Landing gear
Transcription
Landing gear
GraSMech Course: Computer-Aided Analysis of Rigid and Flexible Multibody Systems Modelling and simulation of a simplified landing gear Contact: O. Brüls ([email protected]) After the design and the prototyping phase, a landing gear is always submitted to numerous tests in severe working conditions. Real-size drop tests are performed in laboratory when the landing gear is fixed to a test-rig. In order to reproduce the actual load exerted by the plane in real landing conditions, an equivalent mass is attached to the test-rig. X O Z The figure represents a simplified nose landing gear (this is the auxiliary landing gear at the front of the plane). The system is moving in the plane XOZ, and the gravity force is oriented in the direction of the axis OZ. This mechanism is composed of a barrel, which is hinged to the test-rig. The shock-absorber connects the barrel and the sliding rod. At the impact, the shock-absorber is compressed and dissipates the kinetic energy of the system. The sidestay should resist against the large horizontal force, which results from the wheel/ground contact (especially at the impact, since the wheels are first sliding before rolling on the ground). Before the impact, the gravity force is compensated by the aerodynamic forces, so that the plane is subject to a constant descent speed. After impact, we assume that the aerodynamic forces are kept constant. We ask to: 1. Determine the number of kinematic degrees-of-freedom before and after landing. 2. Establish a rigid-body model of the system (excepted for the wheel, which is flexible). 3. Simulate and analyze the impacts in the following cases: • Case 1: Horizontal speed: 0.m/s - Vertical speed: 0.8m/s • Case 2: Horizontal speed: 60m/s - Vertical speed: 1.8m/s • Simulation time: 1.2s • Initially, the wheel is in contact with the shock table (the ground), and the shock-absorber is extended. 4. Adapt the assumptions of the model to simulate a more realistic landing procedure, and discuss the simulation results. Centre de la masse réduite Origine du repère de conception CM c O X Z Fut Contre-fiche Palier supérieur Avant Forward direction Test-rig Equivalent mass = 8000.kg (at point CM) Position CM = (-0.25, 0, -0.3) Position C = (-0.5, 0, -0.1) Palier inférieur Compas Tige B coulissante The test-rig can only move vertically and horizontally, its out-of-plane and rotation motions are forbidden. Roue Charnière Charnière 0.70 m Contre-fiche Barrel - external diameter = 0.130m - internal diameter = 0.114 m 0.1m Charnière 0.15m Charnière Palier inférieur fixe 0.10m Fut 0.1m Sliding rod: • External diameter: 0.114m • Internal diameter: 0.10m Side-stay - Cross-section : 9.E-4 m2 - IX = 2.E-8 m4 - IY = 1.E-8 m4 - IZ =1.E-8 m4 0.5m The sliding rod is mounted on two bearings. The lower bearing is fixed (connected to the barrel), whereas the upper bearing is sliding (connected to the sliding rod). The dry friction coefficient of the sliding bearing is estimated at 0.5. We consider that the shock-absorber is attached to the barrel at point O, and to the sliding rod at point B. In the extended configuration, its maximal length is 1.35m, with a maximal stroke of 0.45m. At the extreme configurations, the local stiffness of the stops is 1.E8. The shock-absorber is modelled as a damper and a nonlinear spring in parallel. The damping coefficient is roughly estimated: 8.E4 N.s/m, whereas the variations of the spring force with respect to the compression of the shock-absorber are described below: Charnière T Rotule 0. 3 m 0.15 m B 0.1m Charnière 0.1m U (m) F (N) 0.05 16 E3 0.0 18 E3 -0.1 20 E3 -0.2 25 E3 U (m) F (N) -0.3 40E3 -0.35 70 E3 -0.4 14 E4 -0.45 22 E4 The torque links are modelled as rigid bodies with inertial properties: Masse IXX IYY IZZ Kg kg.m2 kg.m2 kg.m2 1 0.1 0.2 0.1 In extended configuration, the position of point T is (0.25, 0, 1.1) The mass of the wheel is 50 kg, and its nominal (i.e. undeformed) radius is 0.3m. The relation between the radial deformation and the radial contact force is characterized by: d (m) 2.E-2 5.E-2 8.E-2 1.E-1 Fr (N) 1.3E 4 5.E4 8.E4 1.E5 µ Frottement pneu/sol 0.7 0.65 0.4 0.14 0.17 0.20 1 Vh/V0 est la vitesse horizontale du centre de la roue Vh V = hslipping horizontal velocity est la vitessevelocity horizontale à l’impact Vo V = 0horizontal of the centre of the wheel Two behaviours are possible for the wheel/ground contact: sliding or rolling. During the sliding phase, the friction coefficient depends on the sliding velocity at the contact point, as described in the figure. When Vh/V0 = 1, the sliding is maximal (this occurs at the impact), when Vh/V0=0, the wheel rolls on the ground without sliding.