LOUDSPEAKER ROCKING MODES MODELLING AND ROOT CAUSE ANALYSIS. William Cardenas and Wolfgang Klippel. Presented by Stefan Irrgang. KLIPPEL GmbH.

Transcription

1 LOUDSPEAKER ROCKING MODES MODELLING AND ROOT CAUSE ANALYSIS William Cardenas and Wolfgang Klippel Presented by Stefan Irrgang KLIPPEL GmbH Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 1 Content 1. Problematic and causes of rocking modes 2. Modal Analysis 3. Practical Diagnostics 4. Numerical and experimental Verification 5. Design Improvements 6. Summary Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 2

2 Signal at IN1 [V] Instantaneous crest higher order distortion (ICHD) k 2k Frequency [Hz] KLIPPEL What are rocking modes? Symmetric forces produce only transversal displacement Desired piston mode F 0 µ Moments produce a tilting of the diaphragm - Undesired rocking mode are effects of rigid body movement! No break up of cone Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 3 Why are rocking modes undesired? end-of line testing PROBLEMS: - Generating voice coil rubbing and impulsive distortion - Generating harmonic distortion - Reducing acoustic output - Causing an asymmetric radiation pattern Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 4

3 i k z What causes rocking modes? Stiffness asymmetries WHAT? WHERE? AND HOW MUCH? Mass Unbalances B( z,, r0 ) i k 1,..., N 1,..., N Asymmetric acoustic loads B field Asymmetries Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 5 Lumped Parameter Model Imbalances Moments µ Mass Inbalance Tilting angles τ Stiffness symmetry µ B-field Inhomogeneity Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 6

4 Rocking Mode Modeling Differential Equation with lumped parameters M ms 1, m 2, m 1, m I 1, m 2, m, m I 2 xcoil R ms 0 R x coil K 0 1 R 2 2 ms 1, k 2, k 1, k K 1, k 2, k xcoil F, k 1 K 2 2 sym 1, Bl 2, Bl Bl 1, Bl i( t) 2, Bl Δ 1,m representing coupling between fundamental piston model with first rocking mode due to mass imbalance Δ 2,m representing coupling between fundamental piston model with second rocking mode due to mass imbalance Δ 1,k representing coupling between fundamental piston model with first rocking mode due to stiffness imbalance Δ 2,k representing coupling between fundamental piston model with second rocking mode due to stiffness imbalance Δ 1,Bl representing the excitation of the first mode by force factor imbalance Δ 2,Bl representing the excitation of the second mode by force factor imbalance Δ τ,m representing the coupling between the first and second rocking mode due to a mass imbalance Δ τ,k representing the coupling between the first and second rocking mode due to a stiffness imbalance Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 7 A New Measurement Technique System Identification µ n,t H n (jω) Φ n (r c ) x n (r c ) Root-causes (Excitation) Modal Resonator Boosting Mechanism Mode Shape Total Vibration Accumulated Acceleration Level AAL Scanner measurement DIAGNOSTICS Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 8

5 SPL [db] for 1.00V, 1.00m Results from Scanner Relative Rocking Level piston mode RRL n,tot = 5.5 db 80 SCN Result Curves - SPL Decomposition Total SPL Acceleration Level Quadrature Acceleration KLIPPEL Second rocking mode f 1 4*10 1 6*10 1 8* *10 2 4*10 2 f [Hz] First rocking mode Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 9 A New Measurement Technique System Identification µ n,t H n (jω) Φ n (r c ) x n (r c ) Root-causes (Excitation) Modal Resonator Boosting Mechanism Mode Shape Characteristics of modes Total Vibration Accumulated Acceleration Level AAL DIAGNOSTICS Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 10

6 Piston Mode AAL 0,E --- Experiment Identified Model Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 11 First Rocking Mode piston mode First rocking mode --- Experiment Identified Model f 1 Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 12

7 Modal Resonator System Identification µ n,t H n (jω) Φ n (r c ) x n (r c ) Root-causes (Excitation) Modal Resonator Boosting Mechanism Gain Damping Properties: Modal Damping or Q-factor Mode Shape Total Vibration Accumulated Acceleration Level AAL DIAGNOSTICS Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 13 How to interpret the Resonators? Piston Mode 1 st rocking mode 2 nd rocking mode F 0 =80 Hz Q 0 =6.97 F 1 =129 Hz Q 1 =34.7 RG 1 =31.7 db F 2 =151 Hz Q 2 =30.3 RG 2 =36.1 db Rocking modes: much less damping than the piston mode!! Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 14

8 How to cope with the problem? System Identification µ n,t H n (jω) Φ n (r c ) x n (r c ) Root-causes (Excitation) Imbalances (K, m, B) Modal Resonator Boosting Mechanism Mode Shape Total Vibration Accumulated Acceleration Level AAL DIAGNOSTICS Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 15 MODAL ANALYSIS Z e -1 I Bl F 0 x H 0 (jω) Φ 0 (r c ) µ 1,M Excitation µ 1,K u + µ 1,T τ H Mode 1 1 (jω) 1 Φ 1 (r c ) + x n (r c ) µ 1,Bl µ 2,M Excitation Mode 2 µ 2,K µ 2,Bl µ 2,T τ 2 + H 2 (jω) Φ 2 (r c ) Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 16

9 Stiffness Contribution RRL 1,K = 1.3 db T k STIFFNESS Imbalance X coil Δk F sym Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 17 Mass Contribution RRL 1,K = -5.9 db T m MASS Imbalance X coil F sym Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 18

10 Force Factor Contribution RRL 1,Bl = db Bl(θ) T Bl X coil Bl Imbalance F sym Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 19 First Rocking mode Stiffness Imbalance is the dominant cause of the first rocking mode Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 20

11 Second rocking mode f measured modelled This mode is relatively low compared to The fundamental, not critical Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 21 Modal Excitation Ratio ER 1,E F n,e Interested in the direction of the maximum tilting of the first mode d ref F 0 Stiffness Harder ER n, E F n,e F0 Fn, E F0 100% F 0 Dominant excitation Stiffness asymmetry Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 22

12 Modal Excitation Ratio ER 2,E F eq Interested in the direction of the maximum tilting of the second mode d ref Dominant excitation Bl Inhomogeneity Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 23 Root Causes Where are the asymmetries and Imbalances located? IR E Direction of Mode 1 ER 1,E Superinpose excitation ratio of the two rocking modes at the mean frequency Direction of Mode 2 ER 2,E f m f 1 f 2 f 1 = 129 Hz f 2 = 151 Hz f m = 139 Hz Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 24

13 Imbalance Ratio IR E Stiffness Harder Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 25 Summary of Diagnostics System Identification µ n,t H n (jω) Φ n (r c ) x n (r c ) Root-causes (Excitation) Imbalances (K, m, B) rel. to piston force Direction Modal Resonator Boosting Mechanism Gain Modal Damping or Q-factor Mode Shape Geometry of effective modes Relative Level to piston mode Total Vibration Accumulated Acceleration Level AAL Scanner Measurement DIAGNOSTICS Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 26

14 Verification of the New Technique 1. Numerical Simulation (FEM) of a virtual loudspeaker with artificial imbalances 2. Practical Experiments with modified loudspeakers Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 27 Numerical Simulation Arbitrary material parameters only rigid body motion interested! Z e (f) Bl, R e, L e X(r i,f) Virtual Perturbation: - Thickness changes - Adding lumped mass - Excitation force changed along the circumference Voice Coil boundary FEA Rocking Mode Simulation Cone Deformation (other analysis) Detect the same root causes of the perturbation! Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 28

15 FEA - Dominant Bl Imbalance Klippel SCN + Virtual SCN and LPM More force at 225 Klippel Rocking Mode Analysis stronger Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 29 FEA Dominant Mass Imbalance Klippel SCN + Virtual SCN and LPM Lumped Mass at 60 Klippel Rocking Mode Analysis Less mass Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 30

16 FEA + Thickness Dominant Stiffness Imbalance Klippel SCN - Thickness Change 300 Virtual SCN and LPM Klippel Rocking Mode Analysis Stiffness harder Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 31 Force Factor Experiment original loudspeaker ~ Energy Direction Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 32

17 Force Factor Experiment loudspeaker with additional magnets AAL ~ Energy Direction stronger Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 33 Mass Imbalance Experiment original loudspeaker Coil leads AAL ~ Energy Direction Less mass 34 Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 34

18 Mass Imbalance Experiment modified loudspeaker with additional mass AAL ~ Energy Direction Less Mass Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 35 Stiffness Imbalance Experiment original loudspeaker AAL ~ Energy Direction Stiffness harder Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 36

19 Stiffness Imbalance Experiment loudspeaker modified by damaged surround AAL ~ Energy Direction Stiffness Harder Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 37 Design Improvements ACTING ON THE ROOT CAUSES 1. Coil leads position 2. Thickness or material properties 3. Gap geometry, magnetization 4. symmetric distribution of back-holes (headphones) ACTING ON THE RESONATOR 1. Increase damping (difficult) 2. Shift resonance frequency to high frequencies, increase rotational stiffness OBSERVE ROCKING MODE ANALYSIS (RMA) PARAMETERS Measure several samples to detect systematic errors in production or assembling process (reduce QC rejected units) HINTS 1. Keep Rocking Level RRL n,e as small as possible 2. Check problems associated to acoustic loads with parametric RMA measurements in vacuum and air. Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 38

20 SUMMARY Rocking modes critical in headphones and micro speakers Few percent of imbalance produces huge mechanical energy of the rocking Improvements based on imbalance reduction and/or resonator modification Laser scanning technique provides sufficient information to identify the problems (diagnostics) Future: Nonlinearities cause imbalances at high amplitudes Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 39 THANK YOU! Loudspeaker Rocking Modes, Part 1 Modelling and root cause analysis, 40