Random Vbraton Fatgue Lfe Smulaton of Bolt-on Metal Brackets usng LS-DYNA Jong S. Park Ramakrshna Dospat Ye-Chen Pan General Motors Amt Nar Lvermore Software Technology Corporaton Abstract Predcton of Vbraton Fatgue Lfe s an mportant mlestone durng product desgn and development of Vehcle Brackets. Bracket n Vehcle s defned as a smple structure fastened to foundaton structure or other brackets supportng mass of varous modules. CAE smulaton for Fatgue Lfe predcton gves useful nformaton early n desgn cycle, and saves consderable tme and cost compared wth physcal Shaker Table tests. LS-DYNA Implct Smulaton technology for Random Vbraton Fatgue Lfe of Bolt-on Metal Bracket s developed. The smulaton provdes flexblty to evaluate multple desgn optons and accommodate desgn changes early n producton development cycle. Bolt Fastenng s ncluded n the Smulaton Process and the Fastenng Stress s assumed to be mantaned as the pre-stress for the assessment of Vbraton Fatgue Lfe. Ths Fastenng Stress s often very hgh and results n sgnfcant effect on Fatgue Lfe. Random loadng s provded va the Power Spectral Densty (PSD), whch descrbes exctaton acceleraton levels n the frequency doman. System response to unt exctaton s calculated usng LS-DYNA s steady state dynamcs analyss. Ths analytcal stress FRF and random loadngs are then combned to calculate the stress response PSD, whch s cyclecounted and used for the calculaton of Fatgue Lfe. Introducton In GM, Bracket desgn can be valdated wth CAE Smulaton of the followng typcal Bracket Performances; (1) Resonant Frequency, (2) Mechancal Shock from Road Loads lke Pot Hole, (3) Mechancal Shock from Mnor Collson, and (4) Random Vbraton Fatgue. GM Bracket Valdaton Specfcatons are documented n many publc GM Documents ncludng GMW3172 (General Specfcaton for Electrcal/Electronc Components Envronmental/Durablty), GMW17010 (Mechancal Shock and Vbraton Durablty Test - Thermal Under Hood Procedure Specfcaton), GMW16390 (General Specfcaton for Analyss/ Development/ Valdaton (A/D/V) of Rechargeable Energy Storage Systems), and etc. Bolt-on Brackets are fastened by specfcaton defned n GMW17000 (GM Global Fastenng Catalogue). The nomnal Standard Dynamc Torque of Torque Specfcatons Table n GMW17000 s used for the smulaton. Bracket Supplers can buy GM Documents onlne at HIS Markt Standards Store, and obtan specfc requrements to valdate ther parts as specfed n GM Documents. In ths paper, only Random Vbraton Fatgue (RVF) s the scope of work. In most cases of Vbraton Fatgue of Vehcle, the loadng s non-determnstc except few parts. In other words, many vbraton envronments are not related to a specfc drvng frequency, and have nput from multple sources such as Road Profles and Powertran Vbratons that requres RVF. For the predcton of RVF, component-level smulaton s chosen n order to (1) utlze the exstng GMW Valdaton Specfcaton of physcal Shaker Table test, and (2) effcently apply to all Brackets ndependent from the parent Vehcle-level performances. In ths paper, a VBM (Vdeo Bypass Module) Bracket s chosen to demonstrate smulaton of RVF usng LS-DYNA Implct. June 10-12, 2018 1
Example of VBM Bracket A 1.2mm Gage CR1 Steel Bracket holds a 200 Gram VBM (Vdeo Bypass Module) through three clps, and undergoes two sets of loads; (1) Two M6 Bolt Torque 9NM as specfed n GM Global Fastenng Catalogue, and (2) PSD Input of Random Road and Powertran Exctaton specfed n a GMW. The bracket s mounted to the vehcle by two Bolts as shown n the Fgure 1. The VBM Bracket holds the VBM Module Assembly through the snap fts. The VBM Bracket Assembly s fastened to vehcle body structure sheet metal part. Fasteners are represented as pre-stress of Bolt Shank to smulate the Fastenng effect. In ths example, two M6 Bolts are used whch s represented n hexa domnant mesh wth Pretenson secton defned at md span of bolt shank length. The VBM Polymer Holder s held by sheet metal wth expanson clp. Expanson clp s modeled wth desgn nference to smulate the clp expanson load. Shaker table was modeled to represent the vehcle fastenng deally representng the fxture scenaro. The LS-DYNA model s composed of 22408 elements and 30441 nodes as shown n Fgure 2. The VBM Bracket s modelled as 1739 shell elements, whle the other parts of VBM Module, Polymer Holder, and Bolt & Nuts are n sold elements. The average mesh sze s 3mm wth the mnmum length of 0.73mm n a few areas to accommodate geometry detal. VBM Assembly Part data s shown n Table 1 n Unts of Kg, MPa, & mm. Snap ft that holds the module and clp that clamps sheet metal to VBM polymer bracket has desgn nterference. Desgn nterferences are represented wth contact nterference - Shrnk. Bolt Fastenng Force s appled to bolt pretenson secton that fasten Sheet metal and Shaker Table. Shaker Table s constraned to represent the grounded fxture as the exctaton zone. Input PSD from GMW16390 s shown n Fgures 3 and 4 as graphs of the dstrbuton of the acceleraton levels over a range of frequences n two dfferent sets of measurng unts. Fgure 1: VBM Module Assembly n CAD Dsplay June 10-12, 2018 2
Fgure 2: Geometry and Mesh of VBM Module Assembly n LSPP Wndow Table 1: VBM Assembly Part data n Unts of Kg, MPa, & mm Fgure 3: GMW16390 Input PSD Plot and Table n Unts of Gravtaton and Hz June 10-12, 2018 3
Fgure 4: GMW16390 Input PSD Table and Plot n LS-DYNA Unts n mm, msec, and KHz LS-DYNA RVF Smulaton Process The process chart shown n Fgure 5 s the LS-DYNA Functons wth Keywords used for the smulaton; Bolt Fastenng, Modal, and Fatgue. These smulaton procedures are seamless wthout beng stopped and restarted, and run as one sngle job launch. Fastenng Force s nput to Bolt Fastenng, and PSD Input data for each X, Y and Z-Drecton are nput to Fatgue. For Fatgue, ndvdual drectonal smulatons as well as a combned PSD Input of X, Y, and Z are run as separate load cases. Fgure 5: LS-DYNA RVF Process Flow Bolt Fastenng The smulaton s performed n Implct LS-DYNA wth nonlnear geometrc and materal effect consdered for the entre loadng. In Step-1 of Bolt Fastenng, the desgn nterference load s appled so that snap and clp area are subjected to stran movement untl the nterference between parts s removed. Ths transton ft s carred out usng *CONTACT_AUTOMATIC_SURFACE_TO_SURFACE_MORTAR wth flag IGNORE n Optonal Card C set to 3 and MPAR1 set to a tme to remove the transton ft. Fgure 6 shows the keyword format. June 10-12, 2018 4
Fgure 6: Contact card defnton for Snap-Ft In Step-2, Bolt Fastenng Force of 8200N s appled to the sheet metal, whch s fastened to the Shaker Table n addton to the Step-1 desgn nterference effect. Fasteners are represented as pre-stress of Bolt Shank to smulate the Fastenng effect. M6 Bolt s used and represented n hex domnant mesh wth Pretenson secton defned at md span of bolt shank length. The pre-stress s appled n LS-DYNA usng the card of *INITIAL_STRESS_SECTION. Fgure 7a shows pre-stress card wth the 90 ms tme-hstory of nput stress wth the max value of 0.373 GPa along wth a *DATABASE_CROSS_SECTION that specfes the Bolt part d. A low of elements that cross the secton plane are shrunk durng the Step-2 to reach the appled stress. The nut s constraned to the shank usng constraned nodal rgd body. The bolt fastens the bracket to the shaker table as shown n the mage below. Whle tghtenng the Fasteners, tenson load s developed n the fastener. The tensle load creates a compressve force n the jont. The stress that developed n the fastened part s called Fastenng Stress, and shown n Fg.7b. The Fastenng Stress observed n ths case for the VBM Bracket s 149 Mpa. Ths stress s the nput to RVF calculaton of the metal bracket. Fgure 7a: Card and Modelng of Bolt Fastenng June 10-12, 2018 5
Fgure 7b: Modelng and Stress Plot of Bolt Fastenng Modal Analyss The modal analyss performed s a fxed normal mode analyss done by constranng the boltng locaton n sx degrees of freedom. Ths modal analyss s carred out after the pre-stress s appled usng the feature ntermttent Egen value analyss. The method can be used anytme the modal response of a structure s requred durng applcaton of a load. It can be used on both statc and transent analyss. A load curve nput controls the output of requred number of modes at specfc tme ntervals. Ths *DEFINE_CURVE n the card *CONTROL_IMPLICIT_EIGENVALUE s nput as a negatve d defnng tme vs the number of Egen modes requred. Fgures 8a, 8b and 8c show the three lowest modes and ther frequences for VBM bracket obtaned from Modal Analyss. Fgure 8a: 23Hz Bendng Mode Fgure8b: 53Hz Lateral Mode Fgure 8c: 69Hz Torsonal Mode June 10-12, 2018 6
Fatgue Analyss LS-DYNA can run SSD (steady state dynamcs) to provde structural response under harmonc or steady state vbraton condton. The results, whch are dependent on frequences, nclude magntude and phase angle of nodal and elemental response. These results are gven n D3SSD fle, as well as NODOUT_SSD, and ELOUT_SSD fles from LS-DYNA output. FRF provdes a transfer functon between load and dynamc response n frequency doman. It s a characterstc of systems under harmonc loadng condtons. Unt Nodal force as a functon of frequency s appled at ponts of Shaker Table Elements, and FRF response n form of Acceleraton s calculated at Bracket Mesh Grds. Fatgue s the progressve and localzed structural damage that occurs when a materal s subjected to cyclc loadngs. Fatgue analyss can be carred out n tme or frequency doman but n LS-DYNA the frequency doman approach s adopted. LS-DYNA can run fatgue analyss for structures under random vbraton or snusodal vbraton. It s based on materal s SN fatgue curve. Upon analyss based on probablty dstrbuton and Palmgren-Mner s Rule of Cumulatve Damage Rato, we can predct the chance of fatgue falure. Where E[ D] E [ D] = s the Expected Damage, n s the number of cycles and n N N s the number of cycles for the falure n are calculated wth the specfed at the gven stress level as specfed by the Materals S-N data. Values of Input PSD exctaton n LS-DYNA. The Random Vbraton Analyss provdes PSD and RMS of nodal and elemental responses. The analyss methods avalable to further calculate E[D] are as follows; Stenbergs s Three Band Method, Drlk Method, Narrow Band, Wrschng, Chaudhury and Dover, Tunna, Hancock, and Lalanne Method [3]. Fgure 9: Materal SN Fatgue Curve For RVF analyss, a modal analyss s performed after completng the Fastenng Load. Modal results are wrtten out nto D3EIGV fle. Ths fle s then used to apply the random vbraton nput. LS-DYNA outputs Stress PSD nto a bnary fle call D3PSD, and Stress RMS output n D3RMS. Fatgue lfe results are calculated and output n D3FTG fle. The unts used n the model are Kg, mm, ms, KN, and therefore the LS-DYNA fatgue lfe results are output n ms. The ms lves are converted to lfe n hours manually. The keyword used for RVF s *FREQUENCY_DOMAIN_RANDOM_VIBRATION_ FATIGUE as shown n Fgure 10 wth the card defntons. June 10-12, 2018 7
Fgure 10: LS-DYNA Keyword for Frequency Doman Analyss To run multple load cases *CASE cards can be used so that the Fastenng and Modal analyses are performed only once smultaneously. Results are processed usng LS-Prepost as t can read n all the bnary fles output by LS-DYNA and process them. D3Plot s read n and FCOMP s set to FRNX. Ths feature sets the value of any frnge component to the maxmum value found durng the entre smulaton. Stress value to be dsplayed should be set to MAX of all the ntegraton ponts for Von-Mses Stress. Stresses can be output for all the frequency values specfed n the PSD data. Ths nput n gven as LCFREQ the keyword *DATABASE_BINARY_ D3PSD. As examples, the PSD Stresses at 8, 16, and 40Hz are shown n Fgure 11, respectvely. Fgure 11: Stresses at 8, 16 and 40Hz June 10-12, 2018 8
Fgure 12: RVF Lfe Plot Drlk s method s used to calculate fatgue lfe. Method selecton s specfed by changng the parameter MFTG n the *FREQUENCY keyword. A 24-Hour exposure tme s set for the analyss. The SN curve for the bracket materal s specfed as a log-log nterpolaton curve n Fgure 9. Fatgue lfe results shown n Fgure 12 are reported n mllseconds, and they are currently manually converted to Hours. RVF Lfe results are 3.6 n X, 508 n Y, 0.12 n Z, and 0.03 Hours n the combned loadcase, respectvely. RVF Lfe contour s set to mn n LS-PrePost as the smallest value s sough. Regons shown n red contour have the lowest lfe. Concluson A smulaton methodology for predctng RVF Lfe of Bolt-on Metal Brackets on vehcles usng LS-DYNA s developed n ths paper. The methodology takes nto account (1) the Bolt Fastenng whch affects the RVF Lfe, and (2) Random Exctaton whch realstcally represents vehcle rough road and powertran vbraton. LS-DYNA features n Modal Analyss and Fatgue were appled after Bolt Fastenng usng DYNA Implct Solver. The RVF Lfe was calculated wth PSD Input, PSD Stress from Steady State Dynamcs, and Fastenng Pre-Stress. In order to buld confdence on LS-DYNA RVF Smulaton, correlaton study s needed to prove ths smulaton provdes results that are realstc representaton of realty. Also new methods of RVF Smulaton wll be studed and varous Bracket Loads wll be refned n the future. June 10-12, 2018 9
References [1] GMW16390 (General Specfcaton for Analyss/ Development/ Valdaton (A/D/V) of Rechargeable Energy Storage Systems (RESS), 2015 [2] GMW17000 (GM Global Fastenng Catalogue), 2016 [3] Arnaud Rngeval, Yun Huang, Random Vbraton fatgue Analyss wth LS-DYNA, 12 th Internatonal LS-DYNA Users Conference, Detrot, 2012 [4] LS-DYNA Keyword User s Manual Verson R9.2, Lvermore Software Technology Corporaton, 2012 [5] Wenxn Qn, Integratng Manufacturng Pre-Stress n FEA Based Road Load Fatgue Analyss, 2013-01-1204, SAE Internatonal, 2013 [6] Govann M Texera, Random Vbraton Fatgue - A Study Comparng Tme Doman and Frequency Doman Approaches for Automotve Applcatons, 2014-01-0923, SAE Internatonal, 2014 [7] Lang Wang, Robert Burger, and Alan Aloe, Consderatons of Vbraton Fatgue for Automotve Components, SAE Internatonal, 2017 Contacts Jong S. Park Jong.s.park@gm.com Amt Nar Amt.nar@gm.com Acknowledgement We would lke to thanks developers Yun Huang of LSTC and Thomas Borrvall of Dynamore. We would also lke to thank Satsh Pathy of LSTC for hs support. Also we would also lke to thank Kurt Munson of ncode and Jeyavendeesh K. S. of GM for hs support. June 10-12, 2018 10