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linear variable differential transformers

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Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005453
EISBN: 978-1-62708-196-2
... every point ( x , y , z ). A set of values ( x , y , z , p , q ) describes a planar element associating the direction numbers p , q , −1 with a point ( x , y , z ). A linear second-order partial differential equation with two independent variables has the form: (Eq 57) L = A...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005413
EISBN: 978-1-62708-196-2
... into a steep, almost linear branch, called stage II. The slope in this stage is athermal: It depends on crystal orientation but not on temperature, except for the temperature dependence of the shear modulus. Stage III follows as the slope of the stress-strain curve decreases gradually, tending toward a...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005431
EISBN: 978-1-62708-196-2
... on the mathematical principles of solving differential equations. It also reviews linear structural problems to illustrate the concept of the FEMs. partial differential equation meshed-solution method finite-element method finite-difference method boundary-element method ENGINEERING...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005451
EISBN: 978-1-62708-196-2
... transforms. laplace transformations THE METHODS OF LAPLACE AND FOURIER TRANSFORMATION and the Heaviside operational calculus are essentially aspects of the same method. This method simplifies solutions of such problems as ordinary differential equations with constant coefficients, linear...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006767
EISBN: 978-1-62708-295-2
... procedure to deal with stress by determining maximum values through stress transformation is described. The article provides the stress analysis equations of typical component geometries and discusses some of the implications of the stress analysis relative to failure in components. It focuses on linear...
Series: ASM Handbook
Volume: 17
Publisher: ASM International
Published: 01 August 2018
DOI: 10.31399/asm.hb.v17.a0006450
EISBN: 978-1-62708-190-0
... this linear change of impedance or reactance with frequency, note the nonlinear change of impedance when the coil has a part within it. First, assume that the part being inspected is a thin-wall tube and that its reference number ω L 0 G is 0.316 at radian frequency ω 1 . This...
Series: ASM Handbook
Volume: 4E
Publisher: ASM International
Published: 01 June 2016
DOI: 10.31399/asm.hb.v04e.a0006277
EISBN: 978-1-62708-169-6
... crystals without contact. Such orientation degeneracy must be differentiated from the so-called transformation pathway degeneracy during a structural phase transformation following a given LC between two phases before and after the transformation. A typical example is the three crystallographically...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005435
EISBN: 978-1-62708-196-2
... a linear-viscous dynamic response, in the three-dimensional dynamic simulation of a cubic-tetragonal martensitic transformation with internal shuffles (improper ferroelastic), giving the sequence of structures depicted in Fig. 9 . Starting from a supercritical embryo of arbitrary shape, the...
Series: ASM Handbook
Volume: 4B
Publisher: ASM International
Published: 30 September 2014
DOI: 10.31399/asm.hb.v04b.a0005936
EISBN: 978-1-62708-166-5
... article also describes the generation of thermal, transformation, and hardening residual stresses. bearing steel case hardening distortion elastic plastic deformation heat treatment linear elastic deformation phase transformation quenching residual stress retained austenite steel...
Series: ASM Handbook
Volume: 4B
Publisher: ASM International
Published: 30 September 2014
DOI: 10.31399/asm.hb.v04b.a0005967
EISBN: 978-1-62708-166-5
... requiring strict dimensional control, such as bearings and gears ( Ref 24 ). Table 7 provides crystallographic data and linear thermal expansion coefficients to calculate the unit-cell volume of each phase present in Japanese grade S45C (JIS G4051) carbon steel. The linear thermal expansion coefficient...
Book Chapter

Series: ASM Desk Editions
Publisher: ASM International
Published: 01 December 1998
DOI: 10.31399/asm.hb.mhde2.a0003238
EISBN: 978-1-62708-199-3
... which it passes. This behavior is expressed as I = I 0   exp   ( − μ t ) where I is the intensity of the emergent radiation, I 0 is the initial intensity, t is the thickness of homogeneous material, and μ is a characteristic of the material known as the linear-absorption...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005426
EISBN: 978-1-62708-196-2
..., and temperature) is transformed into an algebra problem of solving a large system of simultaneous linear equations for discrete unknowns that represent the state of a thermal-fluids system; the latter is amenable to numerical solution on a digital computer. This is a somewhat abstract description of...
Series: ASM Handbook
Volume: 4B
Publisher: ASM International
Published: 30 September 2014
DOI: 10.31399/asm.hb.v04b.a0005968
EISBN: 978-1-62708-166-5
... experimental methods are developed for dealing with multiple-factor variability is known as the design of experiments (which should not be confused with simple linear regression interpolation from empirical data). The key goals in a design-of-experiment (DOE) exercise in heat treating are generally twofold...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005189
EISBN: 978-1-62708-187-0
... solutions of nickel in iron. Fig. 1 Activities of iron and nickel in their binary solutions at 1873 K. Source: Ref 1 , 3 A common characteristic of the activity of a component in solution is the relatively linear portion of the curve as X i → 0. This limiting slope, designated γ i...
Series: ASM Handbook
Volume: 17
Publisher: ASM International
Published: 01 August 2018
DOI: 10.31399/asm.hb.v17.a0006473
EISBN: 978-1-62708-190-0
... search unit is essentially proportional to the area of the bottom of the hole. Therefore, these blocks can be used to check the linearity of a pulse-echo inspection system and to relate signal amplitude to the area (or, in other words, the size) of the flaw. Note that because an FBH is an ideal reflector...
Series: ASM Desk Editions
Publisher: ASM International
Published: 01 November 1995
DOI: 10.31399/asm.hb.emde.a0003052
EISBN: 978-1-62708-200-6
... a description of the comminution process (wet and dry milling methods), it discusses batching and mixing operations and granulation methods. The article also deals with the effect of process variables and the steps involved in chemical synthesis, including preparation from solution and gas-phase...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005428
EISBN: 978-1-62708-196-2
... boundary motion gives some grains an advantage, and they grow to consume the others. Once all the stored energy is consumed, the system reverts to normal grain-growth behavior. The ratio of the stored energy and the interfacial energy is a crucial variable in the system. Differential boundary energies and...
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0009003
EISBN: 978-1-62708-185-6
... ″ where n is the strain-hardening exponent, and K is the strength coefficient. A log-log plot of true stress and true strain up to maximum load results in a straight line if Eq 22 is satisfied by the data ( Fig. 7 ). The linear slope of this line is n , and K is the true stress at ε = 1.0...
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0004017
EISBN: 978-1-62708-185-6
... will result in a straight line if Eq 17 is satisfied by the data ( Fig. 6 ). The linear slope of this line is n , and K is the true stress at ε=1.0 (corresponds to q =0.63). As shown in Fig. 7 , the strain-hardening exponent may have values from n =0 (perfectly plastic solid) to n =1 (elastic...
Series: ASM Desk Editions
Publisher: ASM International
Published: 01 November 1995
DOI: 10.31399/asm.hb.emde.a0003023
EISBN: 978-1-62708-200-6
... semicrystalline polymers; complete liquidlike flow above T g for linear, amorphous polymers; or rubberlike behavior for cross-linked systems). This region of behavior above the transition is called the rubbery plateau, in reference to the high degree of molecular motion possible at these temperatures. Fig...