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What Are the Effects of the Different Design Parameters When Building a Linear Motor?

Good question.

You earn a PhD by the time you get a half good answer :-).More detail about what you are wanting to achieve wouldhelp muchly. Stroke, force, speed, ... . Appliaction?Too much to cover at present. This is just a quick canter and their should be others more expert here. As well as "learned papers" you can get a good idea by using eg Google image search using eg linear motor as search term, looking for manufacturers "strutting their stuff" re new models, advantages, capabilities etc and seeing what they say. But:Air gap is crucial.

Magnetic field varies with inverse cube of distance at a distance (really) due to interaction of two poles working in inverse square. (FWIW few people realise that this is why what happens happens). Magnet shape and thickness and proximity to other magnets affect the field. At distances up to 5 or 10 magnet thicknesses if you want to see what the field is at a point you are best to use one of the many free and far from free simulation programs. For practical purposes for DIY linear motors alternators etc you can use the rule of thumb that the magnet is about as effective as it's going to be out to about half its thickness. eg if you use a really top grade "rare earth" magnet (details later maybe) you can get around 1T at half it's thickness. So for "ironless" coils if you are using 10mm thick magnets then the majority of your coil wants top be no more than 5mm away from the pole faces so if you have a 1mm airgap then you can have 4mm thick coils.

Which is why people use laminations and why ironless construction has very flat coils. Once you add laminations in the windings you "extend the field" at the cost of more mass, eddy current losses, magnetic saturation, saliency (cogging) unless you are very good at mechanical design, and other secondary effects. About all the rest is standard theory at a first approximation. You can find papers on motor design, ampturns, conductor resistance (which affects heating and current you can provide to get the amp-turns that do the work. If you use laminations you are into the wonderful world of saturation, BH curves, losses, fringing effects, ... . But it's all available in the standard motor texts. As a simple simplistic starting position, to get maximum motor force you are trying to use the strongest magnets you cn get, smallest airgaps, flattest coils, and maximise amp turns. Amp turns are affected by the copper (usually) you can fit in the available space and the current you can apply and the heating that results.

â€¢ Related Questions

Fat Tailed risks: do they get fatter when we linearize non-linear systems?

Absolutely! There are many, such as for example:Ahlfeld R, Belkouchi B, Montomoli F, 2016, SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos, Journal of Computational Physics, Vol:320, ISSN:0021-9991, Pages:1-16Montomoli FF, Amirante DD, Hills NN, Shahpar SS, Massini MM. Uncertainty Quantification, Rare Events, and Mission Optimization: Stochastic Variations of Metal Temperature During a Transient. ASME. J. Eng. Gas Turbines Power. 2014;137(4):042101-042101-9. doi:10.1115/1.4028546Ahlfeld R, Montomoli F, Scalas E, Shahpar S, 2016, Uncertainty Quantification for Fat-Tailed Probability Distributions in Aircraft Engine Simulations, Journal of Propulsion and Power Montomoli, F and Massini, M, Gas turbines and uncertainty quantification: Impact of PDF tails on UQ predictions, the Black Swan, GT2013-94306, ASME Turbo Expo 2013Note that there's nothing inherently wrong in using polynomials to model Fat-Tailed risk - the problem is in the pdf of the predictors. Consider a lognormal distribution: strictly speaking this is not fat-tailed, since the tail goes to zero faster than a power, but just heavy-tailed (the tail goes to zero slower than an exponential). The log-normal distribution has an associated family of orthogonal polynomials, but as described in this answer, they are not dense in the space of mean-square integrable functions. This means that expanding the response of a complex system, whose input variables are log-normally distributed, in a series of polynomials which are orthogonal w.

r.

t. the log-normal measure, is not a good idea: the expansion may not converge or converge to a limit which is not actually the response function of the system. However, even with a fat-tailed distribution of the inputs (for example the Cauchy distribution), you can still define numerically a set of polynomials which are orthogonal to the input distribution, as long as you truncate the distribution to some limit. This is an approximation, of course, but it could make sense. Example: you want to model the possibility of a temperature spike at the inlet of a gas turbine nozzle. It might make sense to assume that rare events (very high temperature spikes) have a frequency which is much higher than expected, if the distribution of temperature spikes were Gaussian. Thus, you may want to use a lognormal, t-Student or Cauchy distribution (t-Student with 1 degree of freedom). On the other hand, you clearly don't need to model the risk posed by spikes of, say, \$10^4 K\$: even if, from a theoretical point of view, the untruncated Cauchy distribution would give a "high" (w.r.t. a Normal distribution) probability of such spikes, in practice there's no way at all that you would reach a temperature of \$10^4 K\$ inside a gas turbine, except pheraps if the gas turbine were hit by an atomic bomb :) Thus, you can safely truncate the Cauchy to a limit which is sufficienly higher than any physically plausible temperature, but lower than \$infty\$

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What propulsion system would not pollute the surface when landing on a pristine celestial body?

Wikipedia says that Ryugu (for example) has a mass \$M_ryu\$ of 4.510 kg and a radius \$R_ryu\$ of about 450 meters. With G 6.674 10 m kg s that makes the surface gravity about 1.

48 10 m s. You could use either big ion thrusters using a noble gases angled at /- 45 degrees to bring you within 200 meters of the surface without much ion sputtering. Unlike cold gas thrusters, the ion beams accelerated to say 100,000 eV would have a very narrow emission angle, roughly the square root of the ratio of the ion plasma thermal energy to the acceleration energy for a design optimized for the task. \$\$ theta approx sqrtfrack_B T_ionVe approx sqrtfrac1100,000 approx 0.

2 \$\$1 eV corresponding to about 10,000 K sounds pretty hot for an ion temperature, this is probably a conservative number. See for example JPL/Descanso Fundamentals of Electric Propulsion: Ion and Hall Thrusters Dan M. Goebel and Ira Katz If the ion beam spread out due to self-propulsion, you might start with a wide exit aperture and try to play tricks with attraction to a central electron beam which you need for spacecraft charge neutrality.

For an \$m\$600 kg satellite like Hyabusa 2 at this range, each thruster would need a thrust of\$\$T fracsqrt22 Gfracm M_ryu(R_ryu200)^2 approx 45 textmN \$\$which is only about half the thrust of one of DAWN's three main ion thrusters. Shutting off the thrusters the spacecraft would fall from it's 200 meter hovering altitude towards the surface. We can get the terminal velocity by conserving energy \$Delta T Delta U 0\$.

The kinetic energy gained at impact would be:\$\$Delta T_i -Delta U m M_ryu G left( frac1R_ryu - frac1R_ryu200 right) approx 12.3 textJoules,\$\$and so the velocity at impact is \$\$v_i sqrtfrac2 Tm approx 20 textcm/sec.\$\$As suggested by the OP in the question, you could soak that up with the landing gear. You could do that with some combintation of thing like:You could also add one or three thrusters (noble ion or not) on the backside of the spacecraft pushing you into Ryugu, in order to cancel any possible recoil if you latched your springs too soon or your legs didn't all touch at the same time or there was a more complex landing involving shifting rocks or gravel. You'd use three instead of one to cancel angular momentum resulting from the legs hitting at different times.This is why my favorite option is the linear motor/generator with dynamic braking in each leg. You can wait until you have something like three point contact before starting active deceleration. Servo control can be really smart and fast with modern electronics and inertial sensors

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Mobile robot speed synchronization for straight line moving

There are really two problems here:Suppose you get the "perfect" control scheme that sends exactly the correct signals to the motors. The problem then becomes: What if one wheel runs over a piece of paper and just spins for a little bit instead of generating traction? What if one wheel runs over some dust that sticks to the tire and now it's a little bigger than the other wheel?I'm assuming here that your wheel odometry is coming off of encoders on the motor, but the same arguments are true if you've got an idle wheel to do odometry measurements. Assuming some rotation of the motor \$theta\$, each wheel should traverse a distance of \$rtheta\$, where \$r\$ is the wheel radius. However, if one wheel is slightly larger than the other \$(repsilon)\$, then one wheel traverses \$rtheta\$ while the other traverses \$(repsilon)theta\$, or \$rtheta epsilon theta\$.Your vehicle will then turn (assuming a differentially steered or two-wheel robot) an angle of \$psi epsilon theta / d\$, where \$d\$ is the wheel base (distance between the two wheels. You can see now that the angle your vehicle turns, \$psi\$, is a linear function of how far your wheels turn, \$theta\$. I have posted an answer like this before - The only way you can be sure to drive in a straight line is to measure where the robot is relative to the straight line. This could be LIDAR, a localization routine (like SLAM), overhead webcam watching the robot, compass/magnetometer, etc. There will always be variations that prevent your vehicle from going exactly straight, so you need to be able measure how you're travelling and be able to adjust accordingly. With regards to your original question though, first I'll comment that you're looking to provide only a wheel speed, so if anything it's multi-input single-output. If you're looking for someone to comment specifically on the block diagrams you've provided, then you need to explain what they mean. Typically the symbols \$x\$, \$v\$, and \$a\$ are used for linear position, speed, acceleration, respectively, and \$theta\$, \$omega\$, \$alpha\$ are used for angular position, speed, and acceleration. You use \$v\$* and \$omega\$*, which looks like linear speed and angular speed, so I don't know what your inputs are, or what the star means, or why there aren't any integrator or derivative blocks (how are you getting between position and speed?), or why Structure 1 has G1 and G2 where Structure 2 has G1 and G1, etc.If you want to drive in a straight line without measuring the orientation of the vehicle, send the same speed signal to both motors. That's probably the best you can do

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