Maximum Magnetic Force Research Articles

Power boundaries in resonant electrodynamic wireless power transfer systems

This article focuses on deriving the maximum power that can be transmitted using recent wireless power transfer technology based on an electrodynamic receiver. Analytical derivations reveal two main constraints that can limit transmitted power: the magnetic field safety limit and the maximum stress before breaking the receiver. From these limits, expressions of maximum magnetic forces and power are derived, providing physical insights on how to optimize the transmitted power. Interestingly, the optimal electrical condition and the optimal electromechanical efficiency differ when maximizing the transmitted power under each constraint. In the final section of the paper, the proposed theoretical boundaries are applied to two types of receivers, based on either electromagnetic or piezoelectric transducers. The results demonstrate that the maximum power density achievable with both receivers is inherently limited (<10 mW/cm3) under realistic assumptions regarding electromechanical coupling and electrical circuitry. This value is smaller than some previously reported results involving rotating or magnetoelectric solutions, indicating that clamped-free beams are not the optimal solution for electrodynamic wireless power transfer. This analysis can be extended to other types of receivers and will be useful for optimizing, sizing, and assessing any technological solution for wireless power transfer.

In Situ Changes in Mechanical Properties Based on Gas Saturation Inside Pressure Vessels.

In previous studies, difficulties were encountered in measuring changes within high-pressure vessels owing to limitations such as sensor connectors and sensor failures under high-pressure conditions. In addition, polymer-gas mixtures experience instantaneous gas desorption upon exiting high-pressure vessels owing to pressure differentials, leading to measurement errors. In this study, a device using magnetic sensors was developed to measure the real-time changes in gas-saturated polymers inside pressure vessels. Experiments on polymethyl methacrylate gas adsorption were conducted with parameters including pressure at 5 MPa and temperatures ranging from -20 to 40 °C for 60 and 180 min. It was observed that at -20 °C, the maximum magnetic field force density and deflection were 391.53 μT and 5.83 mm, respectively, whereas at 40 °C, deflection did not occur, with a value of 321.79 μT. Based on gas saturation experiments, a new model for deflection in high-pressure atmospheres is proposed. Additionally, an ANSYS analysis was conducted to predict the changes in Young's modulus based on gas saturation. In previous studies, mechanical properties were measured outside the pressure vessel, resulting in an error due to a pressure difference, while the proposed method is characterized by the ability to directly measure polymer behavior according to gas saturation in high-pressure vessels using a magnetic sensor in real time. Therefore, it is possible to predict polymer behavior, making it easy to control variables in high-pressure polymer processes.

MHD and Thermal Slip Effects on Viscous Fluid over Symmetrically Vertical Heated Plate in Porous Medium: Keller Box Analysis

The heat transfer characteristics along the non-magnetized shapes have been performed in various previous studies numerically. Due to excessive heating, these mechanisms are less interesting in engineering and industrial processes. In the current analysis, the surface is magnetized, and the fluid is electrically conducting, which is responsible for reducing excessive heating along the surface. The main objective of the present work is to analyze convective heat transfer analysis of viscous fluid flow with thermal slip and thermal radiation effects along the vertical symmetric heated plate immersed in a porous medium numerically. The results are deduced for viscous flow along a magnetized heated surface. The theoretical mechanism of heat and magnetic intensity along a vertical surface is investigated for numerical analysis. The nonlinear-coupled partial differential equations (PDEs) for the above viscous fluid flow mechanism with the symmetry of the conditions normal to the surface are transformed and then converted into non-similar formulations by applying appropriate and well-known similarity transformations for integration and solutions. The final non-similar equations are numerically integrated by employing the Keller box method. The discretized algebraic equations are plotted graphically and numerically on the MATLAB R2013a software package. The main finding of the current analysis is to compute physical quantities such as velocity graph, magnetic field graph, and temperature plot along with their slopes, that is, skin friction, magnetic intensity, and heat transfer for different parameters included in the flow model. First, the velocity graph, magnetic field graph, and temperature graph are obtained, and then their slopes are analyzed numerically along the vertical magnetic surface. It is noticed that fluid velocity is increased at lower magnetic force, but minimum velocity is noticed at maximum magnetic force. It is worth mentioning that with the increase in magnetic force, the magnetic energy increases, which extracts the kinetic energy of the fluid and causes the above-said behavior. Furthermore, the current issues have significant implications for the polymer industries, glass fiber production, petroleum production, fiber spinning, plastic film production, polymer sheet extraction, heat exchangers, catalytic reactors, and the production of electronic devices.

2‐D analytical magnetic model for optimal design of an outer rotor permanent magnet synchronous machine

The objective of this paper is to investigate the optimal design of a 120 W outer-rotor permanent magnet synchronous machine for air-conditioning applications to reduce the electricity consumption and machine costs. To this end, a 2-D analytical magnetic model, combined with a teaching–learning based optimisation algorithm is employed. The objectives are to simultaneously maximise the machine efficiency and minimise the material cost. Constraints such as the required output torque, predefined machine volume, maximum allowable torque ripple and unbalanced magnetic force and limitations to avoid iron core magnetic saturation are imposed simultaneously. To find the flux density in iron parts, a new method based on the subdomain technique has been presented. To evaluate the analytical model in terms of accuracy and speed, the results of the 2-D analytical approach are compared with those of the 2-D and 3-D linear/non-linear finite element method. Finally, a prototype of the optimised machine is fabricated and the superiority of the presented approach is demonstrated.

Single Coil Mechano-Electromagnetic System for the Automatic 1-Axis Position Feedback 3D Locomotion Control of Magnetic Robots and Their Selective Manipulation.

3D locomotion of magnetic microrobots requires at least one pair of coils per axis and 3D feedback of the position of the microrobot. This results in voluminous systems with high‐power usage and a small working space, which require complex and expensive controllers. This study presents a single‐coil magneto‐electromagnetic system, comprising a parallel robot and coil, capable of precise 3D locomotion control of magnetic millirobots while requiring only feedback of the vertical position of the millirobot. The coil current creates a 2D magnetic trapping point in the horizontal plane, which depends on the position and orientation of the coil and toward which the millirobot moves, eliminating the need for position feedback at such plane. The vertical position of the millirobot is controlled by varying the coil current while receiving feedback from the vertical position of the millirobot. Feedbackless 2D control and 1‐axis feedback 3D automatic control of magnetic millirobots are experimentally demonstrated, achieving higher speeds and similar position errors when compared to control systems with 3D position feedback. Furthermore, selective control of two millirobots is demonstrated by matching the region of maximum vertical magnetic force and the targeted millirobot, achieving selective levitation and control of such millirobots.

Numerical insights into magnetic particle enrichment and separation in an integrated droplet microfluidic system

Particle concentration and manipulation inside droplets hold great potential in expanding lab-in-a-droplet applications ranging from biological to chemical assays. Herein, we present a numerical model that provides sufficient insights into magnetic particle enrichment in an integrated microfluidic system considering the most possible interactions and forces. The proposed system comprises three distinct interconnected modules: droplet generator, spacer, and splitter with a permanent magnet placed under the splitting zone. Two approaches are developed to predict the particle trajectories inside the droplet, namely, magnetohydrophoretic streamline (static) and multi-particle tracing (dynamic). It is found that although the presence of an external magnetic force may help to improve the separation/enrichment of the magnetic particles in such microfluidic systems, however, the location of the magnet must be carefully determined to avoid the inverse effect of the magnetic field on the separation/enrichment efficiency. Moreover, the full particle enrichment is obtained at a maximum magnetic force to drag force ratio of >0.8% and a magnetophoretic velocity to the mean fluid velocity ratio of >6% for both 2.83 µm and 4.4 µm magnetic beads. The presented accurate numerical model, together with its unique features of low computational cost and broad applicability, such as separating particles with different properties, can further broaden utility in droplet microfluidics.

Finite element analysis on electromagnetic forming of DP780 high-strength steel sheets

In this paper, the effects of strain rate on the mechanical properties of DP780 were analyzed by quasi-static tensile test and Hopkinson bar test; Johnson-Cook constitutive model with high strain rate was established. Based on ANSYS/LS-DYNA finite element program, the finite element simulation of electromagnetic forming process of high-strength steel sheet under the action of driving plate was realized, and the influence of various process parameters on the forming height was studied. The results showed that the yield strength and ultimate tensile strength of the material increased with high strain rate, and DP780 high-strength steel had certain strain rate sensitivity. The drive sheet receives the maximum magnetic field force near the outermost two-turn coil. The deformation of high-strength steel plate mainly occurs under the action of impact inertia. The peak forming height increases with the rise of discharge frequency. The increase of the thickness of the drive sheet can reduce the forming efficiency.

Load carrying capacity of a novel magnetic-liquid double suspension fixed pad thrust bearing

Purpose Proposing a new type of water-lubricated thrust bearing meets the load-bearing requirements of high-power shaft-less rim driven thrusters. Design/methodology/approach The designs were tested by establishing a bearing thermal-fluid-magnetic comprehensive simulation model and developing bearing fluid film force and magnetic simulation. Lubrication performance tests were carried out on the bearing test rig. Findings The Halbach array of magnet blocks is able to reach the maximum magnetic force. The material of sheath can help increase the magnetism. The magnetism is able to reduce wear during low-speed and the start-stop phase, while the eddy current loss at high speeds will lead to a decrease in magnetic force. The experiment found that the bearing was more stable at low speeds and would not demagnetize due to the temperature rise, but it is necessary to pay attention to the running stability at high speeds to prevent rubbing and impact. Originality/value An innovative combination of hydrodynamic pressure and permanent magnetic repulsion was observed to form a magnetic-liquid double suspension bearing with large bearing capacity. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-08-2020-0295

Anomalous out-of-equilibrium dynamics in the spin-ice material Dy2Ti2O7 under moderate magnetic fields

We study experimentally and numerically the dynamics of the spin ice material Dy2Ti2O7 in the low temperature (T) and moderate magnetic field (B) regime (T ∈ [0.1, 1.7] K, B ∈ [0, 0.3] T). Our objective is to understand the main physics shaping the out-of-equilibrium magnetisation vs temperature curves in two different regimes. Very far from equilibrium, turning on the magnetic field after having cooled the system in zero field (ZFC) can increase the concentration of magnetic monopoles (localised thermal excitations present in these systems); this accelerates the dynamics. Similarly to electrolytes, this occurs through dissociation of bound monopole pairs. However, for spin ices the polarisation of the vacuum out of which the monopole pairs are created is a key factor shaping the magnetisation curves, with no analog. We observe a threshold field near 0.2 T for this fast dynamics to take place, linked to the maximum magnetic force between the attracting pairs. Surprisingly, within a regime of low temperatures and moderate fields, an extended Ohm’s law can be used to describe the ZFC magnetisation curve obtained with the dipolar spin-ice model. However, in real samples the acceleration of the dynamics appears even sharper than in simulations, possibly due to the presence of avalanches. On the other hand, the effect of the field nearer equilibrium can be just the opposite to that at very low temperatures. Single crystals, as noted before for powders, abandon equilibrium at a blocking temperature TB which increases with field. Curiously, this behaviour is present in numerical simulations even within the nearest-neighbours interactions model. Simulations and experiments show that the increasing trend in TB is stronger for B‖[100]. This suggests that the field plays a part in the dynamical arrest through monopole suppression, which is quite manifest for this field orientation.

An analysis on the relation between the seed distance and vertical levitation force for the multi−seeded YBCO using the modified advanced frozen image (MAFI) and experimental methods

The higher magnetic levitation force and related stiffness values are very important for Maglev and magnetic bearing applications. Also, larger superconducting surface area is needed for continuous and larger magnetic mediums with different geometries and dimensions in real scale industrial applications of superconducting systems. In this study, the cylindrical YBCO superconductors were fabricated by top−seeded melt growth (TSMG) method in single and two−seeded forms with different seed distances and then the magnetic force and stiffness measurements were carried out by three axes magnetic force measurement system in different cooling heights (CH) of 20 mm and 75 mm. Additionally, a new analytical method, based on the magnetic dipole approximation, is proposed to calculate the levitation force in this study, named as Modified Advanced Frozen Image Method (MAFI), since although the Advanced Frozen Image Method in literature can calculate the levitation force with hysteresis, this method does not include the size effect of the superconductor. In the experimental studies, it is seen that the maximum levitation force values obtained by PMG with three PMs (named PMG−1) are more than two times higher than that of obtained with single PM for all samples with different distance of seeds, because of the higher magnetic flux distribution of related PMG arrangement than the single PM. In addition, the maximum magnetic levitation force value firstly increased and then decreased due to current coupling effect weakness by increasing distance of seeds. The calculated analytical levitation force results are not compatible with the experimental results without current coupling effect, but a well agreement is observed when the current coupling effect is taken into account in calculations. Also the MAFI method was tested with different dimensions of superconductors and the obtained results indicated the success of the proposed method. The maximum levitation force values obtained with MAFI method increased with increasing dimensions of HTS and PMs. Thus, one can say that the MAFI method is useful for the levitation force calculations between multi−seeded superconductors and PMGs with different dimensions and for different CHs. As a result, the analytical levitation force values obtained with the MAFI method are agree with the experimental levitation force sufficiently and this method can give fast calculation results without any divergence problem. This method can be thought as an alternative to the numerical calculation methods, having serious divergence problems for much amount and bigger size superconducting samples, therefore it will be useful to clarify bulk superconducting properties as supporter to the experimental studies.

Magnetic Graphene Oxide Nanocarrier as a drug delivery vehicle for MRI monitored magnetic targeting of rat brain tumors

Introduction: Glioblastoma multiform is the most common malignant brain tumor, with an invasive nature. Despite the development of conventional therapies such as surgery, radiotherapy and chemotherapy, because of high recurrence rates, the prognosis remains very poor. Over the last decade, nanotechnology has represented an innovative method as nanoparticle-based drug delivery carriers to overcome the BBB transport. Multifunctional magnetic nanoparticles are powerful tools for current clinical diagnostics, imaging and therapeutic procedures. Materials and Methods: Magnetic targeting studies were carried out in C6 glioma tumor-bearing Wistar rats using intravenous magnetic nanoparticles administration under permanent magnetic phantom. Animals were placed ventrally on a platform with their head positioned between two blocks of NdFeB permanent magnet (1.3 tesla). Measurements of magnetic density in the space between the two blocks were carried out using a tangential B-probe Teslameter (LEYBOLD, Germany). MNP (9 mg/kg) were injected into the tail vein of rats, seventeen days after implantation and retained in the magnetic field for 2h. To evaluate brain- targeting ability of nanoparticles, the rats were imaged with MRI before the administration of nanoparticles and after the magnetic targeting. Immediately following MRI, the animals were sacrificed and the brains were collected for Prussian blue staining. Results: Magnetic NGO/PLGA nanoparticles with a diameter of 71.8 nm, a zeta potential of -33.07±0.07 mV presented superior superparamagnetic properties with a saturation magnetization of 15.98 emu/g. The results of MR T2 images and Prussian blue staining of rat brains indicated MNPs could overcome the BBB for glioma targeting in the presence of a permanent magnetic field. The measured magnetic density at the GBM area was 450 mT, the value measured 2.5 cm caudal to the tumor was 325 mT, indicating that the tumor would be exposed to a maximum magnetic force. Furthermore, the MRI images demonstrated MNPs could be used in noninvasive MR imaging techniques and enhance the MRI sensitivity to offer better chemotherapy and real time monitoring. Conclusion: In the present study, for the first time, we combined the concepts from these two fields to synthesize magnetic NGO nanoparticles and indicated its high-level specificity to magnetic targeting C6 glioma rats, that its ability to serve as an excellent contrast enhancement agent for MRI.

Magnetic Intramedullary Lengthening Nails and MRI Compatibility.

Magnetic intramedullary nails (IMNs) are fully implantable lengthening devices that became available in the United States in 2011 for the correction of limb length discrepancies. This device represents a major advancement in the field of limb lengthening surgery as it is typically tolerated better than external fixation. Unlike traditional IMNs, surgeons recommend routine removal following limb lengthening. One such reason involves patient safety as it pertains to magnetic resonance imaging (MRI). Theoretical concerns with MRI exposure include implant migration, implant heating, and involuntary elongation of the lengthening mechanism. Our study seeks to investigate the effects of MRI on intramedullary magnetic lengthening nails. Twenty-five intramedullary magnetic nails were studied. One nail was placed within the magnetic field to measure maximum magnetic force. Nails were then scanned using standard knee MRI protocols, 12 in 3 T and 12 in 1.5 T MRI scanners. The following parameters were measured: (1) distraction of the implants after MRI exposure, (2) temperature before and after MRI, and (3) internal distraction force before and after MRI. Maximum magnetic force was found to be 2 lbs. There was no involuntary distraction of the implants after MRI. Temperature increase of 3.3°C was found in the femoral nails and 3.6°C in the tibial nails that were exposed to 3 T MRI. This increase did not reach or exceed physiological temperature of 37°C. Distraction force was reduced by 61.7% in the femoral nails and 89.6% in the tibial nails after subjected to 3 T MRI. There was no reduction in distraction force after exposure to 1.5 T MRI. Recommendations for routine removal of magnetic IMNs for safety concerns should be reconsidered. Exposure to 3 T MRI should be avoided in patients who are still undergoing lengthening or with plans for future lengthening with magnetic IMNs. To assess patient safety and implant function after magnetic IMNs have been exposed to MRI.

Comparison of AC and pulsed magnetization-based elasto-magnetic methods for tensile force measurement in steel strand

AC and pulsed magnetization-based elasto-magnetic measurement methods of tensile force in steel strand are compared in the study. Completely opposite conclusions on the dependency of maximum magnetic induction on the tensile force are drawn from the two modes. The opposite conclusions are consistent with the predicted results before and after the Villari reversal point. Harmonic and spectral analysis techniques are introduced to investigate new feature parameters for tensile force characterization. In AC mode, the distortion factor of the induced voltage signals demonstrates the better stability and force prediction accuracy than the conventional time-domain feature parameters of maximum magnetic induction and coercive force. In the pulsed mode, the linear correlation between the spectral amplitudes of the induced pulsed signals and the tensile force is analyzed. A new parameter, the summation of the spectrum amplitudes in a particular band, is introduced to characterize tensile force. The calibration curve for tensile force measurement with the new parameter shows a lower prediction error and hysteresis error compared to the time-domain analysis results. Conclusions obtained from the comparative study on the performance of the two magnetization modes and two types of parameters may provide new insights into the improvements in the tensile force detection accuracy of the elasto-magnetic methods.

Orientation and thickness dependence of magnetic levitation force and trapped magnetic field of single grain YBa2Cu3O7-y bulk superconductors

The effects of the crystallographic orientation and sample thickness on the magnetic levitation forces (F) and trapped magnetic field (B) of single grain YBCO bulk superconductors were examined. Single grain YBCO samples with a (001), (110) or (100) surface were used as the test samples. The samples used for the force-distance (F-d) measurement were cooled at 77 K without a magnetic field (zero field cooling, ZFC), whereas the samples used for the B measurement were cooled under the external magnetic field of a Nd-B-Fe permanent magnet (field cooling, FC). It was found that F and B of the (001) surface were higher than those of the (110) or (100) surface, which is attributed to the higher critical current density (Jc) of the (001) surface. For the (001) samples with t=5–18 mm, the maximum magnetic levitation forces (Fmaxs) of the ZFC samples were larger than 40 N. About 80% of the applied magnetic field was trapped in the FC samples. However, the F and B decreased rapidly as t decreased below 5 mm. There exists a critical sample thickness (t=5 mm for the experimental condition of this study) for maintaining the large levitation/trapping properties, which is dependent on the material properties and magnitude of the external magnetic fields.

Numerical simulation of adsorption characteristics of magnetic take-up roll for amorphous ribbon

Take-up roll( TUR) is a key component in amorphous ribbon automatic production line.Take-up rate of TUR determines the ribbon quality and production rate. Because the line speed of amorphous ribbon in the ribbon process is fast and the amorphous ribbon suffers from different resistance,TUR should generate enough adsorption force to overcome the different resistance conditions. According to the requirements of ribbon production process,the structure of magnetic TUR with Nd Fe B permanent magnet was proposed. The finite element method was used to analyze magnetic adsorption characteristics in different ribbon steps. The magnetic adsorption force contour and magnetic field distribution were obtained along different axes under different air gaps. The calculation results show that the magnetic TUR can supply enough adsorption force to take up the ribbon when air gap is smaller than 30 mm in specification range. Finally,the maximum magnetic adsorption force under different air gaps were measured by spot tests. It is verified that the test result is consistent with the simulation result.

Evaluation of In-Situ Magnetic Signals from Iron Oxide Nanoparticle-Labeled PC12 Cells by Atomic Force Microscopy.

The magnetic signals from magnetite nanoparticle-labeled PC12 cells were assessed by magnetic force microscopy by deploying a localized external magnetic field to magnetize the nanoparticles and the magnetic tip simultaneously so that the interaction between the tip and PC12 cell-associated Fe3O4 nanoparticles could be detected at lift heights (the distance between the tip and the sample) larger than 100 nm. The use of large lift heights during the raster scanning of the probe eliminates the non-magnetic interference from the complex and rugged cell surface and yet maintains the sufficient sensitivity for magnetic detection. The magnetic signals of the cell-bound nanoparticles were semi-quantified by analyzing cell surface roughness upon three-dimensional reconstruction generated by the phase shift of the cantilever oscillation. The obtained data can be used for the evaluation of the overall cellular magnetization as well as the maximum magnetic forces from magnetic nanoparticle-labeled cells which is crucial for the biomedical application of these nanomaterials.

Maximizing the Magnetic Force Generated by an Actuator with Non-Magnetic Body in a Ferrofluid Pre-Magnetized by Permanent Magnets

The purpose of this paper is to investigate possibilities and means that lead to the increase of the magnetic force generated by an actuator with a non-magnetic body levitated in a ferrofluid pre-magnetized by permanent magnets. The numerical simulations outline the components of the structure, dimensions and magnetic constants of materials that render a maximum magnetic force. The experimental measurements effectuated on an experimental model of the actuator are in acceptable agreement with theoretical and simulation results

Magnetic Force Investigation of High-Tc Superconducting Bulk over Permanent Magnet Railway under Different Lateral Offsets with Experimental Methods

The magnetic levitation transportation system is one of the potential applications of high-Tc superconducting (HTS) maglev system. The prototype HTS magnetic levitation system is composed of one HTS bulk and a permanent magnet railway (PMR). The maglev transportation system performance is influenced by the maximum levitation force, the maximum guidance force and the maximum of external applied magnetic flux density. The applied magnetic field distribution also needs to be considered carefully. In the paper, the magnetic levitation force of cylindrical HTS bulk over PMR is experimentally studied. During the experiment, symmetrical PMR and Halbach PMR are used separately. The levitation force-gap loops of different lateral offset of the HTS bulk above PMRs are obtained experimentally. The results show that the HTS bulk levitation performance is tightly relative to the external applied magnetic field distribution. The maximum magnetic levitation forces of HTS bulk above symmetrical PMR decrease linearly with the lateral offset increasing. When the lateral offset changes from 0 mm to 25 mm, the maximum magnetic levitation forces of HTS bulk above Halbach PMR increase with the lateral offset increasing. When the lateral offset exceeds the center of the Halbach PMR by 25 mm, the maximum force decreases rapidly with the increase of the lateral offset of the bulk sample.

Analytical Model of Magnetic Force for Axial Stack Permanent-Magnet Bearings

Based on magnetic field of plane point magnetic charge, virtual work principle, and superposition theorem, the magnetic force analytical model for axial stack permanent-magnet bearings (PMB) is established. The aim is to solve the problem of the magnetic force analytical model's lack of being convenient in engineering design calculation of axial stack PMB. The relationship between magnetic force and structure parameters of PMB is analyzed. ANSYS simulation is adopted to test the validity of the magnetic force analytical model. The results indicate that the magnetic force of axial stack PMB is proportional to the magnetic annular average perimeter and the square of residual magnetism induction density, and that the magnetic force increases with an increment in the magnetic annular radial width and magnetic annular number. In the case of similar geometric parameters, the magnetic force of the same direction magnetization axial stack PMB is minimum: when the number of stack magnetic ring is 4, the maximum magnetic force of reversal magnetization axial stack PMB is approximately 4 times as much as the maximum magnetic force of equi-directional magnetization axial stack PMB; when the axial offset is only half of the axial length of single magnetic ring, the axial magnetic force is the maximum. Accordingly, the maximum magnetic force of rotational magnetization axial stack PMB is roughly 1.5 times as much as the maximum magnetic force of reversal magnetization axial stack PMB. When the axial deflection is equal to the axial length of single magnetic ring, the axial magnetic force is the maximum.

Magnetic Forces Investigation of Bulk HTS over Permanent Magnetic Guideway under Different Lateral Offset with 3D-Model Numerical Method

Magnetic forces of a cylinder shape bulk high-temperature superconductor (HTS) over a permanent magnet guideway (PMG) are studied mathematically. One cylindrical bulk HTS with a diameter of 30 mm and 15 mm in height is used. Two types of PMG are employed for external magnetic fields consideration. The relationship of magnetic forces of bulk HTS under different lateral offsets over PMG is studied with 3D-model finite element method (FEM). The calculation results show that the maximum magnetic levitation force of bulk HTS over PMG is tightly related to the applied magnetic field distribution. For the symmetrical PMG, the maximum magnetic levitation force decreases linearly with the increase of lateral offset of the bulk sample. For the Halbach PMG, when lateral offset changes from 0 mm to 25 mm, the maximum magnetic levitation force increases with the increase of lateral offset of the bulk HTS. When the lateral offset exceeds the center of the Halbach by 25 mm, the maximum levitation force decreases rapidly with the increase of the lateral offset of the bulk sample.