CN102592020B - Method for determining weak links of reliability of aviation parameter processing device - Google Patents

Method for determining weak links of reliability of aviation parameter processing device Download PDF

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CN102592020B
CN102592020B CN 201210003484 CN201210003484A CN102592020B CN 102592020 B CN102592020 B CN 102592020B CN 201210003484 CN201210003484 CN 201210003484 CN 201210003484 A CN201210003484 A CN 201210003484A CN 102592020 B CN102592020 B CN 102592020B
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equipment
vibration
temperature
emulation
treatment facility
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CN102592020A (en
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陈颖
谢丽梅
曹然
马响
康锐
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Xiamen Lanwei Reliability System Engineering Research Institute Co.,Ltd.
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Beihang University
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Abstract

The invention discloses a method for determining weak links of reliability of an aviation parameter processing device, comprising the following four steps: (1) determining the worst temperature and the vibration environment in a task process of the aviation parameter processing device, wherein the condition of the worst temperature and the vibration environment is the harshest environment condition suffered by the aviation parameter processing device in the task process; (2) performing Flotherm temperature distribution simulation to the aviation parameter processing device; (3) performing ANSYS vibration stress distribution simulation to the aviation parameter processing device; and (4) determining the weak links of the reliability of the aviation parameter processing device. The method of the invention is based on the methods of the finite element temperature distribution simulation and the finite element vibration stress simulation so as to determine the weak links for device designing, provides the basis for the improved design, thereby improving the inherent reliability of the aviation parameter processing device, furtheremore, the method has good practical value and broad application prospect in the technical field of the reliability simulation of a product.

Description

A kind of aviation parameter treatment facility reliability weak link is determined method
Technical field
The invention provides a kind of aviation parameter treatment facility reliability weak link and determine method, particularly relate to a kind of aviation parameter treatment facility reliability weak link based on severe temperatures and vibration stress emulation and determine method, belong to product reliability emulation field.
Background technology
Along with high-speed development of science and technology, the complexity of avionic device improves constantly, also more and more higher to the requirement of reliability simultaneously, need just determine the reliability weak link of equipment from the commitment of design, thereby take measure targetedly to improve design, guarantee device security, work reliably.Aviation parameter treatment facility is to gather aviation parameter go forward side by side line item, processing, measurement, warning, with the electronic equipment of monitoring aircraft running status.Its structure is in the cabinet of sealing various functional circuit module to be installed, and each module is fixed to around the cabinet by draw-in groove and connector, locking strip.Ingredient in the aviation parameter treatment facility is subjected to the effect of various environment and condition of work in the process that aircraft is executed the task, wherein temperature and oscillating load are topmost environmental baselines, and electric load is the most principal work condition.Temperature loading comprises environment temperature and each components and parts heating temp load when work.Under the effect of these load, each ingredient of aviation parameter treatment facility may lose efficacy, thereby may cause the inefficacy of entire product, caused integrity problem.
Traditionally, the engineering staff mainly is the reliability weak link that experiential method is determined aviation parameter treatment facility at the early stage of design, this method depends on engineering staff's subjective judgement, tend to cause the location inaccurate cross design problem or ignore certain weak part and cause owe design problem.Along with numerical value emulation method, as the development of finite element, Finite Volume Method and the maturation of business software, the stress emulation technology has begun to be applied in the design and analysis of various products.By new to looking into of prior art for retrieval, also do not adopt severe temperatures and vibration stress emulation to determine the report of aviation parameter treatment facility weak link aspect both at home and abroad.
Summary of the invention
1, purpose: the objective of the invention is at the deficiencies in the prior art, provide a kind of aviation parameter treatment facility reliability weak link to determine method, it is based on the emulation of finite element Temperature Distribution, finite element vibration stress method of emulation is determined equipment design weak link, provide foundation for improving design, thereby improve the inherent reliability of equipment.
2, technical scheme: the present invention is achieved by the following technical solutions, determine worst temperature and vibration environment in the equipment task process, aviation parameter treatment facility is carried out the emulation of Flotherm Temperature Distribution, aviation parameter treatment facility is carried out the emulation of ANSYS vibration stress, determine the reliability weak link of equipment.
A kind of aviation parameter of the present invention treatment facility reliability weak link is determined method, and its concrete steps are as follows:
Step 1: determine worst temperature and vibration environment in the aviation parameter treatment facility task process.Mainly refer to aviation parameter treatment facility (hereinafter to be referred as " equipment ") in the task process the harshest environmental baseline that may experience, mainly comprise:
A. if provided operating temperature range and the vibration acceleration power spectrum density section of equipment in the designing requirement of equipment, then select high temperature in the temperature range as worst temperature environment, select in the given vibration acceleration power spectrum density section, one of vibration acceleration power spectrum metric maximum as the most abominable vibration environment, if only provide a vibration acceleration power spectrum density section, then this section is defined as the most abominable vibration environment.
B. if do not provide operating temperature range and the vibration section of equipment in the equipment designing requirement, determine worst temperature and vibration environment according to national standard " GBT2423.43-2008 electric and electronic product environmental test ".
Step 2: aviation parameter treatment facility is carried out the emulation of Flotherm Temperature Distribution.Flotherm is a kind of commercial finite integral software of maturation, and major function is to carry out temperature simulation.Mainly comprise:
A. the three-dimensional CAD of introducing equipment (computer-aided design (CAD), Computer Aided Design) model.At first will set up good equipment three-dimensional CAD model and pass through intermediate form, import in the Flotherm software as forms such as IGES, SAT, STEP, this three-dimensional CAD model has been described the structure of aviation parameter treatment facility and has been formed, assembled annexation, comprised that circuit module that aviation parameter treatment facility is all and power consumption surpass the geometry of the components and parts of 0.1W, do not need to set up the geometry of components and parts pad.
B. define equipment is formed the Temperature Distribution artificial material parameter of each several part.Mainly comprise: the specific heat capacity of each composition material, coefficient of heat conductivity.
C. device model being carried out grid divides.Utilize Flotherm software to carry out automatic mesh and divide, the grid length breadth ratio should be controlled in 20.
D. apply temperature loading and boundary condition.Temperature loading mainly comprises the reality of work power consumption of rugged surrounding temperature and components and parts, utilizes the temperature of Flotherm to apply order, and the severe temperature environment condition of determining in the step 1 is applied in the device model.With the actual power loss of the components and parts surface area divided by components and parts, obtain the face heat flow density, utilize the heat flow density of Flotherm to apply order, be input in the Flotherm software.Utilize the Flotherm temperature boundary that order is set, the NATURAL CONVECTION COEFFICIENT OF HEAT of components and parts and air phase-contact surface is set.
E. implement Temperature Distribution emulation.Utilize the order of finding the solution of Flotherm to carry out the Temperature Distribution emulation of this equipment under severe temperatures condition, finally can obtain the equipment each several part, the Temperature Distribution of each location point.
Step 3: aviation parameter treatment facility is carried out ANSYS vibration stress distributed simulation.ANSYS is a kind of commercial finite element emulation software of maturation, can carry out power spectrum density emulation.Mainly comprise:
A. the three-dimensional CAD model of introducing equipment.At first will set up good equipment three-dimensional CAD model and pass through intermediate form, import in the ANSYS software as forms such as IGS, STEP, this three-dimensional CAD model has been described the structure of aviation parameter treatment facility and has been formed, assembled annexation, comprised that circuit module that aviation parameter treatment facility is all and weight greater than the geometry of the components and parts of 0.1 gram, do not need to set up the geometry of components and parts pad.
B. define equipment is formed the vibration stress artificial material parameter of each several part.Mainly comprise: the density of each composition material, elastic modulus, Poisson ratio.
C. device model being carried out grid divides.Utilize ANSYS software to carry out automatic mesh and divide, the grid length breadth ratio should be controlled in 5.
D. apply vibration acceleration power spectrum density and boundary condition.Mainly comprise, utilize the acceleration power spectral density of ANSYS to apply order, the most abominable vibration acceleration power spectrum metric and the frequency value corresponding thereof determined in the step 1 are input in the ANSYS software, and be applied to the position, fixed position of equipment, apply direction perpendicular to the installation direction of equipment.Utilize the displacement boundary of ANSYS to apply order, position, equipment fixed position is applied the null displacement constraint of X, Y, three directions of Z.
E. implement vibration stress emulation.The vibration damping value of equipment is set, according to the general quantity of selecting between 0.03 to 0.05 of engineering experience.Utilize the order of finding the solution of ANSYS to carry out the stress emulation of this equipment under the most abominable vibration condition, find the solution the response that can obtain each position of equipment after the end, comprise displacement, speed and acceleration-root-mean square.
Step 4: the reliability weak link of determining equipment.Mainly comprise:
A. determine the reliability weak link under the severe temperatures condition.Temperature Distribution and the value thereof of the equipment each several part that obtains according to step 2 emulation are determined device temperature reliability weak link.Mainly be to determine at the components and parts heat-resistant quality, for discrete devices such as integrated circuit (IC) chip, diode, transistors, if the quality grade of chip is technical grade, then when emulation obtained its surface temperature above 85 ℃, this integrated circuit was the reliability weak link; If the chip quality grade is army's grade, then when emulation obtained its surface temperature above 100 ℃, this integrated circuit was the reliability weak link; For components and parts such as resistor, capacitors, if it is surface mount with the connected mode of circuit board, then when emulation obtained its surface temperature above 90 ℃, these components and parts were decided to be the reliability weak link.
B. determine the reliability weak link under the most abominable vibration condition.According to vibration equipment stress, the displacement that step 3 emulation obtains, determine the vibration reliability weak link of equipment.The position of power taking source module, CPU module, AD modular converter, data processing module top offset root mean square, acceleration-root-mean square maximum is the vibration reliability weak link.
In sum, technical thought of the present invention is: at first determine worst temperature and vibration environment in the equipment task process; Secondly the cad model with equipment imports among the Flotherm, sets material parameter, applies temperature or power loading and boundary condition, carries out Temperature Distribution emulation; Cad model with equipment imports among the ANSYS then, sets material parameter, applies oscillating load and boundary condition, carries out vibration stress emulation; The kind of last selected components and parts and quality grade are determined the hot weak link of equipment and vibration weak link.As can be seen, aviation parameter treatment facility based on Temperature Distribution and vibration stress emulation, can obtain to produce in its use the position of integrity problem at the commitment of design, thereby be conducive to the designer and take the design improvement measure, avoid equipment failure, improve the inherent reliability of equipment.
3, advantage and effect: a kind of aviation parameter of the present invention treatment facility reliability weak link is determined method, has the following advantages:
A. utilize worst temperature and vibration condition emulation to obtain the equipment weak link.The temperature that equipment is subjected in the task process and vibration condition have a variety of, utilize extreme conditions to carry out emulation, guarantee to find issuable problem under the most extreme condition, thereby guarantee to have taked the product after the design improvement under other conditions, also similar problem can not take place.
B. utilize the method for numerical simulation to determine the equipment weak link.The weak link of product can be determined by the method for experience and equipment link in kind test.In the design phase, adopt empirical method usually, adopt test method at the principle prototype Qualify Phase.When the designer lacked experience, the weak link of location tended to take place deviation.And adopt test method to determine that weak link needs long test period and change in design time at Qualify Phase.Utilize the method for numerical simulation to provide equipment quantitative stress distribution situation for the slip-stick artist in the design phase, the location weak link is comparatively accurate, and saves experimentation cost, shortens the equipment R﹠D cycle.
Description of drawings
Fig. 1 is the inventive method FB(flow block).
Fig. 2 is the composition frame chart of the aviation parameter treatment facility of the embodiment of the invention.
Fig. 3 is the vibration section of the aviation parameter treatment facility of the embodiment of the invention.
Embodiment
The present invention is described in further detail below in conjunction with drawings and Examples.
Following examples are to implement according to flow process as shown in Figure 1, mainly comprise determining worst temperature and vibration environment in the equipment task process, carry out the emulation of Flotherm Temperature Distribution, carry out ANSYS vibration stress distributed simulation, determining the reliability weak link of equipment.Aviation parameter treatment facility hardware is formed as shown in Figure 2, comprises cabinet, power module, CPU module, AD modular converter, data processing module, motherboard.
See Fig. 1, a kind of aviation parameter of the present invention treatment facility reliability weak link is determined method, and these method concrete steps are as follows:
Step 1: determine worst temperature and vibration environment in the equipment task process.The operating temperature range that has provided this equipment in the designing requirement of equipment is-40 ℃~70 ℃, selects 70 ℃ as worst temperature environment.Give the vibration acceleration power spectrum density section of aircraft under the three kinds of conditions of taking off, cruise, land in the designing requirement of equipment, as shown in Figure 3.Acceleration power spectral density value in the time of owing to take off is maximum among the three, and the acceleration power spectral density section when therefore selecting to take off is worst vibration environment.
Step 2: equipment is carried out the emulation of Flotherm Temperature Distribution.Mainly comprise:
A. the three-dimensional CAD model of introducing equipment.The equipment three-dimensional CAD model that at first will utilize PRoE software to set up imports in the Flotherm software by intermediate form IGES.This three-dimensional CAD model has described that the structure of aviation parameter treatment facility is formed, the assembling annexation, has comprised that circuit module that aviation parameter treatment facility is all and power consumption greater than the geometry of 0.1W components and parts, do not set up the geometry of components and parts pad.
B. define equipment is formed the Temperature Distribution simulation parameter of each several part.What cabinet adopted among the embodiment is aluminum alloy materials, and circuit board adopts FR4, and the components and parts material comprises plastic packaging material and pottery according to the difference of its encapsulating material.Specific heat capacity, the coefficient of heat conductivity of each material are as shown in table 1.
Material properties in the emulation of table 1 Temperature Distribution
Material Specific heat capacity (KJ/kg ℃) Coefficient of heat conductivity W/ (m ℃)
Aluminium alloy 0.88 200
FR4 1.63 0.20
Capsulation material 1.27 0.67
Pottery 0.95 16.7
C. device model being carried out grid divides.Utilize Flotherm software to carry out automatic mesh and divide, the length breadth ratio through measuring the grid maximum is 10.3, and number of grid is 2,180,000.
D. apply temperature loading and boundary condition.Utilize the temperature of Flotherm to apply order, the severe temperature environment condition of determining in the step 1 is applied in the model for 70 ℃.With the actual power loss of the components and parts surface area divided by components and parts, obtain the face heat flow density, utilize the heat flow density of Flotherm to apply order, be input in the Flotherm software.Table 2 has been listed the actual power loss of part components and parts and the heat flow density value that applies.The radiating mode of equipment is natural heat dissipation, and convection transfer rate is made as 5W/ (m ℃).
Table 2 part components and parts actual power loss and heat flow density
Sequence number Code name The position Actual power loss (W) Heat flow density (W/m 2)
1 U4 Power module 1 816.3
2 U5 The CPU module 0.05 694.4
3 D1 The AD module 0.52 5200
4 D2 The CPU module 0.52 5200
5 D3 The CPU module 0.52 5200
6 R12 Power module 0.1 388.2
E. implement Temperature Distribution emulation.Utilize the order of finding the solution of Flotherm to carry out the Temperature Distribution emulation of this equipment under severe temperatures condition, finally obtain the Temperature Distribution of equipment each several part, each location point.Table 3 is the shell temperature of high-temperature device in the equipment.
The high-temperature device that the emulation of table 3 Temperature Distribution obtains
The device item Type of device Encapsulation Quality grade The shell temperature (℃) The position
U4 Integrated circuit (IC) chip Pottery Army's grade 102.4 Power module
U5 Integrated circuit (IC) chip Plastic packaging Technical grade 86.8 The CPU module
D1 Diode Plastic packaging Army's grade 90.4 The AD module
D2 Transistor Plastic packaging Army's grade 92 The CPU module
D3 Diode Plastic packaging Army's grade 91.7 The CPU module
R12 Resistor Surface Mount- Army's grade 90.6 Power module
Step 3: equipment is carried out ANSYS vibration stress distributed simulation.Mainly comprise:
A. the three-dimensional CAD of introducing equipment (computer-aided design (CAD)) model.At first will set up good equipment three-dimensional CAD model imports in the ANSYS software by intermediate form IGS, this three-dimensional CAD model has been described the structure of aviation parameter treatment facility and has been formed, assembled annexation, comprised that circuit module that aviation parameter treatment facility is all and weight greater than the geometry of the components and parts of 0.1 gram, do not set up the geometry of components and parts pad.
B. define equipment is formed the vibration stress simulation parameter of each several part.Mainly comprise: the density of each composition material, elastic modulus, Poisson ratio, as shown in table 4.
The material properties that will define in the table 4 vibration emulation
Title material Elastic modulus (MPa) Poisson ratio Density (kg/m 3)
Aluminium alloy 72000 0.3 2700
FR4 12000 0.3 2900
Capsulation material 15600.0 0.25 1206
Pottery 351645 0.17 2601
C. device model being carried out grid divides.Utilize ANSYS software to carry out automatic mesh and divide, the maximum mesh length breadth ratio is 4.8, and number of unit is 280,000.
D. apply vibration acceleration power spectrum density and boundary condition.Mainly comprise, utilize the acceleration power spectral density of ANSYS to apply order, the most abominable vibration acceleration power spectrum metric and the frequency value corresponding thereof determined in the step 1 are input in the ANSYS software, and be applied to the position, fixed position of equipment, apply direction perpendicular to the installation direction of equipment.Utilize the displacement boundary of ANSYS to apply order, position, equipment fixed position is applied the null displacement constraint of X, Y, three directions of Z.
E. implement vibration stress emulation.The vibration damping value that equipment is set is 0.035.Utilize the order of finding the solution of ANSYS to carry out the stress distribution emulation of this equipment under the most abominable vibration condition, find the solution the response that can obtain each position of equipment after the end, comprise displacement root mean square, speed root mean square and acceleration root-mean-square value.Provided the vibratory response root-mean-square value of each module of equipment under the takeoff condition as table 5.
The vibratory response value of each module of equipment under table 5 takeoff condition
Figure BDA0000129092580000071
Step 4: the reliability weak link of determining equipment.Mainly comprise:
A. determine the reliability weak link under the severe temperatures condition.Temperature Distribution and the value thereof of the equipment each several part that obtains according to step 2 emulation are determined device temperature reliability weak link.
By table 3, U4 is the integrated circuit (IC) chip of army's grade, and the shell temperature has surpassed 100 ℃; U5 is the technical grade integrated circuit (IC) chip, and the shell temperature has surpassed 85 ℃; D1, D2, D3 are the discrete device of military products level, and shell Wen Junwei is above 100 ℃; R12 is army's grade surface-mount resistor, and the shell temperature has surpassed 90 ℃.Therefore determine that U4, U5, R12 are the reliability weak link under the temperature conditions.
B. determine the reliability weak link under the most abominable vibration condition.The circuit board place, right side of CPU module is the maximum position of displacement root-mean-square value that emulation obtains, and AD modular converter centre is the position of acceleration-root-mean square maximum, so this position is vibration equipment reliability weak link.
By aviation parameter treatment facility is carried out temperature and vibration stress emulation, can determine the weak link of equipment in the initial stage of design, take means to avoid equipment thereby be conducive to the designer, improve the reliability of equipment.
The present invention has set up a kind of aviation parameter treatment facility reliability weak link based on severe temperatures and vibration stress emulation and has determined method.Utilize this method, can carry out temperature and vibration stress emulation to aviation parameter treatment facility, in the weak link of quick positioning equipment of design phase, save the cost of development, shorten the equipment R﹠D cycle.

Claims (1)

1. an aviation parameter treatment facility reliability weak link is determined method, and it is characterized in that: these method concrete steps are as follows:
Step 1: determine worst temperature and vibration environment in the aviation parameter treatment facility task process; Wherein, in the aviation parameter treatment facility task process worst temperature and vibration environment refer to aviation parameter treatment facility in the task process the harshest environmental baseline that may experience, comprising:
A. if provided operating temperature range and the vibration acceleration power spectrum density section of equipment in the designing requirement of aviation parameter treatment facility, then select high temperature in the temperature range as worst temperature environment, select in the given vibration acceleration power spectrum density section, one of vibration acceleration power spectrum metric maximum as the most abominable vibration environment, if only provide a vibration acceleration power spectrum density section, then this section is defined as the most abominable vibration environment;
B. if do not provide operating temperature range and the vibration acceleration power spectrum density section of aviation parameter treatment facility in the equipment designing requirement, determine worst temperature and vibration environment according to national standard " GBT2423.43-2008 electric and electronic product environmental test ";
Step 2: aviation parameter treatment facility is carried out the emulation of Flotherm Temperature Distribution; Flotherm is a kind of finite integral software, and its function is to carry out temperature simulation; Comprise:
A. import the three-dimensional CAD model of this equipment; At first will set up good equipment three-dimensional CAD model and pass through intermediate form, IGES, SAT, STEP form import in the Flotherm software, this three-dimensional CAD model has been described the structure of aviation parameter treatment facility and has been formed, assembled annexation, comprised that circuit module that aviation parameter treatment facility is all and power consumption surpass the geometry of the components and parts of 0.1W, do not need to set up the geometry of components and parts pad;
B. define this equipment and form the Temperature Distribution artificial material parameter of each several part; Comprise: the specific heat capacity of each composition material, coefficient of heat conductivity;
C. this device model being carried out grid divides; Utilize Flotherm software to carry out automatic mesh and divide, the grid length breadth ratio is controlled in 20;
D. apply temperature loading and boundary condition; Temperature loading comprises the reality of work power consumption of rugged surrounding temperature and components and parts, utilizes the temperature of Flotherm to apply order, and the severe temperature environment condition of determining in the step 1 is applied in the device model; With the actual power loss of the components and parts surface area divided by components and parts, obtain the face heat flow density, utilize the heat flow density of Flotherm to apply order, be input in the Flotherm software, utilize the Flotherm temperature boundary that order is set, the NATURAL CONVECTION COEFFICIENT OF HEAT of components and parts and air phase-contact surface is set;
E. implement Temperature Distribution emulation; Utilize the order of finding the solution of Flotherm to carry out the Temperature Distribution emulation of this equipment under severe temperatures condition, finally obtain the equipment each several part, the Temperature Distribution of each location point;
Step 3: aviation parameter treatment facility is carried out ANSYS vibration stress distributed simulation; ANSYS is a kind of finite element emulation software, can carry out power spectral-density analysis; Comprise:
A. the three-dimensional CAD model of introducing equipment; At first will set up good equipment three-dimensional CAD model and pass through intermediate form, IGS, STEP form import in the ANSYS software, this three-dimensional CAD model has been described the structure of aviation parameter treatment facility and has been formed, assembled annexation, comprised that circuit module that aviation parameter treatment facility is all and weight greater than the geometry of the components and parts of 0.1 gram, do not need to set up the geometry of components and parts pad;
B. define equipment is formed the vibration stress artificial material parameter of each several part; Comprise: the density of each composition material, elastic modulus, Poisson ratio;
C. device model being carried out grid divides; Utilize ANSYS software to carry out automatic mesh and divide, the grid length breadth ratio is controlled in 5;
D. apply vibration acceleration power spectrum density and boundary condition; Comprise, utilize the acceleration power spectral density of ANSYS to apply order, the most abominable vibration acceleration power spectrum metric and the frequency value corresponding thereof determined in the step 1 are input in the ANSYS software, and are applied to the position, fixed position of equipment, apply direction perpendicular to the installation direction of equipment; Utilize the displacement boundary of ANSYS to apply order, position, equipment fixed position is applied the null displacement constraint of X, Y, three directions of Z;
E. implement vibration stress emulation; The vibration damping value of equipment is set, according to the quantity between the engineering experience selection 0.03 to 0.05; Utilize the order of finding the solution of ANSYS to carry out the stress emulation of this equipment under the most abominable vibration condition, find the solution the power spectrum density response that finishes each position of back acquisition equipment, comprise displacement power spectrum density, speed-power spectral density and acceleration power spectral density response;
Step 4: the reliability weak link of determining equipment; Comprise:
A. determine the reliability weak link under the severe temperatures condition; Temperature Distribution and the value thereof of the equipment each several part that obtains according to step 2 emulation are determined device temperature reliability weak link; It is to determine at the components and parts heat-resistant quality, and for integrated circuit (IC) chip, diode, transistor discrete device, if the quality grade of chip is technical grade, then when emulation obtained its surface temperature above 85 ° of C, this integrated circuit was the reliability weak link; If the chip quality grade is army's grade, then when emulation obtained its surface temperature above 100 ° of C, this integrated circuit was the reliability weak link; For resistor, capacitor components and parts, if it is surface mount with the connected mode of circuit board, then when emulation obtained its surface temperature above 90 ° of C, these components and parts were decided to be the reliability weak link;
B. determine the reliability weak link under the most abominable vibration condition; According to vibration equipment stress, the displacement that step 3 emulation obtains, determine the vibration reliability weak link of equipment; The displacement power spectrum density that emulation obtains in the taking equipment, speed-power spectral density and three maximum positions of acceleration power spectral density response are the vibration reliability weak link.
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