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.
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
Origine du repère
Equivalent mass = 8000.kg (at point CM)
Position CM = (-0.25, 0, -0.3)
Position C = (-0.5, 0, -0.1)
The test-rig can only move vertically and
horizontally, its out-of-plane and rotation
motions are forbidden.
- external diameter = 0.130m
- internal diameter = 0.114 m
• External diameter: 0.114m
• Internal diameter: 0.10m
- Cross-section : 9.E-4 m2
- IX = 2.E-8 m4
- IY = 1.E-8 m4
- IZ =1.E-8 m4
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
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
The torque links are modelled as rigid bodies with inertial properties:
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
µ Frottement pneu/sol
0.14 0.17 0.20
est la vitesse
du centre de la roue
est la vitessevelocity
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