Shear and bending moment diagrams are analytical tools used in conjunction with structural analysis to help perform structural design by determining the
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Shear and bending moment diagrams are analytical tools used in conjunction with structural analysis to help perform structural design by determining the
A Bode plot is a graph used in control system engineering to determine the stability of a control system. Combined with the Gain Margin and Phase Margin, a Bode plot maps the frequency response of ...
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Moment of inertia Newton's second law, Force = mass x acceleration, relates the acceleration that an object of a certain mass experiences when subject to a given force. There is an analogous relation between torque and angular acceleration, which introduces the concept of moment of inertia: Just as mass is a measure of how readily an object accelerates due to a given force, the moment of inertia of an object measures how easily an object rotates about a particular point of rotation. Thus, objects with a larger moment of inertia about a given point will be harder to rotate with a set torque. Correspondingly, a larger torque will cause a larger acceleration on a particular body. The moment of inertia of a body, which is always measured relative to a point of rotation, depends in general on the object's mass and on its shape. It is perhaps evident that for a single mass going in a circle of fixed radius, the greater the radius the harder it is to change the angular velocity. This is because the actual displacement, and hence linear velocity of the mass is proportional to the radius, so greater radius, for a given angular displacement means greater linear displacement. In an extended object the parts that are further from the axis of rotation contribute more to the moment of inertia than the parts closer to the axis. So as a general rule, for two objects with the same total mass, the object with more of the mass located further from the axis will have a greater moment of inertia. For example, the moment of inertia of a solid cylinder of mass M and radius R about a line passing through its center is MR2, whereas a hollow cylinder with the same mass and radius has a moment of inertia of MR2. Similarly when a spinning figure skater pulls her arms in to her body she places more of her body weight closer to the axis of rotation and decreases her moment of inertia. Moment of Inertia Formula The Moment of inertia is the property by the virtue of which the body resists angular acceleration. In simple words we can say it is the measure of the amount of moment given to the body to over come its own inertia. Its all about the body offering resistance to speed up or slow down its own motion. Moment of inertia is given by the formula Where R = Distance between the axis and rotation in m M = Mass of the object in Kg. Hence the Moment of Inertia is given in Kgm2.
Shear and bending moment diagrams are analytical tools used in conjunction with structural analysis to help perform structural design by determining the
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We know the meaning of Hysteresis loop or B-H curve. Let discuss in detail the Magnetic properties of the material or in other word we can say that let discuss basic parameters of Hysteresis loop. Please visit my previous blog to know more about; B-H curve or Hysteresis loop Below picture shows, B-H curve (Hysteresis loop) in detail. B-H curve Below are the magnetic properties of the material; Permeability When a magnetic field is applied to a soft magnetic material, the resulting flux density is composed of that of free space plus the contribution of the aligned domains. B = μ₀H + J or B = μ₀ (H + M) Where; μ₀ = 4πx10¯⁷H/m, J is the magnetic polarization M is the magnetization. Absolute permeability The ratio of flux density and applied field is called absolute permeability. μabsolute = B/H = μ₀ [1+(M/H)] It is usual to express this absolute permeability as the product of the magnetic constant of free space and the relative permeability (μᵣ). B/H = µ₀ µᵣ There are several versions of μᵣ depending on conditions the index ‘r’ is generally removed and replaced by the applicable symbol e.g. μᵢ, μₐ, μΔ etc. Relative permeability Relative permeability shows that how the presence of a particular material affects the relationship between flux density and magnetic field strength. The term 'relative' arises because this permeability is defined in relation to the permeability of a vacuum. Initial permeability Initial permeability describes the relative permeability of a material at low values of Magnetic Flux Density (below 0.1T). Low flux has the advantage that every ferrite can be measured at that density without risk of saturation. It is helpful for the comparison between different ferrites. μᵢ = [(1/µ₀) x (ΔB/ΔH)] (ΔH → 0) Initial permeability is dependent on temperature and frequency. Effective permeability If the air-gap is introduced in a closed magnetic circuit, magnetic polarization becomes more difficult. As a result, the flux density for a given magnetic field strength is lower. Effective permeability is dependent on the initial permeability of the soft magnetic material and the dimensions of air-gap and circuit. µₑ = µᵢ / {1+ [(G x µᵢ)/lₑ]} Where; G is the gap length and le is the effective length of magnetic circuit. This simple formula is a good approximation only for small air-gaps. For longer air-gaps some flux will cross the gap outside its normal area (stray flux) causing an increase of the effective permeability. Comparison of hysteresis loops for a ferrite core with and without an air gap Apparent permeability The definition of µₐᵨᵨ is particularly important for specification of the permeability for coils with tubular, cylindrical and threaded cores, since an unambiguous relationship between initial permeability µᵢ and effective permeability μₑ is not possible on account of the high leakage inductances. The design of the winding and the spatial correlation between coil and core has a considerable influence on µₐᵨᵨ. A precise specification of µₐᵨᵨ requires a precise specification of the measuring coil arrangement. µₐᵨᵨ= L / L₀ = Inductance with core/ Inductance without core Amplitude permeability It is the relationship between higher magnetic field strength and flux densities; it is the permeability at high induction level. At relatively low induction, it increases with H but as the magnetization reaches saturation, it decreases with H. Helpful to find high permeability level of a material. µₐ = (1/µ₀) x (^B/Ĥ) Since the BH loop is far from linear, values depend on the applied field peak strength. Incremental permeability The permeability observed when an alternating magnetic field is superimposed on a static bias field, is called the incremental permeability. μΔ = (1/µ₀)[ΔB/ΔH]Hᴅᴄ If the amplitude of the alternating field is negligibly small, the permeability is then called the reversible permeability (μᵣₑᵥ). Complex permeability To enable a better comparison of ferrite materials and their frequency characteristics at very low field strengths (in order to take into consideration the phase displacement between voltage and current), it is useful to introduce μ as a complex operator, i.e. a complex permeability ͞µ, according to the following relationship: ͞µ = μs' – j . μs" Where, in terms of a series equivalent circuit, (see figure 5) μs' is the relative real (inductance) component of ͞μ and μs" is the relative imaginary (loss) component of ͞μ. Using the complex permeability ͞μ, the (complex) impedance of the coil can be calculated: ͞Z = j ω ͞μ L₀ Where L₀ represents the inductance of a core of permeability μr = 1, but with unchanged flux distribution. Complex Permeability vs Frequency Figure at above shows the characteristic shape of the curves of μ' and μ" as functions of the frequency, using a NiZn material as an example. The real component μ' is constant at low frequencies, attains a maximum at higher frequencies and then drops in approximately inverse proportion to f. At the same time, μ" rises steeply from a very small value at low frequencies to attain a distinct maximum and, past this, also drops as the frequency is further increased. The region in which μ' decreases sharply and where the μ" maximum occurs is termed the cut-off frequency fcutoff. This is inversely proportional to the initial permeability of the material (Snoek’s law). Reversible Permeability In order to measure the reversible permeability μᵣₑᵥ, a small measuring alternating field is superimposed on a DC field. In this case μᵣₑᵥ is heavily dependent on Hᴅᴄ, the core geometry and the temperature. Power loss It should be considered for high frequency/excitation application. It is the addition of Hysteresis losses, Eddy current losses and Residual losses. It should be <1. PL = Physteresis + Peddy current + Presidual Saturation flux density It is how much magnetic flux the magnetic core can handle before becoming saturated and not able to hold any more. It should be high. Use minimum number of turns in winding. Remanence The magnetic flux density remaining in a material, especially a ferromagnetic material, after removal of the magnetizing field. It measures the strongest magnetic field ferrite can produce. There should be low retentive. So, ferrite should not magnetize easily without the application of magnetic field. Coercivity It is the magnetizing field strength required to bring the magnetic flux density of a magnetized material to zero. It should be low, so that it requires low magnetic field thus low opposite current to bring it back to the non-magnetic state. Hysteresis Material constant It is useful for estimating ferrite core losses. It is a constant that represents hysteresis loss when a magnetic material is operating in the Rayleigh region (low magnetic field region - behaviour of magnetic materials at low field). It should be less. Hysteresis Constant is given by: ηв = (Δ tanδm) / [μe × Δ(^B)] Disaccommodation Factor Disaccommodation occurs in ferrites and is the reduction of permeability with time after a core is demagnetized. This demagnetization can be caused by heating above the Curie point by applying an alternating current of diminishing amplitude or by mechanically shocking the core. The value of dis-accommodation per unit permeability is called disaccommodation factor. It is a gradual decrease in permeability. It should be low and should be <2. DF = (µ₁ -µ₂)/ [log₁₀ (t₂/t₁)] (1/µ₁²) (t₂>t₁) Where; µ₁ = resulting complete demagnetization, the magnetic permeability after the passing of t₁ seconds. µ₂ = resulting complete demagnetization, the magnetic permeability after the passing of t₂ seconds. Curie temperature The transition temperature above which a ferrite loses its ferromagnetic properties. It should be high. Resistivity High resistivity makes eddy current losses extremely low at high frequencies. Resistivity depends on temperature and measuring frequency. Ferrite has DC resistivity in the crystallites of the order of 10⁻³Ωm for a MnZn type ferrite, and approx. 30 Ωm for a NiZn ferrite. Relative loss factor With the frequency increase, core loss is generated by the changing magnetic flux field within a material. Core-loss factor, is defined as the ratio of core-loss resistance to reactance, and consists of three components; namely, hysteresis loss, eddy-current loss and residual loss. Addition of an air gap to a magnetic circuit changes the values of its loss factor and effective permeability. The amounts of change are nearly proportional to each other. It should be less. This factor is defined as the loss angle tangent divided by permeability, Relative loss factor = tanδ/μᵢ The loss angle tangent, tanδ, is decreased by an air gap in proportion to the ratio of permeability’s before and after air gap presence. tanδₑ = (tanδ/µᵢ) µₑ Where; tanδ and μᵢ : permeability and loss angle tangent without an air-gap μₑ. tanδₑ: permeability and loss angle tangent with an air-gap. Hence, the relative loss factor, tanδ/μᵢ does not depend on air gap size, when the air-gap is small. Quality Factor It is the reciprocal of loss angle tangent. Q = ωL/R˪ = 1/tanδ = reactance / resistance Temperature factor of permeability Temperature coefficient is defined as the change of initial permeability per °C over a prescribed temperature range. Temperature factor of permeability is defined as the value of temperature coefficient, per unit permeability. The measured value should be less. It is the ratio of “Temperature factor for initial magnetic permeability” to the “initial magnetic permeability“. αµ = αµ₁/µ₁ = [(µ₂-µ₁)/µ₁] [1/(T₂-T₁)] (T₂>T₁) αµγ = [(µ₂-µ₁)/µ₁²] [1/(T₂-T₁)] (T₂>T₁) where, µ₁ = initial magnetic permeability at temperature T₁ µ₂ = initial magnetic permeability at temperature T₂ Density It is calculated by; d = W / V (g/cm³) Where; W = Magnetic core weight V= Magnetic core volume Conclusion Magnetic properties of material help us to select perfect material according to application. Even in the case of failure of application we can analysis the material properties and cause of failure easily we can find. Also, it helps us to find maximum working limit of a material.
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Micrometer Screw gauge Micrometer Screw gauge. Introduction Micrometer screw gauge is a form of calipers used for measuring small dimensions. Screw gauge in extensively used in the engineering field for obtaining precision measurements. The article describes the principle and main parts of a basic micrometer screw gauge. Micrometer screw gauge (or micrometer caliper) is an instrument or device for measuring the length of an object which is more precise than a ruler and vernier caliper. It because a micrometer screw gauge has the smallest scale of 0.01 mm. The device is widely used in mechanical engineering for measuring small diameter, thickness, or angles to a high degree of accuracy. Screw gauge or micrometer screw gauge is a measuring instrument used for precision measurement. Micrometer Screw Gauge Frame of Micrometer screw gauge Anvil Spindle Measuring faces Main scale, Barrel or Sleeve Thimble, Micrometer Scale Ratchet stop Spindle lock nut Least count of Micrometer Thimble one round. 1 mm displacement micrometer Discount calculation Micromete screw gauge Micromete screw gauge Micromete screw gauge Micromete screw gauge Micromete screw gauge Objects measurement with Micrometer Measuring of object with micrometer screw gauge Measuring of object with micrometer screw gauge Measuring of object with micrometer screw gauge Measuring of object with micrometer screw gauge Measuring of object with micrometer screw gauge Measuring of object with micrometer screw gauge Measuring of object with micrometer screw gauge Measuring of object with micrometer screw gauge Measuring of object with micrometer screw gauge Measuring of object with micrometer screw gauge Measuring of object with micrometer screw gauge Measuring of object with micrometer screw gauge Measuring of object with micrometer screw gauge Measuring of object with micrometer screw gauge Measuring of object with micrometer screw gauge Measuring of object with micrometer screw gauge Measuring of object with micrometer screw gauge A screw gauge consists of a “U” shaped metallic structure, which is attached to a hollow cylindrical tube on one end. The hollow tube has a uniformly threaded nut inside it. A long stud with a plane face is fitted into this nut. Exactly on the opposite side of this nut and on the other end of the U shaped frame, a smaller stud with a plane face is also attached. Faces of both the studs are exactly parallel to each other. This U shaped metallic structure is known as the frame of the micrometer screw gauge. the smaller stud is known as the anvil and the longer one is known as the spindle. the anvil is the fixed part of the device, whereas the spindle moves as and when the head is moved. the frame carries both the anvil and barrel, and is also heavier than the rest of the parts. The object to be measured is held between the anvil and the spindle. The Barrel or sleeve is connects the frame to the cylindrical tube. It is a non-movable part of the screw gauge and has a scale inscribed over it which is the main scale of the device. Moreover, it also carries the most important part of the micrometer the screw. The screw is the heart of the micrometer and is located inside the barrel. The screw converts small dimensions into measurable distance using a scale. The thimble or head is the end of the cylindrical tube and is turned to move and adjust the spindle. The thimble carries the vernier or secondary scale. There is one more part called the ratchet which is provided at the end of the tube. The ratchet is kind of limiting device which applies a pressure by slipping at a predetermined torque and thus prevents the spindle from moving further. Some screw gauges also consist of locking devices which holds the scales at a particular position for prevent any kind of error while taking readings. A micrometer screw gauge also uses two scales –main and secondary scales. The secondary scale is provided on the thimble and is the measurement of the pitch of the screw. This means that the reading on the secondary scale measures the distance moved by the thimble per rotation. The scale on thimble is divided into 100 equal parts and measures hundredths of a millimeter. The thimble scale rotates over the spindle or the main scale. The main scale is a millimeter scale subdivided into equal parts with half a millimeter distance. When the object is to be measured, it is placed in between the anvil and the spindle. Readings from both the scales are taken into account for arriving at the final measurement. Micrometer screw gauge is a delicate device and thus special care should be taken while handling it. Moreover, it is also important that the micrometer is well calibrated to prevent any kind of error in the final reading. Precaution Steps The spindle and anvil are cleaned with a tissue or cloth, so that any dirt present will not be measured. Watch video to Learn reading of Micrometer screw gauge reading without the help of tutor. It is very easy to understand. Micrometer screw gauge:
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