Optimization Design and Comprehensive Evaluation of Screw Contact of Space Battery Based on ANSYS

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Shanghai Institute of Spacecraft Equipment，Shanghai 200240，P.R.China

Abstract: In order to improve the safety of the battery of satellite side mounting，and prevent the screw from producing excess due to frequent assembly and disassembly，the YS-20 material replacement and structure optimization design of the screw body are carried out under the premise of not changing the original tooling. The double?shear test of YS-20 bar is carried out，and the ANSYS optimization design module is used to design 7×7×6，a total of 294，calculation cases of D1，D2，T，the three important dimension parameters of screw structure. The actual bearing state of screw composite structure is accurately simulated by using asymmetric contact model. Three comprehensive evaluations are established，and the calculation examples satisfying the conditions are evaluated comprehensively. The final results are T=12.2 mm，D1=16 mm，D2=2 mm. The stress verification and contact analysis are carried out for the final scheme and the bearing state and contact state optimized screw structure are obtained.

Key words：space battery；screw；ANSYS；optimization design；contact analysis；comprehensive evaluation

0 Introduction

Screw is the key fastener of space battery，which plays a key role in the protection and sup?port of the battery. At present，the main purpose of using nylon 1010 screw on the battery is to bear the pulling force caused by the weight of the bat?tery，and at the same time，avoid surplus materi?als caused by frequent disassembly and assembly.In a large number of practical applications，nylon 1010 screw can bear the pulling force caused by the weight of the battery well. However，some types of satellites require the battery to be installed on the side. At this time，the screw mainly bears the shear force caused by the weight of the battery and the pressure on the screw surface. According to the results of simulation，it is found that the force state of nylon 1010 screw under both tension and shear force is very poor，and the maximum stress is 16 MPa and the displacement of screw composite structure is 1.104 mm. The yield strength of nylon 1010 bar is about 50 MPa，and the safety margin is very low，which cannot meet the requirement of satellite AIT（Assembly inte?gration and test）. The yield strength of polyimide plastic is about 100 MPa，which can replace the nylon 1010 rod. At the same time，the structure of the screw body can be optimized without changing the original tooling further. Before the design and optimization of polyimide screw，it is necessary to conduct shear test on this kind of YS-20 bar. The optimization design module of ANSYS can assist the simulation analysis of multi-objective and scheme［1-6］. The distribution of stress and displace?ment in different levels of optimization parameters is obtained. The contact analysis of structural as?sembly parts can also be carried out in ANSYS，so as to obtain the contact state and change of the contact parts. Although the optimization design ex?ploration can give the calculation results of each ex?ample，when there are too many optimization in?dexes，it is impossible to give a better recommen?dation scheme，and the recommended scheme may not be the desired one. Therefore，some compre?hensive evaluation and decision making methods should be used to assist the engineers，such as grey correlation analysis［7-12］，comprehensive evalu?ation method based on fuzzy mathematics［13-17］，etc. Feng et al.［18］introduced a new grey correla?tion model to analyze heterogeneous data，and pro?posed a comprehensive safety risk factor identifica?tion method，which was applicable to the identifica?tion of safety risk factors of heterogeneous sparse small reservoirs. Liu et al.［19］proposed a multi-lev?el fuzzy comprehensive evaluation method，which could be used as a reference for gas enterprises to develop urban gas monitoring and data acquisition system infrastructure.

Therefore， some comprehensive evaluation and decision-making methods can be used to assist the scheme evaluation when the recommended scheme cannot be given by ANSYS or the given scheme is not desired. In this paper，three compre?hensive evaluation methods： Relative deviation fuzzy matrix evaluation method，relative superior membership degree fuzzy matrix evaluation meth?od，and variable weight grey correlation degree eval?uation method，are used to conduct comprehensive evaluation and decision-making for the calculation examples. And the double shear test of YS-20 bar screw is carried out，and the shear stress of the screw is obtained. The structural optimization de?sign of the screw based on ANSYS is carried out，and 294 kinds of calculation examples are obtained.The stress verification and contact analysis of the op?timized model are carried out，and the screw struc?ture meeting the engineering requirements is ob?tained.

1 Double Shear Test of YS?20 Polyimide Bar

Before designing and optimizing the polyimide screw，it is necessary to know the shear perfor?mance of the bar. Referring to the metal compres?sion test method，the design of the test fixture is shown in Fig.1. The grade of the designed test bar is YS-20，the design diameter is 6.65 mm，and the design theoretical shear area volume is 2×π×6.652. The lower cutter is fixed on the fixed block，and the feed speed of the upper cutter is composed of four groups：0.03，0.3，0.6，and 0.9 mm/min，in which the cutter feed rate is 0.03，0.3，0.6，and 0.9 mm/min for one time，three times，three times，and one time，respectively.The upper cutter and the fixing block are fixed on the machine frame.

Fig.1 Shear test tooling of YS-20 polyimide bar

In the test，the bar diameter for 0.03 mm/min cutter is 6.62 mm，while those for 0.3，0.6，and 0.9 mm/min are 6.64 mm. The maximum shear yield strength of the bar is shown in Fig.2，and the failure of the test bar when the cutter feed speed is 0.3 mm/min and 0.6 mm/min are shown in Fig.3. It can be seen that when the rate of cutter feed is 0.03 mm/min，the maximum shear yield stress is larger，which is related to the slow feed rate. With the increase of the speed，the maximum shear yield stress decreases. But it can be seen from Fig.3 that the test bar has produced obvious fracture phenome?non，and the data point dispersion at the speed of 0.3 mm/min is larger than that of 0.6 mm/min，and the data points at the speed of 0.6 mm/min are basi?cally unchanged，thus indicating that the test has en?tered the steady state region，and the maximum shear yield stress in this region can best reflect the shear strength of the material. The shear stress rang?es from 78.722 7 MPa to 81.799 3 MPa. The aver?age maximum shear yield stress of each group of tests is fitted by cubic polynomial. It can be seen that the maximum shear yield stress of cutter feed rate from 0.3 mm/min to 0.9 mm/min has been ba?sically unchanged，and the stress change value is about 79 MPa，which is basically consistent with the actual test results. According to the fitting data，the minimum value of the maximum shear yield stress is 78.972 0 MPa.

Fig.2 Maximum shear yield strength of YS-20 bar

Fig.3 Shear failure of YS-20 bar

2 Optimization Parameters of Screw and Comprehensive Eval?uation

2.1 Parameters and optimization

Without changing the original tooling， the main contact and support parts of the screw are ex?tracted as shown in Fig.4. The overall structure in?cludes screws，nylon bushing and aluminum alloy support parts. There are eight symmetrically distrib?uted screws in the tooling，so one screw can be cal?culated according to the average load in ANSYS simulation. According to the structural model，the ANSYS simulation model is established. It can be seen that the structure has two support surfaces Ⅰand Ⅱ，and six groups of contact pairs，as shown in Fig.5. In the simulation model，the friction coeffi?cient is 0.2，the normal stiffness factor of the con?tact surface is 0.1，the contact method is asymmet?ric，and the tension and the shear force of the screw surface areFl=60 N andFy=60 N，respectively.Set three optimization parameters（unit：mm）：D1the diameter of the Ⅱsupporting surface；D2the ax?ial gate thickness of Ⅰand Ⅱ；andTthe diameter of the Ⅰsupporting surface. There are seven opti?mization levels for the optimization parameterD1，six optimization levels forT，seven optimization lev?els forD2，and 294 for each parameter level in AN?SYS optimization design.

Fig.4 Screw and its combination structure

Fig.5 Optimizing parameters

The mesh division of the screw composite structure is shown in Fig.6. The mesh of the surface fixed on the ground can be roughly processed to im?prove the calculation efficiency. The mesh refine?ment treatment is carried out at the contact surface，and the sweeping grid division is carried out for the cylindrical structure（e.g. aluminum alloy support）.The average skewness of the overall structure grid is 0.224，which has a high grid quality.

Fig.6 Mesh of screw composite structure

2.2 Comprehensive evaluation method

The constituent factors of many decision-mak?ing problems are interrelated and mutually restrict?ed. Some indicators are difficult to quantify and oth?ers contradict each other，resulting in the complexi?ty of decision-making. Therefore，it is necessary to manually evaluate the calculation results or schemes.

2.2.1 Fuzzy comprehensive evaluation

Relative deviation fuzzy matrix evaluation method is a kind of fuzzy comprehensive evaluation method，which is the specific application of fuzzy mathematics. Its basic idea is：on the basis of fuzzy mathematics，using the principle of fuzzy relation synthesis，quantifying some factors with unclear boundary and difficult to quantify，and comprehen?sively evaluating the subordinate level of the evaluat?ed thing from multiple factors. The basic evaluation steps are as follows：

（1）Determining evaluation index and level

Assume thatU=［u1，u2，…，um］is the factor of the evaluation object，and the boject hasmmem?bers；V=［v1，v2，…，vn］is the evaluation level，and the evaluation level hasnmembers.

（2）Constructing fuzzy comprehensive evalua?tion matrix

The membership degreerijof the evaluation in?dexuican be rated as gradevj.rijcan be understood as the membership degree of indexuito gradevj，and it is usually used in normalization. The fuzzy comprehensive evaluation matrix is obtained as

（3）Determining the weight of evaluation index

In order to obtain the weight of the index，we can use the coefficient of variation method. Firstly，we should calculate the mean and variance of theiindex.

whereaijis the specific value ofjin theiindex.

（4）Fuzzy synthesis

Fuzzy comprehensive evaluation uses weight vectors to synthesize different rows，so as to obtain the overall membership degree of the evaluation ob?jects to each level. The calculation needs to be real?ized by fuzzy synthesis. The operators of fuzzy syn?thesis are as follows

In Eq.（4），getting small and large values oper?ations are represented by ∧，∨，respectively.

2.2.2 Relative deviation fuzzy matrix evaluation method

Firstly，assume an ideal schemeu. Then，the weightAof each evaluation index is determined. Fi?nally，the comprehensive distanceFof each scheme is obtained by weighted average ofAandR，and the schemes are sorted according to the size ofF.The main steps of this method are as follows：

（1）Virtual ideal scheme

（2）Establishment of relative deviation fuzzy matrixR

The elements inR

（3）Weighted averaging of deviations for each scheme

2.2.3 Grey relational analysis

The method of judging the degree of correla?tion between data series based on grey correlation degree is called grey correlation analysis. Building evaluation objects and evaluation indexes which hasmandnmembers，respectively. The signature se?quencex0=［x0（k）|k=1，2，…，n］，and the related factors sequencexi=［xi（k）|k=1，2，…，n］，i= 1，2，…，m. Order thatXi=［xi（1），xi（2），…，xi（n）］are data sequences，XiD=［xi（1）d，xi（2）d，…，xi（n）d］. The elements ofXiDcan be obtained as follows：

Initial image

Mean image

Interval-valued image

In order to reduce the influence of extreme val?ues，a resolution coefficientξis set in the grey corre?lation degree，and a formula for calculating the grey correlation coefficient is obtained

The calculation formula of grey correlation de?gree can be obtained by weighted average of each grey correlation coefficient

Grey correlation degree is an index to measure the degree of correlation between data series. The weight of each evaluation index is equal，which is 1/n（nis the number of indicators），and the weight of each index can also be determined ac?cording to the coefficient of variation method. It should be noted that different comprehensive evalu?ation methods have different ranking results for the same problem. Therefore，several comprehensive evaluation methods should be applied to evaluate a same problem at the same time in order to improve the reliability and persuasion of the evaluation re?sults.

3 Simulation Results and Scheme Decision

3.1 Simulation results of screw composite structure

The distribution of stress，displacement and strain of the screw composite structure with the opti?mized parameters is obtained，as shown in Figs.7—9. It can be seen from Fig.7 that the stress of screw composite structure has obvious nonlinear change with the change of optimization parameters，and the regularity is weak，which is consistent with the actu?al situation. The maximum value of stress is 22.214 MPa，and the minimum value is 12.666 MPa.The regions with small stress are mainly concentrat?ed in the range ofT≤12.5 mm，D1≥16 mm，D2≤12 mm，and the comprehensive evaluation re?sults are the most likely to fall into these regions.

Fig.7 Stress distribution of screw composite structure

It can be seen from Fig.8 that the displacement distribution of screw composite structure is nonlin?ear and the regularity is weak. The maximum dis?placement value is 1.291 mm，and the minimum val?ue is 0.413 mm. The regions with small displace?ment are mainly concentrated in the range ofT≥12.5 mm，D1≥15 mm，D2≥8 mm. At the level ofT= 13 mm，D2= 8 mm is the boundary layer.WhenD2> 8 mm，the displacement decreases with the increase ofD2，and whenD2≤8 mm，the dis?placement increases with the decrease ofD2. There?fore，the displacement has a strong linear law in some local regions. It can be seen from Fig.9 that the strain distribution of the screw composite struc?ture is nonlinear，and the maximum strain is 0.012 2and the minimum strain is 0.003 6. The region with small strain is mainly concentrated in the range ofT≥12.5 mm，andT=12.5 mm is the boundary lay?er with obvious strain distribution.

Fig.8 Displacement distribution of screw composite struc?ture

Fig.9 Strain distribution of screw composite structure

The distribution of stress，displacement and strain of the screw structure with the optimized pa?rameters is obtained，as shown in Figs.10—12. It can be seen from Fig.10 that the stress of screw structure has obvious nonlinear change with the change of optimization parameters，and the regulari?ty is weak，which is consistent with the actual situa?tion. The maximum stress is 21.972 MPa and the minimum is 10.326 MPa. The smaller stress re?gions are mainly concentrated in the range ofT≤12.5 mm，D1≥16 mm，D2≤12 mm.

Fig.10 Stress distribution of screw structure

It can be seen from Fig.11 that the displace?ment distribution of the screw structure is nonlinear，and the maximum displacement is 1.291 mm，the minimum displacement is 0.413 mm，which is the same as that of the composite structure. The smaller displacement regions are mainly concentrated in the range ofT≥12.5 mm，D1≥15 mm，D2≥8 mm.At the level ofT= 13 mm，D2= 8 mm is the boundary layer of this level. It can be seen from Fig.12 that the strain distribution of screw structure is nonlinear，the maximum strain value is 0.005 and the minimum value is 0.002 3，and the regions with small strain are mainly concentrated in the range ofT≤12.5 mm，D1≥16 mm，D2≤10 mm.

Fig.11 Displacement distribution of screw structure

Fig.12 Strain distribution of screw structure

3.2 Comprehensive evaluation and decision?making

According to the simulation results，nine pa?rameters of screw structure sizeT，D1，D2，stress，displacement and strain of screw composite struc?ture and screw stress，displacement and strain are taken as optimization indexes. The nine parameters selected are all cost indicators. TheFdistribution of each evaluation method with the optimization param?eters is obtained as shown in Figs.13—15. Accord?ing to Fig.13，theFdistribution changes at different levels with the change of optimization parameters.The regions with smallerFvalue are mainly concen?trated in the range ofT≤13 mm，D1≥15 mm，D2≤4 mm，the minimum value ofFis 0.185 9，and the corresponding optimization parameter value isT= 12.2 mm，D1= 16 mm，D2= 2 mm.

Fig.13 F distribution of fuzzy matrix evaluation method with relative deviation

According to Fig.14，the regions with smallerFvalues are mainly concentrated in the range ofT≤13 mm，D1≥15 mm，D2≤3 mm，the maxi?mum value ofFis 0.795 14，and the corresponding optimization parameter values areT= 12.2 mm，D1= 16 mm，D2= 2 mm.

Fig.14 F distribution of fuzzy matrix evaluation method with relative superior membership degree

According to Fig.15，the regions with smallerFvalues are mainly concentrated in the range ofT≤13 mm，D1≥15 mm，D2≤3 mm，the maxi?mum value ofFis 0.804 3，and the corresponding optimization parameter values areT= 12.2 mm，D1= 16 mm，D2= 2 mm.

Fig.15 F distribution of variable weight grey correlation evaluation method

Take the six top schemes of the three evaluation methods to get theFranking and corresponding opti?mization parameter values，as shown in Table 1. It can be seen that the optimal schemes obtained by the three evaluation methods are allT= 12.2 mm，D1=16 mm，D2= 2 mm. TheFvalues of the first two schemes of the relative deviation fuzzy matrix evalua?tion method and the relative superior membership de?gree fuzzy matrix evaluation method are not signifi?cantly different，so the scheme withT= 12.4 mm，D1=16 mm，D2=2 mm can also be considered.

Table 1 F ranking of evaluation methods and corresponding optimization parameter values

4 Structural Verification and Con?tact Analysis

Taking the optimal schemeT= 12.2 mm，D1= 16 mm，D2= 2 mm，the structural verifica?tion and contact state analysis are carried out in AN?SYS，and the stress verification of screw composite structure and screw is obtained，as shown in Fig.16.It can be seen that the maximum stress of screw composite structure is 14.236 MPa，which is nearly 2 MPa less than that before optimization，and the maximum stress of screw body structure is 10 MPa.At the same time，the bearing capacity of the screw is significantly improved compared with that before optimization，which meets the expectation of opti?mal design.

Fig.16 Screw composite structure and screw stress verifica?tion

The contact state of screw composite structure is obtained as shown in Fig.17. It can be seen from Fig.17（a）that the contact state of some contact ar?eas of 1，2，4 and 6 contact pairs of the composite structure is embedded，which corresponds to the magnitude and direction of the force on the struc?ture，indicating that the materials in this part of the region have large contact pressure，which results in the mutual embedding of materials. The other con?tact surfaces are basically sliding or close，such as the contact surfaces corresponding to contact pair 3 and contact pair 5. According to the contact gap shown in Fig.17（b），the contact state between con?tact pairs can be further understood. The contact gap of contact pair 3 and contact pair 5 is about 0.5 mm，which is close to the contact state. Fig.17（c）shows the contact pressure distribution of each con?tact surface. The contact pressure of the embedded contact surface is larger，and the maximum contact pressure appears on contact pair 1 and it is 7.902 MPa，corresponding to the magnitude and di?rection of the stress on the structure. According to the contact slip situation in Fig.17（d），the sliding distance of contact surface corresponding to contact pairs 1 and 3 is relatively large. The main reason is that the screw moves along the radial direction after being stressed，resulting in the larger sliding dis?tance of contact surface corresponding to contact pair 3. At the same time，the cylinder surface of the screw head is in contact with the nylon bushing，re?sulting in larger contact pressure and a larger sliding distance in some regions of the contact surface.Comprehensive analysis shows that the contact state of screw composite structure under the design load is in line with the actual change.

Fig.17 Contact state of screw composite structure

5 Conclusions

The material substitution and structural contact optimization design of a load-bearing screw of space battery are studied. The double shear test of YS-20 bar is carried out，and the maximum shear stress is obtained，which verified the possibility of replacing nylon 1010. Without changing the original tooling，the screw structure is optimized and 294 schemes are obtained. The final scheme is obtained by using three comprehensive evaluation methods. The stress verification and contact analysis of the final scheme show that the comprehensive stress and shear stress meet the requirements. The screw can bear the weight of the battery body well in actual use，and can continue to be used after several work?ing cycles. It has strong anti-fatigue performance and long service life.