designv11-1.json

[
    {
        "image_filename": "designv11_1_0003991_jor.1100170218-Figure1-1.png",
        "original_path": "designv11-1/openalex_figure/designv11_1_0003991_jor.1100170218-Figure1-1.png",
        "caption": "FIG. 1. Description or remoral geometry. H is the center of thc fcmoral hcad, 0 is thc ccntcr of the femoral neck. P is the attachment of the posterior cruciate ligament, and L and M are the posterior aspects of the lateral and medial condylcs, respectively. Antcvcrsion (a) is the angle between the plane of the neck axis (NA) and the plane of the condylar axis (CA). Hip rotation occurs about the axis (RA), which is derined by the point H and the midpoint of a line joining thc mcdial and latcral condylcs. Ucrotation occurs about an axis parallel to the femoral shaft axis (FA) but located at the centroid o f the intertrochanteric. subtrochantrric, or supracondylar cutting planes. (Adapted with pcrniission from Murphy SB, Simon SR, Kijewski PK. Wilkinson RH, Griscom NT: Femoral anteversion. J Bone Joint Surg [Am] 69:1171, 1987.)",
        "texts": [
            " dylar levels, and these procedures alter the femoral geometry and muscle lines of action in different ways. In addition, the anteversion angle of the femur, the rotational position of the hip, and the amount of femoral derotation all potentially influence muscle lengths, and their effects are not entirely independent. The length change of a muscle with derotation depends on the distance between the muscle line of action and the axis of derotation; thc muscle line of action, in turn, depends on the anteversion angle of the femur and the rotational position of the hip (Fig. 1). These length changes are difficult to assess on the basis of radiographic measurements because the planar projections do not accurately characterize the three-dimensional musculoskeletal geometry. The purpose of our study was to determine how surgical correction of anteversion deformities affects muscle lengths. We have developed a three-dimensional computer simulation of derotational osteotomies to examine how femoral anteversion, hip internal rotation, and external rotation of the distal limb segment affect the lengths of the muscles about the hip",
            " Our undeformed model has an anteversion anglc of 20\". We altered thc antcvcrsion anglc of thc modcl to represent a range of deformities by rotating the bonc vcrticcs that comprisc thc femoral head and ncck about thc femoral shaft axis. We assumed that the deformity takes place entircly within thc fcnioral ncck and not along thc fcmoral shaft. Dcrotational ostcotomies at the intertrochantcric. subtrochantcric, and supracondylar levels were simulatcd by cutting the femur perpendicular to the remora1 shaft axis (Fig. 1). The distal segment was externally rotated about an axis oricnted parallel to the femoral shalt axis and located at the centroid of the bone at the cutting plane. J Orthup Rcs, Vul. 17, No. 2, 1999 281 UEROTATIONA L OSTEOTOMIES OF T H E F E M U R TABLE 1. Skeletul dimensions for the two specimens und the model Skeletal dimcnsion Spccimen 1 Spccimen 2 Modcl Maximum anterior-posterior dimension of lateral condyle (mm) 66 59 58 Maximum medial-latcral dimension of distal femur (mm) 80 78 80 Superior-inferior dimension from greater trochantcr to lateral epicondyle (mm) 374 343 379 Anteversion angle\" (\") 10 5 0-60 \" A tabletop measurcment of femoral anteversion (1 1) was taken for each specimen"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_1_0003996_s0142-1123(98)00040-1-Figure2-1.png",
        "original_path": "designv11-1/openalex_figure/designv11_1_0003996_s0142-1123(98)00040-1-Figure2-1.png",
        "caption": "Figure 2 Different casses of load distribution along the tooth width",
        "texts": [
            " Also, the deformation of the housing should be considered, since this indirectly influences the gear shaft and bearing deformations. Asymmetry of contact loads on gear teeth can be avoided with proper crowning of gear teeth flanks during the gear production process. However, since crowning is often omitted in general production of gears, the load distribution along the tooth width is in practice usually non-uniform. In this paper only gear teeth without crowning are analysed. A non-uniform load distribution along the tooth width is the consequence of such influential parameters (Figure 2), which directly influences the stress distri- bution and the initiation and propagation of a crack in the tooth root. The non-uniform load distribution is reflected in the shape of the contact area, which could be elliptical, triangular, etc., and which can be located in the middle or at the edge of the gear tooth. In the process of experimental testing of gears with fatigue crack in the tooth root, the results are recorded as pairs of data (a, N), where a is the crack length and N is the number of loading cycles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_1_0003985_027836499901800504-Figure8-1.png",
        "original_path": "designv11-1/openalex_figure/designv11_1_0003985_027836499901800504-Figure8-1.png",
        "caption": "Fig. 8. Two modes of motion under contact friction: (a) rolling, in which the contact force F points to the interior of the contact friction cone; and (b) sliding, in which F points along one of the edges of the cone.",
        "texts": [
            "2. However, such ambiguities can often be resolved by detecting a third contact u2 on the finger at time t2 > t1 and verifying against u2 the finger contacts at t1 resulting from all ambiguous s0 values. This section extends the results in the previous sections to include contact friction between the finger and the object. Now we need to consider two modes of contact: rolling and sliding, according to whether the contact force lies inside the contactfriction cone or on one of its two edges (see Figure 8). Each mode is hypothesized and solved; then the obtained contact force is verified with the contact-friction cone for consistency. This hypothesis-and-test approach is quite common in solving multi-rigid-body contact problem with Coulomb friction. (See, for instance, the work of Haug, Wu, and Yang 1986.) at MICHIGAN STATE UNIV LIBRARIES on March 26, 2015ijr.sagepub.comDownloaded from When rolling contact occurs, the contact force F may lie anywhere inside the contact-friction cone. Let \u00b5c be the coefficient of contact friction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_1_0003977_s0301-679x(99)00035-3-Figure1-1.png",
        "original_path": "designv11-1/openalex_figure/designv11_1_0003977_s0301-679x(99)00035-3-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of journal bearing with rough surfaces.",
        "texts": [
            " The effect of surface roughness patterns on bearings with different b/d ratios has also been studied [1,3]. However, the influence of surface roughness parameter C, which is a ratio of half total range of random film thickness variable to the radial clearance, on the performance of hydrodynamic journal bearings is seldom reported in the literature. The purpose of this study is to see the influence of the roughness parameter on bearing characteristics. The governing equation in the rotating coordinate frame of reference (see Fig. 1) for pressure distribution using linear analysis can be written in non-dimensional form as [4]: * Corresponding author. 0301-679X/99/$ - see front matter  1999 Elsevier Science Ltd. All rights reserved. PII: S0301- 67 9X( 99 )0 0035-3 \u2202 \u2202qSh\u03043 \u2202p\u0304 \u2202qD1Sd bD2 \u2202 \u2202z\u0304Sh\u03043 \u2202p\u0304 \u2202z\u0304D56(122f\u0307l) \u2202h\u0304 \u2202q 112l \u2202h\u0304 \u2202T (1) The dimensionless nominal film thickness is: h\u0304511e cos q (2) For small roughness slopes the Reynolds type equation where roughness is modelled as done by Christensen and Tonder [1] can be written as [3]: \u2202 \u2202qSy1 \u2202p\u0304 \u2202qD1Sd bD2 \u2202 \u2202z\u0304Sy2 \u2202p\u0304 \u2202z\u0304D56(122f\u0307l) \u2202y3 \u2202q (3) 112l \u2202y4 \u2202T In the one-dimensional longitudinal roughness type, where roughness is assumed to have the form of long narrow ridges and valleys in the direction of sliding, y1=E(H3), y2=1/E(H3), y3=E(H), y4=E(H) and H=h\u0304(q, z\u0304)+h\u0304s(z\u0304, x)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_1_0003985_027836499901800504-Figure6-1.png",
        "original_path": "designv11-1/openalex_figure/designv11_1_0003985_027836499901800504-Figure6-1.png",
        "caption": "Fig. 6. A circular finger pushing a polygonal object.",
        "texts": [
            " The interior of one edge e of B maintains contact with F throughout the pushing.10 We assume that e is known, since local observability is concerned, and since a sensing strategy can hypothesize all edges of B as the contact edge and verify them one by one. Let h be the distance from the centroid O of B to e. Choose s as the signed distance from the contact to the intersection of e, and its perpendicular through O such that s increases monotonically while moving counterclockwise (with respect to B\u2019s interior) on e. See Figure 6. The orientation of B is \u03b8 = u/r \u2212 \u03c0/2.11 The tangent and normal of F at the contact are T = \u03b1\u2032 = (\u2212 sin u r , cos u r )T and N = r\u03b1\u2032\u2032 = \u2212(cos u r , sin u r )T , respectively. The system is governed by the following nonlinear equations as special cases of eqs. (7)\u2013(10), respectively:12 u\u0307 = \u03c9r, s\u0307 = T \u00b7 (v \u2212 vF) \u2212 \u03c9(r + h), \u03c9\u0307 = s s2 + \u03c12 ( \u03c92(r + h) \u2212 2\u03c9T \u00b7 (v \u2212 vF) \u2212 T \u00d7 aF ) \u2212 \u00b5g A(s2 + \u03c12) T \u00d7 0, (24) 10. This is easily realizable in a real pushing scenario. 11. Given a different contact edge e1, it follows \u03b8 = u/r \u2212 \u03c0/2 + \u03b8e1 for some constant \u03b8e1 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_1_0003996_s0142-1123(98)00040-1-Figure4-1.png",
        "original_path": "designv11-1/openalex_figure/designv11_1_0003996_s0142-1123(98)00040-1-Figure4-1.png",
        "caption": "Figure 4 Holding device (1, gear; 2, shoe; 3, roller; 4, positioner)",
        "texts": [
            " The loading spectrum (Table 2) of a gear, which defines the loading cycle of a gear during 1000 km of covered transporting distance, was determined with measurements on the truck with 11 tons total weight5. From Table 2, the number of loading cycles N in Equations (1\u20136) can then be substituted with the number of loading spectrum. Experimental tests of fatigue crack propagation were conducted on a universal INSTRON 1255 testing machine, which is controlled by a PDP 11/04 computer. A special holding device (Figure 4) was constructed, which allowed for the exact positioning of the acting force in the outer point of single engagement (point B in Figure 5) and at the same time allowed for setting the desired contact area along the tooth width4,5. The experimental measurements were conducted for two load cases, as shown in Figure 5. In load case 1, the loading force was uniformly distributed along the tooth width, while in load case 2 the force was concentrated on one half of the tooth width, which is often load case encountered in practice where teeth crowning is omitted",
            " When measurable crack is initiated in a gear tooth root, it usually appears through whole case-hardened layer, of which depth is generally not equal along the tooth width and also differs for each gear specimen. Therefore, different initial crack lengths have been recorded during the crack initiation period (see Figure 7). After the formation of the initial crack, the loading was reduced and thereafter followed the loading spectrum as defined in Table 2. In gears the loading normally drops to zero between loadings. However, in experiments presented here there was always a minimal load present due to the testing device configuration (Figure 4). The gear tooth loading was hydraulically driven and the reversal of the pressure in the hydraulic cylinder, needed to fully unload the tooth and then to reload it, would induce unacceptable dynamic loadings and the results from such tests would not be correct. Nevertheless, the lover load Pmin was relatively small (Pmin = 0.1 \u00d7 Pmax) and it has been assumed, that its influence on the experimental results is small and can be neglected. The crack length was measured with a magnifying glass (10 \u00d7 magnification) only on the front face of each loaded gear tooth for both load cases"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_1_0003995_41.807999-Figure3-1.png",
        "original_path": "designv11-1/openalex_figure/designv11_1_0003995_41.807999-Figure3-1.png",
        "caption": "Fig. 3. Two-link BMR model in simulations.",
        "texts": [
            " It is required to get a controller for the real robot in fewer iterations, because computer simulations can easily repeat the trials until the solution is found, but, using the real robot, the robot durableness and the time cost are limited. In such a case, this algorithm shows the utility of finding the feasible solutions that satisfy an order in fewer iterations, instead of finding the best solutions. The BMR is a mobile robot, which dynamically moves from branch to branch like a gibbon (Fig. 1), that is, a long-armed ape, swinging its body like a pendulum [12]\u2013[17]. Fig. 3 shows the two-link BMR model used for a computer simulation in this paper. The robot has no body and two symmetrical arms, the joints of which are driven by a rotational actuator. There are two grips at the ends of the links to catch bars. The arm holding a bar is called a first link, and the other arm is called a second link. The angle between a vertical line and the first link is defined as , and the angle between the second link and an extension line of the first link is defined as . In this simulation model, the mass of the robot is simplified into two components; the actuator has rotational inertia and adhesive friction whose coefficient is , while the grips are also assumed to have adhesive frictions whose coefficients are "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_1_0003946_60.815091-Figure3-1.png",
        "original_path": "designv11-1/openalex_figure/designv11_1_0003946_60.815091-Figure3-1.png",
        "caption": "Fig. 3: Magnetic Circuit, Layout and Axis Labelings",
        "texts": [],
        "surrounding_texts": [
            "IEEE Transactions on Energy Conversion, Vol. 14, No. 4, December 1999 1465\nA TIME-STEPPING COUPLED FINITE ELEMENT-STATE SPACE MODEL FOR INDUCTION MOTOR DRIVES - PART 1 : MODEL FORMULATION AND\nMACHINE PARAMETER COMPUTATION\nN. A. Demerdash, Fellow J. 1;. Bangura, Student Member A. A. Arkadan, Senior Member Department of Electrical and Computer Engineering\nMarquette University, Milwaukee, Wisconsin 53201-1881, U.S.A.\nKeywords: Time-stepping, Finite Elements, State-Space Model, abc Frame of Reference, Adjustable Speed Drives, Induction Machines. Abstract: A Time-stepping coupled Finite Element-State-Space model for induction motor drives is developed. The model utilizes an iterative approach lo include the effects of magnetic nonlinearities, and space harmonics due to the machine magnetic circuits' topology and discrete winding layouts. Model formulation and development, which include an improvement in the layout of the cage circuit representation, are given in this paper. This improvement leads to an enhancement of the \"wellposedness\", that is, reduction ofill-conditioning in the overall numerical convergence of the model. Meanwhile, in a companion paper results or induction motor performance simulation are compared with no-load and load tcsts for sinusoidal and inverter operating conditions. Particular attention is given to comparison between sinusoidal and inverter operating losses obtained from this generalized model.\nI. INTRODUCTION A reliable and rigorous simulation model for predicting the performance and operating characteristics of induction motor drivcs is presented. Thc uniqueness of this model lies in the fact that it is based on much fewer idealizing assumptions than conventional induction motor modeling techniques [1-3]. The simulation model takes into account the full impact of inherent nonlinearities and space harmonics due to the machine magnetic circuit configuration, discrete winding layouts and nonlinear magnetic circuit material properties. Moreover, the model is capable of incorporating different configurations of rotor and stator fault conditions. At the heart of this model is thc implementation of magnetic fieldlfinite element based motor winding parameter calculation techniques. It is well recognized that the Finite-Element (FE) method offers considerable advantages. This is the case because it allows the modeling of intricate magnetic circuit topology, discrete windings layouts, as well as nonlinear magnetic material properties. Therefore, it has the capability to model magnetic saturation to a high degree of accuracy for any given set of winding excitation conditions [4- 91. Accordingly, a Time (Rotor Position)-Stepping Finite Elemcnt (TSFE) based machine parameters (inductances) computational algorithm, which utilizes the well-established energylcurrent ( S E ) perturbation method of inductance calculations [7,8], constitutes one key part of the complete simulation model. One of the characteristics of Time-Stepping Finite Element models [4-91 is the relatively considerable amount of computing time and memory requirements.\nPE-1376.EC-0.04-1998 A paper recommended and approved by the IEEE Electric Machinery Committee of the IEEE Power Engineering Society for publication in the IEEE Transactions on Energy Conversion. Manuscript submitted Janualy 22, 1998; made available for printing April 24, 1998.\nThis is because for each time-step in the ac cycle thcre IS a corresponding rotor position for which a complete nonlinear magnetic field FE solution is performed. This is particularly the case with regard to time and memory requirements in the simulation of the induction motor and any associated controller under load conditions, where the rotor (cage) bar currents are nonsinusoidal waveforms with many frequency components ranging from the fundamental slip-frequency component to its highest significant harmonic [9]. However, the pace of progress in computational hardware technology with respect to its CPU speeds, indicates that computational time is increasingly becoming a mute point, and even more so in the not too distant future. This modeling approach is necessary if motor load losses caused by space harmonics in the flux density distribution become a significant factor in the overall motor drive efficiency. These space harmonics are a result of the machine's magnetic circuit topology and discrete winding layouts. Also, these space harmonics can be due to the time harmonic components in the stator phase and rotor (cage) bar currents of the motor resulting from the synergistic interaction between the motor and its power conditionerlsupply. Furthermore, when field based calculation techniques are utilized, it is much more straight-fonvard and easier to use the actual (natural) machine winding flux linkages, currents and voltages. Accordingly, a second portion of the comprchensivc model is a State-Space (SS) algorithm for time-domain simulation of the steady-state performance. This model is based on the circuit relationships between the motor windings' flux linkages and terminal voltages. Contrary to the present model, previously developed modeling techniques based on the conventional d-q transformation [1,2] inherently neglect all space harmonics higher than the fundamental in the winding mmfs, flux linkages, and airgap flux density waveforms. Thus, these d-q transformation based models leave much to be desired with regard to space harmonic representation and thc synergism between time and space harmonics. This is particularly the case if torque pulsations (noise) and core losses arc the subjects of analysis and quantification. That is, a natural abc flux linkage frame of reference is used throughout. The key parameters in this SS model are the nonsinusoidal periodic winding inductance profiles, which are obtained from the TSFE model [4-91. These winding inductances, that is, all the apparent self and mutual inductances, depend on the rotor position as well as the stator and rotor winding cuments at a given instant in the operating ac cycle. These two models, the TSFE model and the SS model, are coupled together to form the so-called Time-Stepping Coupled Finite Element-State Space (TSCFE-SS) algorithm depicted helow in the flow chart ofFig. (I).\n0885-8969/99/$10.00 0 1998 IEEE",
            "1466\nUpdate Ciirrent Initial Waveforms to Mast Estimates of\nRecent Values\nFlux Linkage-Based Slate. Space (SS) Model-Flux Linkagcs and Ciinent (TSFE) Algorithm- wCaiwlationr Induolance Caloulations Time (Rotor Position) Stepping Finite Element\nlNo+ye%jT Cslcalatians, etc.\nFig. 1 : Fiow Chart Representation of the TSCFE-SS Model\nIn order to start the TSCFE-SS simulations the initial conditions must be appropriately estimated in order to enhance the on-set of numerical convergence of the machine winding cui-rents. A good estimate of these initial conditions is a major contributor to obtaining quicker and correct convergence, particularly in the case of the inverter model simulations under no-load and load conditions. These initial conditions, which are primarily the set of initial estimates of all the machine winding currents of the stator and r o t o r circuits, are best determined fiom knowledge of the spatial distribution of the current, mainly the rotor bar currents as detailed in [9]. These initial estimates of the winding currents are used to excite the finite element grid, shown in Fig. (Z), for the rotor position (time) samplings in the first round of the TSCFE-SS iteration. The iterative process follows in a time (rotor position)-stepping fashion covering a complete ac cycle. The output of the TSFE model is mainly the set o f all winding inductance profiles versus rotor position. These profiles are used in the SS model to numerically compute thc nonsinusoidal periodic current profiles of all the machine armature phases, and rotor (cage) bars and connectors, respectively. The resulting winding currents are then used to update the excitation currents in the next FE computation of the inductance profiles, and the iterative process, in Fig. (I) , is repeated until the chosen convergence criterion is achieved. Once convergence is achieved, the laminated iron core and ohmic losses, instantaneous and average developed torque, as well as power, and other performance characteristics are readily computed. Naturally, these include average values of developed torque and power.\n11. MODEL DEVELOPMENT In three-phase induction motors, the three-phase stator armature shown in Fig. (3), can be represented by three electrical windings which are magnetically coupled to each other, and to the rotor circuits. Contrary to the stator armature, the rotor (cage) has no distinct windings, and thus no representation is universally agreed upon. Unlike the \u201cconcentric nested\u201d loop \u201cd-q representation\u201d (not to be confused with the d-q transformation) modeling approach used in [4], here the cage is represented by a set of \u201cadjacent\u201d loops [9]. The coupling bctween the loops is both magnetic and conductive. The magnetic coupling between these loops is obvious. Meanwhile,\nthe conductive coupling exists because each of these loops is formed by two adjacent bars electrically connected through the end-ring segments connecting them on both ends of the rotor cage. Also, each loop shares a bar with adjacent loops on both sides, see Fig. (4). The approach given in this paper and its companion [IO] has significant modeling advantages over the previous \u201cd-q representation\u201d detailed in [4], in that it is quite general, allowing for any asymmetrical and symmetrical configurations of breakages in the rotor cage, see [9] for details. It also enhances both the numerical \u201cwell-posedness\u201d of the formulation, and the corresponding numerical convergence characteristics of the overall model [9]. The squirrel-cage rotor of the 1.2hp case-study motor has 34 bars, connected at both ends through end-ring connectors. Thus, the complete rotor cage can be represented by 34 rotor circuits. The respective currents flowing in these circuits, shown in Fig. (4), are labeled z r l though ir3., . These 34 rotor circuit currents are used to compute the rotor cage individual bar currents which, for a symmetrical rotor, should be of equal magnitude with regular phase angle shift progression around the circumference of the rotor cage, as will he verified later in the results given in the companion paper [IO].",
            "1467\nmachine flux linkages and currents. Again, it should be pointed out that, because of the assumed constant speed of the motor, every time sampling instant is associated with a specific rotor angular position in the steady-state ac cycle. Each converged SS solution is then followed by a TSFE set of solutions to obtain the inductance profiles over a steady-state ac cycle. This iterative process is repeated as shown schematically in Fig. (1) till the chosen convergence criterion described in section (IV) of this paper is achieved. The inductance profiles are computed by utilizing an energylcurrent perturbation-finite element field solution technique detailed earlier in many references such as [7,8]. For the sake of completeness, the expressions used in the computation of these apparent inductances are given below:\nAccordingly, the 34 rotor circuits plus the 3 stator armature circuits constitute a total of 37 circuits by which the case-study induction motor can be represented in the SS portion of the model. Therefore, the case-study motor has 37 state variables (degrees of freedom). These 37 degrees of freedom eliminate the conventionally accepted simplifying assumptions of sinusoidally distributed mmfs, current sheets and other similar concepts associated with d-q frame based models, and d-q transformations (not lo be confused with \"d-q representation of 141'') [1,2]. These assumptions of sinusoidal flux and mmf distributions, on the basis of which d-q transformation models are formulated, obscure the true nature of the spatial distribution of the flux density and mmf waveforms, and consequently distort the time harmonics in the bar and stator winding currents. This is because of the inherent neglect in d-q transformations of the space harmonics higher than second order affecting all the motor inductances. In other words, d-q transformation based models [1,2] hinder the natural inherent and synergistic coupling between space and time effects in machine winding flux linkages, inductances, currents, and associated performance calculations such as developed torque, ohmic and core losses, etc.\n111. THE TIMEROTOR POSITION-STEPPING FINITE ELEMENT MODEL The time (rotor position)-stepping Finite Element based portion of the model is used to compute all of the machine parameters of interest. These parameters include, but are not limited to, the winding inductance profiles versus rotor position (in space and time), midgap radial flux density profiles and profiles of elemental flux densities (radial and tangential components) which are used in core loss computations [9,10]. The crucial machine parameters linking the TSFE algorithm to the SS model are the machine winding inductance profiles. The inductance profiles are directly utilized in the SS model to compute the steady-state periodic nonsinusoidal current waveforms of all the 37 circuits. The computation of the inductance profiles requires a Finite Element grid of the machine cross section, as shown in Fig. (Z), in which forward rotor position stepping (counter clockwise) is performed over an entire ac cycle. This grid is excited by the updated instantaneous winding current profiles (waveforms) in a time-stepping sampling fashion covering the complete ac cycle. That is, each set of current samplings in these profiles corresponds to a specific rotor position. These updated instantaneous profiles are the most recent current profiles obtained from a complete round of a converged SS solution. The updating of the current profiles occurs once one achieves a converged SS solution of the motor's time-domain steady-state flux linkages and currents. That is, the updating takes place upon obtaining the steady-state forced response of the set of differential equations governing the\n2 (1) L!pp = [ W ( i . - A i ) - 2 W ( i .)+ W ( i , + A i , ) ] / ( A i j ) ,\nU I i I I 1\nL y f p = [ W O . + A i . i + A i , ) - W ( i j - A i i , ' , + A i , ) I I ' k\nHere,j=1,2,3,~~~,37andk=l,2,3,~~~,37. Also-tAij andiAik\nare the current perturbations around the quiescent solution point obtained for the j-th and k-th winding currents at the given instant of time (rotor position) under consideration. Also, the W's are the energies computed from the perturbed field solutions. These inductances, under steady-state conditions, are periodic nonsinusoidal functions of time, t, (that is rotor angular position, B = Bo + or t , where eo is the initial rotor position [5,9] and or is the constant rotor angular speed). Therefore, each of these inductance profiles can be numerically analyzed from the samplings, and expressed in harmonic Fourier series form as follows:\n(3)\n(4)\nwhere, h is the harmonic order, and Nh is the highest order of a significant harmonic. Here, k' is related to the synchronous speed for all the stator self and mutual inductances. Meanwhile, k' is related to the rotor's angular speed, and hence slip speed, for all the rotor self and mutual inductances, as well as the stator to rotor (rotor to stator) mutual inductances. Again, these Fourier series expressions are obtained from numerical Fourier series analysis of the various inductance profiles resulting from the TSFE computed magnetic field solutions at all the discrete rotor angular positions (samplings) covering a complete ac cycle.\nIV. THE MOTOR STATE-SPACE MODEL Applying Faraday's law and KVL formulation, the terminal voltages in terms of the flux linkages and winding currents of the 37 circuits of the motor can be written in compact matrix form as follows:"
        ]
    },
    {
        "image_filename": "designv11_1_0003985_027836499901800504-Figure3-1.png",
        "original_path": "designv11-1/openalex_figure/designv11_1_0003985_027836499901800504-Figure3-1.png",
        "caption": "Fig. 3. Finger F translating and pushing object B.",
        "texts": [
            " Coulomb\u2019s friction law is assumed, and the coefficient of support friction, that is, friction between B and the plane, is everywhere \u00b5. For simplicity, let us assume uniform mass and pressure distributions of B. Let us also assume frictionless contact between F and B at present, and deal with contact friction exclusively in Section 5. Let vF be the velocity of F, known to F\u2019s controller; and let v and \u03c9 be the velocity and angular velocity of B, respectively, all in the world coordinate frame (Fig. 3). Let F\u2019s boundary be a smooth curve \u03b1, and B\u2019s boundary be a piecewise-smooth closed curve \u03b2 such that \u03b1(u) and \u03b2(s) are the two points in contact in the local frames of F and B, respectively. Following convention, moving counterclockwise along \u03b1 and \u03b2 increases u and s, respectively. Assume that one curve segment of \u03b2 stays in contact with \u03b1 throughout the pushing. That F and B maintain contact imposes a velocity constraint vF + \u03b1\u2032u\u0307 = v + \u03c9 \u00d7 R\u03b2 + R\u03b2\u2032s\u0307, (1) where R(\u03b8) = ( cos \u03b8 \u2212 sin \u03b8 sin \u03b8 cos \u03b8 ) is the rotation matrix associated with the orientation \u03b8 of B, which is determined by u, s, and the orientation of F"
        ],
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    {
        "image_filename": "designv11_1_0003980_1.2834407-Figure1-1.png",
        "original_path": "designv11-1/openalex_figure/designv11_1_0003980_1.2834407-Figure1-1.png",
        "caption": "Fig. 1 (b) Measurement of friction force",
        "texts": [
            " Each disk is mounted on the spindle of a three-phase a- Contributed by the Tribology Division of THE AMERICAN SOCIETY OF MECHANI CAL ENGINEERS and presented at the Joint ASME/STLE/IMechE World Tribology Conference, London, England, September 8-12, 1997. Manuscript received by the Tribology Division June 27, 1996; revised manuscript received January 25, 1997 Paper No. 97-Trib-7. Associate Technical Editor: S. loannides. c motor, and a wide range of speed\u2014i.e., 1000 to 14000 rpm\u2014 is accomplished by varying the supply frequency. The motor I (see Fig. 1(a)) is fixed to the machine housing, and the motor II is connected to the frame via two sets of hydrostatic bearings along an axis normal to the rotational axis of the motor. Thus, motor II has two degrees of freedom. The translation about this transverse axis provides the desired normal load via a pneumatic loading system. Second, the rotation about the transverse axis primarily converts the motor assembly into a dynamometer, and the friction force between the disks is measured using a stiff load cell (see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv11_1_0003932_21.8.1391-Figure1-1.png",
        "original_path": "designv11-1/openalex_figure/designv11_1_0003932_21.8.1391-Figure1-1.png",
        "caption": "Fig. 1. The free body diagram for a freely swimming copepod in water. G stands for the body force due to gravity which acts at the center of mass; B stands for the buoyancy force which acts at the center of volume; Fpd stands for the force due to the integral of the flow pressure (the flow-induced pressure deviation from the hydrostatic pressure) over the whole body surface; Fvd stands for the force due to the integral of viscous stress over the whole body surface. The distributed force due to the flow pressure or viscous stress can be represented by an integrated force and a torque. The point of application for the force is arbitrary (we chose the center of mass), but the torque must be calculated about the point of application for the force. The curved arrow labeled Tpd indicates the torque on the copepod by the flow pressure distribution on the surface of the body. The curved arrow labeled Tvd indicates the torque on the copepod by the viscous stress on the surface of the body.",
        "texts": [
            " Moreover, the effects of the distribution of forces and the copepod\u2019s body shape on the drag and the viscous dissipation are investigated. Conclusions are presented in the final section. Dynamics, force analysis and numerical method Consider a freely swimming copepod in water with the flow around it, and assume that the flow is generated by the animal. The forces acting on the body include the buoyancy force, the body force due to gravity, and the forces exerted by the flow on the copepod due to the distributions of the flow pressure and the shear stress around the surface of the copepod. Figure 1 shows schematically the free body diagram for the copepod. A \u2018free body diagram\u2019 represents the body under consideration with the physical constraints removed and replaced by the forces and torques they exert. Detailed descriptions of the forces and torques are given in Table I. The governing equations of the feeding current around the copepod are the Navier\u2013Stokes equation and the continuity equation: \u2202u r \u2014\u2014 + ru \u00b7=u = \u2013=p + \u00b5=2u (1) \u2202t and = \u00b7u = 0 (2) where r is the density of the fluid (~1"
        ],
        "surrounding_texts": []
    }
]