Design and Manufacturing solutions through Digital Prototyping and Interoperability

Category Archives: Simulation

Engineering Notes: Curved Area Calcs Using Limited Information

In order to determine how fast the High-Pressure Compressor can safely spin, we need to determine how much stress the blades and hubs are experiencing. If I throw something together and build the CFD (computational fluid dynamics) and FEA (finite entity analysis) models, I would end up with a complete overhaul to the design, and have to repeat the build processes. By employing some basic 2D calculations of selected stress concentrations which the HP compressor will experience can save considerable revision time.

Stress is defined as Force/Area. One such stress that needs to be determined is how much stress is acting on the root of the compressor blade. I tried to approximate the area with a few coefficients, but unfortunately, as the blades grow in size and camber, the approximations lose considerable accuracy.

What we can do is to approximate the blade inner and outer curve parameters, calculate the areas under each, and then subtract these to get the net result thereof. If you are using CAD, such as AutoCAD, you can query radii, areas, and centroid parameters graphically. However if you are generating the shapes using CAD parameters, or linked Excel tables, then you are going to have to do some math.


What we know

From our basic blade flow calculations, we know the centerline (mean camber line) chord length and camber angle of each blade, from root to tip. We also know that the blade thickness factor is 0.1, which indicates that the maximum blade thickness is 10% of the chord length.

Blade Chord Length (C)=0.0194m

Blade Thickness Thick=0.00194m

Mean Blade Camber (or Delta) Angle =51.15°Δ or 0.89274 radians Θ

Note: To avoid confusion of mean camber line with other references to the mean line design of the flow cross section, I’ll refer to the mean camber line as the centerline of blade (c/l).


CAD Curve Area Calculations Centerline

What we need to determine

The equations we will use are basic trigonometry relationships in a circular arc. We would be wise to use some calculus to determine these, but trig will be easier in a spreadsheet or CAD parameter field.

Radius: R =  C/(2*Sin(Θ/2))

Mid Ordinate: M = R(1-Cos(Θ/2))

Camber or Delta angle: Θ = 4*ATan(2 * M/C)

Area under the curve: Area = R^2/2 * (Θ – Sin(Θ))

Note: Area is the area between the curve and the chord.


symbols will include:

R = Radius

Rcl = Radius of centerline

M / Mo / Mi / Mcl = Mid-Ordinate and subscripts for outer, inner, and centerline curves

Θ / Θo / Θi = Delta or Camber angle, in radians, with subscripts for outer and inner curves

AREA = Net area between curves

AREAo / AREAi = Area under respective curves, with subscripts for outer and inner curves


C/l Curve Calculations

Our first step is to determine the radius and mid-ordinate of the c/l curve.

Why the mid-ordinate you may ask. Because, it is easiest to jump to the inner and outer curves as we already know the offset from the centerline at the thickest point. That would approximately be half the thickness of the blade.

CAD Curve Area Calculations Mid Ordinate

R =  C/(2*Sin(Θ/2))

  • Rcl = 0.0194 / (2*Sin(0.89274/2)) = 0.02247m


M = R(1-Cos(Θ/2))

  • Mcl = 0.02247*(1–Cos(0.89274/2)) = 0.00220m

Outer and Inner Curve

As mentioned easrlier, if the blade centerline lies in the middle of the inner and outer curves, then the offset between these is 1/2 the thickness.

CAD Curve Area Calculations Outer

The following calculations are for the outer curve, with subscript _o.

Mid Ordinate:

Mo = Mcl + 0.5*thickness

  • Mo = 0.00220 + 0.5*0.00194 = 0.00317m

Using the Chord length and Mid Ordinate, we can determine the remaining values.

Camber Angle:

Θ = 4*ATan(2 * M/C)

  • Θo = 4 * ATan(2 * 0.00317/0.0194) = 1.26345 rad


R =  C/(2*Sin(Θ/2))

  • Ro = 0.0194/(2 * Sin(1.26345/2)) = 0.01643m

For the inner curve, with subscript _i, we’d subtract the half thickness instead of adding, then repeat the remaining calculations.

Mi = 0.00220 – 0.5*0.00194 = 0.00123m

  • Θi = 4 * ATan(2 * 0.00123/0.0194) = 0.50452r
  • Ri = 0.0194/(2 * Sin(0.50452/2)) = 0.03886m


Now that we have Radius and Camber, we can determine the area under the curve.

CAD Curve Area Calculations Difference

Area = R^2/2 * (Θ – Sin(Θ))

  • AREAo = 0.01643^2 /2 * (1.26345 – Sin(1.26345) = 0.000042 m^2

Now, we can repeat the entire process for the inner curve and get it’s area:

  • AREAi = 0.03886^2 /2 * (0.50452 – Sin(0.50452) = 0.000016m^2
  • Area of blade cross section = AREAo – AREAi
  • Area = 0.000042 – 0.000016 = 0.000026m^2


That seems like a lot of work that some calculus could simplify; very true. However if you are working in Excel or CAD parameters, you need something that’s algebraic (plus I’m not the best at Calculus).

Our old coefficient estimation of this curve was 0.000031m^2, which is about 20% off. That difference applied into three factors of the principle stress calculations should be enough to cause considerable uncertainty. With a safety factor of 3+, 20% starts eating up our usable design room quickly. If each stress estimation is out by 20%, the design stability is overestimated tremendously.

I’ll bring other ways of determining some of this information, as well as centroid calculation, second moment of area, bending moment, stress calculations and more. Keep checking back at Engineering Notes.


While the standard arc trigonometry equations are real, the application for applying these for compressor blade root area cross sections is approximate. If you simply need the trig information for circular arcs, then you are set. If you are applying these factors to DCA airfoil calculations, which can vary shape somewhat, be aware that these are only close estimations intended to get you running quickly.

The entire trigonometry equation for Excel

If you want to simplify things a bit, the following is the whole enchilada, in one equation. You can paste that into Excel if you like, and it only needs you to supply the Chord, and the inner and outer Mid Ordinates.

Area = (((C/(2*SIN(ATAN(2*M)/C)))^2)/2)*((4*ATAN((2*M)/C))-SIN(4*ATAN((2*M)/C)))


Review: solidThinking Inspire 2014 Test Drive

Recently we revisited our New Features Review for solidThiking Inspire 2014. After writing that, we decided that since we love 3D printing, additive manufacturing technology, and topological optimization, we were ultimately responsible to test drive this software. Actually, it just looked so cool… and it is!

Inspire is a topological optimization software that allows users to optimize their parts for mass or strength. Inspire is different in that it can not only optimize existing design concepts to be lighter, it can develop lighter and stronger components as a starting point for a new design process. Don’t miss out on this really amazing technology and a well refined interface in our Full Review of solidThinking Inspire 2014.

Review: solidThinking Inspire 2014

What’s New: solidThinking Inspire 2014

In light of recent and upcoming enhancements from solidThinking (both Inspire and Evolve), I wanted to dust of our recent review of the the new additions of solidThinking Inspire 2014. Inspire is a topological optimizer capable of developing amazing shapes intended to be lighter and stronger than traditionally designed components. The company has increased productivity with more feature enhancements as well as some big ticked additions:

  • Geometry simplification tools
  • Smoothing options
  • Linear static analysis
  • Concentrated mass parts
  • more…


When you are done reading about the changes this year, check out our test drive of solidThinking Inspire 2014 as well.

solidThinking Inspire 2014 Infographic

Autodesk Simulation 2016 Portfolio

As part of  Autodesk Design, Lifecycle, and Simulation’s 2016 Manufacturing Launch, the company has unveiled their next push in an expanding end-to-end engineering solution, which includes their Simulation portfolio alongside Product / Factory Design Suites and Inventor HSM.

The following highlights are only the tip of the iceberg, and more information will be available shortly.

Simulation Software Titles

  • Simulation Mechanical
  • Nastran and Nastran In-CAD
  • CFD and Flow Design
  • Robot Structural Analysis Professional
  • Moldflow and Moldflow Design
  • Helius PFA and Helius Composite

Dropped Simulation from the Name

Autodesk Simulation software titles will no longer be prefixed with the word ‘Simulation’ with the exception of Simulation Mechanical; Autodesk Simulation CFD is now simply ‘Autodesk CFD’ and so forth.


I am rather excited about this product. SimStudio is a new product available to Moldflow, CFD, and Simulation Mechanical subscribers. This nifty toolset was developed from the Autodesk Labs Arrow project, and essentially replaces the old desktop version of Inventor Fusion, which served as one of the best defeaturing technologies ever.

New Autodesk SimStudio 2016

SimStudio is a new software build designed specifically for defeaturing and direct editing. It has a streamlined toolset that appears (in demonstrations) to seamlessly repair and simplify complex surfaces, as well as search and remove common manufacturing features like rounds, fillets, chamfers, holes and more.  One really sweet feature demonstrated was the geometry replacement tool, where small detailed electronic components were swiftly replaced by simple geometric shapes. Model data is handed back and forth between SimStudio and simulation products, as well as acting as a go-between for Inventor and simulation.

Task automation can further be enhanced with 3rd party applications and custom scripting. Customized in-app geometry and data extraction tools can be applied using JavaScript and Python.


  • Increased pre-processing efficiency
  • User feedback driven UI refinements, such as having all tabs permanently available on the Ribbon
  • Completely integrated CFD for conformal cooling studies
  • New processes and additional controls
  • Copy settings to a new study
  • Controlled valve gate opening rate – evaluate the results of injection speed across valve gates to study flowfront and injection pressure profiles.
  • Induction heating – RocTool partnership enables this new feature in 2016
  • Advanced Material Exchange – map data to Abaqus and ANSYS


Export Warped Model

My favorite MoldFlow addition so far is the ability to export the simulated warpage of cooled, molded plastic parts back into the overall product design process as a new model. Users can then check the fit in the assembly as well as better collision detection.

Autodesk Moldflow Export Warped Part


  • New Graphics engine delivers large model performance with >15X frame rate increase
  • New scalable solver – delivers ~80% scaling ratio per networked station
  • External radiation model enhancements
  • New turbulence models – enable more accurate solutions with high curvature flows

External Surface Wrapping and Geometry Fault Detection

CFD now offers an automated process to create simplified mesh that incorporates multiple bodies into a single externally wrapped mesh. Ideally this would substantially improve solving times in models with even moderate complexity.

Autodesk CFD 2016 New Features and Error Detection

Geometry faults can be detected inside CFD. Gaps and seams with poor geometry definitions are highlighted within both the part geometry and assembly component levels. While these functionalities might fit well within the SimStudio product, CFD model preparation and gapless flow channel challenges require both of these processes. Having them seamlessly integrated as part of CFD core functionality is a real blessing.


Nastran and In-CAD have made themselves at home and finally make their debut as part of the Design, Lifecycle, and Simulation product launch. No new features have been announced for these products but I suspect some new enhancements will be arriving shortly.

Simulation Mechanical

2016 will represent the first official product launch with Autodesk Nastran as part of the solving capabilities. I have heard that there is some degree of expanding use of Nastran in Simulation Mechanical. I expect more specifics about enhancements will be coming to light soon.


There was a lot of things happening with simulation this year considering the Nei Nastran purchase, and determining how the products would sit within the company’s growing portfolio. That said, MoldFlow and CFD received some valuable improvements, and as a subscriber, since you will still be using the products, enhancements are simply a good reason to keep subscribing.

We spend a little time with Nastran In-CAD last year, and found it to be quite a nice addition to Autodesk Inventor and am happy to see it emerge in an official launch. This year I am really looking forward to spending some well-deserved, concentrated research time with CFD 2016, as well as SimStudio.

Autodesk Software Information and Downloads

Simulation software portfolio

These products are available now!

Images courtesy of Autodesk, Inc.


Autodesk Manufacturing 2016 Product Launch

Autodesk has officially released (April 13, 2015) their Product Design Suite and Factory Design Suites for 2016, in concert with their Simulation software lineup, and Inventor HSM. This package represents a very large range of solutions for its manufacturing industry customers, and includes some great updates to existing products as well as a few new features too.

Autodesk Inventor took the Lion’s share of improvements in what the company is calling an open, connected, end-to-end seamless product development ecosystem. The following are a few highlights from these portfolios.

Product Design Suite (PDS) and Inventor

Recently, we detailed the enhancements in Autodesk Inventor 2016; 387 additions and valuable enhancements such as multi-body sheet metal and model to free-form tools. One addition that stood out was the 3D Printing Environment within Inventor. This allows users to prepare their components for specific vendor’s machines, orienting and partitioning their parts in print spaces that are too limiting. The partition tools include alignment tabs, and the ability to reposition the remaining portions of the part in the void areas of the printer’s effective printing space. Watching the company’s demo of this functionality was kind of cool.

Autodesk Print Studio 2016

Once a print is prepared, users can then send the oriented parts from the 3D Printing Environment to Autodesk’s new 3D Print Studio, an application that helps users build supports and prints the project directly to the large list of known commercial printers.

AnyCAD, Autodesk’s name for their new technology for importing and maintaining most popular CAD model formats inside Inventor assemblies. This allows users the option of importing almost any CAD model for use in their designs, and maintaining the relationship between the original file and the model. If the original file is modified (or overwritten), the imported model is updated dynamically.

Autodesk Inventor 2016 AnyCAD

Buzz Kross, senior vice president, Design, Lifecycle and Simulation at Autodesk noted:

“The new AnyCAD technology in Inventor alone is worth moving to the 2016 version, but we’re also improving every part of the product workflow from concept through product delivery to help companies meet the challenges that lie ahead”


Watch Scott’s great video of AnyCAD in action.


Other really nice areas of improvement include Sheet Metal environment, 2D Sketching, Drawing Environment, and Presentation Environment (yes, believe it or not).


Product Design Suite Software Titles

PDS Premium includes:

  • Inventor
  • AutoCAD( + Mechanical)
  • AutoCAD Raster Design
  • ReCap
  • Vault Basic
  • 3ds Max Design
  • Navisworks Simulate
  • Showcase (downloaded separately)
  • 3D Print Studio
  • Fusion 360

PDS Ultimate adds:

  • Inventor Professional
  • AutoCAD Electrical
  • Navisworks Manage (replaces Simulate)
  • Alias Design (downloaded separately)


Factory Design Suite

Additional enhancements for Factory design Suite include:

  • Batch convert legacy CAD items into Factory Assets
  • Quickly convert AutoCAD facility layouts to 3D in Navisworks.
  • Point Clouds display laser scan location map and synchronize across AutoCAD, Inventor, and Navisworks.
  • Create Factory Design Suite assets from Point Clouds

Factory Design Suite Softare Titles

FDS Standard includes:

  • AutoCAD( + Mechanical +Architecture)
  • AutoCAD Raster Design
  • Factory Design Utility
  • ReCap
  • Vault Basic
  • Showcase (downloaded separately)
  • 3D Print Studio

FDS Premium adds:

  • 3ds Max Design
  • Navisworks Simulate
  • Inventor

FDS Ultimate adds:

  • Navisworks Manage (replaces Simulate)
  • Inventor Professional

The Complimenting Simulation and InventorHSM

I’m tempted to call these the landscape after all the money the company has sunk into the technologies. Think back 5 or so years ago and compare… You can’t; there was nothing there.  Autodesk’s end-to-end manufacturing solution is intertwined with continually expanding simulation and CAD/CAM software solutions.

Simulation Portfolio

The Autodesk Simulation portfolio for 2016 has a few changes you don’t want to miss as well as a brand new application. We have more details here.

Inventor HSM

We still do not have the complete picture for the changes in Inventor HSM, but there is one really sweet addition to the product, and more information coming soon. What we can say is…

Autodesk Inventor HSM 2016 gets Turning!

Autodesk added the much awaited turning capability to InventorHSM. The turning addition includes traditional toolpaths with facing, roughing, profiling, grooving and drilling operations. The applications support programming for twin-turret and twin-spindle lathes, plus mill/turn machining.

Autodesk InventorHSM 2016 Gets Turning

What does this mean for Subscribers?

I think Inventor’s improvements alone represent a significant value to engineers and their customers (I won’t rehash these here), and are worth the costs of renewing. I cannot personally speak for specific enhancements within the remaining titles in these suites, but I can attest to the level of detail applied to Autodesk Inventor, and how happy I was to see this much attention paid to a veteran product that we depend on.  Potentially more wonder and technological goodness surrounding Inventor are on the horizon, but I am under oath of silence and secrecy… (first born child and all that).

The integration of Inventor and Nastran In-CAD speaks to the company’s connected, all-encompassing mantra. With regard to the complete end-to-end digital prototyping (and physical prototyping), Autodesk’s Simulation offerings for 2016 hold a few nice features as well. More on that is coming soon.


Autodesk Software Information and Downloads

Autodesk Product Design Suite

Autodesk Factory Design Suite

Autodesk Inventor HSM

These products are available now!

Images courtesy of Autodesk, Inc.


Autodesk Nastran In-CAD: Results

During our test drive with Autodesk Nastran In-CAD, we prepared a simple linear static analysis, the setup of which went smoothly. The biggest benefit was at the very least learning how Autodesk expects Inventor users to behave around a more robust simulation model and Inventor acting as a pre-processor for Nastran. In this article I will take a look at those results using Inventor now as the post-processor, how they were configured, and then some closing comments regarding the entire experience.


The results were consistent with what you’d expect.  Each results plot can be configured with the typical smoothed and contoured visualization. A well simplified configuration dialog allows users to configure the results plots with a basic set of options. I know that the company is looking at how users feel about this particular part of the UI; I feel that it is pretty easy to pick up on and use.

Autodesk Nastran In-CAD Stress Results Plot

Tip: You can turn off your mesh view for specific components using the Mesh Table

Each 3D results plot is stored in the overall template, and can then be employed in any of the case studies as desired. The standard array of plot types are available including displacement, Von Mises stress, principle stress, and more. Cross sectioning is configurable within the plot setting, permitting the particular plot to always section the model. Additionally, models can be sectioned through the Inventor interface, and then view the results.

Autodesk Nastran In-CAD Display Options

Tip: Configuring cross section in the saved results plot template permits additional information such as the element results along the cross section to be reviewed graphically. This is not the case when simply reviewing plots with Inventor’s section views enabled.

 Nodal information per plot style can be reviewed by turning on the nodal display, and passing the cursor over the nodes.

Autodesk Nastran In-CAD Results Plot

 Tip: Nodal label displays can be turned on by right clicking the Mesh categories Node header, and picking Query Display.

XY plots can be made by nodal results (such as displacement) and by element (stress, etc.). These need to be added by picking the respective node(s) or element(s), by a defined group of these, or by picking a model entity, such as an edge.

Autodesk Nastran In-CAD Simple XY PLOT

The user interaction in this process was a bit awkward, and definitely not on par with the foregoing UI experience. Moreover, the configuration of the plots was limited, and once a plot was created, there seemed to be no manner in which to change it. If you wanted something different, you have to discard the unwanted plot, and start over with a new one (multiple plots can be saved).

Note: It occurred to me that it might be possible to establish the plot by group, and then alter the group, thereby altering the plot criteria. I have not confirmed this possibility.

Reporting was similar to other reports I have experienced with Autodesk analysis software. The basic model information is provided, along with basic narratives that contain maximum type results data. These narratives can be configured during the report generation, which is then saved to the hard drive in an HTML format, with associated 3D colored plot images.

Autodesk Nastran In-CAD Report clip

The plots images are cut from the current model state, which may or may not be sufficient to deliver a respectable report. This is also typical of most Autodesk analysis software. I have never developed reports from a stock report plot (from any post-processor), but instead use them as a starting point to create a final report. I believe that most analysts do this, as it is impossible to predict exactly what aspect is important in any particular study, and that Autodesk understands this. As such we often see little enhancement of the results engines. This could be enhanced by an option to designate pre-formatted plots for reporting (see my mote in the comments below).

I do like that the report system previews each narrative in an editable window before it is finalized, which can allow users to develop a more substantiate report to start from. While some reporting options are configurable (in the overall options of the In-CAD software), this is limited.

Tip: Remember to create a new Analysis subset! (Like a new Inventor ‘Scenario’) Subsequent runs of the same analysis will overwrite the previous results. If you (like I just experienced) get a failure and overwrite your previous good results, you will feel quite foolish.

Closing Thoughts

Nastran is a fabulous analysis solution, no doubt. Having the ability to reach out to Nastran directly from Inventor is also a welcomed reality now. In-CAD is easy to learn and you can be up and running in less than an hour.

You will need some hardware to run In-CAD. Meshing can rapidly become quite complex without having to beg for it. While you may be used to running Inventor comfortably on a machine, In-CAD will suck up resources quickly, depending on how carefully you limit your model DOF and mesh complexity. Without trying it, I feel safe in predicting that you won’t be doing anything substantiation on a standard CAD station while solving studies with plasticity in non-linear analyses. (Cloud solving anyone?)

In-CAD model setups will increase your assembly and model file size. This is something that should be considered and a reasonable strategy imposed from the start. It stores the results separately, but the Inventor files still take on a large amount of data compared to the original file size, but not outrageous.

I did find some areas that I either expect to see adjusted soon, or desire to have available. These include (but not limited to):

  • Nodal results labels color can’t be read through results color plots, nor can it be altered; contrasting colors should be more dynamic
  • Need tools to pick all nodes from component, entity, or element selection, including a concext menu option
  • Need component groups
  • Need Results Properties Sets – Users should be able to create a ‘results property set’ that is characterized by a result plot style, which will act as a container for components. You simply identify your desired components in the set. Results only show up for those components. Very handy for studies that involve numerous components, but where the results are focused on select areas
  • Make it easier to exclude specific components from the results; meshes can be turned off, but the results continue to consider those bodies
  • More comprehensive and editable XY plot results
  • Ability to save 3D results plots in state (e.g. components, view angle, cross sectioned, criteria, etc.) and designate these as well as XY plots for reporting, thereby automating the process a bit more.

While this UI is not tuned for diehard analysts, I think In-CAD is a good tool to allow Inventor users (that don’t want to leave Inventor and learn a very complex interface) to have access to the power that Nastran offers, as well as analysts that need a CAD platform for their studies. There are limitations using In-CAD, in that some features in the Autodesk Nastran solver are not accessible without another pre-processor.  In-CAD will not easily replace a full-featured pre-post-processor that analysts may be relying on currently.

Companies purchasing Nastran should consider the type of pre and post processor that they require. As I understand it, the Inventor In-CAD Nastran deck is compatible with any Nastran pre-processor. In areas where both CAD users and analysts will be using Nastran, a strategic purchase of both Nastran and Nastran In-CAD licenses would be a wise choice. While the cost is the same, companies would still need a processor for the Nastran only license.

Note: The Autodesk Nastran Editor is not available for the Nastran In-CAD license.

I feel it is important to mention here that Autodesk included the Nastran solver as an option to their subscribers of Autodesk Simulation Mechanical, their full featured Pre-Post processor and solving package. The last information I was given indicated that the company was doing so free of charge. If users need Nastran and more pre-post capabilities, they might be wise to consider Simulation Mechanical as a viable alternative.

Join the Community