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# 2015 12-02-optiwind-substructure-decoupling-ku leuven

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Substructure decoupling with inconsistent experimental data (Pepijn Peeters, KU Leuven)

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### 2015 12-02-optiwind-substructure-decoupling-ku leuven

1. 1. Optiwind meeting Substructure decoupling with inconsistent data PhD student Pepijn Peeters Promotor Wim Desmet 02.12.2015
2. 2. Overview Substructure decoupling with inconsistent data - Substructuring: what and why ? - Principle of decoupling - Problems in decoupling - Current focus
3. 3. Substructuring : Predicting the behaviour of an assembled system based on the behaviour of its components and connections between the components 3 Introduction: what is substructuring ? Substructure decoupling Substructure coupling
4. 4. Based on “A dual approach to substructure decoupling techniques” by S.N. Voormeeren and D.J. Rixen What ? • The identification of a substructure from an assembled system is addressed. • Substructure A and AB are known. Substructure B is unknown Why ? • E.g. when a component is too heavy or fragile to measure in free-free, or part of a test rig. • No simulations are required, in theory • No need to measure (rotational) connection DoF 4 Decoupling: introduction
5. 5. 5 - = 𝑢 𝐴𝐴 = 𝐻 𝐴𝐴 𝑓 𝐴𝐴 − 𝑔 𝐴𝐵 𝑢 𝐴 = 𝐻 𝐴 𝑓 𝐴 + 𝑔 𝐴 - We introduce a (dis)connection force g - We enforce compatibility (at the interfaces): 𝐶 = 𝐶 𝐴𝐴 𝐶 𝐴 = 0 I 0 | 0 − I 𝐶𝑢 = 𝐶 𝐴𝐴 𝐶 𝐴 𝑢 𝐴𝐴 𝑢 𝐴 = 𝑢 𝑐 − 𝑢 𝑐 𝐴 = 0 - We enforce equilibrium (at the interfaces): 𝐿 = 𝐿 𝐴𝐴 𝐿 𝐴 = I 0 0 0 0 0 0 I 0 0 I 0 0 0 I 0 0 0 0 I 𝐿 𝑇 𝑔 = 𝐿 𝐴𝐴 𝑇 𝐿 𝐴 𝑇 𝑔 𝐴𝐴 𝑔 𝐴 = 0 0 0 0 𝑔 𝑐 − 𝑔 𝑐 𝐴 = 0 Decoupling: principle
6. 6. 7 𝐻 𝑑𝑑𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 𝐻 𝐴𝐴 − 𝐻 𝐴𝐴 𝐸 𝐴𝐴 𝑇 𝐶 𝐴𝐴 𝐻 𝐴𝐴 𝐸 𝐴𝐴 𝑇 − 𝐶 𝐴 𝐻 𝐴 𝐸 𝐴 𝑇 + 𝐶 𝐴𝐴 𝐻 𝐴𝐴 - = - = Decoupling: principle a = DoF on test-rig c = DoF on connections b = DoF on gearbox  Analytical solution ! Compatibility: C Equilibrium: C
7. 7. 8 𝐻 𝑑𝑑𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 𝐻 𝐴𝐴 − 𝐻 𝐴𝐴 𝐸 𝐴𝐴 𝑇 𝐶 𝐴𝐴 𝐻 𝐴𝐴 𝐸 𝐴𝐴 𝑇 − 𝐶 𝐴 𝐻 𝐴 𝐸 𝐴 𝑇 + 𝐶 𝐴𝐴 𝐻 𝐴𝐴 - = - = Compatibility: A + C Equilibrium: A + C  Inverted matrix can become redundant  pseudo-inverse  Rotational DoF ?  can be replaced by other DoF  Improvement of the condition of the inversion, a = DoF on test-rig c = DoF on connections b = DoF on gearbox Decoupling: principle e.g. analytical: 1e10 redundant: 2e3
8. 8. 9 - Noise on the FRFs 𝐻 𝐴𝐴 − 𝐻 𝐴𝐴 𝐸 𝐴𝐴 𝑇 𝑪 𝑨𝑨 𝑯 𝑨𝑨 𝑬 𝑨𝑨 𝑻 − 𝑪 𝑨 𝑯 𝑨 𝑬 𝑨 𝑻 + 𝐶 𝐴𝐴 𝐻 𝐴𝐴 = 𝐻 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 LocalproblemsGlobalproblems - Mass loading and frequency shifts between different input collums - = - Difference of assembly and empty test rig are not exact + Δ𝑬 - The condition of the inversion is very high 𝐻 𝑎𝑎 𝐴𝐴 𝐻 𝑎𝑎 𝐴𝐴 𝐻 𝑎𝑎 𝐴𝐴 𝐻𝑐𝑐 𝐴𝐴 𝐻𝑐𝑐 𝐴𝐴 𝐻𝑐𝑐 𝐴𝐴 𝐻 𝑏𝑏 𝐴𝐴 𝐻𝑏𝑏 𝐴𝐴 𝐻 𝑏𝑏 𝐴𝐴 Problems in decoupling
9. 9. 10 - Noise on the FRFs LocalproblemsGlobalproblems - Mass loading and frequency shifts between different input collums 𝐻 𝑎𝑎 𝐴𝐴 𝐻 𝑎𝑎 𝐴𝐴 𝐻 𝑎𝑎 𝐴𝐴 𝐻𝑐𝑐 𝐴𝐴 𝐻𝑐𝑐 𝐴𝐴 𝐻𝑐𝑐 𝐴𝐴 𝐻 𝑏𝑏 𝐴𝐴 𝐻𝑏𝑏 𝐴𝐴 𝐻 𝑏𝑏 𝐴𝐴 Current focus
10. 10. Thank you for your attention 11