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Twin gap magnetorheometer using ferromagnetic steel plates—Performance and validation
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10.1122/1.3302804
/content/sor/journal/jor2/54/2/10.1122/1.3302804
http://aip.metastore.ingenta.com/content/sor/journal/jor2/54/2/10.1122/1.3302804

Figures

Image of FIG. 1.
FIG. 1.

Schematic cross section of the magnetocell MRD180/1T (rotor and inserts removed). Circle indicates the location of the specific inserts (TG or SG, see Figs. 2 and 11).

Image of FIG. 2.
FIG. 2.

Schematic of the TG magnetocell insert (compared to the horizontal dimensions, the vertical dimensions are blown up by a factor of 2). For details of the geometry, see text.

Image of FIG. 3.
FIG. 3.

Magnetic flux density versus solenoid current as measured for the TG magnetocell (radial position of the probe’s sensitive area ). Unfilled squares: both gaps empty; full circles: MRF I in both gaps; full triangles: MRF II in both gaps. MAXWELL®2D predictions for empty gaps are denoted by stars, for the MRF I filled gaps by crosses, respectively.

Image of FIG. 4.
FIG. 4.

Simulated radial flux density profiles in the middle of the shear gaps (upper gap: squares; bottom gap: circles) filled by MRF I at a solenoid currents of 1 and 3 A, respectively. Radial dimensions of rotor shaft, upper yoke, and rotor plate are indicated by the hatched areas. Broken lines represent calculated flux densities in the middle of the Hall probe channel, while the arrow indicates the radial location of the probe’s sensitive area.

Image of FIG. 5.
FIG. 5.

Rheology-relevant average flux density versus flux density at the Hall probe position. Data points (full circles) stem from MAXWELL®2D simulations for solenoid currents 1–5 A and MRF I loaded into the TG magnetocell. Full line has slope .

Image of FIG. 6.
FIG. 6.

TG flux density correction factor versus weight percentage CIP in the MRF as determined by FEM simulations for various solenoid currents (compare Fig. 5). FEM data are represented by circles; straight line depicts Eq. (2).

Image of FIG. 7.
FIG. 7.

Shear stress overestimation factor versus nominal shear stress as given by Eq. (16). The pre-factor 0.05 causes at .

Image of FIG. 8.
FIG. 8.

Comparison of measured normal forces versus magnetic flux density measured by the Hall probe at a shear rate of for the TG magnetorheometer (TG, full symbols) and the corresponding SG magnetorheometer (SG, unfilled symbols), respectively, loaded by MRF I or MRF II. Data are average values from three independent runs.

Image of FIG. 9.
FIG. 9.

Time dependence of the apparent (rim) shear stress in the TG magnetorheometer for MRF I and MRF II, respectively, at constant shear rate after a step from zero magnetic flux density to 0.55 T (flux density correction applied) at time . Data points are averages from three independent runs.

Image of FIG. 10.
FIG. 10.

Apparent (rim) shear stress versus magnetic flux density for MRF I and MRF II, respectively, measured at constant shear rate in the TG magnetorheometer (various symbols indicate independent runs). Both the flux density correction Eq. (2) and the torque correction Eqs. (16) and (17) have been applied. For comparison, the average uncorrected data for each sample are represented by broken lines.

Image of FIG. 11.
FIG. 11.

Schematic of the SG magnetocell (compared to the horizontal dimensions, the vertical dimensions are blown up by a factor of 2). For dimensions, see text.

Image of FIG. 12.
FIG. 12.

Simulated radial flux density profiles in the middle of the shear gap (symbols) filled by MRF I at solenoid currents of 1, 2, and 3 A. Broken lines represent calculated flux densities in the middle of the Hall probe channel (arrows indicate radial location of the probe’s sensitive area).

Image of FIG. 13.
FIG. 13.

Rheology-relevant average flux density from FEM versus flux density calculated for the Hall probe position. Data points (full circles) stem from MAXWELL®2D simulations for solenoid currents 1–5 A with MRF I loaded into the SG magnetocell. Full line has slope .

Image of FIG. 14.
FIG. 14.

Time dependence of the apparent (rim) shear stress in the SG magnetorheometer for MRF I and MRF II, respectively, at constant shear rate after a step from zero magnetic flux density to 0.55 T at time . Data points are averages from three independent runs.

Image of FIG. 15.
FIG. 15.

Measured gap height of the SG (full symbols) and of the bottom gap of the TG magnetocell (unfilled symbols) versus normal force . Data for MRF I are represented by circles, those for MRF II by triangles. Straight line represents an axial rheometer compliance of .

Image of FIG. 16.
FIG. 16.

Apparent (rim) shear stress versus magnetic flux density for MRF I and MRF II, respectively, measured at constant shear rate in the SG magnetorheometer (various symbols indicate independent runs). Flux density correction Eq. (19) and gap opening corrections Eqs. (21) and (22) have been applied. For comparison, the average uncorrected data for each sample are represented by broken lines.

Image of FIG. 17.
FIG. 17.

Direct comparison of the apparent shear stress versus flux density data at shear rate from the TG (full symbols) and SG (unfilled symbol) for MRF I and MRF II (all corrections listed in Table I applied). Drawn lines represent the average of the TG data.

Image of FIG. 18.
FIG. 18.

Same data as in Fig. 17 but with logarithmic scale for the apparent shear stress to provide an improved shear stress resolution for the low flux density regime.

Image of FIG. 19.
FIG. 19.

Shear rate sweeps on (a) MRF I and (b) MRF II at over the full range of shear rates. Stars (first up-sweep), diamonds (down-sweep), and circles (second up-sweep) represent apparent shear stress versus rim shear rate. Dotted line: fit by Eq. (24) to gray circles. Full squares: true rim shear stress from Eq. (5). Full line: fit by Casson law Eq. (26).

Image of FIG. 20.
FIG. 20.

Apparent shear stresses of MRF I versus shear rate from successive up-sweeps with stepwise increase of the flux density. Unfilled symbols: measured data points; drawn line: fit by Eq. (24).

Image of FIG. 21.
FIG. 21.

True shear stresses of MRF I versus shear rate from successive up-sweeps with stepwise increase of the flux density. Full symbols: measured data points; drawn line: fit by Casson model Eq. (26). Arrow indicates the true stroke of 3970 for and 0.84 T.

Image of FIG. 22.
FIG. 22.

Full symbols: true rim shear stress of MRF I versus rim shear rate (data from Fig. 21) at (squares) and (diamonds), respectively. Unfilled symbols: apparent rim shear stress for a calibration oil. Thin straight line: expected response from Eq. (28). Arrow indicates the onset of the oil viscosity decrease due to dissipative heating.

Image of FIG. 23.
FIG. 23.

Magnetic flux lines and magnetic flux density field simulated by MAXWELL®2D for the TG magnetocell filled with MRF I at 1 A solenoid current (nonmagnetic housing at the rim not shown).

Image of FIG. 24.
FIG. 24.

Magnetic flux lines and magnetic flux density field simulated by MAXWELL®2D for the SG magnetocell filled with MRF I at 1 A solenoid current.

Image of FIG. 25.
FIG. 25.

Magnetic flux density versus radial position (SG filled with MRF I, solenoid current 2 A). Symbols: middle plane of the MRF; lines: vertical position of Hall probe. Nominal gap 0.3 mm: squares and dotted line, gap 0.315 mm: circles and broken line, gap 0.33 mm: triangles and full line. Sensitive area of the Hall probe is located at . Vertical bars denote .

Image of FIG. 26.
FIG. 26.

Effective flux density factor versus effective gap height for the SG filled with MRF I at 2 A solenoid current. Unfilled squares calculated from Eq. (A2), full square stems from Fig. 13. Full line: Eq. (A3) using .

Tables

Generic image for table
TABLE I.

Overview on the applied corrections (example MRF I, data from Fig. 17).

Generic image for table
TABLE II.

Parameters of the Casson model used for Fig. 21 (MRF I at ).

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/content/sor/journal/jor2/54/2/10.1122/1.3302804
2010-03-09
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Twin gap magnetorheometer using ferromagnetic steel plates—Performance and validation
http://aip.metastore.ingenta.com/content/sor/journal/jor2/54/2/10.1122/1.3302804
10.1122/1.3302804
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