Modular Multibody Formulation for Simulating Off-Road Tracked Vehicles

Abstract

This paper presents a formulation and procedure for incorporating the multibody dynamics analysis capability of tracked vehicles in large-scale multibody system. The proposed self-contained modular approach could be interfaced to any existing multibody simulation code without need to alter the existing solver architecture. Each track is modeled as a super-component that can be treated separate from the main system. The super-component can be efficiently used in parallel processing environment to reduce the simulation time. In the super-component, each track-link is modeled as separate body with full 6 degrees of freedom (DoF). To improve the solution stability and efficiency, the joints between track links are modeled as complaint connection. The spatial algebra operator is used to express the motion quantities and develop the link's nonlinear kinematic and dynamic equations of motion. The super-component interacts with the main system through contact forces between the track links and the driving sprocket, the support rollers and the idlers using self-contained force modules. Also, the super-component models the interaction with the terrain through force module that is flexible to include different track-soil models, different terrain geometries, and different soil properties. The interaction forces are expressed in the Cartesian system, applied to the link's equation of motion and the corresponding bodies in the main system. For sake of completeness, this paper presents dynamic equations of motion of the links as well as the main system formulated using joint coordinates approach. 78Accounting for the distributed nonlinear inertia forces of the track is another challenge in modeling tracks using spatial multibody codes.Some CSP have developed multibody dynamic simulation capabilities for modeling metal tracks (MSC Software, 2007). Most of these implementations simplify the contact detection algorithms by using primitive geometries for modeling the contacting bodies leading to less accurate force prediction. Other CSP utilized general purpose algorithms for modeling tack-link dynamics and the contact detection is based on full CAD geometry leading to computationally intensive simulation and time consuming analysis. Other packages implemented a simplified representation of the tracks using pre-computed parameters and pre-determined track-link path. Although the computational efficiency greatly improved, the inertial link dynamics and contact forces are not captured accurately. McCullough and Haug 1985 proposed one of the early models for tracked vehicles. The equations of motion for the vehicle, suspension system and road wheels were derived. A mechanical system super-element that represents spatial dynamics of high mobility track vehicle suspension systems was derived. The track was represented as a complex internal force element that acts between ground, wheels, and the chassis of the vehicle. Track tension was computed from a relaxed catenary. Vol. 1, No. 2; 2014 80 Studies in Engineering and Technology ...

Grousers Effect in Tracked Vehicle Multibody Dynamics with Deformable Terrain Contact Model

“…Rubber tracks, reinforced with a steel core, are usually classified as flexible whereas tracks made of steel links are classified as rigid. The latter are composed of rigid links [27] usually connected in multibody models with rotational joints [28] or bushing elements [29]. Bushing elements can also damp the system to limit numerical errors [30].…”

Multibody simulation of a tracked vehicle with deformable ground contact model

“…Tracks with steel links are instead classified as rigid and are mainly used in military or agricultural fields for high size machines. Steel tracks are usually modelled with rigid links 18 connected by different types of joints: revolute joints, 14 bushing elements 19 or beams. 17 Impulsive forces may take place in tracked vehicles due to the contacts between the track links and the sprockets, the front idle wheels and the road wheels, as well as the ground.…”

Decoupling Kinematic Loops for Real-Time Multibody Dynamic Simulations

“…In the joint-based multibody dynamics formulation, chord-joints could be modeled by introducing a massless chord-body that is rigidly attached to a marker on the parent body of the chord-joint. The chord-body is then connected to the child body of the chord joint by kinematic joint, as shown in Figure 2, [1,2,9]. In order to maintain the integrity of the chord joint, 6 kinematic constraints are used to represent the rigid connection between the chord-body and chord-joint parent body at the joint locations.…”

“…The other loops are modeled similarly as shown in Figure 2 Figure 2. using the loop description in Table 1. In joint-coordinates multibody dynamics formulation, the equation of motion of system with closed loop could be written as follows [2,9]:…”

“…Real-time simulation for such systems poses a challenge for software developers and for analysts [4,5,6,7]. This paper presents an approach for replacing the linear actuator and rigid link bodies in the multibody system model with passive force and constraint elements whose kinematic and dynamic equations are expressed in terms of the attached body state variables [8,9]. The spatial displacement and velocity of any number of markers fixed in the element are computed, and this information is used to compute interaction between the element and other parts of a model.…”