Impact Experimental Analysis and Computer Simulation Yucheng Liu Department of Mechanical Engineering, University of Louisville

Transcription

1 Impact Experimental Analysis an Computer Simulation Yucheng Liu Department of Mechanical Engineering, University of Louisville Abstract In this paper, an automotive bumper system (a bumper connecte to a frame through joints/connections) is set up for small impact tests (nonestructive tests). During the tests, a steel bar is raise to certain highs then release from there an hit onto the bumper system, the bumper system is fixe to the groun through fully constraining the en of two shocks, the reaction forces at the en of shocks uring the whole impact process are measure an investigate in orer to etermine how they are transferre to the joints then to the rest part of the frame. Also, other important experimental ata are collecte an stuie to reflect the actual impact process. A finite element moel is create for the automotive bumper system an the impact test is also simulate on the computer using ANSYS. The results from the experimental tests are compare an correlate to the finite element simulation. From the comparison, it is foun that the experiment results an FEA results matches very well an the valiity of the computer moel is then verifie. Aitionally, this paper also inclues a han calculation of the impact problem, where the bumper system is moele as a simple spring-amping system an solve using classical ynamic theory; the han solutions are also compare to the experimental results an the FEA results to verify the correctness an reliability of the impact tests an computer simulation. Introuction This project is to compare an correlate the experimental results, the computer FEA results an the theoretical results for a small impact case, then to show that for any small impact case a reasonable computer moel can be foun to simulate it. In the project an automotive bumper system is use to perform the impact tests, some important experimental ata such as reaction forces an isplacements at certain locations are recore, an a computer FEA moel is create for the bumper system. A transient ynamic analysis is performe to simulate the impact tests, an the corresponing computer results are obtaine. Finally, the bumper system is moele as a simple spring-amping system an a han calculation is one to get the theoretical results, all the three results are compare an correlate, an the strengths an the weaknesses of the project are iscusse. The objectives of the project are to verify the efficiency of the computer moel an the computer simulation, an to prove that there always existe a computer moel that can be use to simulate any small impact cases. At the same time, the behavior of the bumper system uring the impact process is stuie an how the impact forces are transmitte to the joints an how they are transferre from the bumper to the frame are explaine through the project. Literature Review Before starting this project, some of publishe literatures an previous researches have been reviewe buil up a soli backgroun in the area of experimental analysis an finite element analysis. Toshiyuki Sawa, Yoshihito Suzuki, an Shoichi Kio use finite element metho to analyze the stress wave propagations in ahesive joints of similar hollow cyliners uner static an impact tensile loaings in elastic eformation range. They use DYNA3D to start the analysis an applie the impact loaing to the joint by ropping a weight. The effects of the Young s moulus of the ahesive on the stress wave propagation at the interfaces were examine an finally they foun that the characteristics of the joints subjecte to impact loaings were opposite to those subjecte to static loaings. [9] Thomas J. Trella, Rana Rawan, Samaha (1995) escribe the evelopment an valiation of a computer base moel of the moving eformable barrier evelope for sie impact safety performance simulations using LS-DYNA3D. They investigate the effects of important factors central to FEA moeling such as

2 material noe merging, mesh ensity, an element type an then foun that the material amping coefficient an compacte Young s moulus both ha a strong influence on the simulate impact responses. [7] Davi H. Johnson, Richar B. Englun, Brian C. McAnlis, Kevin C. Sari, an Davi Colombet presente a moeling technique use to create a mostly-brick meshe 3D moel of a nut an bolt joint using ANSYS an the create 3D moeling can simulate the conitions of joint tightening an sliing along the helical threa flanks when the nut is turne. [4] For engineers (2001) evelope a target-vehicle moel use for computer simulation of vehicle crash compatibility. For the target-vehicle moel they chose five frontal impact moes to test it, which inclue full frontal impact an corner frontal impact. After running the analysis the moel woul provie the vehicle responses an component characteristics such as compression, tension, bening stiffness an rate effects which were use to compare with the results of vehicle-to-vehicle test. The target-vehicle moel was then be calibrate an optimize base on the results of comparison until an ieal target-vehicle was reache in the en. The methos an ieas utilize in the moeling process were kin of enlightening. [5] S. W. Kirkpatrick, J. W. Simons, an T. H. Antoun (2000) evelope an valiate a high fielity finite element moel of a full size car for crashworthiness analysis, which was part of an overall program to evelop a set of etaile finite element moels for various vehicles. In the program, they selecte the For Crown Victoria as the representative full size car an briefly escribe the moeling proceure incluing the vehicle tearown an igitization an moel generation. The techniques use in vehicle igitization; the mesh an the element type use in the FE moel were introuce, an the evelope FE moel was presente too. The authors performe the component crash tests an vehicle crash tests separately an obtaine a set of ata from the tests for valiating the crash moel. In their paper, they introuce the test conitions an analyze an compare the test results thereby conclue the overall collision response of the vehicle an verifie the valiity of the evelope moel. [5] From above emonstration, tremenous avancements have been mae on the computer simulation of impact analysis an the FEA methos an the CAE tools ha been intensively applie for solving such problems. An in this project, the path put forwar in those previous literatures is followe to create an valiate a computer moel an it is prove that the methoology use in the project coul be sprea into other impact problems. Methos an Materials Experimental Analysis Experiment setup In the experimental part a series of small impact tests have been performe on the bumper system. During the tests, the reaction forces at the en of two shocks are measure, an the isplacements at the connections between the shocks an the bumper are recore either. The whole experiment system is set up like this: a bumper system is obtaine an hel by a bracket, a long steel pipe is hel vertically to serve as a guie through which the hitting object can vertically rop onto the bumper. A 10.5, 8.4 lb iron bar with a long nylon string tie on its en is use as the hitting object, the nylon string is marke at ifferent locations such as 3, 4, etc. in orer to control the iron bar s initial position. Thus, with the initial position of the iron bar, h, the bar s initial velocity when it hit on the bumper can be easily etermine using the formula v 2 = 2gh. The bumper system use in the tests is etache from a 1980 Volkswagen. Since the original shocks are almost faile so they have been taken away an two soli steel cyliners are use to replace the shocks that connect the bumper an the frame together. Two ynamic loa transucers, whose type is 208 A03 an limit is 800lb, are use to measure the reaction forces; the loa transucers are installe at the en of the shocks an are fixe to the bottom plate of the bracket using bolts an nuts. A sensitive isplacement sensor (DVRT) is applie for capturing the isplacements at the connections between the bumper an the shocks, the tip of the sensor just contacts the bumper s surface where the isplacement woul be measure, an then is glue to the surface using epoxy to avoi it separating from the surface uring the impact process. All the transucers go to an amplifier, an the output signals come

3 out as voltage. A ata acquisition system is use to collect all the experimental ata, an a special labview program (Bumper.vi) is create to isplay these signals on a computer an store them on the isk. The last experimental ata isplaye on the reports shoul have been transferre from the volts to corresponing pouns (for reaction forces) or inches (for isplacements) by a certain scale. Figures 1 to 3 show the bumper system an the experimental setup. Figure 1. Bumper system installe on the bracket Figure 2. Experimental set up for impact test

4 Figure 3. Displacement transucer (DVRT) Impact tests First of all, the iron bar is roppe onto the center of the bumper surface from three heights 3, 4, an 6 to measure the reaction forces. Different initial heights are chosen here so that the effects of initial velocities on the impact test can be stuie while it has to be promise that the maximum impact force woul not excee the transucer s limit. At each height, the iron bar is roppe three times to remove the unexpecte external interferences. Special Labview program is running uring the tests an for each ropping the reaction forces curve is isplaye on the computer an save to the isk. Thus, overall 9 plots are obtaine from the tests, an these plots will be compare an use later. After measuring the reaction force, the force transucers are remove an the DVRT is installe. The locations where the isplacement is measure are marke an the DVRT is glue to the point to make the sensor keep touching with the measure locations uring the whole test. This time the iron bar is only roppe from 10 high an similarly, it is roppe three times at both positions. After all ropping tests finishe, the experimental ata an relate curves are save an ocumente for further analysis. Experimental results an analysis Because the bumper system is a symmetric structure, so the reaction forces shoul be the same for either en of shocks, therefore, the reaction forces at either sie can be taken for analysis. Here the left han sie reaction forces are taken as samples. Figure 4 shows one of the reaction force plots when the bar is roppe from 6 inches high. As compare to other plots, it can be foun that for ifferent initial positions, both of the shape of the force curves an the times at which the peak reaction force appeare are similar, an only the peak force values change. This means that in the low velocity impact cases, the velocity oesn t change the bumper s behavior but changes the impact force. (The comparisons are shown in table 1). Also, as compare the reaction force plots that roppe from the same initial position, it is observe that the peak force appears at the same time, an the peak force values are close to each other (varie within ± 20 lbs range because of the uncontrollable factors uring the impact).

5 Figure 4. Reaction force curve for 6 ropping Table1. The effects of initial positions on the reaction forces (average value liste) Initial position (in) Initial velocity (in/sec) Peak force (lb) Time (sec) After measuring the reaction forces, the loa transucers are remove an the isplacement transucer DVRT is mounte to measure the isplacements. In orer to have an obvious isplacement, the impact bar is raise to 10 high an roppe from there. The isplacements at both connections between the bumper an the shocks are measure an similarly, the object is roppe three times at each position to verify the reproucibility of the impact. From the resulting plots, it can be seen that the isplacements at either connections are almost the same because the bumper system is perfectly symmetric about its center axis. Thus, the isplacement measure at left connections is selecte for further stuy, which is shown in figure 5. Figure 5. Displacement curve for 10 ropping

6 Figure 5 isplays the isplacement variation at the left connection uring the impact process. The first peak isplacement is , which happene at secon, an the secon peak isplacement is that happene at secon. The big ecrease between the first two peak values shows that the bumper system ha a large amping ratio value (the amping value will be calculate later), an the increase in the fourth peak value is because that the bar reboune after it impacte onto the bumper an hit the bumper again. Thus, from the figure 4 an figure 5, the bumper s behavior uring the impact test can be roughly outline. During the impact tests, as the ropping bar impacte to the center of the bumper, the bumper is compresse by the impact force uring the first secons an move own, then returne back through the static position by a much smaller amplitue in another shorter time. After that the bumper experience several small oscillations until it reache its static position. However, the DVRT measure the maximum isplacement at , which might be oubte an will be explaine later. Computer Simulation CAD Moel In computer simulation, a CAD bumper moel is first create using IDEAS. All the geometric imensions of the bumper system incluing the two shocks are measure an special moeling techniques such as reflecting, lofting, sweeping, an shell are applie to create the structure with a long curve surface. Figure 6 shows the bumper s CAD moel. Figure 6. Bumper s CAD moel Finite Element Moel (FE Moel) After finishing the CAD moel, the bumper moel s atabase is then transporte to an IGS file an importe into ANSYS environment to provie the original geometric information for the new finite element moel. In creating the finite element moel, the 2D shell element, shell 181, is use to mesh the bumper surface, an the 3D elastic beam element, beam 188, is use to mesh the two shocks. The impact bar can be meshe with 3D soli elements, since the impact bar s eformations or stress istributions are not concentrate in this problem, so the element shell 181 can be still use to mesh the iron bar. The material of the bumper surface is aluminum, an the materials of the impact bar an shocks are steel. The real constants correspon to each element is etermine from the measure imensions. Figure 7 shows the create FE moel, which inclue 230 elements an 357 noes.

7 Figure 7. Bumper s FE moel Computer Analysis The whole impact process will be simulate on a computer by running a transient analysis. In the transient analysis, the impact test that the bar was raise to 6 high then roppe onto the bumper system is simulate to get the reaction force. As set up in the experiment, both ens of shocks are fully constraine; the initial velocity of the impact bar is assigne as in/sec, an acceleration 386 in/sec 2 is applie on the entire environment to simulate the gravity. As a contact problem, the front surface of the bumper is efine as the target surface, an the surface of the impact bar is efine as the contact surface. The solution time is set to 0.04 secons accoring to the sampling time in the experiments so that both results can be easily compare. At last the steppe loa is use an the number of the substeps is set to 80. To fin the isplacements, the same settings are still use except that the initial velocity is reset to in/sec to simulate the effect of a 10 high ropping. Accoringly the solution time is set to 0.05 secons an the number of the substeps is set to 100. In orer to truly reflect the actual experiments, uring the computer analysis, the large eformation option (nlgeom) is turne on, a numerical amping ratio is ae, an the elasto-plastic moel is use in efining the real constants. After all the analyses finishe, the ynamic reaction force at the en of the left shock an the ynamic isplacements at the connection between the left shock an the bumper are plotte out, an liste in the time-history postprocessor. Figures 8 an 9 isplay the reaction force curves an the isplacement curves respectively. Figure 8. FE results for reaction force of 6 ropping

8 Figure 9. The FE results for isplacement of 10 ropping Comparisons an Analysis As compare the computer results to the experimental results, it can be seen that for the reaction forces of 6 ropping, the computer analysis yiels the maximum force 468 lb that appeare at sec, which matches to the experimental results very well. The comparison verifies that the computer moel can preict the peak force value an its appearing time accurately, which is very meaningful in stuying how the impact force is transferre from the bumper to the rest part of a vehicle uring crashes. While the weakness of the computer simulation is that it i not truly reflect the entire impact process, instea of many small oscillation curves shown in the experimental results, the computer moel only yiels a smooth curve an omits all the small oscillations an waving. However, the figure 9 gives out the maximum isplacement as 1.33E-4 inches at secon, which significantly iffers from what has been obtaine in the experiment ( ). To evaluate the actual isplacement, two extreme conitions are consiere. First of all, the shock is looke as a spring whose stiffness is EA/L. If the shock is applie by a static force that equals to the maximum reaction force uring the 10 ropping which is lb (obtaine from the computer analysis), the maximum isplacement will be = F/ (EA/L) = 4.59E-5 inches. Also, if the shock rops from 10 high to the groun, the maximum eformation can be calculate using = vl / a. Where the v is the impact velocity which can be calculate as in/sec, an a is efine by the shock s young s moulus an ensity as a = E / ρ 5. Then the can be calculate as 3.56E-3 inches. Base on the evaluations, the actual isplacement shoul lay within 4.59E-5 an 3.56E-3 inches an it can be foun that the computer result is in this range while the experimental result seems much higher. The possible reason maybe ue to the shaking of the bumper system uring the impact process, since the isplacements measure in the tests are very small, so any tiny shakings of the bumper system can cause big ifferences. To overcome this shortcoming, an obvious isplacement such as the eflection at the center of the bumper nees to be measure. Theoretical Solution The han calculation of the impact problem is accomplishe by applying classical ynamics theories. At first, the bumper system is moele as a simplifie support beam structure with both ens fully constraine. From the mechanics of materials, the stiffness of the beam is EI 48 L 3 when the external loas applie on its center. Where the young s moulus, E of the aluminum bumper is 10E6 psi, the total length L is measure as 55 in, an the moment of inertia I is rea from the ANSYS output file as in 4. So the stiffness K of the bumper system can be evaluate as lb/in.

9 Figure 10. The equivalent beam structure of the bumper system Thus, the whole bumper system can be consiere as a spring amping system whose stiffness is lb/in, an the impact problem can be moele as figure11. Figure 11. The equivalent spring amping system The governing equation for figure 11 is... x + kx = W m x+ c (1) Where the W is the weight of the impact bar an the bumper itself, which is 24.4 lb in this project. Now this problem is reay to be solve to fin the maximum reaction force, the maximum isplacement an the corresponing time. Actually such kin of problem has been mostly solve by V. I. Babitsky [17], from his theories the maximum isplacement is solve as X ( t1) = n v 2 1 ξ exp[ An the corresponing time t1 is 1 1 t1 = tan ξ n (3) ξ tan 2 1 ξ ξ ]sin tan ξ ξ ξ (2) Starting from (2) an (3), the reaction force then can be erive. From equation (1), the reaction force formula can be written as F = c x+. kx (4) An from the force balance theory, the function of isplacement x can be expresse by the equation (2) as X (t) except to use general time t instea of the special time t1. In orer to fin the maximum reaction force F, it is only nee to solve the ifferential equation F/t = 0 to fin the corresponing time t2, then substitute the t2 back into the equation (4) to fin the maximum reaction force. Following these steps the time t2 is solve as

10 1 t2 = tan 1 Cξ n + k ξ nk C + (5) An the maximum reaction force F is F Cv kv exp( ξ nt2 )( cos t2 ξ n sin t2 ) + exp( ξ nt2 ) sin t = 2 W + k Thus, the equations (2), (3), (5), (6) will be the governing equations in this han calculation, where the n = k / m, C = 2ξ n, an the 2 = n 1 ξ. The parameters that will be use in the equations are: K = lb/in; W = 24.4 lb; g = 386 in/sec 2 ; V is the initial velocity that liste in table 1; an for the amping ratio,ξ it can be calculate from the isplacement plots (see figure5) by using the logarithmic y1 ecrement metho, which isδ = ln = 2πξ 2 y2 1 ξ, where the y 1 an y 2 are the two successive peak amplitues which are measure from the figure 5. Then the amping ratio value is etermine as 0.28 (as mentione before, because the experiment may not give the correct isplacement result, the amping ratio value use here is still nee to be verifie). Substitute all the parameters into the equations an all the results can be calculate using Microsoft Excel. Table 2 lists the han calculation results an the corresponing experimental results for reaction forces. From the table it can be seen that the reaction forces obtaine from the impact tests an calculate in this section are correlate very well (with maximum error only about 5.5%), while the appearing times show some ifferences, which means that the simplifie numerical moel can represent the actual impact system in a certain level consiering all the simplifications an assumptions taken in the moeling process. Table2. The theoretical results an the experimental results for reaction force Initial position (in) Peak force (lb) Time (sec) Experimental Theoretical Error (%) Experimental Theoretical (6) For those impact cases that have not been one in the experiment, the maximum reaction force value can also be evaluate by using the han calculation as well as computer simulation. For example, even the reaction force of ropping the bar from 10 inches high has not been measure because of the limitation of the loa transucers, it still can be evaluate on the computer an be calculate using above equations as well. The computer moel gives the maximum force was lb at secon while the theoretical results is lb at secon, the error of the maximum force value is only about 3.4%. Parametric Stuy As emonstrate in theoretical solution, it can be seen that the system stiffness k an the system s amping ratioξ are the two most important parameters, which etermine the maximum reaction force an its appearing time. To fin how they affect the results separately, ifferent k an ξ values are substitute into above equations, an relate maximum reaction forces an times then can be calculate using Excel. For an

11 example, in the 6 ropping test, the stiffness is firstly kept unchange, an theξ value is set to change from 0.05 to 0.5 with equal increment of 0.05 then calculate the maximum reaction forces an the appearing times. Figures 12 an 13 show the relationships of ξ - time an ξ - reaction force. Figure 12. Relationship between amping ratio an peak value time Figure 13. Relationship between amping ratio an maximum reaction force From the figure 12 an 13, it can be seen that the increase in the ξ will ecrease the time, which means that the larger is theξ, the sooner the maximum force appears. Nevertheless, the ξ value oes not obviously affect the maximum force. From figure 13, it can be foun that the ξ -force plot is a smooth curve that varies gently. The peak force value goes own with the increasingξ till it reaches the lowest value at about 457 lb when the ξ equals to 0.3 an then it rises up with the increasingξ. After that, the ξ value is fixe at 0.28, as the value use in the theoretical calculation, an the stiffness value is change from 1000 lb/in to lb/in with the same increment 1000 lb/in. Figures 14 an 15 show the relationship of k- time an k- reaction force.

12 Figure 14. Relationship between stiffness an peak value time Figure 15. Relationship between stiffness an maximum reaction force From figure 14, it can be seen that similar to the amping ratio, the increase in the k will ecrease the time too. However, unlike the amping ratio, when the stiffness increases from 1000 lb/in to lb/in, the maximum reaction force value also increases from about 200 lb to above 700 lb, which increases by 3.5 times. Conclusions an Evaluations Base on above emonstrations, it is conclue that the computer moel can correctly preict the reaction force in nonestructive impact test. The hypothesis of the project is then testifie through comparing the experimental results an computer results, an also is confirme by theoretical evaluation. Tables 3, 4, 5 isplay the results of comparisons among the experimental results, the computer results an the theoretical results of the reaction forces of 3, 4, an 6 ropping tests. From these tables it can be seen that the experiment an computer moel yiel very close results incluing the force an the time, an the reaction force can also be verifie through the theoretical solution. Table3. Reaction force of 3 ropping test Maximum force (lb) Error (%) Time (sec) Experimental results Computer results Theoretical results

13 Table4. Reaction force of 4 ropping test Maximum force (lb) Error (%) Time (sec) Experimental results Computer results Theoretical results Table5. Reaction force of 6 ropping test Maximum force (lb) Error (%) Time (sec) Experimental results Computer results Theoretical results From above results, it can be conclue that the reaction forces obtaine from the computer moel, the experiment, an the theoretical solution correlate very well. As for the peak value time, the computer moel an the experimental give very close values an the ifferences cause by the theoretical solution may ue to the simplifications an assumptions that have been taken uring the calculations. Through the experiments an the computer analysis, the behavior of the bumper uner a low velocity impact can be etermine. During the impact, the transferre force reaches its peak value shortly after the impact then reuces own an unergoes a series of smaller fluctuations until achieves to its static value. Though the effectiveness of the computer moel has been verifie, there still exist some isavantages in the project except the weakness of the experimental isplacement plot. That is, as mentione before, the computer moel can expect the maximum reaction force well but it is not goo in simulating the entire impact process. Therefore, the create computer moel is still nee to be moifie an refine, an some avance moeling techniques are require to improve the quality of the current computer moel. On the other sie, as presente in the paper, the force that transferre from the bumper to the frame uner low velocity impact is stuie, but how it is transferre into the entire vehicle? What its response might be uner a estructive impact such as buckling? An is it possible for us to evelop a generous moeling methoology that can be use for eveloping the computer moel for any impact cases instea of only for vehicle crashworthiness? All these questions nee to be answere in future works. References 1. Abullatif K. Zaouk, Nabih E. Beewi, Cing-Dao Kan, Dhafer Marzougui, Development an evaluation of a C-1500 pick-up truck moel for roasie harware impact simulation. 2. H. Shakourzaeh, Y. Q. Guo, J. L. Batoz, Moeling of connections in the analyses of thin-walle space frames. Journal computers an structures 71 (1999) S. Moura, A. Ghobarah an R. M. Korol, Dynamic response of hollow section frames with bolte moment connections. Journal of Engineering Structures. Vol. 17. No. 10, PP , Davi H. Johnson, Richar B/ Englun, Brian C. McAnlis, Kevin C, Sari, Davi Colombet, Three-imensional moeling of a bolte connection. 5. Front bumper component test. Applie Research Associates, Inc. 6. Composite an metallic crash performance.

14 7. Trella, Thomas J.; Samaha, Rana Rawan (1995), Finite element moel of a Moving Deformable Barrier for Feeral Motor Vehicle Safety Stanar 214 sie impact collision. Journal: ASME, Applie Mechanics Division, AMD, v210, C. L. Li, K. M. Yu, T. W. Lam (1997), Implementation an evaluation of thin-shell rapi prototype. Journal: Computers in Inustry 35 (1998) Toshiyuki Sawa, Yoshihito Suzuki, Shochi Kio, FEM stress analysis an strength of ahesive butt joints of similar hollow cyliners uner static an impact tensile loaings. Journal of Ahesion Science an Technology, v16, n11, 2002, p A. N. Palazotto, E. J. Herup, L. N. B. Gummai, Finite element analysis of low-velocity impact on composite sanwich plates. Composite Struictures, v49, n2, 2000, p Woo Jong Kang, Hoon Huh, Crash analysis of thin-walle structures with an elasto-plastic finite element metho. Key Engineering Materials, v , ptl, S. H. Choi, S. Samaveam, Visualization of rapi prototyping. Rapi prototyping Journal, v7mn2, 2001, p S. Timoshenko, D. H. Young, W. Weaver, Jr., Vibration problems in engineering. 14. Mario Paz, Structural ynamics (theory an computation). 15. I. Bykhovsky, Funamentals of vibration engineering. 16. C. E. Cree, Shock an vibration concepts in engineering esign. 17. V. I. Babitsky, Theory of vibro-impact systems an applications. 18. Yu Chen, Vibrations theoretical methos. 19. Robert K. Vierck, Vibration Analysis. 20. Robert D. Cook, Finite element moeling for stress analysis.