texts: Transformers and systems with gears have similar computation when having quantities refer to different parts. What is the general concept?

texts:
In rotational mechanical systems, there is a common ratio used when transferring quantities to different shafts.

$$ \frac{N_D}{N_S} $$
Let's generalize number of teeth into number of a physical parameter associated with a connection.
The ratio then represents the number of the physical parameter of the destination over the source.
This ratio is used in different manners depending on the type of quantity.
Rotational Mechanical System

Gears link connections.

The loop connection is the connection.

The number of teeth is the physical parameter.

For torque, you multiply by the ratio.

For angle, you divide by the ratio.

For impedance, you multiply by the square of the ratio.

Now get this, in the transformer this concept also applies. Now I know there are analogous quantities such as torque and voltage, angle and current and the two impedances for rotational mechanical and electrical networks. But I didn't notice at once that even this concept of transferring and referring quantities to connections it is not originally part of is also the same.
Transformer in Electrical System

Windings link connections.

The current connection is the connection.

The number of turns is the physical parameter.

For voltage, you multiply by the ratio.

For current, you divide by the ratio.

For impedance, you multiply by the square of the ratio.

I haven't seen any source say it blatantly as I did, but if you are familiar with the lessons you can verify if my concepts are correct. My question is, is there an overarching concept that covers why these two systems have a similar behavior? Are there formal terminologies and would such concept be extendable to other systems provided that they would also have analogs to the quantities mentioned above.


texts: Why are variations zero on the endpoints of a beam?

texts:
On Wikipedia derivation on Timoshenko beam equation we arrive at this:

$$ \delta U = \int_L \left[-M_{xx}\frac{\partial (\delta\varphi)}{\partial x} + Q_{x}\left(-\delta\varphi + \frac{\partial (\delta w)}{\partial x}\right)\right]~\mathrm{d}L $$

then:

  Integration by parts, and noting that because of the boundary conditions the variations are zero at the ends of the beam, leads to

$$ \delta U = \int_L \left[\left(\frac{\partial M_{xx}}{\partial x} - Q_x\right)~\delta\varphi - \frac{\partial Q_{x}}{\partial x}~\delta w\right]~\mathrm{d}L $$

But why are the variations on the angle $\delta\varphi$ and displacement $\delta w$ zero at the ends? If we have a beam resting on two supports at the ends, then I can understand why the displacement variation would be zero since the beam is bound there, but I don't see how the angle variation could be zero, since more the beam is displaced along its length, bigger the change in angle at the ends. And if we are dealing with a beam, say, attached to a wall with one end free, the one of the ends experiences a difference in both the angle and the vertical displacement.


texts: Why this torque is not considered into the virtual work principle equation?

texts: In the picture above you can see a SCARA robot, with its end effector (the point x,y). The torques c_a and c_b are the ones of the motors in the joints, while f is an external force. My teacher has written the virtual work principle equation (for the static case) without considering the opposite c_b torque acting on the first link (the red one, which I drew). My question is why? They are internal torques but are on two different links that also have different virtual angular displacement, so I think we have to consider it.


texts: How to constrain stepper motor inside case?

texts:
I have a stepper motor linear actuator assembly like this for example, but the stepper shaft seems able to move axially back and forth - hence when I change direction it has to do a few rotations, forcing the ballscrew against one end or the other, before the rail platform itself starts moving. Why could this be happening and what can I do to fix this?

If anyone has a diagram showing the internals of a NEMA stepper motor that would be really helpful also. I've seen many on the internet but none showing me enough to understand this problem. Many thanks!


texts:
I got a terrible error in the Ansys when I try to create a new project.

I couldn't be able to open the geometry. Every time i open it i get the error "Geometry editor was closed abnormally"

I looked for the solution but didn't get the proper answer.

I useing:

Windows 10;

Ansys 19.2;

notebook Specifications:
Lenovo ideapad 320

Intel Pentium 4415U (2.3 ГГц)

RAM 4 ГБ

nVidia GeForce 920МХ


texts: What is this captive screw and barrel nut adjustment assembly called? Picture attached

texts:
I'm designing a precision adjustment bracket, and I'd like to have a component that allows the field tech to make small adjustments to push and pull on each axis of adjustment.

I went looking to see how others have solved this problem and found an assembly that seems common to several precision adjustment assemblies. I'm a bit embarrassed to say that, as a degreed mechanical engineer.... I don't know what these are called.

I would say that this is a captive screw that threads into a barrel nut, but that doesn't seem to be it. At least, I can't turn up anything suitable on McMaster's site when I try it. Pro tip - Probably don't Google "captive bolt." Apparently that name is more commonly used to refer to the device used to slaughter animals.

I also can't seem to find barrel nuts that have a threaded end as pictured in the assembly; barrel nut seems to be exclusively the drop-in fastener used for a lot of flat-pack furniture.

Here's another view of the same item from above:

And then what I believe is the same style assembly in a different product:

In all the brackets where it's not just "loosen the nut and tap with a wrench until it's generally correct," the assemblies I've shown seem to be the standard solution. I'd like to incorporate it into my solution, but I need to know what it's called to be able to source the parts.


texts: Steady state approximation for compressible fluid flow (manifolds and other pressure vessels)

texts:
I've been puzzling over a question / class of questions I'd like to solve via rough estimate before turning to CFD analysis.

Say I have a pressure vessel with one inlet and one outlet. The pressure vessel is at some initial pressure $P_0$. The outlet is at some fixed pressure $P_{out}$. The inlet has some mass flow rate, $\dot{m}$ (assume it's attached to an infinite upstream reservoir and a mass flow controller).

With a compressible fluid, a known mass flow rate, and a set volume in the vessel, what mechanism would you use to approximate the final steady state (volume-average, we'll say) pressure in the vessel? Assume that the outlet pressure is such that the flow will choke. Assume no heat transfer to the walls and that the gas is ideal.

One solution I have thought of is to perform a dumb iterative solution:

Pick some time step, $dt$
Add $\dot{m} * dt$ mass to the tank
Compute the new pressure in the tank via the ideal gas law
Use choked pipe flow equation to determine $\dot{m}$ at exit (knowing exit area)
Subtract $\dot{m}_{exit} * dt$ mass from the tank
Repeat until "convergence"

Possibly you could do some Bernoulli-streamline-style analysis, but I'd like to also apply this sort of approximation to a multi-inlet / multi-outlet problem. This feels like some form of the Hardy Cross method might be applicable as well. Interested in anybody's suggestions.

Graphs of what the above technique gets me for a 1 kg/s flow rate into a 5 m^3 volume vessel, initial conditions T = 290K & P = 1 Pa in the vessel:

Edit: Added a few figures from my "estimation."


texts: Does a transformer use power when devices aren't attached?

texts:
I have just purchased a 45 W 12 V transformer with an integral photocell for landscape lights. I measured the voltage while it was plugged in and the photocell closed the circuit (off) and there was still about 3 volts across the terminals.

The question is, since the transformer is delivering 3 volts to the terminals, how much energy is it consuming just by being plugged in with no lights attached? Is this normal or bad design?

Input 120VAC 60Hz 52VA
OUTPUT 12VAC 3.75A 45VA


texts:
What is the simplest way if you have a shaft rotating clockwise for it to have an extension that rotates anti clockwise. Least loss of energy is best so i think a mechanical mechanism would be best.

I am thinking is there a way you could use the main shaft in a turbo fan engine to drive another fan in the opposing direction in front of the original fan.


texts: How to get laminate stiffness matrices (ABD) in APDL ANSYS?

texts: I am trying to perform structural analysis of composite pressure vessel in APDL/ANSYS. I have completed the solution and now I want to extract ABD matrix.Do anyone have an idea about this?


texts: Shape with highest difference of Drag Coefficients on opposite sides

texts:
What would be the shape having the highest difference of Drag Coefficients regarding opposite sides?

For example, as per the following table, a hollow semisphere would have respectively Cd=0.38 on one side, and =1.42 on the opposite side. Would there be another shape with greater Cd differences? (with similar Reynolds, around 10^4)

(from Sighard Hoerner's book "Fluid Dynamic Drag", Chapter 3)


texts: What are the disadvantages of cylindrical residential buildings?

texts: I've been spending an hour finding references for my research, but unfortunately I can't see useful information. So, I would really appreciate it if you could give me some references about the disadvantages of cylindrical residential buildings. Thank you!


texts: What factors besides nozzle geometry and propellant's affect engine ISP? How can one optimize ISP?

texts:
In the design of a Rocket engines, it is understandably desirable to have a more efficient engine.

Ensuring the gasses coming out of the engine comes out straight, and the chemistry of the propellants are all straight forward methods of improving ISP, but how can engines with identical propellants and similar nozzles have different specific impulses?

What are the major factors besides nozzle geometry and propellant that allow for higher specific impulses, and how can one optimize an engine to improve specific impulse?

(Obviously I wont compromise other engine parameters for microscopic increases in isp, but I want to build an engine that gets at least 70% efficiency of theoretical Kerosene LOX combustion)


texts:
Why does chilled water emerge from the water pipe of air conditioner?

I feel that instead, lukewarm water should come out, the reason being the air conditioner air from the room and also, electricity produces heat energy so as a result warm water should come out. So what is the correct reason for this?


texts:
I'm trying to analyze a simple shaft supported by two bearings and subject to a single point load. But I keep coming across assumptions that only consider the vertical reactions and neglect the moment reactions of the bearings.

This article states this assumption in examples: 5-73 and 5-86. I've tried to find an explanation for this but keep finding examples that just state the assumption.

I'm at a loss not having my textbooks with me at the moment but from looking at examples I've noticed in some cases that the bearings take the form of a simple pin support hence the bending moment is zero at those points. See here for an example (although no assumption stated).


texts: how much force is required to drive a fence post 2ft into soil or sand using a hydraulic press?

texts:
I'm building a post driver for the farm and it got me thinking:
what force is required to drive a 6ft(1.8 m) 4 inch (100 mm) post 2 ft into the ground? I'm wondering how different soils affect driving ability and where I could find information on soil resistive force.
I have a spare 20 ton hydraulic cylinder that I'm going to use to press the posts into the soil. imagine the tractor has infinite mass and the output force of the cylinder will be fully transferred into the post.
thanks for any help!!!


texts: Principal on gaining more height based on nested poles?

texts:
How do people design height gaining based on nested poles ?

Consider this picture (I made them) :

If I want to achieve height based on these 3 poles, how they should behave?

Is this how the behave?

I had been searching over the internet I haven't found the related material, and it's kinda hard what to type. I'm doing some tasks on designing a simple robot (no foundation knowledge but with will) and my English is sort of limited, especially to technical stuff but I hope you understand it .

*Imagine like there's somehow an auto increasing portable stair to get over the tree, the poles(both sides) are consisted of  poles fragment on each of them, how the fragments behave in this case.


texts: When using an o-ring as a face seal, are the faces flush together?

texts: I'm using an o-ring in a face seal, external pressure configuration as a seal between two metal parts. Are the two faces being compressed and sealed going to be flush together or will there be a gap due to the volume of the o-ring? Diagrams I've seen make it look like they'll be flush but I'm not sure if that's the case in practice. Thanks!


texts: Insufficiently constrained structural model in Ansys

texts:
I want to analyze this model that is stressed and deformed. I fixed the lowest of points in the x, y, and z directions, and I pulled top of points upward (y direction). When I run the model in Ansys I got the following error:

  Check for insufficiently constrained model.

I tried to cut the model to make it smaller, and analyzed the model like this. I fixed all points in the x and z directions. The lowest of elements are all fixed in x, y, and z. This didn't work.

I then cut the model to one element. It worked.

How can I analyze this model?
What is the error and how do I need to set the boundary conditions?


texts: Calculate output pressure of a syringe pump

texts:
I've built this syringe pump following those instructions. Now I would need how do I calculate the output pressure given the step rate of the stepper motor, and vice-versa.

I don't know if it is helpful anyway but I know that the relationship between the torque exerted by the motor and the linear force upon the syringe plunger is given by:

$$M = F r_a \tan(\alpha), \; \tan(\alpha) = \frac{p}{2 \pi r_a}$$

where $r_a$ is the radius of the threaded rod, $\alpha$ the thread angle and $p$ the pitch.

Thus we have:

$$M = \frac{F p}{2 \pi} = \frac{P r^2 p}{2}$$

where $r$ is the syringe radius. Is it right until now? Moreover, is it any useful? I found myself unwillingly stuck in this project but I never studied such cases.

The problem here is that the exerted torque depends on the load so I wouldn't know how to link output liquid pressure with motor step rate.


texts:
I don't know if this is the correct forum as I can't find any suitable tags.

We operate some of our equipment in fields inside tents.   Our big problem is thrips/thunder flies.  They somehow make it into the inside of the LCD monitors.  This happens to laptops too.

It is quite amusing and an the same time annoying that these creatures crawl around inside the screens.  If you press the monitor behind the thrip, it makes them move somewhere else.  If you press too close, it squashes the thrip and its corpse will be there forever.  Sometimes they just die in there.

We have a bunch of monitors with dead thrips inside which are for field use only.  The main problem is when you look at data and wonder is that 112 or 1.2 because the thrip is over the 1 or .  You have to move the text up or down to make sure - wastes a lot of time.  Also when you are looking at charts, the thrip corpses obscure the display.

We have tried sealing the edges with duck/duct tape but still the little buggers manage to get in.  The only way in I can think of is through the air vent which must not be covered.

I'm just wondering what I can cover the vents with that will still allow airflow but stop the thrips from entering.


texts: Zero-state observability and strictly passive systems

texts:
I'm currently studying passivity theorems of nonlinear systems, and I find it difficult to understand the difference between the different kinds of strict passiveness.

Are there any intuitive examples of the difference between state, output and input strictly passive systems?

Further, the passivity theorems use zero-state observability to prove global asymptotic stability for feedback-connection systems.

(Definition 6.5, Khalil nonlinear systems)

Σ is zero-state observable if
no solution of x˙ = f(x,0) can stay identically in
S = {x ∈ R
n
|h(x,0) = 0} other than the trivial solution x(t) = 0.

This thread:

How can I check whether a nonlinear system is zero-state observable?

States that the system state x and y should be 0 at the same time when u = 0. Why is this important?


texts: Finite Element software for chemical diffusion in liquid

texts:
I'm an engineer who needs to do FEA for the first time.  I need to model chemical diffusion in a liquid in a container with specific geometry.  For now fluid is assumed to be not flowing.

What features do I need to look for in FE software to get this done?  Diffusion doesn't fall under fluid dynamics does it?  It's not thermal (though I think it may be mathematically similar) or structural either.

Specific software suggestions are also welcome.  I suspect my needs are basic so ease of use would be nice too.


texts: Why does the orientation of a floor joist affect its strength?

texts:
When building things like floors to walk on, we use materials like 2"x10" wood joists or steel I-beams. I'm primarily interested in knowing why a 2"x10" piece of wood resists bending downward when you have it "standing up" (ie, the 2" side facing the sky) as opposed to when you have it "laying down" (ie, the 10" side facing the sky).

It seems intuitive to me based on experience, but I can't actually explain why we orient floor joists the way we do even though it seems obvious that will lead to a stronger floor. I imagine whatever the reason is, it also explains why I-beams have such a thin webbing between the two sides.


texts: simple supported Beam deflection question involving two point loads and a UDL

texts:
so i was given a problem by my mechanical principles teacher to work out the max vertical deflection of a simply supported beam with two point loads one a distance of 5.3 away from A and another 5.9 away from a on a 6m beam.

the point loads are  both 15.7KN and the UDL is 1.2Kn/M

Now ive worked out most of the constants using the double integration method but the main problem im getting is that c1=c3=c5 = a positive number when an online calculator shows me that its meant to be negative.


texts: Trying to get a plane at a certain distance and angle

texts:
I'm working with solidworks and trying to make a plane at a certain distance and angle from another plane.

Just for some context, I want to do something like this:

My plan was to create a plane at the reference and then make a sketch on the new plane and convert entities so that the feature on the bottom right extends to the back.

I know I can do it like this, and extrude out the sketch, then make another sketch on the side face:

But Im wondering if theres a more direct/efficient way?


texts: What is the effective depth of a beam with two layers of tension reinforcement?

texts: In EC2 for calculating crack width and deflection, does the effective depth d refers to the depth from compression face to centroid of the tension reinforcement or is that calculated to the centroid of outermost tension reinforcement? It seems from output file that software OASYS Adsec 8.4 uses the latter definition. So I need to confirm which is correct.


texts:
Is there some regulatory body/inspection that verifies the AISC specified Moment(s) of Inertia for steel I-Beams?  So for example, if a mill produces a W8x21 and says hey, it meets the specs, it's 8 in Deep and is 21 lbs/ft, and because I say so, it has Moment Of 75 in^4.

Does anybody actually go in a caliper the flange width/thickness web thickness/depth and fillet profile to get some idea whether this manufacturer is within a percent +/- of the spec? Like particularly if their fillet building process ends up putting an extra half pound per foot of material?


texts: Controlling torque required to turn a shaft

texts:
I have an shaft/crank that will be turned by the user.
I want to precisely and dynamically control the torque required to do so.
For simplicity we can think of it as a exercise machine (so the torque will be pretty high, depending on the length of the crank arm).
User rotates a crank, computer controls how hard it is to do so.
Like a hand powered crane with a simulated load.
I'm looking for advice on how to do that.
Simplest solution, where the rope with a weight at the end is attached to the shaft lacks gradual control.
Solutions I was thinking about:

Disc brake, even from a bicycle and a servo controlling the clamping force. - I think this will be very hard to precisely control (in terms of the torque needed to turn).
Backdrivable electric motor with gearing - But for high torque that would require a lot of gearing / a powerful motor,
plus that would mean the motor is constantly being backdriven, which would probably increase the risk of damaging it (or the controller).
Some combination of weights and motors where most of the torque is provided by the weight, but motor is there to adjust it.

I need your opinions, suggestions and ideas.
Thanks!


texts: Sound level emissions (IEC 60704-1) spectrum?

texts:
I have a very noisy air conditioner that have a 10kHz peak at 75 dB, the rest (fan/compressor/pump) are under the regulation limit.

I would like to understand what is the measurement spectrum. I think 10kHz is out of the measurement spectrum, but I am not sure.

What is the procedure to measure household appliances noise level?


texts:
I'm looking at the option of running two blinds motors in one tube, running in alternate rotations so that they can help to lift more weight.

My understanding is that the dominant motor will slow to the other motor but when under load (lifting blind) they will kick in together. These motors are 1.1Nm but struggle to lift the blind, we tried a hard wire running at 1.5Nm but still it struggled.

So if I put two of the battery ones together it should run about 2Nm?

Thanks


texts:
Hello, I've been asked to show that:
$$d\Gamma=\tau 2\pi r^2 dr$$

Where $\Gamma$ is the torque applied to the shaft and $\tau$ is the shear stress of the sample fluid at radius $dr$. So, I know that $d\Gamma= Force\cdot dr$ and that $Force = \tau \cdot Area$ and this is where I start encountering issues. If we're looking at some radius $dr$, isn't the area $2\pi dr $ or just the circumference of the local circle? So I end up with $d\Gamma = \tau 2 \pi dr\cdot dr$ which isn't right, can someone help?


texts: Using electricity to heat up a slab through post-tension cables?

texts:
Would a passive and controlled amount of electricity fed through post-tension cables, heat up a slab, without ruining the dependability and health of the post-tension cables, and the concrete itself?

I am wondering because I coat concrete slabs with different types of paint, and in the winter, it is super slow to add layers of coats on top of one another because of the waiting time for drying and curing of the paint. If I could heat up the slab through the post tension, then re-grout the post tension ends, it would totally change the game for me. I am just afraid of possible snapping the cables. In the winter I can get away with only one coat for the whole day. In the summer I can put down 5 coats of paint over a 7,200 square foot area with ease.


texts: How to define the Clothoid Constant in Clothodial Arc ( Spiral Curve)?

texts:
Referring to the  document here on IfcClothoidalArcSegment2D, we have ClothoidConstant, which is defined as

  The constant $A$ (not $A^2$), that determines the rate of curvature
  change along the clothoid.

I wonder what it actually is?

From the wiki page about Euler Spiral, I found a symbol $a$, which is calculated to be

$a={1\over \sqrt{2R_cs_o}} $

It has the same dimension of the above ClothoidConstant, $A$.

Are they actually the same? If not, how should the ClothoidConstant be defined?


texts: Sketching an engineering system in healthcare

texts:
I am about to do a project about engineering systems in a Systems Engineering course.

I need to sketch an engineering system in which clinical decision support systems are being used to diagnose patients by a medical doctor/physician. It doesn't have to be fully correct. I just need to show that I understand how different actors/subsystems interact with each other, and who have economic/political/social interest in this system.

I have tried to sketch something, but I'm not sure if it makes sense.

I imagine that a patients contacts his/her doctor. They cooperate to figure out what is wrong with the patient. The doctor enters some information into the (intelligent) decision support system (=IDSS). The IDSS has a user interface, an inference engine and a knowledge base. The knowledge base gets its information both from doctors entering stuff but also from the internet.

In order for this to work, there must be some software developers who build, maintain and control the system, but also some insurance companies who will cover any costs if something goes wrong.

Outside of the system, there are students or researchers who potentially can benefit from using the system, both by learning but also by searching for patterns in the huge amount of data. There are also politicians who are interested in this system since the system potentially is more efficient and reduces human mistakes. But there are also hackers or IT criminals who want to gain access to this data.

I know this is kind of a fluffy assignment, but I just need some good advice, so I really hope that you will help me out.

Have I forgot something in this system? Is there something that doesn't make sense at all?


texts: Why does my motor model match the actual data in transient but not steady state response?

texts:
I have created a model of a DC Servo motor using electromechanical system modeling. I simulated the motor in Simulink (MATLAB) and compared the data with data obtained from a real motor having similar characteristics. Just to be sure, I also derived the equations and used laplace and ilaplace transforms to get the response in MATLAB. I obtained the following characteristics:

As expected, the model from Simulink and that of MATLAB (Simulated) are virtually the same. But, I see that the real motor model has a different steady state response. I can see that it has very less transient error, but high steady state error. Any idea why is this happening and if my method of analysis is right at the first place?
I feel there are some non-linear components coming into play here.
The control system used is a PID Controller with filtered derivative (But, just for this example, I've used Kp = 1, Ki = 0, Kd = 0, N = 100, the same constants are even on the real motor). The motor is modeled as having a permanent magnet on rotor to produce a constant magetic field.
I used the following for Simulink Model

The PWM block looks like this:

Kp, Ki and Kd are for PID, N is for the bandwidth of low pass filter on derivative.
And the Motor block looks like this:

sQ(s) is the speed of motor, Ea is the applied EMF. Jm, Dm and Km are the loads acting on the shaft of the motor (not the gearbox output, the motor shaft internally). Nm/No is the gear ratio for getting the speed to the output shaft (output of the gearbox). Ra and La are the resistance and inductance of armature. Kt and Kb are touque and back emf constant of the motor.


texts: Active suspension with accelerometers and displacement observer/estimator problem

texts:
I faced a logical dilemma, while designing and simulating Active suspension system.

This is what I have planned:

My system will be controlling actuators of a vehicle, using PI.
It is 2nd order mechanical system with mass-spring-damper-actuator.
In Matlab and Simulink, I am using Transfer Functions for analysis (to manage overshoot, settling time, etc.) and State Space representation (to design observer/estimator).
Sensors used are ONLY accelerometers, that will produce acceleration of the suspension displacement. However, I require a displacement, which will be Observed/Estimated by designed estimator and fed back to compare with the reference point.
I cannot use double integration as drift occurs.
I have 2 states from 2nd order system. (x1 = displacement and x2 = velocity)
We are dealing with LTI SISO system.

My mechanical system matrices are as follows:

A = [0 1; (-ks/ms) (-bs/ms)];
B = [0; (1/ms)];
C = [1 0];
D = [0];

Problem:

How can I use an Observer/Estimator states to estimate the suspension displacement (in Simulink) from the acceleration that is provided from the accelerometer, if in my opinion, acceleration state does not exist?

Let me know, If you would like to see some of my code or derivations, but I think this is one of the Logical Understanding problems, so any clarification will help to get me back on track.


texts: What would be a practical way for removing thousands of padlocks from valuable bridge railings?

texts:
Inspired by this story about Paris authorities ordering removal of thousands of "love lock" padlocks from bridge railings. This is not a DIY SE question because it's not DIY scale in the first place.

So suppose we have several dozen meters of valuable metalworks (perhaps some one hundred years old forged or cast railings) and so we cannot just melt the whole thing and produce new railings. We have to remove the padlocks and place the railings back. And we'd be happy to do all of that over a week or so, not waste a year.

Let's assume that we're not required to work on the bridge and can remove the railings for a while (and install cheap looking temporary railings for that period).

What would be an adequate technological process for that? Cutting with boltcutters? Cutting with angle grinder? Cutting with gas welder? Anything else?


texts: I am trying to find the easiest way to cut a thick glass pattern (glass thickness of 1-3 mm thick) without breaking. I am considering laser cutting but I don't know if I can cut glass of this thickness. Can anyone suggest an easy way to cut curved shapes precisely into glass?


texts: Solving a linear mass balance equation in the form of Ax = 0 with variables in vector x

texts:
I have been tasked with solving a series of linear equations in the form of Ax = b, where b is the zero vector. Specifically, I have a matrix E which is 4x7 and a column vector r which is 7x1, as pictured:

I must solve for Er = 0.I'm having difficulty finding a function in GNU Octave that will solve this equation for me. I went to the documentation page at https://octave.org/doc/v4.0.0/index.html#SEC_Contents and failed to find any functions that would accept column vectors with variable elements.

I found nothing of use in 1.2.4-Solving Systems of Linear Equations.

linsolve() looked promising, but it doesn't work with variables as far as I can tell.

I found nothing of use under 16-matrix manipulation, 18-linear algebra, nor 25-optimization.

Any advice or suggestions would be appreciated.


texts: What system of pde's models ice melt flow?

texts:
Suppose I have a block of ice resting on an insulated surface in a closed room.  Suppose the room also contains air at a temperature above the ice's melting point.  I want to simulate the transient behavior of the ice melting and flowing (due to gravity) onto the insulated surface over time.  Particularly, I'm interested in tracking the evolution of the interfaces between each phase (solid, liquid, and gas) over time.

I'm sure that the heat equation and navier stokes equations will be involved, but I'm not sure how to adjust them to account for the existence of three phases (solid ice, liquid water, and air) and how to model the transition between phases (e.g. equation of state).  What are the complete set of equations that I need to model this situation?  More importantly, what is the best approach to handle the evolution of the interfaces over time?


texts: Rotational and translation DoFs in structural mechanics

texts:
I'm a computational person, and I don't quite understand how rotational DoFs are manifested in the linear elasticity equations. I understand the translational DoFs are simply the displacement components. When specifying boundary conditions for linear elasticity simulations, we typically specify the displacement and/or traction boundary conditions at the boundaries. Where do the rotational boundary conditions come in? Are they manifested in the traction boundary conditions?

This is not very intuitive to me and I was hoping someone can explain.


texts:
I'm trying to calculate the axial force that is generated in a vertical threaded axis (arrow in picture) when a force of 100N is applied to a handle perpendicular to the axis (circled in picture).

I've found various websites and calculators but I'm not sure which one is correct as they give me different solutions.

The torque generated in the axis is 14.35Nm and the thread is an M30x2. How can I calculate the correct axial force?


texts: Evaluating replacement pulley axle strength

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Repairs... My garage door has counterweights, and the weight of the door is connected to the counterweights with a steel cable which runs over two pulleys. The original (cast iron) pulleys had needle roller bearings, but lacked any lubrication, and probably incorrect termination/hardening of the outer ring caused excessive wear, and I had to replace them.

I found size-compatible replacements, but they have 'normal' ball bearings, which should be able to bear the load. I've been trying to find a way to tell if the axis will stand hold the narrower load though. The simplified configuration is now:

White is the axle, blue is the fixed hardware, and green is the bearing of the new pulley. All measures are in mm. The extra space is because the original roller bearing was wider.

This is the path the cable follows:

I've looked over many pages, and I'm not sure how to tackle this. The problem is not completely shearing stress. I've found precious little info on 'bending' limits of round bars (axle). The weight of the door is about 60 kg (same as weights, of course) and the load is distributed at each side of the door.

Intuitively I suspect this will hold, but then my mechanical intuition isn't as developed (I'm an electronics engineer). In short, will the (mild steel) 10 mm axis bear the weight? Or do I need some more hardened material?


texts: Distillation modelling McCable Thiele, Chemical Engineering

texts: I am using an extractive distillation column to seperate ethanol and ethylene glycol. I am trying to find Rmin however its proving difficult as the the top operating line, q-line and bottom operating line do not to intercept the VLE curve. I have to use McCabe-Thiele for this before I can proceed onto using Aspen HYSYS. Please help in working out Rmin, thank you


texts: How does the DERIVATIVE term slow down the signal?

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I look at PID controler and do not understand derivatve term. I know it's used in order to not let the signal to overshoot the set value. BUT when the sigal is arising, its derivative is positive. So when we add the positive derivative term, the signal gets even higher, so its derivative becomes even higher!
I think that if the signal is rising too fast it should be slowed down by derivative term, which means that derivative term should produce NEGATIVE value to DECREASE the signal that controlls the object. How does it work in reality? Is there any good simulation online of how PID works? I've seen some simulations, but they weren't very informative.

One more question: I want to check if I understand the integral term properly. Let's assume our PV is arising and getting closer and closer to the SP. During that time integral part of the PID output is GROWING all the time, until the PV reaches SP, than the integral part has already grown so much that the PV overshoots the SP. So PV rises above SP and the integral part becomes smaller and smaller (but still bigger than zero), and finally it becomes so small, that it gets negative smaller than zero). That casues the PV to start decreasing. It gets smaller and smaller and again, integral part is so big (on the minus part this time) that the PV goes down too much and gets smaller than the SP.
And that's why integral part causes oscillations. Was my example right? Is that how it really works?


texts: Drinking Water Treatment R&D: Mechanical or Civil Engineering Degree?

texts: I will be a freshman in University next year. After graduating, I would like to get a job in the R&D sector of drinking water treatment technologies. I'm unsure if I should get a degree in ME or CE. ME seems to better prepare students for the development of new technologies, but CE deals a lot more with drinking water management.


texts: How does a dimension like "2-Ø12X25L" describe an oval hole?

texts: This is a schematic for a plastic piece that has an oval hole on it. I understand that the Ø12 part of the measurement is for a diameter, but I do not understand what the "X25L" at the end is indicating nor do I understand the "2-" at the beginning. What is the meaning of those numbers?


texts: How to number section and detail view for a same drawing

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For a given 2D print, is it recommended to number section views and details views with the same alphabetical list, i.e. Section views A,B and C followed by detail views D, E and F,

or go with different alphabetical list, i.e. Section views, A, B and C, followed by detail views, A, B and C?


texts: Is the relative acceleration with respect to a translating frame equal to that with respect to a fixed one?

texts:
My book, written by Beer, states that the rate of change of a vector is the same with respect to a fixed frame and with respect to a frame in translation.
But while it says the derivative ˙rB/A represents the rate of change of rB/A with respect to the frame Ax′y′z′, as well as with respect to the fixed frame, it says the derivative ˙vB/A defines  the acceleration aB/A of B relative to the frame Ax′y′z′.(aB/A of B relative to the frame Oxy isn't mentioned on the same page of the book.)


texts: Use of Absolute vs. Differential Pressure Transducers to Calculate Flow Through Annular Restriction

texts: If using a laminar flow element, in conjunction with Poiseuille's equation, to calculate mass and volumetric flow rate, what would the benefit be to using two absolute pressure transducers to measure dP instead a single differential transducer? I am currently using a single differential sensor and a single absolute (for STP & mass flow calculations), but have become aware of an instrument that uses 3 absolute sensors to accomplish the same calculations. Why would this be done?


texts: How to describe the rotation of opposite ends of a body due to an applied moment

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Summary
A short way to phrase this question is:
Shear describes the translation of one part of a body relative to another given an applied force.  What is the equivalent rotational term?  That is,
What describes the rotation of one part of a body relative to another given an applied moment of force?
In more detail:
I'm trying to find the right word for a particular type of distortion.  I have an assembly of items connected to be approximately solid.  I mount one flat to a wall, and put some force or moment onto the opposite flat side so that the assembly distorts.  In particular, I want to correctly describe the relative rotation of the two flats (in any direction), and I want this term to describe only the rotation, and exclude any translation (so that if it only shears without twisting I'd like the quantity to be zero).

I thought of torsion, but definitions of torsion always seem to refer to a bar or an elongated axis of some type.  Is a bar required for "torsion" to be meaningful?  I thought of twist, but that doesn't necessarily imply a dynamic quantity, so, for example, one could freeze in a twist, and something can be twisted without forces applied.  I don't think bend is correct because that could just refer to translation.  Is there a better word that I'm not thinking of, or even a concise phrase?
If there is a word that matches my needs, a reference that I could review would be very helpful.

Why "bending" is not the word I need
Below is a sketch of two objects that are bending along the same curve (both by intuition and the equations), yet the rotation of the ends is different in each.  I'm interested in a word or phrase for describing the rotation of the ends (or a tendency for the ends to rotate or not, etc).

Also, according to wikipedia, bending "characterizes the behavior of a slender structural element" under load, but I'm not interested in slender elements (and only drew the above to illustrate bending).  The first is the common way a beam would bend, but not everything bends like a beam, and I am hoping to find a word that characterized the particular difference illustrated here.
Things that don't bend like normal beams
A reasonable model is a highly anisotropic material, rigid in one axis but less so in the others.  For example, a bundle of parallel fiber optic cables.
I think another would be a tube filled with water at high pressure, like a fire hose.  (I don't know how this bends, but I doubt it bends like a beam.)
Here's a sketch of a structure that doesn't bend like a beam, in that the side parallel to the wall stays parallel, even though the rest of the structure bends in a normal way.  The black dots are meant to represent rotating joints.  Even if this item were long and slender I think the ends would stay parallel.  The point of the third picture is that you don't necessarily get to see what's on the inside (but it could still be important to describe that the two walls don't rotate with respect to each other in response to an applied force).


texts: Is hardened steel better than tough steel?

texts: During the heat treatment process, people use clay to harden the steel in certain areas like the spine. Then they have to go through another process to make the steel tough. I need very hard steel and want to know will the hard steel be brittle and able to withstand large amounts of pressure? I ask because the steel is heavily stressed from the forging process. Also, can I make a thinner piece of steel as hard as a thicker piece with this method?


texts:
I'm building a motorized standing desk and am trying to calculate what linear actuators I need. If I have 4 linear actuators (one on each corner) each able to lift 25kg does that mean that the desk would be able to lift a full 100kg?

In other words, when linear actuators are sharing a load is the total drive force equal to the sum of the actuators individual drive force? Or is it more complicated than that?


texts:
So I need to design a cylindrical cam (aka barrel cam I think). I'm an aerospace engineer so I've never had a course on cams/gear design (wish I had though). Is there a general equation for the curve (path) on a cylindrical cam of known radius?

Here's a picture of my application; it's basically like a fishing reel. I need to use it to wind thread from a bigger spool to a smaller spool that will work on my sewing machine. The top rod with the purple thing is the input and the black thing is a rubber belt that turns the green drum. The green drum is the part I need to have a cam path on so that it moves the red arm. Any help or pointing to references is greatly appreciated!


texts: What are the general consideration for tendon profile in a post tension slab?

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How the tendon profile is calculated for banded-distributed disposition? In the following figure why is the tendons profile one in the top fiber and the second in the bottom fiber? If the location is at the middle of the slab why do we place them opposite to each other doesn't that cancel the effect of the lower tendon?

maybe this picture will clear my question


texts: Usticking two glass elements fused by vacuum

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I have an interlocking set of parts (1 and 2) which are used under vacuum. The last time I used it, the interface was wet with a mixture of water and ethanol. When the vacuum was removed, the two parts stayed firmly fused and no amount of force that I can apply can pull them apart. I suspect I will break the glass neck before I break the connection.

Can anyone suggest some tricks I could try to use to unstick them? I have tried heating the interface, which had no effect, and I have tried lubricating it, but the connection is too tight to allow the lubricant to penetrate.

Here is a crudely drawn picture of the fused pieces:


texts: Buckingham Pi theorem, repeating variables

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I'm having trouble understanding the 4th step to the Buckingham Pi theorem.

My variables are:

weight ($\text{N}$) : $\text{MLT}^{-2}$
h ($\text{m}$): $\text{L}$
Diameter ($\text{m}$): $\text{L}$
Orifice diameter ($\text{m}$): $\text{L}$
flow rate Q ($\text{m}^3/\text{s}$) : $\text{L}^3\text{T}^{-1}$
density ($\text{kg/m}^3$) : $\text{ML}^{-3}$
fluid viscosity ($\text{Ns/m}^2$) : $\text{ML}^{-2}$

From this $k = 7$, $r = 3$, $\text{number of Pi groups} = 4$

I know the criteria for repeating variables, but I'm not 100% sure.

For instance, if i picked weight, height and flow rate will that have fulfilled all the criteria? I don't understand the dependent variable criteria.


texts: Car trajectory with angled rear wheels (non-Ackerman)

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Consider a four-wheel steering vehicle in which:

The front wheels follow Ackerman condition
The rear wheel are rotated with a fixed angle (dir == dor in the picture below, and such angles do not change if the driver moves the steering wheel)

Actually, this is similar to a classic front wheel steering vehicle, but the rear wheels are not "straight", they are angled.

What kind of trajectory would this vehicle follow? Is there any closed-form equation to describe it?


texts: Is my understanding of the Chernobyl explosions correct?

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I have been reading technical reports and whatnot about Chernobyl for some time, and I'm feeling that they-or their wording-is not quite letting me understand it. For lack of a better way to present my many questions, I am requesting an evaluation of one of my current understandings of the Chernobyl explosions; mainly if it is consistent with published research and what parts are and are not.

01:23:44-Power in a hotspot in the lower southeast quadrant of the reactor causes these fuel channels to explode.
The channels are depressurized and the resulting boiling of water forms steam that is released into the empty space between the channels and the graphite. Aiding greatly is the positive void coefficient kicking in at the broken area of the channel.
01:23:46/7-This causes a lifting force on the reactor lid which lifts it up somewhat, jamming the control rods, tearing apart the remaining fuel channels (which are attached to it) releasing their steam in the same way as in #2.
01:23:46/7-The lid moves so high it floats above the reactor hall floor. The steam bursts through the gap thus formed. This is the first explosion
With the steam gone, pressure in the reactor drops and the lid begins settling down. Meanwhile, the loss of water is allowing an outrageous power surge.
01:23:49/50-power is 300 gigawatts. A hydrogen or nuclear explosion blows the lid through the roof, and kills Valery Khodemchuk. This is the second explosion.


texts: Why do (some) high-speed trains have curved (convex) walls?

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Comparing the cross-section of modern high-speed trains to old train waggons, which had straight walls and were limited to speeds around 200 km/h, I notice that most of them have curved outer walls. The width of the cabin decreases with height (and at heights occupied by passengers) and this obviously reduces space and comfort inside the cabin. So my question is, what are the main benefits of this? I am thinking of:

lower cross section of the train, i.e. reduced aerodynamic drag.
lower center of gravity. This is not bad with strong side winds!
lower moment of inertia for rolling around the longitudinal axis between the wheels for driving with high speed trough curves.

So what are the main benefits of curved outer walls? Is a circular shape the best?


texts: Does adding cold water to evaporative air coolers actually produce colder air?

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Or should it be the other way around, because hotter water evaporates easier than cold water?
I know this sounds stupid, so just hear me out.
I use an evaporative cooler and add normal room temperature water. Someone told me to add cold water to get better results. I intuitively thought that indeed cold water will produce colder air.
But as we all know evaporative coolers cool air by using the air to evaporate water which takes away heat from the air. So, we need the water to evaporate to cool the air. But we know that hotter water evaporates easier than cold water.
So, should it not be the case that colder water will actually not evaporate as efficiently and hence not produce cooler air than in case of hotter water?
For what its worth, i tried both and could not feel any noticeable difference, but of course it was nowhere close to a controlled experiment. So, I would appreciate an answer about what does the physics predict about what would happen?


texts: how do you calculate viscocity from torque arm load cell measurements?

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I have a piece of company developed equipment that uses a pot mounted on a rotating base plate with a 0.15m torque arm and load cell, a mixing paddle is used to stir the mixture while the controller calculates torque from the motors rpm and force applied to the load cell.

My question is considering a servo viscometer and many other digital viscometers calculate viscocity based upon torque can this be achieved using the setup with what principles would you require?


texts: Difference between continuous wave laser and a pulsed laser

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I understand the difference between the two in terms of how they function; one will release all of it's energy in small pulses with the other creates a constant stream of radiation.

My question is for materials processing such as marking or cutting.  Why would I use one over the other?


texts: What is the structural factor in context of wind loads?

texts:
Coefficient called "structural factor" appears in building codes when calculation of wind loads in discussed. The wind load is proportional to this factor.
I have a lot of trouble understanding its meaning. One definition from here says:

The structural factor takes into account the absence of pressures simultaneity to the surface of the construction and of vibration of the structure caused by the turbulence.

Eurocodes, for example gave no clearer explanation. Could somebody explain the meaning in more detail? What is meant by "absence of pressure simultaneity", and how does a multiplicative factor account for this?


texts: how to calculate the angle in Nyquist plot

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Does anyone know how i can read the angle on the Nyquist plot
without knowing the open loop transfer function?
So by only having the plot.


texts:
Say you have a metal rod with a square cross section (say 10cm by 10cm) of a certain length. You'd like to make it less prone to bending. Is it better to:

keep it the way it is

or

remove material so that it has a T shaped cross section

I wonder if removing material would actually make it more rigid from a bending perspective simply due to the T shaped cross section.

Thanks


texts: Constrained optimization using Lagrangian

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I'm trying to optimize the weight of a truss with the constraint that the trusses don't face more stress than the material resistance.

Here is a sketch of my truss:

I have a Python function that given the list of X,Y coordinates for my fours nodes, gives the weight of the truss. Let's call it Weight(X).

I've also a function that calculates the stress in each truss: Stress(X).

Using a classical unconstrained gradient approach I've minimized the weight of my truss. I only act on Node 2's x and y coordinates (lower right node). Here is the configuration I get:

I would like now to be sure that the stresses in my trusses are not higher than the material resistance.

I've read some things on the Lagrangian dual approach. Here is an example:

The problem is to minimize $\frac{1}{2}(x_1-1)^2+\frac{1}{2}(x_2-1)^2$ with $x_1+x_2 < 1$ and $x_1>0$.

First here is the Lagrangian of the problem:

$$L(x_1,x_2,\lambda_1,\lambda_2)=\frac{1}{2}(x_1-1)²+\frac{1}{2}(x_2-1)^2 + \lambda_1(x_1+x_2-1)-\lambda_2 x_1$$

We have to find the root of derivate of $L$ regarding the prime-variables $x_1$ and $x_2$. The following are called the "primal-dual relations":

$$\begin{align}
\frac{\partial L}{\partial x_1} &= (x_1-1)+\lambda_1 x_1 - \lambda_2 \\
\frac{\partial L}{\partial x_2} &= (x_2-1)+\lambda_1 x_2 \\
\therefore x_1 &= 1 - \frac{\lambda_1 - \lambda_2}{2} \\
x_2 &= 1 - \frac{\lambda_1}{2}
\end{align}$$

Whith these relations, the dual fonction can be written as:

$$l(\lambda_1,\lambda_2)= -\frac{\lambda_1^2}{2}-\frac{\lambda_2^2}{4} + \frac{\lambda_1 \lambda_2}{2} + \lambda_1 - \lambda_2$$

We have then to maximize the function in terms of $\lambda_1$ and $\lambda_2$. When this $\lambda$ couple is found and with the primal-dual relations, we get back to the optimal $x_1$ and $x_2$.

Here are some questions:

Can I solve my optimization problem following this methodology?

I don't know how to do it because my cost and constraints functions are implicit (I cannot analytically derivate them toward the X-Y coordinates of my moving node).

I've writting my Lagrangian function as follows:

$$\begin{align}
L(X,\lambda_1, \lambda_2, \lambda_3, \lambda_4) = &\mathrm{weight}(X) - \\
&\lambda_1(400-\mathrm{abs}(\mathrm{stress1}(X))) -\\
&\lambda_2(400-\mathrm{abs}(\mathrm{stress2}(X))) -\\
&\lambda_3(400-\mathrm{abs}(\mathrm{stress3}(X))) -\\
&\lambda_4(400-\mathrm{abs}(\mathrm{stress4}(X)))
\end{align}$$

I have a Lagrangian multiplier per truss and the stress() functions give the nominal stress in each truss.

Do you think this is properly defined?

I've set $l_1\ldots l_4=1$ at the beginning, I've found the $x\ast$ and $y\ast$ that root the derivative toward $x_1$ and $x_2$. But then, I don't know what to do with these values because these are implicit relations, I don't have my primal-dual relations, isn't it?

Also, do I have to do something when my Lagrangian multipliers are negative or something?


texts: Is tunnel boring considered groundworks?

texts: The wikipedia page for groundworks (earthworks) does mention contour trenching and cut & fill but not a word about bring tunnels. Is a bored tunnel part of groundworks discipline/field? If not what discipline does it belong to.


texts:
16 Examples of Tensile Strength has a list of items and their tensile strength.

bamboo has these tensile strength ratings
Bamboo  MPA 350 PSI 50,763

If I needed to have a hydraulic motor to shred bamboo, the hydraulic motor ratings are in Nm, example
cc/rev 492
Nm/bar 6.86

cc/rev 197
Nm/bar 2.51

With the second hydraulic motor rated at 197 cc/rev and 2.51 Nm/bar

at 20bar system pressure the motor should output 50.2Nm of torque.

How do I calculate the required Nm needed to crush bamboo.
Newton Meters and MPA are different.


texts: How to handle reflections when cutting metal with a laser?

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I have heard of lasers being used to cut metal, however all laser cutting machines I've found can't cut metal, I'm guessing because it reflects the light?

What is different in the designs of such machines between those that can and can't cut metal? Is it just accepted that energy is lost in reflection, and has a safe way of absorbing reflections?


texts:
How much could this motor lift and how fast? If I connect a belt to its axis about 1cm away or even 10cm away from its tip.

Torque: 1.5Nm
Peak Torque: 10Nm
Power: 9-30A, to 1000W.

https://www.alibaba.com/product-detail/86BLF40-24v-48v-1000W-big-brushless_60644013087.html?spm=a2700.7724838.2017115.56.f5f862211YuM1C

What kind of motor would I need to be able to lift 50kg about 1m high, in say 4 seconds? And to control finely the exact position within the 1m, sometimes it should lift to 20cm sometimes to 30cm. Is a stepper or servo motor capable of this task? Would a linear actuator be better, but I read those have low duty cycle, and they are slow so they would lift it slowly and wait for next time?


texts: How to use the intersect tool for two components in an assembly with solidworks?

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I have an assembly file in Solidworks 2019 with two components, the green, and yellow rectangular prisms.

I'm having trouble understanding the instructions I found online about making an intersection with these two components. Can someone help me with this?
They form a subassembly in a larger file, and I'm really just interested in the volume that they share.
Edit
I just found out how to make a 3D sketch outlining the intersection. Tools > Sketch tools > Intersection curve. But I'm not sure how to take this further and extract the intersected volume.

Edit 2
I am looking to take these two parts from the subassembly and make a new single part where they intersect.
Yes, they ultimately do need to be an assembly, but if it can be converted temporarily that's fine. It can be saved under a new name first as a file with a multibody if necessary.
The only remaining part should be the intersection of yellow and green. (Although if I think about it carefully, it might be important not to remove the portion of green below the intersection in the final part.) The leftovers can be removed as long as it's in a separate file. I still need the subassembly for other things in the larger assembly I mentioned.


texts: Oblique cutting implemented in Industrial applications

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Oblique cutting generates transverse cutting force which reduces tool life. Oblique cutting involves principal and auxiliary cutting edges in the cutting action which increases friction and advances wear in the cutting tool.

Orthogonal cutting doesn't have those complexities, but oblique cutting is found to be used in more often in an industrial setting.

Why are oblique cuts made instead of orthogonal cuts when it is more efficient to make an orthogonal cut?


texts: Can't tesla turbine work on air heated by solar concentration?

texts:
If we heat air along a pipe that's tilted at 30° to the horizontal using parabolic troughs, the air should rise upwards (I'm not sure how fast or powerfully) and then connect the outlet at the top into a Tesla turbine, shouldn't it generate power?
Please explain the heat engine concepts here, because in my understanding, there SHOULDN'T be a need for an air pump (to pump air in the CSP piping) as the hot air rising up will inevitably create low pressure and cooler air will replace it from under. And there SHOULDN'T be a need for a cooling fluid as the hot air should just exit from the Tesla turbine, giving up (if not 90% efficiently) it's kinetic energy to the turbine?
Is there something I misunderstand? Also correct me about such: as write this, I am starting to believe the air will not exit from the turbine at all and a "suck back" effect will happen at the bottom, i.e. the hot air will build up pressure and exit from the bottom, destroying my whole idea.


texts: How to supply hydrogen to a fuel cell at a pressure lower than the atmospheric pressure?

texts: I have purchased a fuel cell, and the supply pressure must not exceed 0.55 bar. My question is how can I supply the hydrogen at this pressure given that it is below atmospheric pressure.


texts: Is Belytschko beam defined for 3D or 2D?

texts:
from the paper in this link , which is the Belytscko beam. I could not figure out if it is a 3D beam or a 2D one.

if you don't have access to that paper, please check the page 73 on this link.

what confused me was the schematics on the original paper and the second link. in the beginning the general movements start from 3D but I don't see all the DOFs in the above image


texts: Formula for "ram rise" that works all the way to orbit

texts:
True Airspeed (TAS) is the vehicle speed relative to the surrounding air. My assumption is that if I am in orbit say at 120 km altitude with an instantaneous velocity of 8 km/s my TAS would be fairly close to 8 km/s even though my Indicated Airspeed (IAS) shows zero.

Assuming the above holds true, the "ram rise" (RR) formulas I find are all based on Mach (which, in turn, is based on TAS) or TAS directly. They do not appear to take into account the static pressure or atmospheric composition, only the adiabatic index. Therefore, my TAT (OAT plus ram rise) is in the thousands of degrees Kelvin ... which makes no sense because there are practically no molecules of air to hit!

So are these RR=TAS²/87 formulas assuming to be used below a specific altitude? I can't find anything for orbit or reentry. I also can't find any space shuttle telemetry to corroborate the TAS assumptions I made above. I am aware there is also a Mach-based RR formula and it has the same problem.

Your help is sure appreciated!


texts: Overcoming limitations of a snap in joint

texts:
I have a medical device I am designing which will lie under the patient bed.

I need to add a "connector/joint" on this device to permit the attachment of some consumable.

Here is a quick overview of the process:

Blue part is low cost injected plastic disposable part that will be assembled and disassembled only 2-3 times before being disposed.
Orange part is the device, can contain more complex parts (springs...).
Orange part must last thousands of assembly/disassembly.
Orange part is not movable, only blue part can be moved when assembling.
When assembled, it must resist to at least 100N force in all direction, including rotation around the "snap axis".
Orange part must be around 3cm which is a good side to apply pressure with two fingers.
Disassembly pressure force should be low as only two fingers will be use, other hand will retain blue part.
It should be easy to assemble/disassemble with "closed eyes" as the device will be under a bed and there might be no visibility on the device itself.

As my drawing might be a bit confusing, here is a common device that is similar (aka a buckle).

The main problem with buckle design is the require pressure force for disassembly which is way too high, it's also too hard to assemble and not robust enough. But it is a good example for the "general principle".

What I am looking for is not for someone to design the assembly for me, but I am looking for exiting systems that are an alternative to a snap in joint and any pointer that would help me design it.


texts:
I'm attempting to calculate the clamping force from a u-bolt. This arises from an existing support configuration that is being re-qualified due to the installation of new equipment. I am stuck with this configuration unless it turns out to be truly impossible to re-qualify.

$\hspace{4cm}$

$\hspace{7cm}$Figure 1

The u-bolts, as shown in Figure 1, are supporting a vertical load. This vertical load is being resisted only by the clamping force which exists from the 2 u-bolts around the vertically oriented 2" dia. Schedule 40 pipe.

My initial thoughts are to approach the qualification as I would for a bolt and nut in a slotted hole. That is to say, use the installation torque to calculate the bolt preload, and then use the preload along with an appropriate coefficient of friction to calculate the clamping load. This approach seems inadequate to me, but I don't really have a good reason why I feel that way.

Has anyone ever dealt with a similar issue? What method was used to calculate the clamping force?

Thanks.


texts: How are passive houses made in very hot regions (like Saudi Arabia)?

texts:
I think, here is the main problem the difference between the internal and the external temperature.

For example, in Saudi Arabia, in 50 C, a passive house needed probably much sophisticated planning as in Paris.

Compared to the traditional cooling systems, in the second case is enough only to get a cooling system with bigger power. I think, they are much more scalable.

Is it anyways possible?


texts: How can I calculate the power and torque required for the motor on a wheeled robot/vehicle?

texts: How can I calculate the power and torque required for the motor on a wheeled robot or vehicle if a particular acceleration or movement up an incline is required?


texts: Designing of a tissue stretching device using a linear actuator

texts:
I'm trying to design a device that can stretch a tissue sample of set length, right now about 2 mm, to desired stretch ratios. This will be controlled using a interface where the user can input their desired ratio, and the controller will tell a 6 in stroke WindyNation linear actuator to move to a position based on the input ratio. The controller also needs to communicate with a force sensor and display the force that is being exerted on the sample.

For this type of problem, is it better to use an Arduino, Raspberry Pi, or both to power the controller? I've found that the Pi won't be very good due to issues with timing. Will this be a serious issue?


texts: Avoid snapping an electric cable from too much rotation

texts:
I recently built the basic construction for a crane out of lightweight material. Basically the head of the crane contains an electric servo motor which spins the head of the crane by pushing itself away from the tower (the rotor is fixed to the axis which is fixed to the tower. The axis isn't fixed to the head in any way).

All electronics required to operate the motor and more are inside the head. The only thing I should extend to the rest is a 240 V cable.

Since the head is allowed to make multiple rotations (preferably limitless), how do I avoid snapping my cable by rotating it too often? I'm aware such solutions exist, but I have no experience in this area so I have no idea what to ask for specifically.

/---------------------\
|                     |
|        motor        |
\----------|----------/
           |
___________|___________
\          |          /
 \         |         /


texts: What does this bandpass signal equation indicates?

texts:
This is the equation for bandpass signal from transmitter. What are the values for different parameters present in this equation. For example, what should be the value of P, Sl(t), Fc etc. Also what is the meaning of j in this equation.

Source for context.


texts: What materials absorb water and release it steadily when compressed?

texts: Absorbent cotton wool is a good bio-compatible example, but it has low availability in the US and is not reusable.


texts: How to determine the characteristic length in reynolds number calculations in general?

texts: I understand that the reynolds number is given by the expression $Re=\frac{\rho v L}{\mu}$, where $\rho$ is the density, $v$ is the fluid velocity and $\mu$ is the dynamic viscosity.  For any given fluid dynamics problem, $\rho$, $v$, and $\mu$ are trivially given.  But what exactly is the characteristic length $L$?  How exactly do I calculate it?  What can I use from a given problem to determine the characteristic length automatically?


texts: Is compressed air energy storage economically viable in the home?

texts:
If I install a small air compressor/engine, generator, and tank in my garage, and I charge it up at night when electricity costs $\frac{5.4p}{kWh}$ and use it during the day to power my house when electricity costs $\frac{12.5p}{kWh}$ would this be able to save money on the electricity bill or not?

The tank, engine, and generator should be sized to charge up over 7 hours between 01:00 and 08:00 and release the energy during the other 17 hours of the day. I'm assuming that regardless of when during the day the energy is actually released it is either used by me or goes back into the grid and runs the meter backwards to offset my day-usage.


texts:
a long time back at school, I had a difficult excercise which was named X, Y and Z bodies.
They were drawings where both the front view and the top view were fully given. We had to find the view from the left plus the body in a sketch drawing.
Unfortunately, I don't remember the solutions anymore and I don't find out them anymore.
Could anyone help?
As an example, I added the Y body with below link.

Ah, yes: the forms are squares and the middle of the Y is the middle of the squares - in both views.

Thanks for your help and hints in advance!

Best
Tom


texts: What type of control system is this? open loop?

texts: Suppose I have a liquid in a container, the type of liquid is such that it expands when its temperature rises. The contrainer is marked with scale to measure the height of liquid expanded. There is a controller that maintains the temprature at it desired value. Temprature sensor feedback the temprature value to generate error signal into the controller. But the main purpose of the system is to maintain the height which does not have any feedback sensor. The only way to find out is through scale reading which is done by human observer. To maintain the height, the observer changes set point temprature. So first, what is the actual name of this kind of system, an open loop system for height control? Second is this block diagram correct in control theory?


texts: I'm stuck trying to find the resultant of the force system. Here it is said to find the angle θ the resultant manes with the horizontal. But θ here is narked relative to F₂. How do I find the resultant and θ


texts:
Suppose I have a small stepper motor, and for reasons (like wiring considerations) it is advantageous for me to not actually have the motor's body fixed as the shaft rotates, but rather have the shaft fixed in place while the entire mechanism of the motor rotate around the shaft. Are the two schemes equivalent if we assume that the shaft is perpendicular to the ground?
My ultimate case is to have a stepper motor rotate while it is upside down, without using additional gear wheels or any other component other than a coupler which secures the shaft to a solid base.


texts: Stability issues in gateleg table design

texts:
This is a table with two wings that fold down, and two legs per side that swing out for support. I'm pretty confident about this design being stable:

The green section at the top is the only surface that remains in place. The vertical green section at the back is another wing on the opposite side, shown folded down. For the yellow wing, the legs are shown fully rotated outward to their stop position.

The total measurement of the surface is 22" (wing) + 6" (stationary section) + 22" (other wing) = 48". The total height is 24".

Here is an alternate design. I would like to find a way to reduce the overall weight and only include one swing-out leg (other wing removed for illustrative purposes):

The swing-out leg is shown here fully extended to its resting position. It would have some kind of ball/socket mechanism to lock in place.

Alternatively, the single leg in the alternate design could swing out from the center to form a T-shaped frame underneath, which is probably more expected:

My question is: how can I calculate this table's stability? I worry that in the second design, there would be stability issues in the corners. I'm an amateur builder and not sure how to go about this.

Oak would be the surface material, with the legs being 1" square steel.

There is a similar table from Crate and Barrel that I can't link to due to being a new user ([A], [B]):


texts: Deformation of a fixed-fixed beam with perfectly plastic yield stresses

texts:
Here's the setup:

The problem asks to find the relationship between the force $P$ and the displacement of B ($u_B$). I have done this correctly:

$$P = \left(\dfrac{E_1A_1}{L_1}+\dfrac{E_2A_2}{L_2}\right)u_B$$

Now imagine that members AB and BC both have yield stresses ($\sigma_{Y_1}$ and $\sigma_{Y_2}$) and are perfectly plastic after yield.

I need to find the relationship between $u_B$ and $P$ in the following cases:

No member yields - ($0 < u_B < \sigma_{Y_1}$) & ($0 < P < P_{y_1}$)
Member AB yields, but not member BC - ($u_{Y_1} < u_B < u_{Y_2}$) & ($P_{y,1} < P < P_{y,2}$)
Both members yield - ($u_B > u_{Y_2}$) & ($P > P_{y,2}$)

I'm having trouble finding explicit expressions for $P_{y_{1/2}}$ and $u_{Y_{1/2}}$. I'm not quite sure how to relate yield stress to elongation and displacement of the members.

To be honest, this problem has tied my brain in a knot and I believe my conceptual understanding (or misunderstanding) of the problem is limiting my ability to solve it mathematically. Any help at all would be greatly appreciated!

Edit: Here is the exact problem


texts: How to calculate the pressure loading of a vented silo explosion?

texts:
I would like to independently check a vendor's silo design for proper explosion venting. Worst case, it is essentially cylinder filled with a stoichiometric mixture atomized sugar dust and atmospheric oxygen initially at atmospheric pressure. The roof of the cylinder is designed to detach from the structure with, lets assume, zero force. The roof also has some amount of mass per square inch.

Lots of different ways to go about it, but initially to skip transient calcs I was thinking I could calculate the worst case by assuming 100% of oxygen reacts instantly. Put that energy into the ideal gas law and calculate the final pressure if unvented. Not sure if this will truly be the max pressure or if the transient shock wave pressure would exceed this?

The minimum pressure would be the psi required to lift and accelerate the roof up. The vented roof pressure loading should be pretty easy, again not considering transients.

Any thoughts on how to better roughly calculate wall pressures without cfd? Thanks!


texts: 3D Transformation Between Two Cartesian Coordinate Systems Using Euler Angles

texts:
I am trying to transform any arbitrary vector $\bf{v_{1}}$ in a Cartesian frame $\mathscr{F_{1}}$ into a different Cartesian frame $\mathscr{F_{2}}$. Both $\mathscr{F_{1}}$ and $\mathscr{F_{2}}$ have the same origin. I have consulted Aircraft Flight Dynamics and Control by Wayne Durham, and understand that book's solution as follows:

Use the standard yaw-pitch-roll $ z,y,x$ $/$ {$\theta_{z},\phantom{s} \theta_{y},\phantom{s} \theta_{x}$} (usually called {$\psi, \theta, \phi$} respectively) / $3 2 1$ order. There exist three transformation matrices, one for each axis. First, rotate about the z axis of $\mathscr{F_{1}}$. Call the transformation matrix $T_{\mathscr{F'},1}$ since it goes from $\mathscr{F_{1}}$ to an intermediate frame $\mathscr{F'}$. $T_{\mathscr{F'},1}$ is given as

$$T_{\mathscr{F'},1}=\begin{bmatrix}
    cos(\theta_{z})       & sin(\theta_{z}) & 0 \\
   -sin(\theta_{z})       & cos(\theta_{z}) & 0 \\
    0                     & 0               & 1 \\
\end{bmatrix}$$

To go from $\mathscr{F'}$ to $\mathscr{F''}$, you then rotate about the y' axis using
$$T_{\mathscr{F''},\mathscr{F'}}=\begin{bmatrix}
    cos(\theta_{y})       & 0 & -sin(\theta_{y})              \\
    0                     & 1                & 0              \\
    sin(\theta_{y})       & 0               & cos(\theta_{y}) \\
\end{bmatrix}$$

Finally, to go from $\mathscr{F''}$ to $\mathscr{F_{2}}$, you then rotate about the x'' axis using

$$T_{\mathscr{F''},\mathscr{F'}}=\begin{bmatrix}
    1       & 0 & 0             \\
    0                     & cos(\theta_{x})       & sin(\theta_{x})   \\
    0       & -sin(\theta_{x})               & cos(\theta_{x}) \\
\end{bmatrix}$$

A composite transformation matrix $\bf{T}$ can be made by multiplying these transforms together. Individual transform steps on a generic vector $\bf{v}$ are given in the book (and I reproduced them below) to show order determination.

$$\bf{v'}=T_{\mathscr{F'},1} \bf{v}$$
$$\bf{v''}=T_{\mathscr{F''},\mathscr{F'}} \bf{v'}$$
$$\bf{v_{2}}=T_{\mathscr{F_{2}},\mathscr{F''}} \bf{v''}$$

$$\bf{v_{2}}=T_{\mathscr{F_{2}},\mathscr{F''}} T_{\mathscr{F''},\mathscr{F'}} T_{\mathscr{F'},\mathscr{F_{1}}} \bf{v}$$

$$\bf{v_{2}}=\bf{T}v_{1}$$

So $\bf{T} = T_{\mathscr{F_{2}},\mathscr{F''}} T_{\mathscr{F''},\mathscr{F'}} T_{\mathscr{F'},\mathscr{F_{1}}}$ (strictly in this order).

My problem arose when I coded this transformation into MATLAB and tested some examples which I could verify qualitatively (with some coordinate axes I made out of wood).

The transformation matrix $\bf{T}$ that works is $\bf{T} =  (T_{\mathscr{F'},\mathscr{F_{1}}}   T_{\mathscr{F''},\mathscr{F'}}  T_{\mathscr{F_{2}},\mathscr{F''}})^{T}$. Thus, in order for the transformation to work the way I expect it should, I need to multiply the matrices in reverse order and take their transpose. What has gone wrong?


texts: How to calculate meters per pixel for a given camera?

texts:
I am stuck on this problem for a while:

I have a square-shaped camera, with:

1000 pixels on vertical side
1000 pixels on horizontal side

I want to know the number of meters per pixel depending of the distance, I mean:
If I have a 1 meter long object which is 100 meters far from the camera, how many pixels of the resulting picture will be occupied by the object?

I am not sure if it is useful, but we can estimate the length and size of the camera:

0.05 meters vertical
0.05 meters vertical

How to calculate the number of meters per pixel as defined above?

EDIT:

From first answers and the given formula, I am wondering:

Does the formula depends of how far from the lens is the pixel device?

SECOND EDIT:

I have this data: The Optical Form Factor of the camera is: 1/2.5''

Is it related to the lens focal length? I did not find a definition on wikipedia and only this blog article that I don't understand


texts:
I'd like to calculate the max contact pressure in the below assembly, just before contact loss between the beam and the wall.
The beam is clamped to the wall with a pretensioned screw, and sustaining a force at his gravity center.

I'm assuming all bodies dimensionnaly stable (no distorsion).

I wonder about few questions...
how to calculate the maximum force at center of gravity before contact loss ?
how to work out the composed pressure profile...

Here are some sketches that may help understanding the problem :

Thanks a lot for any kind of help (calculation steps...).
Have a good day !


texts:
I just started my BEng, so I actually don't feel ready to assess real cases.

Upper floor of my quite standard British terraced house.
We would like to hide an existing drainage pipe which is currently running along the wall.
To do that, I cannot find other ways but running it through the pictured floor joist (I already removed the plywood underfloor, as you can see).

Now, I am very wary of introducing possible structural weakenings when boring the joist: its sizes are 7cm (parallel to the floor) by 20cm (perpendicularly to the floor).
Since the outer diameter of the drain pipe is 43mm (even less if use solven weld), I should be fine according to the information I found from multiple sources on the internet (maximum 1/3 of the height of the joist, hole centered and away at least 2" from the highest and lowest faces of the joist).

However, I'd really like to have further certainty for my specific case: maybe somebody who knows about these things could have a look at the picture and the data I provided and confirm this is the case?
Alternatively, should I hire a (real:) structural engineer for a proper consultation on this single issue? Or would that be overkill?

I'll be glad to hear anything you might have to suggest/explain/add.

Thanks!


texts: What is this pressure gauge on the London Underground measuring?

texts:
I noticed this pressure gauge on the Piccadilly Line of London Underground yesterday. It was located on the side of a row of seats.

Close-up of the gauge at hand:

click for larger version of image

The pressure gauge seemed to randomly fluctuate between 0.5 and 1.5 bar when the train was in motion, with no significant correlation with the acceleration or the speed of the train. However, when the train was in stations and the door opened, the gauge reads out as ~3 bar. The close-up was taken when the train was stopped at a station.

What is this pressure gauge measuring, and why is it helpful to have it displayed in such a prominent location in direct sight?


texts: Analog PID Controller/Filter delay and stability

texts:
recently I had an exercise where I had to build and measure an analog PID controller/filter. The starting point was this circuit.

This is a tamed PID controller implemented with a single opamp. Resistor and capacitor values are calculated regarding the crossover frequency and a 40 degree phase margin.
First question I have:
When this circuit is connected to a power supply and given an input voltage(sine wave while manually editing the frequency) the output voltage slowly but surely goes up to the supply voltage level where it stands which draws the conclusion that the analog PID controller is unstable right? Or am I interpreting something wrong here? If I am right, that means that it is BIBO unstable(Since the only thing bounding the output is the opamp not the controller)
However, after a new Resistor is added parallel to R3 and C2 which makes it a PID-Controller/filter(not sure about this formulation when it is mentioned as an analog filter) it becomes stable and these are the bode plot and step response of the circuit with a new resistor.

My next question would be, does an analog controller has delay? Looking at the step response I would conclude that there is no delay. Nevertheless the delay from the step response should be calculated and compared to the delay measured from the bode plot.


texts: Response time and time constant of Mercury thermometer

texts:
I searched to find differences between response time and time constant of a thermometer. So I found that those two are not same and we have to get 99.3% of the total step change to find response time and we have to get 63.2% of its total step change to find time constant of thermometer... Is this correct or not and are those percentages are correct or not? Can you explain why that is...
Thanks in advance...


texts: From an engineering point of view what are the downsides of a too accurate model?

texts:
I was wondering, from an engineering point of view, for what reasons can too much accuracy in modeling be detrimental?

From a scientific point of view it seems like it's almost always a benefit, apart from when you need to take less computation time.

So from an engineering point of view, besides time (or computing power) why should you avoid that?


texts: Calculating Flow rate and Water Velocity of a pipeline

texts:
Background
I am trying to assess the Power output of a Pumped Hydro project based on this website. I have all the required inputs except the flow rate (m3/s).
Problem
However, this is where I think I'm getting confused,

When I looked up how to calculate the flow rate (here), I need to first know the water velocity,
When I looked up how to calculate the water velocity (here), I first need to know the flow rate

How would I go about calculating this, when both are unknowns?
Known Information
What I do know is

Pipeline Diameter (762 mm)
Pipeline length (38,000 m)
Pipeline hydraulic head / drop (176 m)
Pipeline Roughness (concrete lined, operating 0.3mm)
Upper Reservoir volume (78.8m m3)
Water density (1000 kg/m3)
Gravity (9.81 m/s^2)

is that sufficient information to be able to calculate either water velocity or flow rate?
Note
This question has been asked before (here) but it previously went unanswered.


texts: How to convert ASCII to binary to facilitate a UART to SPI bridge for an MSP430?

texts:
I am currently working on project where the commands for a PC to the MSP430 will be communicated via UART. These commands need to be converted to binary to be able to written to the SPI bus.

For example 'a' from PC is translated to 0x61 on the microcontroller. What is really needed is hex 'a' Thus
ASCII 'a' from PC = 0x61 => need to translate hex 0x0A

Question : What is the most simplest way to convert ASCII to binary? I am using "C".


texts:
I am working on an assignment and I have a doubt in a step in my problem. Could someone please help me understand it?

Question and its solution is:

.
My doubt is in the part which is underlined. How did the 2nd term become zero? Also. how did they calculate external moment vector. If someone can explain these steps it would be very helpful.

P.S: If this is not the correct forum to ask such question, I apologize.


texts:
I would be appreciate if anyone can solve problems below for this beam.

・Find the all sectional forces $F_x,F_y,M_x,M_z$ for both elements① and element②.
・Find elastic strain energy of element① and element②.
Flexural rigidities  of two elements are both $EI$ and torsional rigidities of them are $GJ$.


texts: How to calculate rotations from displacements?

texts:
I'm trying to develop a finite conical shell element with six dof at each node. I want to express the rotations $\phi$, $\theta$ and $\psi$ in terms of the displacements $u$, $v$ and $w$. The displacements are functions of $x$ and $y$.

Using the geometric relations and small angle approximation, I have found $\phi\approx \tan(\phi)=\frac{dw}{dv}$, $\theta\approx \tan(\theta)=\frac{dw}{du}$ and $\psi\approx \tan(\psi)=\frac{dv}{du}$. But I'm not yet convinced that this is the way to go.

Do you know any other general approach to express the rotations in terms of the displacements?

Edit: I have attached a picture of the geometry of the cone and its coordinate system. $x$ is the meriodional coordinate along the generator of the cone which is presumed to be zero at the apex of the cone. $y$ is the circumferential coordinate.


texts:
I am studying the mixed sensitivity design for control systems, and I have seen that the control effort has limitations given by the bandwidth of the process and by the bandwidth of the sensitivity function. In particular I have seen that if we plot the control sensitivity function, we have that if I am above the bandwith of the process I have an increase of the control effort, while if I am below it decreases. And also I have a lower limitation given by the bandwidth of the sensitivity.

But I don't understand why. Also, does the controller bandwidth impose some limitations? Can please someone explain this to me? Thanks in advance.

[EDIT] I recognize that my question was to shallow, so I will try to do more reasonings and add more argumentations as I search for answers.

I will use an approch based on the mixed sensitivity for my discussion.

Suppose I have the following plant and controller:

s = tf('s');
G = 10/((s+10)*(s+1));
K1 = 0.5/s;

Now I define the following mixed sensitivity controller, where I used a weight for the sensitivity in order to achieve my desired specifications, which are a 60 dB attenuation at high frequency, a cross over frequency of 0.66353 and a maximum resonance peak of 2 dB. I also inroduce a weight for the control effort, which I use to limit the amount of effort the control has to do. In particular, I use a constant weight, so by doing so I am hopefully trying to limit the control effort to increase too much:

W_bs2 = 0.66353;   %same cross over frequency as the previuos point
M = 2;           %peak of the sensitivity
A = 0.001;      %attenuation
Ws2 = (s/M + W_bs2)/(s+W_bs2*A);%sensitivity weight
%bodemag(1/Ws),grid;
Wu = tf(1);
[K2,CL,GAM2] = mixsyn(G,Ws2,Wu,[]);  %define the controller with the mixed
sensitivity
display(GAM2);
K2 = minreal(K2);  %define a minimal order controller

some of the comments may not make sense because they refer to some previous code.

Now, I define the control effort:

Q1 = K2/(1+G*K2); %control effort

and I plot the control effort and the weight of the control effort, which should impose a limitation:

in this case I used a control effort weight equal to 1, but probably an higher value would have been better.

Now, the bandwith of the controller is 0.9879, so if I go above it the control effor shoulb be increasing instead of decreasing. Let's try:

I define a second sensitivity weight which gives an higher cross over frequency to the control  effort when defining the controller:

W_bs3 = 2;   %same cross over frequency as the previuos point
M = 2;           %peak of the sensitivity
A = 0.001;      %attenuation
Ws3 = (s/M + W_bs3)/(s+W_bs3*A);%sensitivity weight
%bodemag(1/Ws),grid;
Wu = tf(1);
[K3,CL,GAM3] = mixsyn(G,Ws3,Wu,[]);  %define the controller with the mixed
sensitivity
display(GAM2);
K3 = minreal(K3);  %define a minimal order controller

and if I plot the control effort of it and confron it with the previous result:

the second mixed sensitivity controller gives me the yellow line, while the first gives me the red line.

Now, I am not sure I am going to the right direction, but hopefully I am getting closer.

Can someone help me? Thanks again.

[EDIT 2] So,after a lot of searching and thinking I think the point is that I haven't really understood the concept of bandwisth and how it influences the system. I am in particular looking at sensitivity bandwidth and complementary sensitivity bandwidth.

At this point, my idea is that the sensitivity bandwidth an the complementary sensitivity bandwidth should be limited by the fact that $S+T=1$. But still not really clear what happens. So it should be that if S is large, T cannot be too large. But is the bandwidth related to this?


texts: Is a gear usually held to a shaft by friction or an adhesive?

texts:
So, where I work, we have this arcade game, which is a classic claw machine.  IN order to raise the claw up and down the machine makes use of a worm gear, like so:

(although for the meticulously curious, this is actually the drive that moves the trolley the claw rests on back and fourth but it is almost identical to the part in question.)

I noticed that the gear seems to be on little grooves here.  On one of our machines , the gear has actually come off of the grooves on the horizontal shaft.  This has been causing the gears to slip whenever the motor tries to rise the claw.  I assume this can happen because the vertical gear puts friction on the other gear that makes it tend to slide in the direction of rotation along the shaft, so my question is this:

Is this gear on the horizontal shaft held in place by friction (if I slide it in place until it is hard to move from pressure between the shaft and diameters of the gears, am I good) or do I need to clean the shaft and apply some adhesive in order to expect it to stay?  It works okay now, but I didn't exactly test it extensively.


texts: How do bike wheels keep turning when the rider stops pedalling?

texts:
I am very confused with something regarding bikes...

How is it that a bike wheel continues to spin (either from momentum or from going downhill) when the rider is not pedalling, without also spinning the pedal?

Similarly, what mechanism allows the addition of this spin from momentum with to the spin from the pedalling that makes the wheels spin faster than they would with just one or the other?

I've literally searched all over the internet for this and have found nothing, so I'd really appreciate the help.


texts: How does the strength of a square tube depend on the side size?

texts:
There are two square tubes of the same length, material and wall thickness, one being 40x40mm, the other 20x20mm. How does their strength against bending compare?

On the one hand, the cross-sectional area of the 40mm tube is 4 times bigger. On the other hand, I guess it is mostly the two walls that are in the same plane as the bending force that work against it. The other two walls provide very little resistance comparing to the first two. And because the surface of the "working" walls of the 40mm tube is twice as much bigger as those of the 20mm one, I am inclined to think that the 40mm tube is roughly twice as much stronger. How does this conclusion stand?

More specifically, this question is about galvanized steel tubes with 1.6mm thick walls:

I am looking at using them as two or more horizontal beams 2.4m long which will take some evenly distributed load. The vertical space is limited so that I would rather use four/eight/sixteen 20mm tubes than two 40mm ones. But how many 20mm tubes would be roughly equal to two 40mm ones?


texts: How to use excel spreadsheet formulas to find optimal camshaft profile

texts:
I have a 600cc 4 cylinder Honda engine that my race car team uses.
The rules of the race mandate that we install an intake that is substantially smaller than the stock factory intake size to limit power.
This year, we want to optimize the stock camshaft profile to increase power across the whole curve (or at least the low end).
The engine is running on stock factory cams but its air intake is much more restricted that stock so the current camshaft profile is not optimal. So this means we need to reduce duration/overlap on intake and exhaust camshafts. I am looking for help on how to find the new profile.
(I'm guessing it will be something like this but I need to calculate actual numbers).

How do I go about doing this? (Using spreadsheets)
Thank you


texts: How can I approach the application of control theory to real control systems?

texts:
I am an engineering student and I took my second dedicated controls class last semester. It was cool math and whatnot, but after all was said and done: I still have no idea how to make an actual working control system.

In other words, there was no tie-in to reality at all; it was all Laplace-domain mathematics that somehow affected our result.

What I want to know is: how do I go from real-space, to controls-space, and back to real-space? To help with understanding, I have prepared an example:

I have platform that is supported by a vertical rod. This rod can freely move up and down, or rather, it would be able to if it was not held in position by a motor (either a servo or a gear). The job of this motor is to keep the platform at the same height. E.g., if I place a mass on the platform, the motor must be able to adjust to it and respond accordingly such that after the response, the height of the platform is the same as before. (Of course, with a specified rise time, maximum overshoot, yada yada...).

This might sound trivial to you controls engineers out there, but I really don't know how to do this. I get that it is a closed loop system, but what I don't know is what all these laplace-space block diagrams correlate to in the real world. How do I get the block diagram for this system, and how do I build a controller inside of it?

The point of this example is to extend it to other problems, like airplane control, but I figure if I don't understand this I probably won't be able to do those other (cooler) things!


texts: How does free space path loss change with receiver's antenna's height

texts:
I have a question which seems like an easy one, but I couldn't find anything on Internet to be 100% sure.

The free space path loss equation is:

$$FSPL=20\text{log}(d)+20\text{log}(f)+20\text{log}(\frac{4\pi}{c})$$

Now, if the receiving antenna is at the same height as the transmitting antenna, $d$ is just the horizontal distance between the two. But if we now move the receiving antenna up and down (without increasing $d$), the straight line between the two antennas is this:

and the path loss equation becomes:

$$FSPL=20\text{log}\bigg(\sqrt{(h_{T_x}-h_{T_r})^2+d^2}\bigg)+20\text{log}
(f)+20\text{log}(\frac{4\pi}{c})$$

is this correct? Maths seems to agree, but I don't know if I am not missing somthing obvious here. Thanks.


texts: Check valve with precise cracking pressure

texts: I have two containers of air, one at 100 kPa and rising, the other at 30 kPa and decreasing. I need a valve that lets air through when the pressure difference is >70 kPa. Where would I find a valve like that? If nowhere, do you have any pointers on how to make one?


texts: From Single to Multiple Input (from SISO to MISO)

texts:
I have the following SISO (Single Input, Single Output) system:

$$
\begin{bmatrix}
\dot{x}_1 \\ \dot{x}_2
\end{bmatrix}
=
\begin{bmatrix}
0 & 1 \\ -1 & -1
\end{bmatrix}
\begin{bmatrix}
x_1 \\ x_2
\end{bmatrix}
+
\begin{bmatrix}
0 \\ 1
\end{bmatrix}
u
$$
$$
y = \begin{bmatrix}
1 & 0
\end{bmatrix} \begin{bmatrix} x_1 \\ x_2
\end{bmatrix}
$$
I know how to calculate the step response of that system (open loop and closed loop).

Now, I have the same system but another control variable:
$$
\begin{bmatrix}
\dot{x}_1 \\ \dot{x}_2
\end{bmatrix}
=
\begin{bmatrix}
0 & 1 \\ -1 & -1
\end{bmatrix}
\begin{bmatrix}
x_1 \\ x_2
\end{bmatrix}
+
\begin{bmatrix}
0 \\ 1
\end{bmatrix}
u
+
\begin{bmatrix}
-40 \\ 0
\end{bmatrix}
\omega
$$
$$
y = \begin{bmatrix}
1 & 0
\end{bmatrix} \begin{bmatrix} x_1 \\ x_2
\end{bmatrix}
$$
And I have to calculate the step response for open loop and closed loop (I suppose I have to use integral action, but maybe another technique is better). That's a MISO system and I don't know how to do it.

EDIT: I know that the system is linear so maybe I can calculate assuming that first B = [0 1] (transpose) and then B = [-40 0] (transpose) and then applying superposition or something like that


texts: X Axis Sign Convention for Axially-Loaded Rods

texts: (Simple Mechanics of Materials) Is there a sign convention for where x=0 is and x=L is on a simple horizontal axially-loaded rod? It seems that no matter where the fixed end is, the x=0 end is always on the left end of the rod, so is that a defined convention or can we choose either end to be where x=0?


texts: Calculating heath exchange for custom boiler

texts:
I am playing with the Idea that I should make a my own heath exchanger to generate warm water.

But as a hobbyist I would like to calculate the potential of my design and here is the question for me, how do I do this?

I need to calculate the heat transfer of a pipe passing trough liquid.

For example: I have a boiler containing 100liters of water, in this boiler there is a spiral with length of 10 meters with liquid of 50°C. How do you calculate the heath transfer from the liquid in the pipe to the water inside the boiler ?

Lets forget the fact that my boiler water is loosing heat to it's surrounding.

Additional info: the spiral pipe will be made out 1/2" (Ø21.3mm) x sched. 5 (1.65mm)

And the liquid speed is 1m³/h