Analysis of shock force measurements for the model based dynamic calibration

Transcription

1 8 th Worshop on Analysis of Dynamic Measurements May 5-6, 4 Turin Analysis of shoc force measurements for the model based dynamic calibration Michael Kobusch, Sascha Eichstädt, Leonard Klaus, and Thomas Bruns Nationales Metrologieinstitut

2 Introduction Motivation Dynamic force measurements still purely rely on static calibrations Static calibration not sufficient for dynamic applications when precision is important Establishment of an infrastructure for dynamic force calibration needed Guidelines and standards for dynamic calibration still lacing Objectives of Research Development of dynamic calibration devices with primary traceability Development of validated dynamic measurement methods with specified measurement uncertainties Lining of calibration results from different devices or methods (sine and shoc) Joint Research Project EMRP IND9 Traceable Dynamic Measurement of Mechanical Quantities

3 Introduction Dynamic Calibration Devices Sinusoidal Forces Shaer excitation using seismic mass (primary method, max. N, Hz) Hydraulic exciter with load frame (secondary method, max. N, Hz ) Shoc Forces Collision of two mass bodies applying interferometric measurement of inertial forces (primary method) Advantages of shoc calibration realization of large forces broad frequency range short measuring time N Shoc Force 5 N Shoc Force 3

4 Introduction Shoc Force Calibration Device N Shoc Force Calibration Device Vibrometers probe the end faces of the mass bodies (on axis measurement) 4

5 Shoc Force Calibration Principle of Primary Shoc Calibration Collision of two airborne mass bodies with force transducer Traceability of dynamic force by measurement of inertia forces F i (t) = m i a i (t) Mass values m i determined by weighing Dynamic signals accelerations a i (t) of both mass bodies m i measured by laser vibrometer force transducer output 5

6 Shoc Force Calibration Analysis of Shoc Pulse Data Pulse analysis in time and frequency domain (pea amplitude, pulse width, signal form, spectral content) Resonances of transducer set up seen in signal ringing! Typical results of shoc calibrations are based on pulse pea ratios shoc sensitivity S defined as ratio of pea amplitudes e.g. in ISO 663 standard for shoc calibration of acceleration transducers results depends on pulse duration, signal shape, spectral content shoc calibrations on different calibration set ups will produce differing results pea fitting Approach of model based calibration with identification of the dynamic parameters of the transducer 6

7 Dynamic Characterisation Simple Model Dynamic Characterisation of a Force Transducer Mechanical model spring mass model describes dynamic behaviour (most simple model: DOF, no damping) model parameters: masses m H, m B stiffness Head Mass Force Vibration x(t) Resonant frequency Measuring Spring f Res = π m fundamental resonance along the measuring axis force transducer rigidly fixed at its base, no loads or coupled mechanical environment specified in German guideline VDI/VDE 638 values specified in some datasheets H Base Mass Base Plate A general dynamic characterisation requires the model parameters. 7

8 Dynamic Characterisation Model of Calibration Device Model of the Calibration Device Calibration device with mounted FT modelled by a series arrangement of masses Basic Model of Force Transducer Basic Model of Shoc Calibration Device 8

9 Modelling and Parameter Identification Model of the Calibration Device Calibration device with mounted FT modelled by a series arrangement of masses Models of different complexity investigated 3, 4 or 5 model masses adaptation of FT to MB differently modelled (rigid/elastic coupling) viscoelastic springs (stiffness, damping d) Model Masses M. Kobusch et. al., Investigation for the model based dynamic calibration of force transducers by using shoc forces,imeko 4, South Africa. 9

10 Force Transducers under Test Devices under Test Investigation of various strain gauge force transducers different type, size, weight, mechanical design, adaptation force applied via threaded bolts with spherical end face (for compression/tension forces) HBM U9B / N Interface 6 /. N Transducers HBM U9B / N: 63 g (head < 3 g), Ø 6 mm, M5 rods at both ends, f Res > 4 Hz Interface 6 /. N:.57 g (incl. connector/cable), Ø 5 mm (see IMEKO 4) HMB UB / N: ca. 3 g (without base adaptor), Ø 5 mm, rigid base coupling, earlier dynamic tests M. Kobusch et. al., Comparison of shoc and sine force calibration methods,imeko 7, Mexico. HBM UB / N

11 First Tests Overview Test Conditions Shoc force generated by the impacting mass body of g hard metallic contact (no pulse shaper) for short pulses (high frequency content) shoc amplitude ca. % to % nominal load Modification of the mechanical configuration (HBM U9B / N) additional load button increases the small head mass (< 3 g) to lower the fundamental resonance no load button (Fore more details see IMEKO 4) plus 3. g plus 7. g

12 First Tests Overview Shoc Force Measurements: HBM U9B / N Force Acceleration a Acceleration a smooth force pulse with very small ringing acceleration signals with strong ringing components at Hz noise and transducer resonance in the same range > problem of signal filtering analysis of spectral content to understand transducer s shoc response model fitting and parameter identification without satisfying results filtered with Hz low pass (Fore more details see IMEKO 4)

13 New Investigations Questions Why is it difficult to model and identify the parameters of the small HBM U9B / N? Where is the measurement information needed? Is it a problem when we have very smooth force pulses? Does the noise harm the identification process? New Analytical Research Simulation of the transducer s shoc response using multi mass models Simulation of the shoc response of the cubic shaped g mass bodies FE analysis of the force transducer Calculation of the resonance frequencies of coupled masses New Experiments Auxiliary device with small pendulum masses for shorter pulses Auxiliary data using 3 rd vibrometer New set of small load masses Variation of mounting torque 3

14 Simulation of Shoc Response Simulation of the Transducer s Shoc Response Multi mass model using 4 masses: impacting mass, transducer (base, head), reacting mass Transducer mass values extracted from CAD data (m B = 6 g, m H =.65 g) Total stiffness of force transducer set up c FT adjusted to match with observed force pulse: c FT = N/m (agrees with sine calibrations) Impact velocity not changed Calculations ) Variation of nonlinear Hertzian contact stiffness ) Variation of impact mass 3) Variation of transducer s head mass 4) Variation of stiffness ratio between base coupling and measuring spring 4

15 Simulation of Shoc Response Simulation of the Transducer s Shoc Response Variation of contact stiffness: stiff base coupling, no load masses, g impact mass Hertzian contact radius R of impact surfaces varied (flat > large radius) pulse amplitude slightly increases for flatter surfaces and pulse width slightly decreases strong vibrations on impacting mass for hard impacts signal ringing of force signal depends on the conditions at the moment of decoupling R =.97 m R =.6 m R =.8 m R =. m 5

16 Simulation of Shoc Response Simulation of the Transducer s Shoc Response Variation of impact mass: stiff base coupling, no load masses pulse width decreases with smaller impact mass ringing amplitude of head mass vibration not dependent from impact mass but relative ringing increases with smaller mass pronouncing higher frequency contents m = g m =. g m =. g m =. g 6

17 Simulation of Shoc Response Simulation of the Transducer s Shoc Response Variation of head mass: stiff base coupling, g impact mass ringing amplitude increases with larger head mass and resonant frequency decreases superposed contact vibrations strongly pronounced for larger masses m H = 3 g m H = 8 g m H = g m H = 5 g 7

18 Simulation of Shoc Response Simulation of the Transducer s Shoc Response Variation of stiffness ratio: g impact mass, no load masses dynamic effects due to the elastic base coupling become visible for stiffness ratios < two vibration frequencies for lower ratios beat signal Ratio = Ratio = 3 Ratio =.4 Ratio = 4. 8

19 Finite Element Analysis Modal Shapes for Soft Mounting Two axial modes bul vibration at.6 Hz head vibration at 7. Hz Bending modes down to 75 Hz.75 Hz double threaded base connector fixed at end face.3 Hz 6.9 Hz double Design data supplied by manufacturer HBM..6 Hz.8 Hz double 7. Hz 9

20 Finite Element Analysis Modal Shapes for Rigid Mounting Two axial modes bul vibration at 6.4 Hz head vibration at 7.9 Hz Bending modes down to Hz. Hz double threaded base connector fixed at full circumference.9 Hz.5 Hz double Design data supplied by manufacturer HBM. 6.4 Hz 9.4 Hz double 7.9 Hz

21 Resonances of the multi mass model Basic model of DOF mass model Multi-Mass Model m f π = = + + x x x x m m && && Resonance frequency ODE system of equations of motion... in matrix notation Eigenfrequencies x K x M = + &&.5 / 4 π + + ± + + = m m m m m m f ( ) M K / eig π = f Calculation of eigenvectors gives the corresponding resonance shapes

22 Resonances of the multi mass model 3 mass model Multi-Mass Model = x x x x x x m m m && && && Eigenfrequencies ( ) M K 3 / / eig π = f ODE system

23 New Experiments Measurement Set-Up New Features Auxiliary device for shoc excitation with pendulum small mass bodies: 88.6 g, 7. g pendulum suspended by 4 strings pendulum elongated and released by string original g mass body removed for on axis vibrometer measurements 3

24 New Experiments Measurement Set-Up New Features Set of additional load masses for HBM U9B / N mass values in g:.7,.65, 3., 3.8, 5., 6., 8.75, 8.6 impact occurs on the end face of the threaded connector bolt (not on load button lie before) 4

25 New Experiments Measurement Set-Up New Features Acquisition of additional vibration data 3 rd vibrometer measures at various spots of interest, e.g. adapter, transducer housing, load mass superposition of axial and transversal vibration components due to oblique incidence 5

26 New Experiments Shoc Excitation with Pendulum Shoc Response of HBM U9B / N without load mass Shoc pulse with g mass body Transducer response for different impact masses g mass body: t p =.3 ms 89 g pendulum: t p =. ms 7 g pendulum: t p =. ms Strong ringing for short pulses at least spectral components crucial information for parameter identification Shoc pulse with pendulum of 89 g Shoc pulse with pendulum of 7 g 6

27 New Experiments Shoc Excitation with Pendulum Shoc Response of HBM U9B / N without load mass, 7 g pendulum Spectral analysis of signal ringing strong peas at Hz and 8 Hz different damping, 8 Hz component dominates first better resolution of the DFT analysis reveals double pea structure Resolution 5 Hz Resolution 65 Hz Double pea structure needs explanation! 7

28 New Experiments Shoc Excitation with Pendulum Shoc Response of HBM U9B / N without load mass, 7 g pendulum Auxiliary vibration measurement at the transducers connector bolt strong vibration at Hz with low damping time depending beat structure largest amplitude at the tip agrees with bending mode of the connector bolt from FE analysis measurement positions 8

29 New Experiments Shoc Excitation with Pendulum Shoc Response of HBM U9B / N and varied load mass, 89 g pendulum Spectral analysis of signal ringing several fixed resonances #F > Hz wealy load sensitive resonance # (starting at Hz) strongly load sensitive resonance # (starting at 8 Hz) DFT of ringing of acceleration a (of MB) # #F #F #F DFT of ringing of transducer output # # 9

30 Conclusions Summary Investigation of HBM U9B / N model response, FE analysis experimental tests Shoc tests applying small pendulum additional mass loads tested prominent axial modes mass model not valid for small loads data analysis for parameter identification just started Outloo Further data analysis / measurements to explain the observed modal response Data analysis and parameter identification Comparison with sine calibration results Measurement uncertainty of the parameter identification: many factors, e.g. model type, filtering, fitting algorithm 3

31 Analysis of shoc force measurements for the model based dynamic calibration Michael Kobusch, Sascha Eichstädt, Leonard Klaus, and Thomas Bruns Kontat: Dr. Michael Kobusch Tel.: Anschrift: Bundesallee 386 Braunschweig Acnowledgement: This wor is part of the Joint Research Project IND9 Traceable Dynamic Measurement of Mechanical Quantities of the European Metrology Research Programme (EMRP). The EMRP is jointly funded by the EMRP participating countries within EURAMET and the European Union.