Multi-body simulation optimizes performance of earth moving machinery
Introduction
Dynamic simulation of wheel loaders, backhoes, excavators, dozers, and other earth moving systems is used to support the engineering development process early in new product design programs and make better use of testing downstream. 
Simulation is used to predict the complex non linear dynamic behavior, loads, and motion. Manufacturing companies have used increasingly more complete analyses to verify that the design can tolerate the loads and offer reliable customer performance and safety in all scenarios. The simulations are both accurate and versatile and closely match what was once only possible with physical testing.
Simulating the system
The simulation model is created from solid model geometry for mass and inertia properties of each body in the model. Each body is connected by kinematic joints and nonlinear stiffness and damping force elements. Kinematic joints are used to connect the bodies and define the way the bodies move relative to one another. There are different levels of detail used for each aspect of the model depending on what results are required. In the simplest cases, time varying functions are used to defined the length of each actuator resulting in a kinematic description of the steer, lift, and dump degrees of freedom. At the other extreme is a detailed model of the hydraulic pump, lines, valves, and actuators. The hydraulic system can be modeled using the new LMS Imagine.Lab AMEsim product. There is a convenient way to connect the two simulation models and make take advantage of the power of both working together.
LMS Virtual.Lab Motion is used to create a model of the complete system, describing the 3D kinematics and dynamics of the backhoe. LMS Imagine.Lab AMESim provides an accurate model of the hydraulic subsystem, including the different electro-hydraulic valves, oil pump, fluid properties, etc. To couple both models, the user specifies which physical signals are common between the mechanics model and the hydraulics model. Typically these are the actuator position and velocity on the one hand and actuator forces or torques on the other hand. The coupled simulation allows to correctly calculate the loads acting on each of the components. The resulting load time histories are accessible both in LMS Imagine.Lab and in Virtual.Lab Motion. These provide valuable engineering insight into the dynamic behavior of the backhoe and allow the correct dimensioning of the hydraulic subsystem and the mechanical components to reach the targeted performance. 
Full multi-body dynamic simulation model of a wheel loader
 
Mechanics, powered actuators and electronics are simulated in parallel to predict loads and analyze the overall performance of the backhoe.
Tire force elements are included to compute the lateral, longitudinal, and vertical tire forces moving over terrain profiles. The force relationships are usually nonlinear functions of position and velocity between connected bodies. Again, the tire force nonlinear stiffness and damping can be modeled using the basic level of detail, or taken to a higher level by using the specialized Comfort and Durability Tire from LMS. This more advanced tire characterizes the tire rubber carcass using one of three levels of detail, with the most sophisticated using a coarse Finite Element approach and measure parameters for the tire properties. Ultimately, the geometry, mass, nonlinear stiffness, and damping information are all used to construct the equations of motion.
Multibody formulation
The Virtual.Lab Motion Solver is based on a Cartesian formulation for the translational degrees of freedom along with Euler parameter (quaternions) to represent the rotational degrees of freedom. The bodies are connected together by force and joint elements. The relative degrees
of freedom between two bodies can be constrained by a set of joints or constraint equations. The Newton-Euler equations of motion plus the joint constraint equations form a set of differential-algebraic equations of motion (DAE) in the following form.
Where M is the mass matrix, q are the generalized coordinates, Qa are the generalized forces applied to the rigid bodies in the model, l the so called LaGrange multipiliers, Fq is the Jacobian of the constraint forces and g the second derivative the constraint equations.
Loader operation
Operating tasks for the wheel loader include loading and unloading material from the bucket. During this process, there are safety and performance objectives that manufacturers need to meet. The safety aspects are associated with tip over on slopes and with loads in the bucket at high positions. Rolling can also occur if the loader is steered sharply at high speed. All of these can be simulated to learn what will happen in any scenario using Virtual.Lab Motion.
In addition, the performance tasks are involved with simulating the driving forward and back, steering, and the lift and dump processes. Manufacturers have used Virtual.Lab Motion to improve operational “feel” of the loader and make it more responsive to the operator. Small improvements make a big difference since loaders are used in many repeated operational cycles when moving material. The feel can be improved by making design changes to the powertrain or the control interface.
In many large loaders the control interface is actually a digital signal device that operates hydraulic valves. Tuning the valve and digital control behavior provides a sophisticated and widely adjustable way to alter the feel and productivity of the loader.
Seamless integration of FE results takes the flexibility of the beam into account.
LMS Virtual.Lab Motion post processes simulation results (e.g. Motion RPM vs. Time), by using the powerfull integrated graphic displays.
Results
The simulation is used to represent the main moving bodies and hydraulic system in considerable detail. It was developed in stages and validated at each to create a comprehensive simulation that can provide engineering design insight and provide “what-if” trade-off studies. All aspects of the model are parameterized and can be used for design sensitivity, design of experiments, or optimization. The objective of the simulation is to represent all aspects of the operational cycle and way the operator uses the loader when moving material.
Conclusions
Models can be used to predict all the loads, reaction forces, position, velocity, and accelerations. In general, the multibody dynamic solution from Virtual.Lab Motion provides both more accurate results for transient dynamic events, and ways to represent more complex problems. Simulation provides design insights to eliminate bad designs before making prototypes, and ensures that engineers can make the most of the limited test time once a prototype is available. It is also possible to study misuse and failures scenarios where it might be too dangerous or costly to do physical tests. The Virtual.Lab Motion solver and modeling interface are ideally suited to offroad and construction machinery applications and will be appreciated by any organization that needs to predict total system dynamic performance, safety, and loads.(end)
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