Design and Manufacturing solutions through Digital Prototyping and Interoperability

# Category Archives: Engineering Notes

### Solid Edge Free to New Start-Up Companies

Siemens PLM announced that they will be furnishing Solid Edge free to New Start-Up Companies. This surprise was delivered last week during the General Assembly of Solid Edge University 2016, held in Indianapolis. The company said that they want to help empower new companies, and make design software part of the solution, not the problem.

If you are a new start-up, or are considering a new design or manufacturing endeavor, this great opportunity is for you. Siemens PLM intends to furnish one seat of Solid Edge Premium per engineer at the company. The license will be for a term of one year. The program includes training and co-marketing opportunities (more details to follow when available).

# Who is eligible for Solid Edge Free to New Start-Ups?

The criteria for being considered for the program are quite simple, and are as follows:

• The company must be a legally registered company, less than 3 years old.
• The company must have less than 1 million U.S. dollars of funding
• The Company must have less than 10 million U.S. dollars in annual revenue
• The Company must be formed for the purpose of design and/or manufacturing

# Application Process

The process is simple, and there is no fee. Fill out this Solid Edge Free for Start-ups online application. Once completed, the company will contact you with more information.

### PTC Mathcad Express: My First Look

PTC Mathcad is a symbolic mathematic document software, capable of a vast array of calculations, simultaneously documenting your project in an easy to read manner. I have been using it for about three weeks, and now that the recent round of college exams are over, I have a few minutes to chat about it. It is an interesting piece of engineering software, uniquely beneficial in specific situations.

PTC offers a limited version that is totally free, named PTC Mathcad Express! That is the focus of this article.

# PTC Mathcad software, old and new

The Mathcad line of products recently split:

• PTC Mathcad, the somewhat robust legacy build, has been halted at v15
• PTC Mathcad Prime, the build for the future, is currently at v3.1.

The company decided that it was beneficial to move to a new core platform, giving themselves more room to grow. While Mathcad Prime is in its 3rd major revision, and continues to be improved, the original feature set is being brought over piece-meal, a major criticism by many on the forums.

Mathcad Prime runs in “Express” mode until it has been registered; express mode is de-featured, but it’s a useful tool, free of charge to use perpetually. Since you use Express knowing it’s in a limited, unregistered state, you don’t miss the previous toolset that hasn’t made it to Prime… well, not completely.

Mathcad is simply a symbolic math calculator, capable of performing most varieties of math, and doing so in a document format. What you see is what you get. There are no hidden calculations.

(The image above was formatted as a ledger sheet in portrait orientation. The default math variable and text sizes were rather large, and instead of reformatting the defaults, I simply went to a larger sheet, and plot it reduced to letter sized). The image should offer a feel for the basic software and expectations. It is somewhat like a symbolic version of Microsoft Excel with all the information visible, but with far more mathematic capabilities and an easy to read approach. The format can be appealing to students that are new to mathematic projects, and are uncomfortable with programmatic and spreadsheet type software.

This setup is in English reading style: Left to right; top to bottom. This is the breaking point for many experienced Excel users, which can point to any cell in their spreadsheet. Variables must be defined above, and/or to the left of the calculations referencing them, as if you were reading the report from top to bottom. In many situations, setting up a variables and constants page at the beginning will alleviate this. Organizing a document with this limitation, in an attractive, well laid out manner can be very trying, and not to mention time consuming. This is not a deal breaker, but an inconvenience nonetheless.

The document shell is just that – a shell. You add information to the shell with three major components:

• Add a text block – permits a paragraph style entry, the full width of the page.
• Add a text box – a rectangular-style grouping of text and symbols that word-wraps independently, which can be dragged anywhere on the document. I wished that a border were available for these in certain situations.
• Add a math block -These are the mathematic containers and are similar to fields in other document formats. Apply the math block to the empty shell independent of text, as well as inline within the text containers. Variables defined in these become the variables and constants used throughout the document.

Basic document and text editing is available, including fonts, colors, underscores, etc. What is not available is search and replace. When you rename a variable, downstream variables of the same name do not update, but instead your sheet calculations fail and the document turns red: quite un-cool.

Images can be added, and print out quite nicely.

# Mathcad – Symbolic and slick

Variables, symbols and units

Variables are created on-the-fly with a statement such as this: “mdot:=something”; “mdot” is then ever-present for reference from that point forward. Greek symbols are available within variables, allowing them to remain visibly similar to other references, like say lower case sigma for solidity, or upper-case sigma for sums. Pulling these off the ribbon is cumbersome, but once you learn the associated hot-keys, the process is quite smooth.

Mathcad is unit-aware which is a strength and weakness. Once you define a variable with a unit type, that unit is maintain that throughout the document. When units are multiplied for example, say like m/s and kg/s, Mathcad spits out Newtons. If I wanted that in English units, I can simply type those over top of the SI unit result, and Mathcad will update the result to accommodate the difference. That is pretty cool.

When incompatible unit types come together, the units have to be rendered out and then reapplied. In my opinion, this makes for an ugly document, but these changes become quite apparent for all to understand.

Mathematics and operators in math blocks

Most algebraic mathematics that I can think of off-hand are present, as well as calculus, logic, and matrices. This is where the rubber meets the road, and where Express is lacking. Items like iterative solver blocks are locked until he product is registered.

Calculations involving matrices is both amazing when the system is with you, and utterly painful when it is not; this is largely due to my inexperience with the software. Matrices and lists are divided into two categories, vectors and range variables. Knowing which is used in which situation still remains a mystery to me. I have however learned enough to get by in a case-by-case basis.

Matrices can be dimensioned ahead of time, but Mathcad will dimension variables into matrices on-the-fly where needed. For example, the exit velocity of the stream is calculated from single variables and 1X6 element arrays. The new resulting variable is alutomatically created as a 1X6 matrix to accommodate the straight multiplication.

Matrices and lists can be visibly compressed by dragging their ends up and down save space, or to limit terrifying redundancy where it is not needed.

Subscripts and indexes

These can seem a bit perplexing:

• Subscripts – more characters to use as identification, differentiating mass flow of air “mdota”, from the mass flow of fuel “mdotf”.
• Indexes – index lookups within variables. These look like subscripts, but applied differently, so that Mathcad knows the difference between a variable with a subscript vs. an index of an array. Users can add indexes under subscripts as well. Another example of this is shown in the plots section following.

# Plots and graphing

Plots are a letdown. They are basic at best, and after much reading, learned that most of the advanced functionality and formatting was left behind in v15. The company assured users back before v3.0 that the improvements were coming, however in 3.1 they are still not there.

Adding variables is simple enough. Simply add a trace; the software will drop a placeholder in on the plot for users to enter the desired variable names. Limited formatting can be applied on a trace-by-trace basis.

The image below shows 8 plot types available in the ribbon pulldown. However, the background grid is not available, the axes cannot be formatted for opposing scales, data cannot be shown on the plot, and so forth. Some plot features can be drag adjusted directly, but these are limited.

One nice feature was plotting the data from matrices. In this example, I compared thrust, velocities, Mach thresholds, and internal areas for each of an array of compressor pressure ratios. I identified the x-axis with the equation that would deliver the ratios, and the y-axis with the corresponding variable and index.

# Conclusion

Mathcad Express is a nice tool to do some mathematic documentation, and it really stands alone in that area of engineering. Discussions I had with other engineers have noted that they use it to do certain calculations that need to be documented, and as one engineer put it “I run out my calculations and when I’m completed, there is no need to document anything: the documentation is already done”. There really isn’t any other full capability software that can do this with such ease.

### Pros:

• Awesome documentation of calculations
• Manipulates arrays and performs calculus (which spreadsheets won’t do)
• Creates simple graphs
• Express version is free

### Cons:

• Retail version is expensive (You really gotta need documentation)
• Creates simple graphs
• Document layout methodology wastes a lot of space and requires a lot of pages to do anything fun
• Most employers are requiring knowledge of MatLab
• Mathcad Prime 3.1 is the compatibility cutoff; Mathcad files cannot be read forward or backward of this version, not even Prime 3.0 documents (there are converters available, but the jury is out on whether this is safe or not).

Is it worth the cost?

PTC Mathcad Express – duh! It’s free. You can’t beat this, period.

PTC Mathcad Prime 3.1 – Student ~$100 USD (annual). Still, you can’t beat that for what it provides. PTC Mathcad Prime 3.1 – single user? Last time I checked it was ~$1600 USD (annual). Ummm…. I’m not sure.

Why do I seem unsure? On my end there was a licensing snafu, where in I am still out the registration fee, but cannot register the software. PTC came through with a new registration code last night, so I have not had a chance to work with Prime yet. I will write more about Prime as I begin to use the full feature set.

I think the value largely depends on how you document your calculations. Many will retreat to Excel, but for others the slick documentation, easy on-the-fly format is a no-brainer.

### ASME Y14.5 Free Draft Copy is Available

You can get a draft copy of ASME Y14.5 free and mailed to you. American Society of Mechanical Engineers (ASME) is completing their overhaul of ASME Y14.5 standard for Dimensioning and Tolerancing. If you want a draft copy, you can request it by emailing your name and address to:

Mayra at ANSIBox@asme.org.

They will in turn send out a preliminary hardcopy by mail.

Note: This is not the final revision of the standard, but should serve as a very close copy for those that are either not required to adhere to the standard strictly, or those that want to be part of the review process.

## ASME Y14.5 free

The deadline for requests is 23 Feb 2016. After that they will close the public review process, and you will have to pay \$200 to get the official version (which many of us will have to do anyway).

Official Link to buy old ASME Y14.5-2009 Dimensioning and Tolerancing at ASME Site

### 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.

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).

## 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.

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:

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.

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.

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.

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

## Conclusion

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.

### Disclaimer

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)))

### Engineering Notes: Ideal Gas Law and Gas Constants

There is no such thing as a truly ideal gas; ideal “perfect’ conditions do not exist. However through numerous assumptions and generalizations, scientists derived a hypothetical equation of how gasses would behave without the confusion of inter-molecular forces, by constraining their definition to the Kinetic-Molecular Theory of Gases. This approximation allows us to predict within a certain degree of accuracy, the way a gas will behave in our design.

# Ideal Gas Law using the Universal Gas Constant

Ideal Gas Law [using the Universal Gas Constant] shows the relationship of Pressure, Volume, and Temperature, within all Ideal Gases:

$\boxed{PV = n\bar{R}T}$

Properties (ISA standard conditions at Sea Level):

• p = Absolute pressure (101325)[Pa]
• V = Volume (1)[m^3]
• n = number of moles (42.2925)[mol]
• $\bar{R}$ = Universal Gas Constant (8.314462)[J/mol K]
• T = Absolute temperature (288.15)[K]

Example: reorder the equation to solve for moles.

$\Huge pV = n\bar{R}T$     becomes       $\frac{pV}{\bar{R}T} = n$

$\boxed{ \frac{ 101325 _{[Pa]} \times 1 _{[m^3]} }{8.314462 _{[J/mol K]} \times 288.15 _{[K]} } = 42.2925 _{[mol]} }$

So a cubic meter of a gas at Sea Level will always contain 42.2925 moles, regardless of what gas fills that space. Notice that Universal Gas Constant version of the Ideal Gas Law is dependent on molarity (mol/m^3), as we do not know what gas is filling that space. From the resulting moles we can now calculate the mass of a particular substance within that volume and change the equation to one of molality (mass dependent).

# Determining the Specific Gas Properties

In order to use the Ideal Gas Law within the context of a known gas, we need to calculate the two dependent properties:

• Molar Mass of the gas and the total mass that is contained in the specified volume (m)
• Specific Gas Constant (R)

We can then calculate the density($\rho$) of the gas which will simplify the equation further:

#### Determine the Molar Mass and Total Mass of the Gas

Find a trusted source for referencing Molar mass. Engineering Toolbox did a beautiful job detailing the calculation of the molar mass of dry air, which is one of the gasses I am studying in the Damn Turbofan project.

Molar mass of dry air = 28.97 (or 28.97 g/mol)

Multiply the quantity of moles we initially calculated, and multiply it by the mass/mol of the known gas.

moles x molar mass = mass of specific gas

$\boxed{ 42.29119 _{[mol]} \times 28.97 _{[g/mol]} = 1225.21 g \quad or \quad 1.22521 kg}$

Since we knew the volume of gas previously, we can also calculate the density:

$\rho$ = m / V

$\boxed{ \frac{ 1.22521 _{[kg]} }{ 1 _{[m^3]} } = 1.22521 kg/m^3 }$

#### Calculate the Specific Gas Constant

Change the Universal Gas Constant from a context of molarity to that of mass. We can do this by dividing the Universal Gas Constant by the molar mass of the known gas.

$\boxed{ \frac{ 8.314462 _{[J/mol K]} }{ 28.97 _{[g/mol]} } = 0.287 J/g K \quad or \quad 287 J/kg K }$

Specific Gas Constant (R) for dry air =   287 J/kg K

# Ideal Gas Law using the Specific Gas Constant

Ideal Gas Law [using the Specific Gas Constant] shows the relationship of Pressure, Volume, and Temperature, within a specific Ideal Gases:

$\boxed{ p V = mRT }$

Properties of dry air using ISA standard conditions at Sea Level:

• p = Absolute pressure (101325 Pa)
• V = Volume (1 m^3)
• m = mass (1.22521 kg)
• R = Specific Gas Constant for dry air (287 J/kg K)
• T = Absolute temperature (288.15 K)

Example: reorder the equation to solve for temperature.

$p V = m R T$  becomes  $\frac{p V}{m R} = T$

$\boxed{ \frac{ 101325 _{[Pa]} \times 1 _{[m^3]} }{ 1.225 _{[kg]} \times 287 _{[J/kg K]}} = 288.15 K }$

288.15 K is the ISA standard temperature at Sea Level, which brings us directly back to where we started.

## Simplifying the Specific Version of the Ideal Gas Law

By combining the mass and volume into a density, we can slightly simplify the specific version using $\rho = m / V$:

$\frac{ p V }{ V } = \frac { m R T }{ V }$  becomes

$\boxed{ p = \rho R T }$

# Background

The Ideal Gas Law corresponds to Boyle’s Law and Charles’ Law.

#### Boyles Law – Robert Boyle (1662):

The product of pressure and volume is exactly a constant for an ideal gas.

$pV = k$

#### Charles’ Law – Jacques Charles (1787):

Charles’s law states that if a given quantity of gas is held at a constant pressure, its volume is directly proportional to the absolute temperature.

$\frac{V1}{T1} = \frac{V2}{T2}$

#### Avogardo’s Constant and moles – Amedeo Avogadro et.al: (1811-)

Avagadro’s Constant is 6.02214 x 10^23

Moles is simply a unit of quantity just like a dozen indicates twelve, and is based on Avogardo’s Constant, where a mol contains 6.02214×10^23 particles, or molecules.

#### Initial Ideal Gas Statement – Emile Clapeyron (1834):

Combined Boyle’s Law with Charles’ Law into the first statement of the ideal gas.

$pV = \bar{R}T_{c} + 273.15$

# Consider

All these ideas and constants are extremely important and is rooted throughout fluids engineering and physics. Practice them until you can say them backwards and forwards, and can translate from volumes to masses with ease.

Credits:

Brilliant Ideal Gas Law image was furnished by

### Engineering Notes: Mass Flow

Turbojets develop thrust by accelerating mass. They do this by compressing intake air, mixing it with fuel, combusting the mixture and expelling it in a highly accelerated and controlled manner. The result of this is thrust, and its opposite reaction moves the aircraft. The accelerated fluid (combusted air) is quantified as mass flow.

# Mass Flow

Mass flow is the measure of the mass of a fluid that passes over a control surface, in a specific frame of time.

Consider: A surface has only 2 dimensions, which constitute an area. The third dimension needed to calculate a volume (and then the mass thereof) is represented by the velocity at which the fluid (air) flows past that surface. In our case, that rate is stated as meters per second (m/s).  If we know the area of the inlet, the density of the fluid, and the velocity that it is travelling at, then we can calculate the mass flowing past that surface in one second.

Mass flow is often noted in fluids analysis and engine design as $\dot{m}$, or in text as mdot, and mass dot.

This is equivalent to the following:

$\rho \times A \times V = \dot{m}$.

Where:

$\rho$ [kg/m^3] – the static density of the fluid

A [m^2] – control surface area

V [m/s] – velocity of the fluid.

$\dot{m}$ is then related as mass/time, here as kg/s

# Control Surfaces

Control surfaces are simply a fixed imaginary 2D surfaces that the engineer is using to establish the controls for his/her flow calculations. Literally, a frame of reference that can be established (and re-established) in space. In our study of “the Damn Turbofan”, the initial control surface is located at station 1, the leading edge of the inlet. Knowing the 2D area of the inlet allows me to determine the total quantity of the air entering the engine.

An example of this:

$\rho \times A \times V = \dot{m}$.

$1.225 [kg/m^3] \times 0.011 [m^2] \times 350 [m/s] = 5 [kg/s]$

# Considerations

One important thing to consider is that like energy, mass cannot be created or destroyed. Therefore, the mass entering the engine is the same as the mass leaving the engine (neglecting the added fuel for the scope of this discussion). The mass can’t exit the engine at a faster or slower rate in a static environment. You may accelerate the flow of molecules by reducing the exit control surface area or really pissing the molecules off by adding energy, but the flow rate of mass exiting remains the same as the flow rate of mass entering.

$\dot{m}9=\dot{m}1$

This is the fundamental principle throughout this study.

The other thing to consider is that somewhere in the engine is a point that is the most restrictive to the fluid. No matter why it is so restrictive, no other surface will permit more mass to pass through any faster. This is the entire problem with choking, which we will discuss later.

### Engineering Notes: Turbofan References

Looking for a better understanding of the basics of turbofan design theory? John starts this series with a discusses his favorite references and points out their strengths and weaknesses. Continue Reading

### Engineering: Java Airfoil Tools

I found a great tool for creating and/or reviewing airfoil design and performance. Best of all it’s free. Continue Reading

Join the Community