Multi-Body Dynamic Transient Simulation for a Spray Mechanism

Multi-Body Dynamic Transient Simulation for a Spray Mechanism Satheesh C.

Kaviraj Shinde

Raviteja S.

Design Engineer Infotech Enterprises Ltd. Manikonda Hyderabad-500072,India

Team Leader Infotech Enterprises Ltd. Manikonda Hyderabad-500072,India

Project Manger Infotech Enterprises Ltd. Manikonda Hyderabad-500072,India

Abbreviations : FMBD

Keywords

: Flexible Multi Body Dynamics

DSTIFF

: Differential/algebraic equations (DAE) integrator code

h3D

: Hyper 3D

: Rigid-to-rigid, Point to deformable contact, Flexprep Abstract

The paper deals with a study of kinematic motion of a spray mechanism. MotionView tool is used in constraining multiple bodies with their respective joints and also contacts at the interfaces. Compression & torsion springs are modeled to support the kinematic motion in the mechanism. The simulation is performed in two stage process: Rigid body simulation: Transient load is applied, and the load transferred and displacement in each body is calculated. Flexible body simulation: FE model is created in HyperMesh and imported into MotionView. Transient analysis is carried out in MotionSolve to observe the stress & strains developed in the bodies.

Introduction Different types of spraying mechanisms to spray the fluid generated are the integrated part of some of the current home appliances. The spray mechanism involves number of joints, springs and contacts. The functionality of these joints is to provide the required amount of fluid while in operation. Accessing the Failure modes and stresses in the mechanism due to the applied force by end user is the main objective of the project. A linear transient 3D MBD simulation with rigid bodies and flexible body is carried out by considering the generic material and inertia properties using MotionSolve. HyperMesh and MotionView softwares are used for pre-processing. HyperView and HyperGraph are used for post-processing. Ansys software is used to compare the flexible body results.

Process Methodology (details with figures) For Rigid Body Simulation: After importing the CAD model into MotionView, mass and inertia properties of each components are applied. Joints are modeled for the respective components to achieve the required mechanical function. Please refer the table 1.

TABLE 1

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JOINTS WITH RESPECTIVE DOFS

The calculation method for contacts is selected as poisson contact with coulomb friction on. Contact related properties viz., penalty, restitution coefficient, static and dynamic frictional coefficients are obtained by iterative method starting with the default values defined in MotionView. Stiffness, damping coefficients, preload properties are defined as given. Rigid-to-rigid body contacts are used for rigid body simulation. The frictional force is modeled as a viscous (dynamic) force according to the following law:

.....cnt01 In the above equations: •

is the current slip speed at the point of contact.

•

is the coefficient of static friction.

•

is the coefficient of dynamic friction. is the stiction (static friction) transition slip speed at which the full value of

•

is used for the

coefficient of friction.

•

is the dynamic friction slip speed at which the full value of

•

is the friction force that is to be applied. The friction force opposes the direction of the slip velocity.

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is used for the coefficient of friction.

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Figure 1: 1 Spray Mechanism with Joints and Contacts

The springs are modeled at the required joints. Force and displacement output are requested for the required components/ joints/ springs. Solution run is given as transient with provided end time. The integrator type ype is defined as DSTIFF. Integration tolerance, maximum step size are defined by carrying out number of iterations. The transient analysis is carried out to calculate the response of a multi-body multi body system to time-dependent time loads and motions. The results obtained obtained of a transient analysis are displacements, velocities, accelerations, forces. The responses are usually time-dependent. time

Figure 2:: Force vs. Time curve (Force is applied gradually at the location as shown in figure 1)

The equation of motion is given iven in the following form:

.....em01 The matrix M is the mass matrix, the vector P is the vector of external forces, and the vector q represents the generalized coordinates. Stiffness, damping, constraint forces, external loads, and gravity are all included in the external force vector P. An initial and maximum integration time step, an end time, and integrator tolerance is defined.

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For Flexible Body Simulation: The flexible body is modelled with tetramesh and contact elements are created using rigid elements connected to its center of gravity and joints in the HyperMesh Hyper with OptiStruct interface. The material properties are applied as provided. The The *.h3D file is created using *.fem file of flexible body using Flexprep option in Flextool toolbar. The flex body is overlapped on corresponding rigid body and contact connectivity and contact parameters are defined for the respective interfaces. The corresponding responding deformable contact surfaces are interpreted as Markers as shown in figure 3.

Figure 3: Deformable surface

The further procedure for loads, boundary conditions and solution run is carried same as for Rigid body simulation. Only the contact is used Point to deformable contact The FMBD is carried out for Comp1. Linear static analysis is carried out using the maximum force observed at certain time using ANSYS software. The FMBD results with MotionSolve Motion are compared with the results obtained ined using ANSYS. Results & Discussions With reference to the figure4, the force experienced by the comp2 is similar as the applied force. The variation in the displacement shows the effect of forces and damping factors developed develope by contact parameters, torsion spring and compression spring.

Figure 4: Force, displacement Vs Time plot of Comp2.

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The comp1 is considered for the both rigid body dynamics and flexible body dynamics. The force diagram for the comp1 is as shown in figure 5.

Figure 5: Force diagram for Comp1

The von-mises stress in the Comp1 is observed less than the allowable limit. Refer figure 6.

by ANSYS

by FMBD using MotionSolve olve Figure 6: Von-mises stress contours.

The active force generated for torsion spring is given by the equation .....ts01 where, Tj, Tk are the torque developed in the respective bodies and an partial angular velocity matrices for respective bodies. The maximum torque developed (refer figure 7) in the torsion spring is well below maximum permissible torque as per the designed criteria. Refer the formulae ts01, ts02.

Figure 7: Torque developed in torsion spring

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The maximum permissible torque for the spring is given by the equation,

.....ts02 The maximum allowable bending stress is calculated by .....ts03 The generalized active force on compression spring is given by the equation .....cs01 Where, Vw is partial velocity matrix, fj=fk is forces acting on the respective bodies. The force developed (refer figure 8) in compression spring during operation is observed less than the allowable maximum force of the coil spring. Refer the formulae cs01, cs02, cs03

Figure 8: Force developed in compression spring

The maximum force the spring can take when the spring is deformed all the way to its solid height, ......cs02 The maximum shear stress is calculated in the spring associated with the maximum force is calculated by,

......cs03 Where W is the Wahl correction factor (accounting for spring curvature stress) and C is the spring index (essentially an aspect ratio of the spring cross-section),

,

.....cs04

The torsion and compression spring designs are verified with the above formulae. The designs are estimated further for fatigue calculations.

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Benefits Summary The process reduces the time for meshing for rigid body. It meshes automatically the rigid body components with meshing parameters provided by user. The process for the rigid body simulation is user friendly and cost-effective. The results can be post-processed directly using single GUI of MotionView. Simulation set-up time is more at the initial stage. The process time reduces drastically once the stabilization occurs. The designs of the components, joints, springs, etc. can be verified accurately. Challenges 1. Number of iterations for contact parameters are more to stabilize the transient model. 2. Need to change some of the contact parameters in flexible body dynamics which is used for rigid body dynamic analysis to stabilize the model. Future Plans 1. To carry out the FMBD analysis by considering 2-4 flexible bodies. 2. To carry out the fatigue analysis. 3. To carry out the wear analysis. Conclusions The results obtained from the analysis are comparable in majority of the required aspects. MotionView and MotionSolve softwares will be used for the future plans as well as future projects.

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ACKNOWLEDGEMENTS We would like to acknowledge and extend my heartfelt gratitude to the following persons who have made the completion of this paper possible: From Infotech enterprises Ltd., For vital encouragement and support, Anand Parameswaran - Sr. VP & Head of HTH BU Sujeet kumar - General Manager & PDU Head Rahman Shaikh - AGM From Altair Engineering Inc., For extensive technical support, Ramesha BS - Technical Manager Varun Raj - Technical Support (MBD)

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REFERENCES Altair Engineering Inc., "Introduction To MBD," for overview of MBD implementation using MotionView and MotionSolve software. Farid M. L. Amirouche, " Fundamentals of Multibody Dynamics: Theory and Applications", ebook for Modelling springs and dampers at the Joints. S. Timoshenko, D.H. Young, JV Rao, " Engineering Mechanics", for Rotation of a Rigid Body about a Fixed Axis. Peter Childs, "Mechanical design", for Spring design. Altair Engineering Inc., "Help for HWSolvers-MBD simulations".

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