Fig 1 - uploaded by I-Ming Chen
Content may be subject to copyright.
3-DOF motion of spherical actuator. (a) First tilting motion. (b) Second tilting motion. (c) Spinning motion.
Source publication
This paper has proposed a 3-DOF spherical actuator consisting of a ball-shaped rotor with a full circle of permanent- magnet (PM) poles and a spherical-shell-like stator with two layers of circumferential air-core coils. One key feature of this design is the parametrization of PM and coil poles. Based on the torque model of the PM spherical actuato...
Contexts in source publication
Context 1
... working principle of this spherical actuator is illustrated in Fig. 1. This spherical actuator consists of a ball-shaped rotor with a full circle of PM poles and a spherical-shell-like stator with two layers of circumferential air-core coils. The rare earth PMs can generate high flux density within the actuator, and the air-core coils may simplify the torque model in a linear fash- ion. With pairs of ...
Context 2
... stator with two layers of circumferential air-core coils. The rare earth PMs can generate high flux density within the actuator, and the air-core coils may simplify the torque model in a linear fash- ion. With pairs of coils activated in two longitudinal directions, the rotor creates tilting motions in two orthogonal directions as shown in Fig. 1(a) and (b). By energizing the rest of the circumferential coils, the rotor can spin about its axis. There- fore, through varying the current input of coils, the actuator can produce any desirable 3-DOF rotational motion within the ...
Context 3
... packing pattern of winding affects the number of wire turns placed within a given area. Fig. 10(a) illustrates the regular packing pattern and Fig. 10(b) is the staggering pattern. The density of the patterns can be computed and compared for their effectiveness. Here, the stacking density is defined as the ratio of the occupied cross- sectional area of the wires and that of the designated square space (Fig. 10). For the regular ...
Context 4
... packing pattern of winding affects the number of wire turns placed within a given area. Fig. 10(a) illustrates the regular packing pattern and Fig. 10(b) is the staggering pattern. The density of the patterns can be computed and compared for their effectiveness. Here, the stacking density is defined as the ratio of the occupied cross- sectional area of the wires and that of the designated square space (Fig. 10). For the regular pattern, the stacking density ...
Context 5
... placed within a given area. Fig. 10(a) illustrates the regular packing pattern and Fig. 10(b) is the staggering pattern. The density of the patterns can be computed and compared for their effectiveness. Here, the stacking density is defined as the ratio of the occupied cross- sectional area of the wires and that of the designated square space (Fig. 10). For the regular pattern, the stacking density ...
Context 6
... Reduction of Wire Diameter: Wire diameter affects the number of winding turns. Generally, small diameter of wires allows more turns of winding to occupy the same area. Analysis is carried out to estimate the increased coil turns due to diameter reduction of wires. Based on Fig. 11, the number of turns that occupies the sectional area can be computed ...
Context 7
... on the aforesaid analysis, a research prototype of the actuator has been developed (Fig. 12). The specification is listed in Table II. Eight PM poles are mounted along the rotor equator. Twenty-four circumferential holes are drilled through the stator shell and arranged in two layers symmetrically about the stator equator. Coils are mounted through these holes and point to the stator center. The threads in the holes allow coil ...
Context 8
... the assembly of the spherical actuator, it is required that the rotor is concentric with the stator. Two cylindrical holes separated 90 • apart are drilled at the stator equator plane, as shown in Fig. 13. Likewise, two holes that are separated 90 • apart and pointed to the rotor center are drilled at the rotor equator plane. Two centering pins can be inserted through the holes on the stator shell to the holes on the rotor. In this way, the concentricity of the rotor and the stator can be ...
Context 9
... is housed within the stator directly. Although a low friction coating was made on the stator inner surface, the sliding friction between the rotor and the stator might cause unfavorable effect on the rotor motion. In some spherical motors [5], [9], transfer bearings or analog are used to support the rotor. A typical transfer bearing is shown in Fig. 14(a). This bearing consists of a rolling ball on the top, which can create a rolling motion with respect to the contact sur- face. The screw on the other end can fix the bearing on the stator for adjusting its position. As indicated in Fig. 14(b), to support a spherical rotor stably, at least three transfer bearings are nec- essary. The ...
Context 10
... [9], transfer bearings or analog are used to support the rotor. A typical transfer bearing is shown in Fig. 14(a). This bearing consists of a rolling ball on the top, which can create a rolling motion with respect to the contact sur- face. The screw on the other end can fix the bearing on the stator for adjusting its position. As indicated in Fig. 14(b), to support a spherical rotor stably, at least three transfer bearings are nec- essary. The rolling motion of these transfer bearings produces rolling frictions lower than the sliding frictions. Nevertheless, the friction torque from the transfer bearing relative to the rotor center is large due to the rotor radius. The nonnegligible ...
Context 11
... our spherical actuator, a spherical bearing [ Fig. 15(a)] [16] is employed to support the rotor housed in the stator. This spher- ical bearing can achieve a smooth 3-DOF rotational motion. The tilting motion range of this bearing is up to ±35 • . It can be as- sembled at the rotor center, as shown in Fig. 15(b). Because the friction produced by this spherical bearing is very small and the ...
Context 12
... our spherical actuator, a spherical bearing [ Fig. 15(a)] [16] is employed to support the rotor housed in the stator. This spher- ical bearing can achieve a smooth 3-DOF rotational motion. The tilting motion range of this bearing is up to ±35 • . It can be as- sembled at the rotor center, as shown in Fig. 15(b). Because the friction produced by this spherical bearing is very small and the moment arm of the friction force is less than 4 mm, the friction torque produced by the spherical bearing is negligible. Com- pared with the air bearing, the implementation of this spherical bearing is also ...
Context 13
... workspace of the PM spherical actuator is shown in Fig. 16(a). A series of PM poles are mounted along the rotor equator, whereas the air-core coils are symmetrically mounted on the stator with respect to the stator equatorial plane, with two layers separated by an angular distance of θ s . The rotor shaft can spin about its own z-axis, Z r , in 360 • without constraint. It can also incline to an ...
Context 14
... plane, with two layers separated by an angular distance of θ s . The rotor shaft can spin about its own z-axis, Z r , in 360 • without constraint. It can also incline to an extreme position that the axes of a PM pole and the coil are aligned. Thus, the z-axis of the rotor can move within a conical workspace with a conical angle of θ s as shown in Fig. ...
Context 15
... orientation of the rotor frame with respect to the stator frame can be expressed by using Euler angles. Let the rotor frame be (X r , Y r , Z r ) and the stator frame be (X s , Y s , Z s ). In order to arrive at an arbitrary final orientation within the workspace, three rotor rotations have to take place in sequence [ Fig. 16(b)]. The Euler ZYZ angle expression of the rotor orien- tation can be written as the multiplication of three body rotation matrices R z (φ r ), R y (θ r ), and R z (δ r ) [21] ...
Context 16
... computing process of torque matrix Q from the rotor orientation is carried out as follows (Fig. ...
Context 17
... of the condition numbers can be visualized. By fixing φ r at certain values such as 0 • , 15 • , 30 • , etc., a 3D plot of the condition number, denoted as n c , with respect to the variation of θ r and δ r can be presented visually as a 2-D surface. By choosing different φ r , a set of 2-D surfaces can be obtained, some of which are shown in Fig. 18. Due to the symmetric arrangement of the PM poles about the shaft, only the ranges of φ r = 0 • -45 • and δ r = 0 • -45 • are considered. Referring to Fig. 18, we can find that the condition numbers n c do not vary too much with respect to δ r and φ r because of the evenly distributed PM poles along the rotor equator. It can also be ...
Context 18
... n c , with respect to the variation of θ r and δ r can be presented visually as a 2-D surface. By choosing different φ r , a set of 2-D surfaces can be obtained, some of which are shown in Fig. 18. Due to the symmetric arrangement of the PM poles about the shaft, only the ranges of φ r = 0 • -45 • and δ r = 0 • -45 • are considered. Referring to Fig. 18, we can find that the condition numbers n c do not vary too much with respect to δ r and φ r because of the evenly distributed PM poles along the rotor equator. It can also be found that the minimum value of the condition number is 4.877, whereas the maximum value is 5.145, which is of the same order of magnitude 1. Therefore the ...
Similar publications
Maximum torque per amper (MTPA) control can realize the minimum copper loss control of induction motor, which is often applied below the rated speed. In this paper, MTPA control is firstly extended from the constant torque mode to the constant apparent power mode and the constant voltage mode, and realizes MTPA control of induction motor in the who...
![Fig. 4. Workflow for FEA based optimization [33]](profile/Stjepan-Stipetic-2/publication/318980486/figure/fig1/AS:600136610746368@1520095126126/Workflow-for-FEA-based-optimization-33_Q320.jpg)
This paper presents a method for reducing computational time in constrained single objective optimization problems related to permanent magnet motors modeled using computationally intensive finite element method. The method is based on Differential Evolution algorithm. The principal approach is to interrupt the evaluation of inequality constraints...
Despite the increasing popularity of permanent magnet synchronous machines, induction motors (IM) are still the most frequently used electrical machines in commercial applications. Ensuring a failure-free operation of IM motivates research aimed at the development of effective methods of monitoring and diagnostic of electrical machines. The present...
In this article a hardware topology meant to compare the velocity performance of both an induction motor and a permanent magnet (PM) AC three-phase motor is presented. A variable reference is tracked by the sensorless vector-controlled adjustable speed drive (ASD) that permits, by means of the same type of control, performing the speed control loop...
Permanent magnet (PM)‐assisted synchronous reluctance rotor topologies are investigated by a simplified magnetostatic finite element method (FEM) model. In this model, the slotted stator structure of an original 11‐kW standard cage induction motor is replaced by an air‐gap winding and an iron yoke to avoid time‐consuming transient numerical simulat...
Citations
... where Ns is the number of parallel winding strands, Dw is the wire diameter, dl is the thickness of insulation layer, ρw is the wire resistivity, Rin and Rout are the inner and outer radius of the coil, respectively, dc is the thickness of the coil, and ρd is wire stacking density which can be described as [48] 2 2 ...
... The second type is the complete spherical geometry, which is actuated by external actuators in contact with the surface of the sphere. This design was reported in [29][30][31]. Another design based on this principle was presented in [32], where a pair of sliced orthogonal wheels were placed perpendicularly on the axle. ...
Transforming spherical robots (TSR) has the potential to significantly advance the field of robotics by offering new possibilities for locomotion, kinematics, dynamics, and control. These robots have the ability to transform their shape to suit different environments, which makes them ideal for tasks not feasible with conventional fixed morphology spherical robots, such as those in uneven terrain where vertical mobility is required. This paper seeks to integrate and advance transformation design theory with the design of reconfigurable or TSR. The paper utilises an inductive research methodology to propose an approach to design TSR, by a) identifying the operators for spherical robots and associating relative movement between the parts using kinematic joints, and b) using the existing transformation design theory for mapping the concepts facilitators with the transforming reconfigurable spherical robots. Moreover, design evaluations based on the cost of transformation is proposed based on the mechanical cost of implementation, which consists of additional mechanical complexity and the amount of energy required for transformation. The integrated guidelines provided are demonstrated with the ideation of a spherical robot for monitoring the interior of a duct. The limitation of the proposed design approach for TSR are also highlighted. A proof of concept of TSR for pipe inspection are shown with its experiment.
... The magnetically suspended RSA has a single spherical rotor that can rotate in any direction with spherical angular momentum storage production capability [7,8]. Magnetically suspended RSA produces high torque due to tilting capability of sphere and the vibration is less than other conventional actuators such as the reaction wheel, thruster, and magnetorquer utilizing a magnetic-based mechanism such as a permanent magnet [9], electromagnetic induction [10], and piezo and ultrasonic motors [11]. ...
This paper presents a disturbance observer-based linear quadratic Gaussian (LQG) control strategy to stabilize the flexible spacecraft considering the vibration suppression of flexible appendages using an orthogonal cluster of magnetically suspended reaction sphere actuators. The nonlinear dynamic equation of a flexible satellite is given and then linearized using the Jacobian method to get a linear state-space model. The dynamic equation of the reaction sphere actuators is derived by considering 2 virtual gimbals. A new steering law is designed to produce the tilt angle commands of orthogonal reaction sphere actuators. The proposed disturbance observer-based LQG considers process disturbances and measurement noises, and performs a trade-off search between control efforts and regulation performance. Numerical simulations are performed to evaluate the proposed strategies for an attitude stabilization scenario, and the results illustrate that the disturbances are effectively mitigated.
... This dynamic model receives as control inputs three torque variables which determine rotation by a certain angle around the axes of a cartesian coordinate frame (Xia et al., 2010;Li et al., 2018;Li et al., 2019). These mechanical torque variables are in turn associated with the currents of stator's EMs through an algebraic matrix relation (Yan et al., 2014;Rossini et al., 2013;Yan et al., 2010). Thus, the EMs currents are the final control inputs of the spherical motor (Gan et al., 2020;Yan et al., 2006;Wang et al., 2016). ...
Purpose
Permanent magnet synchronous spherical motors can have wide use in robotics and industrial automation. They enable three-DOF omnidirectional motion of their rotor. They are suitable for several applications, such as actuation in robotics, traction in electric vehicles and use in several automation systems. Unlike conventional synchronous motors, permanent magnet synchronous spherical motors consist of a fixed inner shell, which is the stator, and a rotating outer shell, which is the rotor. Their dynamic model is multivariable and strongly nonlinear. The treatment of the associated control problem is important.
Design/methodology/approach
In this paper, the multivariable dynamic model of permanent magnet synchronous spherical motors is analysed, and a nonlinear optimal (H-infinity) control method is developed for it. Differential flatness properties are proven for the spherical motors’ state-space model. Next, the motors’ state-space description undergoes approximate linearization with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization process takes place at each sampling instance around a time-varying operating point, which is defined by the present value of the motors’ state vector and by the last sampled value of the control input vector. For the approximately linearized model of the permanent magnet synchronous spherical motors, a stabilizing H-infinity feedback controller is designed. To compute the controller’s gains, an algebraic Riccati equation has to be repetitively solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. Finally, the performance of the nonlinear optimal control method is compared against a flatness-based control approach implemented in successive loops.
Findings
Due to the nonlinear and multivariable structure of the state-space model of spherical motors, the solution of the associated nonlinear control problem is a nontrivial task. In this paper, a novel nonlinear optimal (H-infinity) control approach is proposed for the dynamic model of permanent magnet synchronous spherical motors. The method is based on approximate linearization of the motor’s state-space model with the use of first-order Taylor series expansion and the computation of the associated Jacobian matrices. Furthermore, the paper has introduced a different solution to the nonlinear control problem of the permanent magnet synchronous spherical motor, which is based on flatness-based control implemented in successive loops.
Research limitations/implications
The presented control approaches do not exhibit any limitations, but on the contrary, they have specific advantages. In comparison to global linearization-based control schemes (such as Lie-algebra-based control), they do not make use of complicated changes of state variables (diffeomorphisms) and transformations of the system's state-space description. The computed control inputs are applied directly to the initial nonlinear state-space model of the permanent magnet spherical motor without the intervention of inverse transformations and thus without coming against the risk of singularities.
Practical implications
The motion control problem of spherical motors is nontrivial because of the complicated nonlinear and multivariable dynamics of these electric machines. So far, there have been several attempts to apply nonlinear feedback control to permanent magnet-synchronous spherical motors. However, due to the model’s complexity, few results exist about the associated nonlinear optimal control problem. The proposed nonlinear control methods for permanent magnet synchronous spherical motors make more efficient, precise and reliable the use of such motors in robotics, electric traction and several automation systems.
Social implications
The treated research topic is central for robotic and industrial automation. Permanent magnet synchronous spherical motors are suitable for several applications, such as actuation in robotics, traction in electric vehicles and use in several automation systems. The solution of the control problem for the nonlinear dynamic model of permanent magnet synchronous spherical motors has many industrial applications and therefore contributes to economic growth and development.
Originality/value
The proposed nonlinear optimal control method is novel compared to past attempts to solve the optimal control problem for nonlinear dynamical systems. Unlike past approaches, in the new nonlinear optimal control method, linearization is performed around a temporary operating point, which is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector and not at points that belong to the desirable trajectory (setpoints). Besides, the Riccati equation which is used for computing the feedback gains of the controller is new, and so is the global stability proof for this control method. Compared to nonlinear model predictive control, which is a popular approach for treating the optimal control problem in industry, the new nonlinear optimal (H-infinity) control scheme is of proven global stability, and the convergence of its iterative search for the optimum does not depend on initial conditions and trials with multiple sets of controller parameters. It is also noteworthy that the nonlinear optimal control method is applicable to a wider class of dynamical systems than approaches based on the solution of state dependent Riccati equations (SDRE). The SDRE approaches can be applied only to dynamical systems which can be transformed into the linear parameter varying form. Besides, the nonlinear optimal control method performs better than nonlinear optimal control schemes, which use approximation of the solution of the Hamilton–Jacobi–Bellman equation by Galerkin series expansions. Furthermore, the second control method proposed in this paper, which is flatness-based control in successive loops, is also novel and demonstrates substantial contribution to nonlinear control for robotics and industrial automation.
... Early work by [5] developed an active universal joint that mimics the motion of human fingers and is 2-DOF (RR). A 3-DOF spherical (RRR) permanent magnet motor prototype was developed successfully by [6] although reducing the size and weight of the complex actuator design remained a challenge. ...
... To improve power density, the researchers divided the multi-degree of freedom motion into rotation and tilt motion in all directions. 3,4 The generated torque is concentrated in a certain direction of motion to achieve improvement. 5 Gan et al. increased the content of the iron core in the motor, increased the air-gap flux density, and further increased the torque density. ...
A hybrid excitation multi-degree-of-freedom spherical motor (HE-MDOFSM) is designed, which can achieve MDOF motion by cooperatively controlling the excitation current in 12 sets of stator windings. The designed motor has the advantages of high power density and a large motion range. In addition, because the designed motor has an irregular three-dimensional (3D) structure, it is difficult to perform dynamic magnetic field calculations with existing methods. To solve this problem, we propose a modified 3D dynamic magnetic equivalent circuit (3DD-MEC). The proposed method establishes a node network according to the structural edge features of the motor core and the permanent magnet and calculates the reluctance of the connecting branch based on the differential principle. Moreover, a connection strategy of air-gap nodes in 3D space is formulated, and the magnetic saturation characteristics of the iron core are reflected by an iterative calculation of magnetic permeability. Using the 3DD-MEC method, the 3D dynamic magnetic field information of the HE-MDOFSM can be quickly and accurately calculated. Finally, the reliability of the method is verified by simulation and experiment, which provides a reference for improving the design optimization efficiency of HE-MDOFSM.
... By contrast, the novel spherical motor can realize three degree-of-freedom (DOF) of motion at one node. It has broad potential applications in essential fields such as robotics, industrial manufacturing, and precision assembly [1][2][3]. In [4], the shell-like induction motor was concretized as a traction motor in an electric wheel-chair. ...
A multi-degree-of-freedom Permanent Magnet Spherical Actuator (PMSpA) has a special mechanical structure and electromagnetic fields, and is easily affected by nonlinear disturbances such as modeling errors and friction. Therefore, the quality of a PMSpA control system may be deteriorated. In order to keep the PMSpA with good trajectory tracking performance, this paper designs a time delay estimation controller based on gradient compensation. Firstly, the dynamic model of the PMSpA with nonlinear terms is derived. The nonlinear terms in the complex dynamic model can be simplified and estimated by the time delay estimation method. Secondly, for the estimation errors caused by time delay control, a gradient compensator is introduced to further correct and compensate for it. Furthermore, the stability of the designed controller is proved by the Lyapunov equation. Finally, the correctness and effectiveness of the controller are validated by comparison with other controllers through simulation. In addition, experimental results have also shown that the control accuracy of the spherical motor can be effectively improved using the proposed controller.
... (a) SM based on spherical wrist joint (b) Spherical motor (SM) Figure 22. Two examples of spherical motors [111,112]. ...
... More recently, in [115] a new underwater robot was proposed using a pumpedwater-jet primary thruster assisted by two auxiliary S-RMCT, each one dotted with 3-DOF (Figure 25a). This S-RMCT is also based on the spherical robotic wrist joint presented in [68,69] (Figure 18), which was also used in the proposals of Figure 14b ( [64]) and Figure 22a ( [112]). The main differences between the S-RMCT in [115] and that one in [5] are: ...
Manoeuvrability is one of the essential keys in the development of improved autonomous underwater vehicles for challenging missions. In the last years, more researches were dedicated to the development of new hulls shapes and thrusters to assure more manoeuvrability. The present review explores various enabling technologies used to implement the vectorial thrusters (VT), based on water-jet or propellers. The proposals are analysed in terms of added degrees of freedom, mechanisms, number of necessary actuators, water-tightness, electromagnetomechanical complexity, feasibility, etc. The usage of magnetic coupling thrusters (conventional or reconfigurable) is analysed in details since they can assure the development of competitive full waterproof reconfigurable thrusters, which is a frictionless, flexible, safe, and low-maintenance solution. The current limitations (as for instance the use of non conductive hull) are discussed and ideas are proposed for the improvement of this new generation of underwater thrusters, as extending the magnetic coupling usage to obtain a fully contactless vector thrust transmission.
... a) Designed stator, windings and general appearance of the spherical motor, b)Prototype motor By designing stator windings spherically, the aim was to use the structure of the spherical actuator in the most effective way. Figure 2 shows the air core winding used in spherical actuator/motor. R0 is the radius of rotor, R1 is the distance of the inner surface of winding to the centre, R2 is the distance of the outer surface of winding to the centre, ζ0 is the angular diameter of air core, and ζ1 is the angular diameter of winding [28,29]. Stator winding lenght; ...
Today, many applications requiring mass manufacturing are shifting to robotic applications through automation
systems. The actuators used in these robotic systems should be designed according to needs. In this study, an air core
spherical motor which has rotor and stator winding arrangement is described. The spherical motor’s windings are
optimally positioned on the stator made of delrin. Mutual inductance and self-inductance change were examined
according to r=4, 20, 40 and 60 mm radius and the change in the number of stator winding for the spherical motor.
Changes in inductance were found through curve fitting method with the coefficients of cubic equations. Equivalent
circuit with winding inductance model is also given. Torque change according to magnet change was also investigated.
Magnetic flux density change of N52 M magnet 3 winding 2-pole model was examined and the effect of the increase
in overall size on torque was evaluated.
... On the other hand, the abrasion loss is large, and the high-speed rotation is difficult. The 3DOF electromagnetic actuators (3DOFEAs) can generate 3DOF motion without friction [13][14][15][16][17][18][19][20][21]. They have high responsiveness and controllability by the direct drive. ...
Image deteriorations due to vibrations have become a problem in autonomous systems such as unmanned aerial vehicles, robots, and autonomous cars. To suppress the vibration, a camera stabilizer using a gimbal mechanism is widely used. However, the size and weight of the system increase because the conventional image stabilization systems require some actuators and links to drive in multi-axes. In order to solve these problems, we proposed a novel three-degree-of-freedom (3DOF) electromagnetic actuator for image stabilization. The actuator can be driven by only three-phase and has a simple structure and control system. This paper describes the experimental verification of the proposed actuator. The torque characteristics are clarified, and the analysis and measured torque characteristics are compared to verify the analysis validity. For verifying the dynamic performance, the frequency characteristics are measured. The effectiveness of the proposed magnetic structure and operating principle are investigated.
