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Category Archives: Simulation

Modeling Limits: Top-Down or Bottom-Up?

As many of you know, I recently returned to school to complete my engineering degrees; and simultaneously began researching small footprint turbofan engine technologies. As none of this in theory has anything to do with modeling (or fun), I haven’t had a lot of time to write. Modeling this engine is now on my mind, and so is the question of Top-Down or Bottom-Up?

Top-Down or Bottom-Up?

We are nearing the end of the basic mathematical model. I have begun considering how I would bring this beast to life in a digital model; top-down or bottom-up. I am a controlled person and like designing within limits; top-down gives me precisely that. However, in this case I am not so sure that torturing myself by bringing an adaptable model to bear is a good idea, where the limits are still quite uncertain.

Modeling Turbine Blades

Image Courtesy of Stinging Eyes 

The Problem

Stage count is the fly in the ointment. For example, I think we will have 6 low-pressure (LP) fan stages (yes, 6 bloody stages), but am still trying to reduce it to 4. The High Pressure (HP) compressor is equally ugly, and the HP and LP turbines are dependent on the compressor models. If I do not know how many stages will be involved, I will have to constantly return to the master skeleton, and adjust the coefficients to adjust how much space I have to work with. Ugghh!!

However, if I let go of my notions about “how to design something properly”, I might find an easier way. Perhaps if I made my design sections as CAD models with named planes at either end, I can join the design sections end to end, in a bottom-up approach. It will be easier to keep all my section specific design constraints in the respective design sections. Later when I do the bypass and exterior skin sections, I can import key surfaces from each section to work from, and build outward.


Top-down or Bottom Up is one of the first questions I ask prior to modeling. I rarely decide against a master skeleton approach. Moreover building outward is my big fear; since this entire project involves a very small cross sectional dimension limit, it seems counterproductive to work outward. That said, it also seems insane at this point to try and monkey-fart the parameters about in a skeleton file to eventually fit sub-structures that can perform as intended. After much consideration, I think keeping the mathematical design limits tight, and then building the structure outward from the HP compressor will allow the greatest degree of flexibility, and the easiest model to alter, which we expect to do a lot until all aspects of the engine design have been played out.

Your thoughts?


Autodesk Inventor 2016 R2 – Shape Generator

As per John’s recent post (“Inventor: October Update and Move Away from Annual Releases“), subscription customers are in for a treat with the availability of what I like to call the R2 Subscription Bonus Pack. This update provides new tools and features to Inventor’s already extensive “Professional Grade” toolkit.

By claiming Inventor is Professional Grade, Autodesk is aiming to have it be an “end-to-end product development environment.” Part of the reason they are able to accomplish this is by leveraging technology from other products in their ever-growing product portfolio. R2 contains three main “buckets” of enhancements:

  • ForceEffect integration for upfront concept engineering
  • Shape Generation to build structurally efficient parts
  • Improved IDF import

Shape Generation

The Shape Generator was a real “ah-ha” moment for me in that I realized that topology optimization wasn’t just for 3D printing and plastics. There is a potential here for any industry using Inventor. To read more about Autodesk’s path to introducing Shape Generation, take a look at my recent article “The more things change: Generative Design”

Inventor 2016 R2 - Welcome To Shape Generator

According to Autodesk, Inventor is the first product to offer Shape Generation inside the CAD application.

“This release is more than just an update. It’s the future of true ‘computer-aided’ design”

Shape Generation is a conceptual design tool that relies on finite element methods to optimize material for a defined set of criteria. You specify the boundary conditions, the loads, and the target and it figures out how to remove or deform the material to hit the target. The result is a 3D mesh, which you can reference back into your model to refine your design.

Shape Generation in Action

The process of Shape Generation follows the typical FEA process…

  1. Start the Environment
  2. Assign / adjust materials
  3. Apply constraints
  4. Apply loads
  5. Preserve Regions
  6. Adjust the Settings
  7. Generate the shape

To start the process, with the desired part model open, select Shape Generator from the 3D Model ribbon tab. Alternatively, Shape Generator is now an option from the New Study dialog within the Stress Analysis environment… same toolset, just two ways of getting there.

Inventor 2016 R2 - Shape Generation Ribbon Location

The material will default to the material assigned from the modeling environment. To adjust this select Assign from the Material panel and make adjustments as required.

Inventor 2016 R2 - SG Materials

Three options are available for constraints: Fixed, Pin, and Frictionless. These are exactly the same as you would find within the Stress Analysis environment. Use Fixed to remove all degrees of freedom from the selected edge / face / vertex. Pin is used to represent a hole on a cylindrical support.  Frictionless prevents a surface from moving (deforming) in the normal direction… aka, it stays flat (parallel)

Inventor 2016 R2 - SG Fix Constraint

Loads contain many options, that can be applied to vertexes, edges, and faces. The point is to load the model as it will be in the real-world, using whichever combination of loads required.

Inventor 2016 R2 - SG Force

Preserve Region is a tool specific to the Shape Generation Study environment. With this, you specify features that you do not wish to change during the shape generation process. The selected regions are specified as boxes or cylinders.

Inventor 2016 R2 - SG Preserve Shape

Within the Shape Generator Settings specific the target mass reduction and the mesh density. Remember that the greater the density of the mesh, the longer the process will take to run. [Cloud processing is not included in this release, hopefully in the future]

Inventor 2016 R2 - SG Settings

With everything set it times to click the Generate Shape button and wait for the magic to happen. Depending on the density of the mesh and the complexity of the model, this may be a get-up and go-and-get-coffee opportunity.With the analysis complete, you can promote the shape either as an exported STL file (for 3D Printing) or into the active model to compare against the existing model.

If you are interested in more about the theory of Shape Generation the Inventor help includes a section (“Validation Problems”) for reference.

Inventor 2016 R2 - SG Help

Feature Image: Wire mesh” by haru__q

Inventor: October Update and Move Away from Annual Releases

The April 2015 release of Autodesk Inventor was packed with some really nice features. Some of these included AnyCAD to coincide with the previous addition of Inventor’s integrated CAM software, Inventor HSM.

In alignment with the changes to the company’s licensing policies, large annual releases are being moved away from in lieu of smaller release cycles, like quarterly updates.

That said, Autodesk has announced that the first of such large updates is coming at the end of October. This update will be available to Inventor subscribers, as will all updates in the future. Subscription customers already have access to great computing services on the cloud, such as cloud solving, and the company intends on continuing that into the future as well.

3 New Enhancements

Shape Generator

Shape Generator is Autodesk’s Topological Optimization tool. Autodesk has been working with Topological Optimization for about a year now. Topological Optimization is a process by which a finite element model is refined into a shape that has been optimized for mass or strength to perform a specific task. I am quite pleased to see it appear in Inventor.

Inventor 2016 R2 - SG Meshed Part

See Mike’s Inventor Shape Generator overview here (Autodesk Inventor 2016 R2 – Shape Generator)

Force effect

Force Effect, Autodesk’s easy to use 2D statics calculation tool, has been available on mobile devices for some time. It was the second thing I installed on my iPhone, just after my Japanese language references. After much customer requests to have Force Effect in Inventor, it’s finally here.

Inventor 2016 R2 - ForceEffect01

Force Effect will be tied to A360, Autodesk’s cloud collaboration service. Mobile and web users can upload their Force Effect static calculations to A360, and then tie those calculations within an Inventor 2D sketch. Those features can then be constrained to Inventor sketch profiles; any Force Effect changes saved to A360 will update the sketch (and ultimately the Inventor model) when the model is opened. This is awesome! Users are prompted to update or not as they choose.

Electromechanical design

Autodesk continues to push their mechatronics design by including additional functionality within Inventor, a move I think is quite necessary.

Inventor 2016 R2 - IDF Import Options

Inventor’s library database files (.ldf extension) have been updated with additional filtering and options. For example, electronics boards can be imported into inventor, but without components of specified size thresholds (you can filter out all the tiny capacitors, etc.). When asked, the company noted that the Inventor specific harness functionalities were not fully integrated into the library at this time, however they are considering options like this in the future.

Fusion 360 Simulation and September Update

Autodesk’s September update of Fusion 360 will go live today (21 Sep 2015), and brings with it a significant upgrade:


Autodesk had announced the arrival of Simulation at least as far back as November of 2014 when they ran their Ultimate promotion. Since we spent the last year paying for access to simulation that never arrived you might feel a bit put-off, but I’m still happy to see its arrival. Better late than never I suppose.

Integrated Simulation

As of last Saturday, Fusion 360 will include Linear Static and Modal Analyses. These will appear on their own Simulation tab, and the simulation model and study results will stay embedded within the single Fusion design file. The appearance and usability provided will be quite similar (if not identical) to that of the previously retired Sim 360 which Fusion 360 used to include. The spaces, for all practical purposes have been integrated which sort of brings us back to where we were some time ago, but with a complete architecture overhaul.

Fusion 360_Simulation

The integration includes automatic contact generation. I suspect this is facilitated by the assembly joints present in the model, but they might be more powerful than that. I will say that it would be a significant benefit if the joint-to-contact translation could be counted on by the user to deliver concise, expected, and useful contacts in the simulation model. I’ll know more when I try it out.

Integrated Drawing Improvements

Parts list enhancements include balloon alignment and renumbering, the latter of which is distributed back to the Bill of Materials (BOM) as expected. Centerlines and hole-centers will dynamically update as the model changes as well.

Fusion 360 drawings

Accessibility with Autodesk 360 Integration

Fusion 360 models are stored in the A360 cloud space, which permits team design work and collaboration. Some of the A360 changes are a wonderful match for Fusion, and the company has wisely capitalized on these with additional integration.

Fusion Simulation Results – Simulation results will be visible and interactive for invited team members. Controls are available to review the results of studies for each file version, without needing anything beyond the web shell.

Restricted Invitee Viewing – A360 now offers Read-Write and Read-Only access to data stored on the cloud, which is a critical improvement. Fusion team members can now invite non-team individuals to review the model through the web shell, but not have any access to the actual model.

Real-time multi-user design review – Fusion 360 offers a portal that permits team members and invitees to view the model simultaneously, and chatting and driving the model view as desired. This is a great addition, and is available from the web shell or directly within Fusion 360.

A360 has had a large UI overhaul which the company hopes will make the space data-centric, and more usable for teams than in the past.

Usability update

As per user request, Fusion 360 now employs keyboard shortcuts, which some consider to be a key design feature in any CAD software. Command searching will also be available, as well as web accessible tips and training materials for Simulation.

Fusion 360 keyboard shortcuts

Coming Soon…

I asked the company what they intended to do with Fusion 360 and Simulation in the near future, as linear statics are only the tip of the iceberg and that we already had more capabilities in Sim 360 more than a year ago. Surprisingly Autodesk didn’t bat an eye in saying that not only were the remainder of the Simulation 360 studies coming in the very near future, but more were on their way.

The partial list that was discussed included thermal and transient studies. When pressed further, the company was reasonably eager to mention the approach of non-linear studies as well, which is quite encouraging.

What I have yet to gather is how and when the Nastran solvers will be coming. The current solvers are all restricted to desktop applications, however Autodesk has stated that cloud solvers will be coming very soon as well [perhaps by the end of the year]. Adding the Nastran solvers on the cloud would be a fantastic possibility.

The Fusion 360 team stated that they are continuously committed to being open about their plans, and intend to build on drawing capabilities and simulation as time passes. Branching-merging PDM workflows will hopefully be part of the next major discussion on Fusion’s upgrades as A360’s data management possibilities expand.

Images shown courtesy of Autodesk, Inc.

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

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