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Noise and Vibration in Switched Reluctance Machines
Published in Berker Bilgin, James Weisheng Jiang, Ali Emadi, Switched Reluctance Motor Drives, 2019
James Weisheng Jiang, Jianbin Liang, Jianning Dong, Brock Howey, Alan Dorneles Callegaro
where Pr(q,circ,ax) is the amplitude of the harmonic content of the radial force density, which has been discussed in Section 13.6. Force density is in units of N/m2. Therefore, to calculate the force, Pr(q,circ,ax) is multiplied with the area of the surface where the radial force densities have been calculated (usually in the airgap). Hence, the term πDLs is the surface area where D is the inner diameter of the cylindrical shell (for an SRM, it is the inner diameter of the stator) and Ls is the axial length.
Fields in Magnetic Materials
Published in Ahmad Shahid Khan, Saurabh Kumar Mukerji, Electromagnetic Fields, 2020
Ahmad Shahid Khan, Saurabh Kumar Mukerji
The force exerted on individual charged particles ultimately gets transferred to the matter which is subjected to the influence of field(s). If a unit volume of such an affected matter is taken and the force is measured on the basis of per unit volume the resulting quantity is referred to as force density. It is measured in Newtons per cubic meter.
Vector Calculus
Published in Abul Hasan Siddiqi, Mohamed Al-Lawati, Messaoud Boulbrachene, Modern Engineering Mathematics, 2017
Abul Hasan Siddiqi, Mohamed Al-Lawati, Messaoud Boulbrachene
if p has a constant value p0 in the horizontal plane z = 0 (for example, the atmospheric pressure at the ocean surface). We see that the pressure increases linearly with depth −z (the vertical coordinate is directed upward). The total buoyant force on the object is given by the vertical component f3tot of the total force Ftot=f1toti+f2totj+f3totk exerted by the fluid on the object. (This is a single vector, not a vector field.) On the surface Σ, the fluid pressure acts as a force density (force per unit area) of magnitude p and direction −n. Since −pn.k is the vertical component of this force density, the total buoyant force is obtained as the surface integral () f3tot=∫∫Σ−pn.kdσ=∫∫Σ(ρgz−p0)n.kdσ.
Force-sampling methods for density distributions as instances of mapped averaging
Published in Molecular Physics, 2019
Apoorva Purohit, Andrew J. Schultz, David A. Kofke
The calculation approach is to sample the force density during the simulation, and then compute via spatial integration of it. This method significantly enhances the convergence of simulations compared to the conventional counting based method [12]. Additionally, the resolution used for recording the force density as a function of position has no effect on the statistical uncertainty of the calculated density, because only the integral of is required in Equation (1).