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Noise Radiation by a Compound Gear Train
Introduction
This example illustrates the modeling of noise radiation from the housing of a gear train. First, a multibody analysis is performed in the time domain to compute the housing vibrations at the specified driver shaft speed. Then, an acoustic analysis is performed at a selected frequency to compute the sound pressure levels in the near, far, and exterior fields using the housing normal acceleration as a noise source.
Predicting the noise radiation from a dynamic system gives designers an insight into the behavior of moving mechanisms early in the design process. For example, consider a gearbox in which the change in the gear mesh stiffness causes sustained vibrations. These vibrations are transmitted to the gearbox housing through shafts and joints. The vibrating housing further transmits energy to the surrounding fluid, resulting in acoustic wave radiation.
Note: This model requires the Acoustics Module and the Multibody Dynamics Module.
Model Definition
The gear train enclosed in an acoustic domain is shown in Figure 1. The details of the compound gear train is shown in Figure 2.
This model is solved in two steps:
1
 Multibody analysis: In the first part of the model, a transient analysis is performed to compute the dynamics of the gears as well as the acceleration levels on the gear train housing.
2
 Acoustic analysis: In the second part of the model, a spherical domain enclosing the gear train housing is created. The computed accelerations on the housing are used as noise source for the acoustic domain. A frequency domain analysis is performed in order to compute the sound pressure levels outside the gear train.
Note: For the details of the multibody analysis of the gear train, see the model Vibrations in a Compound Gear Train in the Multibody Dynamics Module Application Library.
Figure 1: Model geometry of the gear train enclosed in a spherical acoustic domain.
Figure 2: Details of the compound gear train.
Multibody-Acoustics Coupling
Unidirectional Coupling
When coupling multibody/structural and acoustics physics, unidirectional coupling can be assumed if the exterior fluid is air (or any other lighter fluid). This implies that the vibrations from the gear-train housing impacts the surrounding fluid, whereas the feedback from the acoustic waves to the structure is neglected. This model uses such an approach.
FFT Solver
The multibody dynamics is solved in the time domain, whereas the acoustics is solved in the frequency domain. Therefore, the FFT solver is used to convert the housing accelerations from the time domain to the frequency domain.
Domain Equations
This model solves the problem in the frequency domain using the Pressure Acoustics, Frequency Domain interface. The model equation is a slightly modified version of the Helmholtz equation for the acoustic pressure  p:
where ρ is the density, c is the speed of sound, and ω is the angular frequency.
Boundary Conditions
The following boundary conditions are applied in the acoustic domain:
•
Normal acceleration of the gear train housing is applied on the interior boundaries of the acoustics domain.
where an is the normal acceleration.
•
A spherical wave radiation condition is applied on the exterior boundaries of the acoustic domain.
•
An exterior field calculation is added on the exterior boundaries of the acoustic domain to compute the sound pressure levels in the exterior field.
Model Parameters
The domain material is chosen as air. The following parameters are used in the model:
•
The excitation frequency is set to 2000 Hz.
•
The size of enclosing sphere is set to 0.5 m.
•
Exterior field results are evaluated at a distance of 2 m from the center.
Results and Discussion
Figure 3: Amplitude and phase of normal acceleration of housing .
Figure 3 shows the amplitude (left) and phase (right) of the normal acceleration of the housing at 2000 Hz. The top part vibrates with higher velocity compared to the rest of the housing. This part also has constant phase as indicated by the color distribution in the second plot.
Figure 4: Sound Pressure Level (dB) in the near-field region at 2000 Hz.
Figure 4 shows the sound pressure level (SPL) in the acoustic domain. Different SPL values can be seen at different locations in space, with a maximum at the top of the gear train. The SPL field on the housing/casing surface is shown in Figure 5.
Figure 5: Sound Pressure Level (dB) on the casing surface at 2000 Hz.
The sound pressure levels in the far field at a distance of 2 m are shown in Figure 6, Figure 7, and Figure 8. All these plots show the sound pressure levels in different planes.
Figure 9 shows a three-dimensional plot of the sound pressure level, giving an idea of the dominant directions of noise radiation.
It is also possible to plot the acoustic wave propagation in a domain exterior to the modeled spherical domain. Figure 10 shows a plot of the acoustics waves propagating in the exterior domain.
Figure 6: Exterior-field sound pressure level in the xy-plane at a distance of 2 m.
Figure 7: Exterior-field sound pressure level in the xz-plane at a distance of 2 m.
Figure 8: Exterior-field sound pressure level in the yz-plane at a distance of 2 m.
Figure 9: Exterior-field sound pressure level at a distance of 2 m.
Figure 10: The acoustic wave propagation in the exterior domain.
Notes About the COMSOL Implementation
•
The acoustics is set up in a separate component so that the multibody model setup is unaffected. A General Extrusion nonlocal coupling is used to map the acceleration values between the geometries of the two components.
•
The normal acceleration of the housing is in the time domain. A Time to Frequency FFT study is used to convert it to the frequency domain.
•
The presence of the Multibody Dynamics physics, by default, forces the solver to be nonlinear. Hence it is manually set to linear for the acoustic analysis.
Application Library path: Acoustics_Module/Vibrations_and_FSI/gear_train_noise
Modeling Instructions
Application Libraries
1
From the File menu, choose Application Libraries.
2
In the Application Libraries window, select Multibody Dynamics Module > Tutorials, Transmission > gear_train in the tree.
3
Click  Open.
Enter the required set of parameters for the acoustic analysis.
Global Definitions
Parameters 1
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, locate the Parameters section.
3
In the table, enter the following settings:
Name
Expression
Value
Description
x0
0.07[m]
0.07 m
Sphere offset
R
0.5[m]
0.5 m
Sphere radius
f0
2000[Hz]
2000 Hz
Frequency of interest
Component 2 (comp2)
Create a selection for the exterior boundaries of the gear train housing. The acceleration computed on these boundaries is used as a noise source for the acoustic analysis.
Definitions (comp2)
Explicit 7
1
In the Model Builder window, expand the Component 2 (comp2) node.
2
Right-click Component 2 (comp2) > Definitions and choose Selections > Explicit.
3
In the Settings window for Explicit, locate the Input Entities section.
4
From the Geometric entity level list, choose Boundary.
5
Click  Paste Selection.
6
In the Paste Selection dialog, type 14,38,46,53,65,132,219,220,225,455,456,461,919,920,925 in the Selection text field.
7
Click OK.
8
In the Settings window for Explicit, locate the Input Entities section.
9
Select the Group by continuous tangent checkbox.
General Extrusion 1 (genext1)
1
In the Definitions toolbar, click  Nonlocal Couplings and choose General Extrusion.
2
In the Settings window for General Extrusion, locate the Source Selection section.
3
From the Geometric entity level list, choose Boundary.
4
From the Selection list, choose Explicit 7.
5
Locate the Source section. From the Source frame list, choose Material  (X, Y, Z).
6
Locate the Destination Map section. In the X-expression text field, type X.
7
In the Y-expression text field, type Y.
8
In the Z-expression text field, type Z.
9
Click to expand the Advanced section. From the Mesh search method list, choose Closest point.
Study 1 - Gear 2D
1
In the Model Builder window, click Study 1.
2
In the Settings window for Study, type Study 1 - Gear 2D in the Label text field.
Study 2 - Gear Train
1
In the Model Builder window, click Study 2.
2
In the Settings window for Study, type Study 2 - Gear Train in the Label text field.
Add Component
Right-click Study 2 - Gear Train and choose Add Component > 3D.
Geometry 3
Import 1 (imp1)
1
In the Geometry toolbar, click  Import.
2
In the Settings window for Import, locate the Source section.
3
Click  Browse.
4
Browse to the model’s Application Libraries folder and double-click the file gear_train_noise.mphbin.
5
Click  Import.
Create a domain surrounding the gear train assembly for the acoustic analysis. In order to do this, add a spherical domain of a finite size and remove the gear train assembly from it.
Convert to Solid 1 (csol1)
1
In the Geometry toolbar, click  Conversions and choose Convert to Solid.
2
Click the  Transparency button in the Graphics toolbar.
3
Click in the Graphics window and then press Ctrl+A to select all objects.
4
In the Settings window for Convert to Solid, click  Build Selected.
Sphere 1 (sph1)
1
In the Geometry toolbar, click  Sphere.
2
In the Settings window for Sphere, locate the Size section.
3
In the Radius text field, type R.
4
Locate the Position section. In the x text field, type x0.
5
Click  Build Selected.
6
Click the  Zoom Extents button in the Graphics toolbar.
Difference 1 (dif1)
1
In the Geometry toolbar, click  Booleans and Partitions and choose Difference.
2
Select the object sph1 only.
3
In the Settings window for Difference, locate the Difference section.
4
Click to select the  Activate Selection toggle button for Objects to subtract.
5
Select the object csol1 only.
6
Click  Build Selected.
Add Physics
1
In the Home toolbar, click  Add Physics to open the Add Physics window.
2
Go to the Add Physics window.
3
In the tree, select Mathematics > ODE and DAE Interfaces > Boundary ODEs and DAEs (bode).
4
Find the Physics interfaces in study subsection. In the table, clear the Solve checkboxes for Study 1 - Gear 2D and Study 2 - Gear Train.
5
Click the Add to Component 3 button in the window toolbar.
6
In the tree, select Acoustics > Pressure Acoustics > Pressure Acoustics, Frequency Domain (acpr).
7
In the table, clear the Solve checkboxes for Study 1 - Gear 2D and Study 2 - Gear Train.
8
Click the Add to Component 3 button in the window toolbar.
9
In the Home toolbar, click  Add Physics to close the Add Physics window.
Add Material
1
In the Materials toolbar, click  Add Material to open the Add Material window.
2
Go to the Add Material window.
3
In the tree, select Built-in > Air.
4
Click the Add to Component button in the window toolbar.
5
In the Materials toolbar, click  Add Material to close the Add Material window.
Definitions (comp3)
Outer Boundaries
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, locate the Input Entities section.
3
From the Geometric entity level list, choose Boundary.
4
Select Boundary 1 only.
5
Select the Group by continuous tangent checkbox.
6
In the Label text field, type Outer Boundaries.
Casing
1
In the Definitions toolbar, click  Box.
2
In the Settings window for Box, type Casing in the Label text field.
3
Locate the Geometric Entity Level section. From the Level list, choose Boundary.
4
Locate the Box Limits section. In the y minimum text field, type -0.06.
5
In the y maximum text field, type 0.06.
6
Locate the Output Entities section. From the Include entity if list, choose Entity inside box.
Boundary ODEs and DAEs (bode)
1
In the Model Builder window, under Component 3 (comp3) click Boundary ODEs and DAEs (bode).
2
In the Settings window for Boundary ODEs and DAEs, locate the Boundary Selection section.
3
From the Selection list, choose Casing.
4
Locate the Units section. Click  Select Dependent Variable Quantity.
5
In the Physical Quantity dialog, type acceleration in the text field.
6
In the tree, select General > Acceleration (m/s^2).
7
Click OK.
8
In the Settings window for Boundary ODEs and DAEs, locate the Units section.
9
Click  Select Source Term Quantity.
10
In the Physical Quantity dialog, type length in the text field.
11
In the tree, select General > Length (m).
12
Click OK.
13
In the Settings window for Boundary ODEs and DAEs, click to expand the Discretization section.
14
From the Shape function type list, choose Lagrange.
15
From the Frame list, choose Material.
16
Click to expand the Dependent Variables section. In the Field name (m/s²) text field, type an.
17
In the Dependent variables (m/s²) table, enter the following settings:
an
Distributed ODE 1
1
In the Model Builder window, under Component 3 (comp3) > Boundary ODEs and DAEs (bode) click Distributed ODE 1.
2
In the Settings window for Distributed ODE, locate the Source Term section.
3
In the f text field, type 0.
4
Locate the Damping or Mass Coefficient section. In the da text field, type 0.
Initial Values 1
1
In the Model Builder window, click Initial Values 1.
2
In the Settings window for Initial Values, locate the Initial Values section.
3
In the an text field, type comp2.genext1(comp2.mbd2.an).
Pressure Acoustics, Frequency Domain (acpr)
In the Model Builder window, under Component 3 (comp3) click Pressure Acoustics, Frequency Domain (acpr).
Spherical Wave Radiation 1
1
In the Physics toolbar, click  Boundaries and choose Spherical Wave Radiation.
2
In the Settings window for Spherical Wave Radiation, locate the Boundary Selection section.
3
From the Selection list, choose Outer Boundaries.
4
Locate the Spherical Wave Radiation section. Specify the r0 vector as
x0
x
0
y
0
z
The normal acceleration computed in Study 2 - Gear Train is used as an acceleration source for the acoustic analysis.
Normal Acceleration 1
1
In the Physics toolbar, click  Boundaries and choose Normal Acceleration.
2
In the Settings window for Normal Acceleration, locate the Boundary Selection section.
3
From the Selection list, choose Casing.
4
Locate the Normal Acceleration section. In the an text field, type comp3.an.
Exterior Field Calculation 1
1
In the Physics toolbar, click  Boundaries and choose Exterior Field Calculation.
2
In the Settings window for Exterior Field Calculation, locate the Boundary Selection section.
3
From the Selection list, choose Outer Boundaries.
4
Click the  Show More Options button in the Model Builder toolbar.
5
In the Show More Options dialog, in the tree, select the checkbox for the node Physics > Advanced Physics Options.
6
Click OK.
7
In the Settings window for Exterior Field Calculation, click to expand the Advanced Settings section.
8
Clear the Use polynomial-preserving recovery for the normal gradient checkbox.
Mesh 3
The mesh size is chosen such that there are 5 elements per wavelength at the frequency of interest.
Free Tetrahedral 1
In the Mesh toolbar, click  Free Tetrahedral.
Size
1
In the Model Builder window, click Size.
2
In the Settings window for Size, locate the Element Size section.
3
Click the Custom button.
4
Locate the Element Size Parameters section. In the Maximum element size text field, type 343[m/s]/f0/5.
5
In the Model Builder window, right-click Mesh 3 and choose Build All.
Boundary Layers 1
In the Mesh toolbar, click  Boundary Layers.
Boundary Layer Properties
1
In the Model Builder window, click Boundary Layer Properties.
2
In the Settings window for Boundary Layer Properties, locate the Geometric Entity Selection section.
3
From the Selection list, choose Outer Boundaries.
4
Locate the Layers section. In the Number of layers text field, type 1.
5
From the Thickness specification list, choose First layer.
6
In the Thickness text field, type 343[m/s]/f0/5/10.
7
In the Model Builder window, right-click Mesh 3 and choose Build All.
Add Study
1
In the Home toolbar, click  Add Study to open the Add Study window.
2
Go to the Add Study window.
3
Find the Studies subsection. In the Select Study tree, select Empty Study.
4
Click the Add Study button in the window toolbar.
5
In the Home toolbar, click  Add Study to close the Add Study window.
Study 2 - Gear Train
In the Study toolbar, click  Update Solution.
Study 3 - Acoustics
In the Settings window for Study, type Study 3 - Acoustics in the Label text field.
Transform the time-dependent acceleration data to the frequency domain using a Time to Frequency FFT study step, then use this data as input for the Frequency Domain study step.
Step 1: Time to Frequency FFT
1
In the Study toolbar, click  Study Steps and choose Frequency Domain > Time to Frequency FFT.
2
In the Settings window for Time to Frequency FFT, locate the Study Settings section.
3
From the Prescribed by list, choose Initial expression.
4
From the Input study list, choose Study 2 - Gear Train, Time Dependent.
5
In the End time text field, type 7e-3.
6
In the Maximum output frequency text field, type 1/(7e-5).
7
Locate the Physics and Variables Selection section. In the Solve for column of the table, under Component 1 (comp1), clear the checkbox for Multibody Dynamics (mbd).
8
In the Solve for column of the table, under Component 2 (comp2), clear the checkbox for Multibody Dynamics 2 (mbd2).
9
In the Solve for column of the table, under Component 3 (comp3), clear the checkbox for Pressure Acoustics, Frequency Domain (acpr).
Step 2: Frequency Domain
1
In the Model Builder window, right-click Study 3 - Acoustics and choose Study Steps > Frequency Domain > Frequency Domain.
2
In the Settings window for Frequency Domain, locate the Study Settings section.
3
In the Frequencies text field, type f0.
4
Locate the Physics and Variables Selection section. In the Solve for column of the table, under Component 1 (comp1), clear the checkbox for Multibody Dynamics (mbd).
5
In the Solve for column of the table, under Component 2 (comp2), clear the checkbox for Multibody Dynamics 2 (mbd2).
6
In the Solve for column of the table, under Component 3 (comp3), clear the checkbox for Boundary ODEs and DAEs (bode).
7
Click to expand the Values of Dependent Variables section. Find the Values of variables not solved for subsection. From the Settings list, choose User controlled.
8
From the Method list, choose Solution.
9
From the Study list, choose Study 3 - Acoustics, Time to Frequency FFT.
10
From the Selection list, choose Automatic (all solutions).
Set the solver to linear as by default Multibody Dynamics sets it to nonlinear.
Solution 3 (sol3)
1
In the Study toolbar, click  Show Default Solver.
2
In the Model Builder window, expand the Solution 3 (sol3) node, then click Stationary Solver 1.
3
In the Settings window for Stationary Solver, locate the General section.
4
From the Linearity list, choose Linear.
5
In the Model Builder window, click Study 3 - Acoustics.
6
In the Settings window for Study, locate the Study Settings section.
7
Clear the Generate default plots checkbox.
8
In the Study toolbar, click  Compute.
Results
Study 3 - Acoustics/Solution 3 (9) (sol3)
1
In the Model Builder window, expand the Results > Datasets node.
2
Right-click Results > Datasets > Study 3 - Acoustics/Solution 3 (8) (sol3) and choose Duplicate.
Selection
1
In the Model Builder window, right-click Study 3 - Acoustics/Solution 3 (9) (sol3) and choose Selection.
2
In the Settings window for Selection, locate the Geometric Entity Selection section.
3
From the Geometric entity level list, choose Boundary.
4
From the Selection list, choose Casing.
Study 3 - Acoustics/Solution 3 (10) (sol3)
In the Model Builder window, under Results > Datasets right-click Study 3 - Acoustics/Solution 3 (9) (sol3) and choose Duplicate.
Selection
1
In the Model Builder window, expand the Study 3 - Acoustics/Solution 3 (10) (sol3) node, then click Selection.
2
In the Settings window for Selection, locate the Geometric Entity Selection section.
3
Click  Clear Selection.
4
Click  Paste Selection.
5
In the Paste Selection dialog, type 5-7,10-14,16-27,29-39,43-45,48-49,53-55,57,59,67-69,71,73-96 in the Selection text field.
6
Click OK.
Grid 3D 1
1
In the Results toolbar, click  More Datasets and choose Grid > Grid 3D.
2
In the Settings window for Grid 3D, locate the Data section.
3
From the Dataset list, choose Study 3 - Acoustics/Solution 3 (8) (sol3).
4
Locate the Parameter Bounds section. Find the First parameter subsection. In the Minimum text field, type -2.
5
In the Maximum text field, type 2.
6
Find the Second parameter subsection. In the Minimum text field, type -2.
7
In the Maximum text field, type 2.
8
Find the Third parameter subsection. In the Maximum text field, type 0.
9
Click to expand the Grid section. In the x resolution text field, type 100.
10
In the y resolution text field, type 100.
11
In the z resolution text field, type 2.
Use the following instructions to plot the amplitude and phase of the normal acceleration of the gear train housing as shown in Figure 3.
Housing Normal Acceleration: Amplitude and Phase
1
In the Results toolbar, click  3D Plot Group.
2
In the Settings window for 3D Plot Group, locate the Data section.
3
From the Dataset list, choose Study 3 - Acoustics/Solution 3 (9) (sol3).
4
In the Label text field, type Housing Normal Acceleration: Amplitude and Phase.
Surface 1
1
Right-click Housing Normal Acceleration: Amplitude and Phase and choose Surface.
2
In the Settings window for Surface, locate the Expression section.
3
In the Expression text field, type abs(acpr.nacc).
Surface 2
1
In the Model Builder window, right-click Housing Normal Acceleration: Amplitude and Phase and choose Surface.
2
In the Settings window for Surface, locate the Expression section.
3
In the Expression text field, type arg(acpr.nacc).
Transformation 1
1
Right-click Surface 2 and choose Transformation.
2
In the Settings window for Transformation, locate the Transformation section.
3
In the X text field, type 0.4.
Surface 2
1
In the Model Builder window, click Surface 2.
2
In the Settings window for Surface, locate the Coloring and Style section.
3
From the Color table list, choose Disco.
Housing Normal Acceleration: Amplitude and Phase
1
In the Model Builder window, click Housing Normal Acceleration: Amplitude and Phase.
2
In the Settings window for 3D Plot Group, click to expand the Title section.
3
From the Title type list, choose Manual.
4
In the Title text area, type Surface: Amplitude (m/s^2) Surface: Phase (rad).
5
Locate the Color Legend section. From the Position list, choose Right double.
6
Locate the Plot Settings section. Clear the Plot dataset edges checkbox.
7
In the Housing Normal Acceleration: Amplitude and Phase toolbar, click  Plot.
8
Click the  Zoom Extents button in the Graphics toolbar.
9
Click the  Transparency button in the Graphics toolbar.
Use the following instructions to plot the spatial distribution of the sound pressure level in the spherical domain and on the surface of gear train housing as shown in Figure 4 and Figure 5, respectively.
SPL Near Field
1
In the Results toolbar, click  3D Plot Group.
2
In the Settings window for 3D Plot Group, type SPL Near Field in the Label text field.
3
Locate the Data section. From the Dataset list, choose Study 3 - Acoustics/Solution 3 (8) (sol3).
4
Locate the Title section. From the Title type list, choose Manual.
5
In the Title text area, type Sound Pressure Level - Near Field.
6
Locate the Color Legend section. Select the Show maximum and minimum values checkbox.
Slice 1
1
Right-click SPL Near Field and choose Slice.
2
In the Settings window for Slice, locate the Expression section.
3
In the Expression text field, type acpr.Lp_t.
4
Locate the Plane Data section. In the Planes text field, type 1.
5
Locate the Coloring and Style section. From the Color table list, choose Rainbow.
6
From the Scale list, choose Linear.
Slice 2
1
Right-click Slice 1 and choose Duplicate.
2
In the Settings window for Slice, locate the Plane Data section.
3
From the Plane list, choose XY-planes.
4
In the Planes text field, type 1.
5
Click to expand the Inherit Style section. From the Plot list, choose Slice 1.
Slice 3
1
Right-click Slice 2 and choose Duplicate.
2
In the Settings window for Slice, locate the Plane Data section.
3
From the Plane list, choose ZX-planes.
4
In the Planes text field, type 1.
5
In the SPL Near Field toolbar, click  Plot.
6
Click the  Zoom Extents button in the Graphics toolbar.
SPL Casing Surface
1
In the Results toolbar, click  3D Plot Group.
2
In the Settings window for 3D Plot Group, type SPL Casing Surface in the Label text field.
3
Locate the Data section. From the Dataset list, choose Study 3 - Acoustics/Solution 3 (9) (sol3).
4
Locate the Title section. From the Title type list, choose Manual.
5
In the Title text area, type Sound Pressure Level - Casing Surface.
6
Locate the Color Legend section. Select the Show maximum and minimum values checkbox.
Surface 1
1
Right-click SPL Casing Surface and choose Surface.
2
In the Settings window for Surface, locate the Expression section.
3
In the Expression text field, type acpr.Lp_t.
4
In the SPL Casing Surface toolbar, click  Plot.
5
Click the  Zoom Extents button in the Graphics toolbar.
Follow the instructions below to plot the spatial distribution of the sound pressure level in the exterior-field region as shown in Figure 6, Figure 7, Figure 8, and Figure 9, respectively.
Polar SPL xy-plane
1
In the Results toolbar, click  Polar Plot Group.
2
In the Settings window for Polar Plot Group, type Polar SPL xy-plane in the Label text field.
3
Locate the Data section. From the Dataset list, choose Study 3 - Acoustics/Solution 3 (8) (sol3).
4
Click to expand the Title section. From the Title type list, choose Manual.
5
In the Title text area, type Sound Pressure Level - Exterior Field (xy-plane).
Radiation Pattern 1
1
In the Polar SPL xy-plane toolbar, click  More Plots and choose Radiation Pattern.
2
In the Settings window for Radiation Pattern, locate the Evaluation section.
3
Find the Angles subsection. In the Number of angles text field, type 180.
4
Find the Center subsection. In the x text field, type x0.
5
Find the Evaluation distance subsection. In the Radius text field, type 4*R.
6
In the Polar SPL xy-plane toolbar, click  Plot.
7
Click the  Zoom Extents button in the Graphics toolbar.
Polar SPL xz-plane
1
In the Model Builder window, right-click Polar SPL xy-plane and choose Duplicate.
2
In the Model Builder window, click Polar SPL xy-plane 1.
3
In the Settings window for Polar Plot Group, type Polar SPL xz-plane in the Label text field.
4
Locate the Title section. In the Title text area, type Sound Pressure Level - Exterior Field (xz-plane).
Radiation Pattern 1
1
In the Model Builder window, click Radiation Pattern 1.
2
In the Settings window for Radiation Pattern, locate the Evaluation section.
3
Find the Normal vector subsection. In the y text field, type 1.
4
In the z text field, type 0.
5
In the Polar SPL xz-plane toolbar, click  Plot.
6
Click the  Zoom Extents button in the Graphics toolbar.
Polar SPL yz-plane
1
In the Model Builder window, right-click Polar SPL xz-plane and choose Duplicate.
2
In the Model Builder window, click Polar SPL xz-plane 1.
3
In the Settings window for Polar Plot Group, type Polar SPL yz-plane in the Label text field.
4
Locate the Title section. In the Title text area, type Sound Pressure Level - Exterior Field (yz-plane).
Radiation Pattern 1
1
In the Model Builder window, click Radiation Pattern 1.
2
In the Settings window for Radiation Pattern, locate the Evaluation section.
3
Find the Normal vector subsection. In the y text field, type 0.
4
In the x text field, type 1.
5
In the Polar SPL yz-plane toolbar, click  Plot.
6
Click the  Zoom Extents button in the Graphics toolbar.
3D Polar SPL
1
In the Results toolbar, click  3D Plot Group.
2
In the Settings window for 3D Plot Group, type 3D Polar SPL in the Label text field.
3
Locate the Data section. From the Dataset list, choose Study 3 - Acoustics/Solution 3 (8) (sol3).
4
Locate the Title section. From the Title type list, choose Manual.
5
In the Title text area, type Sound Pressure Level - Exterior Field (3D).
Radiation Pattern 1
1
In the 3D Polar SPL toolbar, click  More Plots and choose Radiation Pattern.
2
In the Settings window for Radiation Pattern, locate the Evaluation section.
3
Find the Angles subsection. In the Number of elevation angles text field, type 50.
4
In the Number of azimuth angles text field, type 50.
5
Find the Sphere subsection. From the Sphere list, choose Manual.
6
In the X text field, type x0.
7
In the Radius text field, type 4*R.
8
Locate the Coloring and Style section. From the Grid list, choose Fine.
9
In the 3D Polar SPL toolbar, click  Plot.
10
Click the  Zoom Extents button in the Graphics toolbar.
Finally, plot the spatial distribution of the sound pressure level in the exterior field as shown in Figure 10.
Pressure Exterior Field
1
In the Results toolbar, click  3D Plot Group.
2
In the Settings window for 3D Plot Group, type Pressure Exterior Field in the Label text field.
3
Locate the Data section. From the Dataset list, choose Grid 3D 1.
4
Locate the Title section. From the Title type list, choose Manual.
5
In the Title text area, type Pressure Exterior Field (xy-plane).
Surface 1
1
Right-click Pressure Exterior Field and choose Surface.
2
In the Settings window for Surface, locate the Expression section.
3
In the Expression text field, type if(sqrt((x-x0)^2+y^2+z^2)>R,pext(x,y,z),NaN).
4
Click to expand the Range section. Select the Manual color range checkbox.
5
In the Minimum text field, type -.04.
6
In the Maximum text field, type .04.
7
Locate the Coloring and Style section. From the Color table list, choose Wave.
8
In the Pressure Exterior Field toolbar, click  Plot.
Slice 1
1
In the Model Builder window, right-click Pressure Exterior Field and choose Slice.
2
In the Settings window for Slice, locate the Data section.
3
From the Dataset list, choose Study 3 - Acoustics/Solution 3 (9) (sol3).
4
Locate the Plane Data section. From the Plane list, choose XY-planes.
5
In the Planes text field, type 1.
6
Locate the Inherit Style section. From the Plot list, choose Surface 1.
7
In the Pressure Exterior Field toolbar, click  Plot.
8
Click the  Zoom Extents button in the Graphics toolbar.
SPL Casing Surface
Click the  Zoom Extents button in the Graphics toolbar.
Thumbnail
1
In the Results toolbar, click  3D Plot Group.
2
In the Settings window for 3D Plot Group, type Thumbnail in the Label text field.
3
Locate the Data section. From the Dataset list, choose Study 3 - Acoustics/Solution 3 (10) (sol3).
4
Locate the Color Legend section. Select the Show maximum and minimum values checkbox.
Surface 1
1
Right-click Thumbnail and choose Surface.
2
In the Settings window for Surface, locate the Coloring and Style section.
3
From the Color table list, choose Wave.
4
From the Scale list, choose Linear symmetric.
Surface 2
1
In the Model Builder window, right-click Thumbnail and choose Surface.
2
In the Settings window for Surface, locate the Data section.
3
From the Dataset list, choose Study 2 - Gear Train/Solution 2 (4) (sol2).
4
From the Time (s) list, choose 0.00301.
5
Locate the Expression section. In the Expression text field, type mbd2.disp.
6
Locate the Coloring and Style section. From the Color table list, choose AuroraAustralis.
Deformation 1
1
Right-click Surface 2 and choose Deformation.
2
In the Settings window for Deformation, locate the Scale section.
3
Select the Scale factor checkbox. In the associated text field, type 1.
Isosurface 1
1
In the Model Builder window, right-click Thumbnail and choose Isosurface.
2
In the Settings window for Isosurface, locate the Levels section.
3
In the Total levels text field, type 11.
4
Click to expand the Inherit Style section. From the Plot list, choose Surface 1.
Filter 1
1
Right-click Isosurface 1 and choose Filter.
2
In the Settings window for Filter, locate the Element Selection section.
3
In the Logical expression for inclusion text field, type y>0.
Thumbnail
1
In the Model Builder window, under Results click Thumbnail.
2
In the Thumbnail toolbar, click  Plot.