, and set the cell electrochemical-thermal coupling model. The model is adjusted to the preset discharge lower limit value;
S6、设置充电截止电压,并以预设的充电电流对电芯电化学-热耦合模型进行充电;S6, setting the charging cut-off voltage, and charging the electrochemical-thermal coupling model of the battery cell with a preset charging current;
S7、采集充电过程中各电荷节点对应的充电开始时刻电压值、充电结束时刻电压值和最大充电电流值;S7, collecting the voltage value at the start of charging, the voltage value at the end of charging, and the maximum charging current value corresponding to each charge node in the charging process;
S8、根据充电开始时刻电压值、充电结束时刻电压值和最大充电电流值计算各电荷节点对应的充电DCR值。S8. Calculate the charging DCR value corresponding to each charge node according to the voltage value at the charging start time, the voltage value at the charging end time, and the maximum charging current value.
优选的,第一测试温度为:25℃或者40℃,第二测试温度为25℃或者40℃。Preferably, the first test temperature is 25°C or 40°C, and the second test temperature is 25°C or 40°C.
优选的,步骤S1和步骤S4中:均通过将待测试电芯正负极极片长度、宽度、厚度、面密度和压实密度输入到电化学模型中,建立电芯电化学-热耦合模型。Preferably, in step S1 and step S4: by inputting the length, width, thickness, areal density and compaction density of the positive and negative pole pieces of the cell to be tested into the electrochemical model, the electrochemical-thermal coupling model of the cell is established .
优选的,步骤S1中,以0.33C电流对电芯电化学-热耦合模型进行充电,直至电芯电化学-热耦合模型调整到预设的充电上限值。Preferably, in step S1, the electrochemical-thermal coupling model of the battery cell is charged with a current of 0.33 C until the electrochemical-thermal coupling model of the battery cell is adjusted to a preset charging upper limit value.
优选的,充电上限值为95%SOC。Preferably, the upper limit of charging is 95% SOC.
优选的,步骤S2中,放电截止电压为2.7V,放电电流为0.33C。Preferably, in step S2, the discharge cut-off voltage is 2.7V, and the discharge current is 0.33C.
优选的,步骤S3中,多个电荷节点分别为:5%SOC、20%SOC、35%SOC.50%SOC、65%SOC、80%SOC、95%SOC。Preferably, in step S3, the plurality of charge nodes are respectively: 5% SOC, 20% SOC, 35% SOC, 50% SOC, 65% SOC, 80% SOC, and 95% SOC.
优选的,步骤S4中,根据以下公式计算各电荷节点对应的放电DCR值:Preferably, in step S4, the discharge DCR value corresponding to each charge node is calculated according to the following formula:
放电DCR值=(放电开始时刻电压值-放电结束时刻电压值)/最大放电电流值;Discharge DCR value = (voltage value at the start of discharge - voltage value at the end of discharge)/maximum discharge current value;
步骤S8中,根据以下公式计算各电荷节点对应的充电DCR值:In step S8, the charging DCR value corresponding to each charge node is calculated according to the following formula:
充电DCR值=(充电开始时刻电压值-充电结束时刻电压值)/最大充电电流值。Charging DCR value=(voltage value at the time of charging start-voltage value at the end of charging)/maximum charging current value.
优选的,步骤S5中,放电下限值为5%SOC。Preferably, in step S5, the discharge lower limit value is 5% SOC.
优选的,步骤S6中,充电截止电压为4.25V,充电电流为0.33C。Preferably, in step S6, the charging cut-off voltage is 4.25V, and the charging current is 0.33C.
本发明提出的一种锂离子电池充放电的最大电流仿真测试方法,通过电芯电化学-热耦合模型的建立,实现了通过模型仿真对锂离子电池充放电过程中最大电流的测试。通过本方法可以快速计算出电池在不同温度、不同SOC范围的最大充放电电流值,避开了实验不断尝试的过程,大幅降低实验数量级规模,保证了测试精度,并缩短了测试周期。The present invention provides a method for simulating and testing the maximum current of lithium ion battery charging and discharging. Through the establishment of an electrochemical-thermal coupling model of the battery cell, the testing of the maximum current during the charging and discharging process of the lithium ion battery is realized through model simulation. The method can quickly calculate the maximum charge and discharge current values of the battery at different temperatures and different SOC ranges, avoid the process of continuous experimentation, greatly reduce the scale of the experiment, ensure the test accuracy, and shorten the test cycle.
附图说明Description of drawings
图1为本发明提出的一种锂离子电池充放电的最大电流仿真测试方法中电池放电测试流程图;Fig. 1 is a battery discharge test flow chart in a maximum current simulation test method for charging and discharging lithium-ion batteries proposed by the present invention;
图2为本发明提出的一种锂离子电池充放电的最大电流仿真测试方法中电池充电测试流程图。FIG. 2 is a flow chart of a battery charging test in a maximum current simulation test method for charging and discharging a lithium ion battery proposed by the present invention.
具体实施方式Detailed ways
参照图1,本发明提出的一种锂离子电池充放电的最大电流仿真测试方法,电池放电测试包括:1, the present invention proposes a maximum current simulation test method for charging and discharging a lithium-ion battery. The battery discharge test includes:
S1、建立与待测试电芯相符合的电芯电化学-热耦合模型,将电芯电化学- 热耦合模型的温度设置为预设的第一测试温度,并将电芯电化学-热耦合模型调整到预设的充电上限值。S1. Establish a cell electrochemical-thermal coupling model consistent with the cell to be tested, set the temperature of the cell electrochemical-thermal coupling model to a preset first test temperature, and set the cell electrochemical-thermal coupling model The model adjusts to the preset charging upper limit value.
具体的,本步骤中,通过将待测试电芯正负极极片长度、宽度、厚度、面密度和压实密度输入到电化学模型中,建立电芯电化学-热耦合模型。然后,以 0.33C电流对电芯电化学-热耦合模型进行充电,直至电芯电化学-热耦合模型调整到预设的充电上限值。Specifically, in this step, by inputting the length, width, thickness, areal density and compaction density of the positive and negative pole pieces of the cell to be tested into the electrochemical model, the electrochemical-thermal coupling model of the cell is established. Then, the electrochemical-thermal coupling model of the battery cell is charged with a current of 0.33C until the electrochemical-thermal coupling model of the battery cell is adjusted to the preset charging upper limit value.
充电上限值可设置为大于或等于95%SOC。The charge upper limit value can be set to be greater than or equal to 95% SOC.
S2、设置放电截止电压,并以预设的放电电流对电芯电化学-热耦合模型进行放电。具体的,本步骤中,放电电流小于或等于0.33C,以保证通过小电流给电芯电化学-热耦合模型放电,从而保证测试的精确,方便放电过程中数据的采集。S2, set the discharge cut-off voltage, and discharge the electrochemical-thermal coupling model of the battery cell with a preset discharge current. Specifically, in this step, the discharge current is less than or equal to 0.33C to ensure that the electrochemical-thermal coupling model of the cell is discharged through a small current, thereby ensuring the accuracy of the test and facilitating the collection of data during the discharge process.
S3、预设多个电荷节点,采集放电过程中各电荷节点对应的放电开始时刻电压值、放电结束时刻电压值和最大放电电流值。S3, preset a plurality of charge nodes, and collect the voltage value at the discharge start time, the voltage value at the discharge end time, and the maximum discharge current value corresponding to each charge node during the discharge process.
具体实施时,多个电荷节点可设置为:5%SOC、20%SOC、35%SOC.50%SOC、 65%SOC、80%SOC、95%SOC。In a specific implementation, the plurality of charge nodes may be set as: 5% SOC, 20% SOC, 35% SOC, 50% SOC, 65% SOC, 80% SOC, 95% SOC.
S4、根据放电开始时刻电压值、放电结束时刻电压值和最大放电电流值计算各电荷节点对应的放电DCR值。S4. Calculate the discharge DCR value corresponding to each charge node according to the voltage value at the discharge start time, the voltage value at the discharge end time, and the maximum discharge current value.
具体的,本步骤中,各电荷节点对应的放电DCR值的计算公式如下:Specifically, in this step, the calculation formula of the discharge DCR value corresponding to each charge node is as follows:
放电DCR值=(放电开始时刻电压值-放电结束时刻电压值)/最大放电电流值。Discharge DCR value=(voltage value at discharge start time-voltage value at discharge end time)/maximum discharge current value.
电池充电测试包括:Battery charging tests include:
S5、建立与待测试电芯相符合的电芯电化学-热耦合模型,将电芯电化学- 热耦合模型的温度设置为预设的第二测试温度,并将电芯电化学-热耦合模型调整到预设的放电下限值。本步骤中,通过将待测试电芯正负极极片长度、宽度、厚度、面密度和压实密度输入到电化学模型中,建立电芯电化学-热耦合模型。S5. Establish a cell electrochemical-thermal coupling model that is consistent with the cell to be tested, set the temperature of the cell electrochemical-thermal coupling model to a preset second test temperature, and set the cell electrochemical-thermal coupling model. The model adjusts to the preset discharge lower limit value. In this step, by inputting the length, width, thickness, areal density and compaction density of the positive and negative pole pieces of the cell to be tested into the electrochemical model, the electrochemical-thermal coupling model of the cell is established.
S6、设置充电截止电压,并以预设的充电电流对电芯电化学-热耦合模型进行充电。本步骤中,充电电流小于或等于0.33C,以保证通过小电流给电芯电化学-热耦合模型充电,从而方便充电过程中数据的采集。S6 , setting the charge cut-off voltage, and charging the electrochemical-thermal coupling model of the battery cell with a preset charging current. In this step, the charging current is less than or equal to 0.33C to ensure that the electrochemical-thermal coupling model of the cell is charged by a small current, thereby facilitating data collection during the charging process.
S7、采集充电过程中各电荷节点对应的充电开始时刻电压值、充电结束时刻电压值和最大充电电流值。S7: Collect the voltage value at the start of charging, the voltage value at the end of the charging, and the maximum charging current value corresponding to each charge node in the charging process.
S8、根据充电开始时刻电压值、充电结束时刻电压值和最大充电电流值计算各电荷节点对应的充电DCR值。S8. Calculate the charging DCR value corresponding to each charge node according to the voltage value at the charging start time, the voltage value at the charging end time, and the maximum charging current value.
计算各电荷节点对应的充电DCR值的公式如下:The formula for calculating the charging DCR value corresponding to each charge node is as follows:
充电DCR值=(充电开始时刻电压值-充电结束时刻电压值)/最大充电电流值。Charging DCR value=(voltage value at the time of charging start-voltage value at the end of charging)/maximum charging current value.
如此,本实施方式通过电芯电化学-热耦合模型的建立,实现了通过模型仿真对锂离子电池充放电过程中最大电流的测试。通过本方法可以快速计算出电池在不同温度、不同SOC范围的最大充放电电流值,避开了实验不断尝试的过程,大幅降低实验数量级规模,保证了测试精度,并缩短了测试周期。例如,本方法可以在一个月时间内完成-25℃、-10℃、0℃、10℃、25℃、40℃不同温度10s、30s脉冲充放电电流能力及DCR估算,而锂离子电池实物实验测试需要一年时间。In this way, the present embodiment realizes the test of the maximum current during the charging and discharging process of the lithium ion battery through model simulation through the establishment of the electrochemical-thermal coupling model of the battery cell. The method can quickly calculate the maximum charge and discharge current values of the battery at different temperatures and different SOC ranges, avoid the process of continuous experimentation, greatly reduce the scale of the experiment, ensure the test accuracy, and shorten the test cycle. For example, this method can complete -25°C, -10°C, 0°C, 10°C, 25°C, 40°C pulse charge-discharge current capability and DCR estimation at different temperatures for 10s and 30s within one month. The test takes a year.
具体实施时,第一测试温度为:25℃或者40℃,第二测试温度为25℃或者 40℃,放电截止电压为2.7V,放电下限值为5%SOC,充电截止电压为4.25V,。In specific implementation, the first test temperature is 25°C or 40°C, the second test temperature is 25°C or 40°C, the discharge cut-off voltage is 2.7V, the discharge lower limit is 5% SOC, the charge cut-off voltage is 4.25V, .
以下结合几个具体的实施例,对本方法中的电池放电测试和电池充电测试做进一步说明。The battery discharge test and the battery charge test in this method will be further described below with reference to several specific embodiments.
实施例1Example 1
第一步:获取电芯正负极极片长度、宽度、厚度、面密度、压实密度等设计参数,输入到电化学模型中,建立电芯电化学-热耦合模型。Step 1: Obtain design parameters such as the length, width, thickness, areal density, and compaction density of the positive and negative pole pieces of the cell, and input them into the electrochemical model to establish the electrochemical-thermal coupling model of the cell.
第二步:将电芯电化学-热耦合模型温度设置为25℃。Step 2: Set the temperature of the cell electrochemical-thermal coupling model to 25 °C.
第三步:以0.33C电流放电545s,调整电芯电化学-热耦合模型到95%SOC;Step 3: Discharge at 0.33C for 545s, and adjust the electrochemical-thermal coupling model of the cell to 95% SOC;
第四步:将放电截止电压设置为2.7V,对95%SOC电芯进行放电,并统计放电过程中,电荷节点5%SOC、20%SOC、35%SOC、50%SOC、65%SOC、80%SOC以及 95%SOC能够支持10s脉冲放电的放电开始时刻电压值、放电结束时刻电压值和最大放电电流值。Step 4: Set the discharge cut-off voltage to 2.7V, discharge the 95% SOC cell, and count the 5% SOC, 20% SOC, 35% SOC, 50% SOC, 65% SOC, 80% SOC and 95% SOC can support the voltage value at the start of discharge, the voltage value at the end of discharge, and the maximum discharge current value of the 10s pulse discharge.
第五步:计算出电芯95%SOC脉冲放电10s的放电DCR值。Step 5: Calculate the discharge DCR value of the 95% SOC pulse discharge of the cell for 10s.
本实施例中,获得的电芯25℃下电芯在各电荷节点5%SOC、20%SOC、35%SOC、50%SOC、65%SOC、80%SOC以及95%SOC处以10s脉冲放电的最大放电电流以及对应的放电DCR值如下表1所示。In this embodiment, at 25° C., the obtained cells are discharged by pulses of 10s at 5% SOC, 20% SOC, 35% SOC, 50% SOC, 65% SOC, 80% SOC and 95% SOC at each charge node. The maximum discharge current and the corresponding discharge DCR value are shown in Table 1 below.
表1:25℃下10s脉冲放电的数据统计表Table 1: Statistics of 10s pulse discharge at 25°C
实施例2Example 2
第一步:获取电芯正负极极片长度、宽度、厚度、面密度、压实密度等设计参数,输入到电化学模型中,建立电芯电化学-热耦合模型。Step 1: Obtain design parameters such as the length, width, thickness, areal density, and compaction density of the positive and negative pole pieces of the cell, and input them into the electrochemical model to establish the electrochemical-thermal coupling model of the cell.
第二步:将电芯电化学-热耦合模型温度设置为40℃。Step 2: Set the temperature of the cell electrochemical-thermal coupling model to 40 °C.
第三步:以0.33C电流放电545s,调整电芯电化学-热耦合模型到95%SOC;Step 3: Discharge at 0.33C for 545s, and adjust the electrochemical-thermal coupling model of the cell to 95% SOC;
第四步:将放电截止电压设置为2.7V,对95%SOC电芯进行放电,并统计放电过程中,电荷节点5%SOC、20%SOC、35%SOC、50%SOC、65%SOC、80%SOC以及 95%SOC能够支持10s脉冲放电的放电开始时刻电压值、放电结束时刻电压值和最大放电电流值。Step 4: Set the discharge cut-off voltage to 2.7V, discharge the 95% SOC cell, and count the 5% SOC, 20% SOC, 35% SOC, 50% SOC, 65% SOC, 80% SOC and 95% SOC can support the voltage value at the start of discharge, the voltage value at the end of discharge, and the maximum discharge current value of the 10s pulse discharge.
第五步:计算出电芯在各电荷节点5%SOC、20%SOC、35%SOC、50%SOC、65%SOC、80%SOC以及95%SOC处放电10s的放电DCR值。Step 5: Calculate the discharge DCR value of the cell at each charge node of 5% SOC, 20% SOC, 35% SOC, 50% SOC, 65% SOC, 80% SOC and 95% SOC for 10s.
本实施例中,获得的电芯40℃下电芯在各电荷节点5%SOC、20%SOC、35%SOC、50%SOC、65%SOC、80%SOC以及95%SOC处以10s脉冲放电的最大放电电流以及对应的放电DCR值如下表2所示。In this embodiment, at 40° C. of the obtained cell, the cells are discharged with pulses of 10s at 5% SOC, 20% SOC, 35% SOC, 50% SOC, 65% SOC, 80% SOC and 95% SOC at each charge node. The maximum discharge current and the corresponding discharge DCR value are shown in Table 2 below.
表2:40℃下10s脉冲放电的数据统计表Table 2: Statistics of 10s pulse discharge at 40℃
实施例3Example 3
第一步:获取电芯正负极极片长度、宽度、厚度、面密度、压实密度等设计参数,输入到电化学模型中,建立电芯电化学-热耦合模型。Step 1: Obtain design parameters such as the length, width, thickness, areal density, and compaction density of the positive and negative pole pieces of the cell, and input them into the electrochemical model to establish the electrochemical-thermal coupling model of the cell.
第二步:将电芯电化学-热耦合模型温度设置为40℃。Step 2: Set the temperature of the cell electrochemical-thermal coupling model to 40 °C.
第三步:调整电芯电化学-热耦合模型到5%SOC;Step 3: Adjust the electrochemical-thermal coupling model of the cell to 5% SOC;
第四步:将充电截止电压设置为4.25V,以0.33C电流对电芯电化学-热耦合模型充电,并统计充电过程中,电荷节点5%SOC、20%SOC、35%SOC、50%SOC、 65%SOC、80%SOC以及95%SOC能够支持10s脉冲充电的充电开始时刻电压值、充电结束时刻电压值和最大充电电流值。Step 4: Set the charge cut-off voltage to 4.25V, charge the cell with a 0.33C current electrochemical-thermal coupling model, and count the charge nodes 5% SOC, 20% SOC, 35% SOC, 50% during the charging process The SOC, 65% SOC, 80% SOC and 95% SOC can support the charging start time voltage value, the charging end time voltage value and the maximum charging current value of the 10s pulse charging.
第五步:计算出电芯在各电荷节点5%SOC、20%SOC、35%SOC、50%SOC、65%SOC、80%SOC以及95%SOC出脉冲充电10s的充电DCR值。Step 5: Calculate the charging DCR value of the cell at each charge node 5% SOC, 20% SOC, 35% SOC, 50% SOC, 65% SOC, 80% SOC and 95% SOC for 10s of pulse charging.
本实施例中,获得的40℃下电芯在各电荷节点5%SOC、20%SOC、35%SOC、 50%SOC、65%SOC、80%SOC以及95%SOC处以10s脉冲充电的最大充电电流以及对应的充电DCR值如下表3所示。In this embodiment, the obtained maximum charge of the battery cell at 5% SOC, 20% SOC, 35% SOC, 50% SOC, 65% SOC, 80% SOC and 95% SOC at each charge node at 40°C with 10s pulse charging The current and the corresponding charging DCR value are shown in Table 3 below.
表3:40℃下10s脉冲充电的数据统计表Table 3: Statistics of 10s pulse charging at 40°C
以上所述,仅为本发明涉及的较佳的具体实施方式,但本发明的保护范围并不局限于此,任何熟悉本技术领域的技术人员在本发明揭露的技术范围内,根据本发明的技术方案及其发明构思加以等同替换或改变,都应涵盖在本发明的保护范围之内。The above descriptions are only the preferred specific embodiments involved in the present invention, but the protection scope of the present invention is not limited thereto. Equivalent replacement or modification of the technical solution and its inventive concept shall be included within the protection scope of the present invention.
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