LINEAR AND NONLINEAR ANALYSES OF A WIND-TUNNEL BALANCE

Transcription

1 LINEAR AND NONLINEAR ANALYSES O A WIND-TUNNEL INTRODUCTION BALANCE R. Kakehabadi and R. D. Rhew NASA LaRC, Hampton, VA The NASA Langley Reseach Cente (LaRC) has been designing stain-gauge balances fo utilization in wind tunnels since its inception. The utilization of balances span a wide vaiety of aeodynamic tests. A foce balance is an inheently citically stessed component due to the equiements of measuement sensitivity. oce balance stess analysis and acceptance citeia ae unde eview due to LaRC wind tunnel opeational safety equiements. This pape pesents some of the analyses done at NASA LaRC. Reseach and analyses wee pefomed in ode to investigate the stuctual integity of the balances and bette undestand thei pefomance. The analyses pesented in this pape ae helpful in undestanding the oveall behavio of an existing balance and can also be used in design of new balances to enhance thei pefomance. As a fist step, maximum load combination is used fo linea stuctual analysis. When nonlinea effects ae encounteed, the analysis is extended to include the nonlineaities. Balance 1621 is typical fo LaRC designed balances and was chosen fo this study due to its taditional high load capacity, igue 1. Maximum loading occus when all 6 components ae applied simultaneously with thei maximum value allowed (limit load). This cicumstance nomally will not occu in the wind tunnel. Howeve, if it occus, is the balance capable of handling the loads with an acceptable facto of safety? Peliminay analysis using Po/Mechanica indicated that this balance might expeience nonlineaity. It was decided to analyze this balance by using NASTRAN so that a nonlinea analysis could be conducted. Balance 1621 was modeled and meshed in PATRAN fo analysis in NASTRAN. The model fom PATRAN/NASTRAN is compaed to the one fom Po/Mechanica. o a complete analysis, it is necessay to conside all the load cases as well as use a dense mesh nea all the edges. Because of compute limitations, it is not feasible to analyze model with the dense mesh nea all edges. In the pesent study, the dense mesh is limited to the suface on the end of the axial sections. APPLIED LOAD Peliminay linea analysis indicated that some of the load cases poduce high stesses on the balance, above yield stess. ou diffeent load combinations ae used fo the cuent analysis. Two of the load cases poduce stesses above yield stess and the othe two esult stesses below yield. Linea analysis is pefomed fo each load case. In the case whee the stess value is above the linea elastic egion, it is necessay to pefom a nonlinea analysis. The limit loads fo this balance wee obtained fom dawing (LD ) and ae shown in Table 1. The loads given ae in the coodinate system shown in igue 1. Tansfomation is necessay since the loads ae applied at Point p and the values given below ae valid fo loads applied at Moment Cente, o. oce and Moment Components oce (lb) and Moment (in-lb) Values Axial (x) 500 Side (y) 1800 Nomal (z) 3000 Roll (Mx) 7500 Pitch (My) Yaw (Mz) 4500 Table 1. Maximum oces and Moments (Limit Loads) fo Balance 1621 ou diffeent load combinations ae consideed and shown below. Case 1: x =-500 i ˆ y =1800 ĵ

2 z =-3000 kˆ M =7500i ˆ ĵ kˆ o Case 2: x =-500 i ˆ y =1800 ĵ z =3000 kˆ M = o î ĵ kˆ Case 3: x =-500 î y =1800 ĵ z =-3000k M =-7500 i o Case 4: x =-500 i ˆ y =1800 ĵ z =3000 kˆ M =-7500 i o ˆ ĵ kˆ ˆ ĵ ˆ k The tansfomation of the loads fom Moment Cente (MC) at point o to Point p is done using equation (1): M p = R + M = 4.1 i ˆ ( + + )+ M Equation (1) po o Moment components fo each case ae obtained afte substituting into equation (1): M p = 7500 î ĵ kˆ Case 1 M p = 7500î ĵ k ˆ Case 2 M p = -7500i ˆ ĵ kˆ Case 3 M = -7500iˆ ĵ kˆ Case 4 p x y z o 2

3 Z " Point o Point p X " 1.75 " igue 1. Balance 1621 with its coodinate axis located at the Moment Cente MODAL ANALYSIS Initial analyses wee pefomed with Po/Mechanica and late analyses with NASTRAN. In ode to bette undestand the stuctual behavio of this balance and compae models geneated in PATRAN with models geneated in Po/E, a modal analysis was pefomed. The natual fequencies and mode shapes wee obtained fom Po/Mechanica and NASTRAN and compaed. Single-pass adaptive (SPA) analysis was used in obtaining these esults fom Po/Mechanica. The fist 3 fequencies ae shown below fom both Po/Mechanica and NASTRAN. The fequencies fom the two models ae close. The esults indicate that the models, Po/E and PATRAN, ae oughly equivalent. Mode equency (HZ) equency (HZ) Mode Shape Po/Mechanica NASTRAN Bending about Z-axis Bending about Y-axis Axial Table 2. equencies fom NASTRAN and Po/Mechanica LINEAR ANALYSIS The pesent model was geneated and meshed using PATRAN. The section of the mateial whee the load is applied is not modeled in ode to educe the numbe of elements. The load is applied at Point p and tansfeed to the balance though a igid element. The esults ae expected to be accuate away fom the applied load due to St. Venant s pincipal. GLOBAL ANALYSIS Because of compute limitations, the model was meshed using a little less than 200,000 elements, all 10-node tetahedal elements, tet10. The esult of this un is used fo Global-Local analysis. Global-Local analysis is used in ode to obtain moe accuate esults fo the selected pats of the model. With this method, a desied section (local model) is meshed and loads and bounday conditions ae obtained fom the esults of the global model analysis. A 3-D view of the meshed global model used in the pesent wok is shown in igue 2.

4 igue 2. A 3-D view of the balance modeled and meshed in PATRAN The von Mises stess and pincipal stesses fo the axial section nea the applied load ae shown in igues 3 and 4, load case 1. As the figues indicate, maximum von Mises stess (267 KSI) and pincipal stess (274 KSI) both occu nea the applied load. It should be mentioned that the values shown ae fo the coase mesh. To obtain moe accuate esults, moe elements ae needed, paticulaly nea the cones. VascoMax C-300 is the mateial fo this balance and accoding to the manual fom TELEDYNE VASCO, it has a yield stess of 287 KSI. igue 3. The von Mises stess fo the balance, load case 1 4

5 igue 4. The maximum pincipal stess fo the balance, load case 1 LOCAL ANALYSIS O AXIAL SECTION NEAR THE APPLIED LOAD Thee ae many cones on the balance and in ode to captue the stess gadient, a dense mesh is equied nea these cones until convegence occus. In ode to use moe elements, because of the compute limitations, the global model has to be divided into smalle local sections. A section nea the applied load was extacted and meshed, igue 5. The esults of the global model wee used as the bounday condition fo this local model. The von Mises and pincipal stesses ae shown in igues 6 and 7. As the esults indicate, the maximum pincipal stess is above ultimate and the maximum von Mises stess is above yield. Hence, nonlinea analysis is needed. igue 5. A meshed view of the section of the balance nea the applied load 5

6 igue 6. Von Mises stess fo the section of the balance nea the applied load MODEL OR NONLINEAR ANALYSIS igue 7. Pincipal stess fo the section of the balance nea the applied load The esults fom the linea analysis indicate that the stess value is above the linea elastic egion; hence, nonlinea analysis is equied. Because NASTRAN tet10 elements do not allow some nonlineaity in the vesion used hee, the model used fo nonlinea analysis is meshed with 4 node tetahedal elements, tet4. The balance is meshed with almost 400,000 tet4 elements, igue 8. Moe elements ae used nea shap cones. A dense mesh is used nea the end of the axial sections, igue 9. Linea analysis was pefomed on the balance with the new mesh and all fou load cases wee consideed. If the linea analysis indicated a maximum stess value below yield stess, nonlinea analysis was not pefomed. 6

7 igue 8. Meshed balance fo nonlinea analysis igue 9. A close-up view of the end of the axial section 1. CASE 1 LOADING The full model is used fo the linea and nonlinea analysis. Also a local model, used in the linea analysis, is used hee again fo compaison. A. GLOBAL MODEL The esults of the analysis fo the load combination of Case 1 ae shown in this section. The full model is used and the esults fom the linea and nonlinea analyses ae shown. 7

8 LINEAR ANALYSIS The von Mises stess fom the linea analysis fo the balance is shown below. As igue 10 indicates, the maximum stess occus at the end of the axial section and is above the ultimate stess. igue 10. The von Mises stess fo the balance fom the linea analysis, Load Case 1 NONLINEAR ANALYSIS The von Mises stess fom the nonlinea analysis of the balance is shown below, igue 11. As expected, the value of the maximum von Mises stess dopped in compaison with the linea case. The maximum stess pedicted by the nonlinea analysis is below the yield point. 8

9 igue 11. The von Mises stess fo the balance fom the nonlinea analysis, Load Case 1 In ode to have an oveall view of the stesses eveywhee on the balance, igue 12 is plotted. igue 12 shows the position vesus von Mises stess fo all points on the balance. The figue clealy indicates that the high stess egions ae localized and the two peak stesses occu at the end of the axial sections. It should be noted that the maximum stess value nea othe cones might incease as moe dense mesh is used nea those cones. Howeve, in the pesent wok, the inteest is at the end of the axial section. igue 12. Axial position vs. von Mises stess fo all points on the balance, Load Case 1 The stess values on the +Y and Y sides of the balance ae plotted individually and shown in igues 13 and 14. As shown, the maximum stess occus on the Y side of the balance fo this load case. 9

10 igue 13. Position vs. von Mises stess fo points located on the +Y side of the balance, Load Case 1 10

11 B. LOCAL MODEL igue 14. Position vs. von Mises stess fo points located on the -Y side of the balance, Load Case 1 The local model of the balance used fo the linea analysis, fom the pevious section, is used hee again fo Global-Local analysis. The local model is meshed with tet4 elements fo the nonlinea analysis, igue 15. The bounday conditions ae obtained fom the linea un. The von Mises and pincipal stesses fo the nonlinea analysis ae shown in igues 16 and 17. The compaison of the linea and the nonlinea uns fo the axial section nea the applied load is shown in Table 3. As expected, stesses obtained fom the nonlinea analysis dopped in compaison with the linea analysis and ae in ageement with the analysis of the global model. Linea Analysis Nonlinea Analysis Von Mises Stess 351 KSI 287 KSI Pincipal stess 312 KSI 249 KSI Table 3. Maximum von Mises and pincipal stesses fom the local model 11

12 igue 15. Axial section of the balance nea the applied load igue 16. Von Mises stess fo the section of the balance nea the applied load fom the nonlinea analysis, Load Case 1 12

13 igue 17. Pincipal stess fo the section of the balance nea the applied load fom the nonlinea analysis, Load Case 1 2. CASE 2 LOADING LINEAR ANALYSIS The von Mises stess fom the linea analysis fo the balance is shown below. As the figue indicates, the high stess occus at the end of the axial section. 13

14 igue 18. The von Mises stess fo the balance fom the linea analysis, Load Case 2 igue 19. The pincipal stess fo the balance fom the linea analysis, Load Case 2 14

15 NONLINEAR ANALYSIS The von Mises and pincipal stesses fom the nonlinea analysis ae shown in igues 20 and 21. As expected, the maximum stess value fo the von Mises and pincipal stesses dopped in compaison with the linea analysis. igue 20. The von Mises stess fo the balance fom the nonlinea analysis, Load Case 2 igue 21. The pincipal stess fo the balance fom the nonlinea analysis, Load Case 2 In ode to have an oveall view of the stesses eveywhee on the balance fo this load case, igues 22 and 23 ae plotted. igue 22 shows the stess fo the von Mises and igue 23 shows the pincipal stess on the balance. 15

16 igue 22. Position vs. von Mises stess fo all points on the balance, Load Case 2 igue 23. Position vs. pincipal stess fo all points on the balance, Load Case 2 16

17 3. CASE 3 AND CASE 4 LOADING igue 24. The von Mises stess fo the balance fom the linea analysis, Load Case 3 igue 25. The pincipal stess fo the balance fom the linea analysis, Load Case 3 17

18 igue 26. The von Mises stess fo the balance fom the linea analysis, Load Case 4 igue 27. The pincipal stess fo the balance fom the linea analysis, Load Case 4 DISCUSSION AND CONCLUSION Modal analysis was pefomed to compae the models fom Po-Engineeing/Po-Mechanica and PATRAN/NASTRAN. ou diffeent load combinations wee used and two of the load combinations equied nonlinea analysis. As the table below indicates, the maximum von Mises stesses pedicted by the nonlinea analysis ae below yield, howeve thee is little o almost no facto of safety. 18

19 Linea Analysis Von Mises (KSI) Linea Analysis Pincipal (KSI) Nonlinea Analysis Von Mises (KSI) acto of Safety Case Case Case Case Table 4. Compaison table between linea and nonlinea analysis RECOMMENDATIONS ANALYSIS It should be noted that not all the balances and not all the load combinations equie nonlinea analysis. o the existing balances, Po/Mechanica, NASTRAN, o othe inite Element softwae can be used fo linea analysis. o a complete analysis, all the load cases need to be consideed. Having the model in Po/Engineeing makes Po/Mechanica a good candidate fo stess analysis. If the maximum stess value obtained is beyond yield, eithe a change in the design is needed o the maximum loads allowed need to be educed. The eduction of the foce can be in cetain components, and this is pactical, since in most cases the wind tunnel tests do not equie the simultaneous application of all maximum load components. In some cases the wind tunnel test may equie some components above thei maximum value while the maximum value of the othe components ae not needed and can be educed. DESIGN o the balances that will be designed in the futue, it is impotant to conside the facto of safety in the design stage. Inceasing the size of the fillets helps to elieve some of the high stesses, which occu locally. In some locations such as the end of the axial section, the shapness on one side can be emoved by taking the unnecessay shap cones out. This can be done on the new o existing balances. Doing so, will educe the maximum value of stess fom those cones with little effect on the oveall pefomance of the balance. 19