CN116127770A - Lorentz force actuator and design method thereof - Google Patents
Lorentz force actuator and design method thereof Download PDFInfo
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Abstract
The invention belongs to the technical field of optimal design of actuators, and discloses a Lorentz force actuator and a design method thereof. The method is based on design indexes of the Lorentz force actuator, and an initialization model of the Lorentz force actuator is established; based on the initialization model, analyzing the relationship between the rotor, the stator and the air gap magnetic induction intensity in the Lorentz force actuator; further, analyzing the geometric parameters of the permanent magnet and the relation between the length of the air gap and the magnetic induction intensity of the air gap, and providing a rapid calculation method of the magnetic induction intensity of the air gap so as to rapidly determine the optimization direction of the geometric parameters of the permanent magnet and the length of the air gap; finally, a Lorentz force actuator parameterized model is constructed, and permanent magnet structures and coil parameters are optimally designed by taking the principle of maximizing the output force of the actuator and simultaneously minimizing the coil quality and heat consumption and taking the outer envelope size of the actuator as constraint conditions. The design method disclosed by the invention can realize maximum output force of the actuator, and meanwhile, the coil quality and heat consumption are minimum, and the method is efficient and accurate.
Description
Technical Field
The invention belongs to the technical field of optimal design of actuators, and particularly relates to a Lorentz force actuator and a design method thereof.
Background
Advantages of lorentz force actuators include fast speed/acceleration response, high thrust and linearity, large stroke, non-contact, compact structure, and easy integration, thus achieving wide application. For example, the method is applied to an ultra-high precision optical effective load, so that the image dimension stability is realized, and the imaging quality is improved; the micro-vibration suppression device is applied to a high-end photoetching machine and a scanning transmission electron microscope, so as to realize micro-vibration suppression and promote the core technical development of the IC manufacturing industry; the method is applied to a spacecraft, realizes track tracking and positioning of the spacecraft, and promotes an on-orbit scientific experiment of spaceflight. Generally, lorentz force actuators are mainly applied to the fields of large-scale precision machining equipment, high-precision measuring instrument equipment, ultra-high-precision operation equipment, aerospace on-orbit precision scientific experimental devices and the like. In addition, lorentz force actuators are also used in the medical and automotive industries.
However, as application scenes continue to go deep, new demands are put on higher precision of devices and higher standards of environments. And then the requirement for the actuator is also long and high. The traditional relatively single dominant element design concept is often not suitable for the actual requirements of new scenes, new environments and new devices. For example, in the conventional lorentz force actuator design process, in order to increase the output force of the actuator, a compromise is made in terms of volume, mass and heat consumption; or while increasing the output force, the volume, mass and heat consumption are partially considered, but not optimally. In addition, in designing an actuator, the design is often performed by more engineering experience. Therefore, an effective Lorentz force actuator optimization design flow and method are established, so that multi-objective optimization output is completed, namely hot spot guidance of future research is achieved, and the method is a reverse of market development. The development of related attempts and exploration is profound.
Disclosure of Invention
Aiming at the improvement demand of the prior art, the invention provides a Lorentz force actuator and a design method thereof, which are based on actuator basic characteristic analysis and construction of a Lorentz force actuator parameterized model, so as to realize maximum output force while minimizing coil mass and heat consumption.
To achieve the above object, in a first aspect, the present invention provides a method for designing a lorentz force actuator, including the steps of:
s1, acquiring design indexes of a Lorentz force actuator, and establishing an initialization model of the Lorentz force actuator;
s2, based on the Lorentz force actuator initialization model, determining the air gap magnetic induction intensity B through simulation s When maximizing, distance D from stator to magnetic field center in Lorentz force actuator along Lorentz force direction 1 And distance D from stator to magnetic field center along magnetic field vector direction 2 Is the optimum value of (2);
s3, analyzing the length l of the permanent magnet m Width w m Thickness t m And air gap length s and air gap magnetic induction intensity B s To determine the air gap induction B s Length of permanent magnet at maximum l m Width w m Thickness t m And the direction of optimization of the air gap length s;
s4, constructing a Lorentz force actuator parameterized model, wherein the Lorentz force actuator parameterized model comprises coil mass m coil And the coil heat loss Q, and boundary conditions of the geometric dimensions of the Lorentz force actuator;
s5, to maximize the air gap magnetic induction intensity B s Minimizing coil mass m coil And taking the coil heat consumption Q as an optimization target, and solving the Lorentz force actuator parameterized model in combination with the optimization direction determined in the step S3, so as to determine the optimal value of each parameter of the Lorentz force actuator.
Further, in the step S1, when the lorentz force actuator initialization model is established, the following needs to be satisfied:
F＝2N coil B s Il≥K F I
wherein: F. n (N) coil 、B s 、I、l、K F The magnetic flux is respectively corresponding to Lorentz force, turns of the coil, air gap magnetic induction intensity, coil current, effective length of each turn of coil and thrust constant.
Further, in S2, the distance D between the stator and the center of the magnetic field in the lorentz force actuator along the lorentz force direction is analyzed by performing 3D parametric simulation analysis in ANSYS 1 Distance D between stator and magnetic field center along magnetic field vector direction 2 With air gap magnetic induction intensity B s To determine the air gap induction B s D when maximized 1 And D 2 Is set to the optimum value of (2).
Further, in the step S3, the following formula is provided to analyze the length l of the permanent magnet m Width w m Thickness t m And air gap length s and air gap magnetic induction intensity B s Is the relation of:
wherein: b (B) r Residual magnetism for the permanent magnet material; k is the equivalent thickening coefficient of the permanent magnet under the condition of considering the reinforcing effect of the magnetic yoke on the magnetic circuit.
Further, in the step S3, the length l of the permanent magnet is set under the boundary condition that the geometry of the lorentz force actuator is satisfied m Width w m Thickness t m And the air gap length s is optimized in the following direction: maximizing permanent magnet length l m Width w m Thickness t m The air gap length s is minimized.
Further, the step S4 includes:
s40, calculating the number of turns N of the coil coil ：
Wherein: F. b (B) s I, l are respectively corresponding to Lorentz force, air gap magnetic induction intensity, coil current and each turnThe coil effective length;
s41, calculating the winding layer number L of the coil:
wherein: d, d 2 For actuator travel, c is the thickness of the coil housing, d coil The diameter of the copper wire;
s42, calculating the number of turns T of each layer of the coil:
s43, calculating the length l of each turn of the coil ij ：
Wherein: l (L) ij Represents the j-th turn coil length of the i-th layer, where i=1, 2, … L, j=1, 2, … T; p and q are the hollow length and width dimensions of the coil respectively;
s44, calculating the total length l of the single-layer coil total ：
l total ＝l i1 +l i2 +l i3 …l iT ＝2T[p+q+4d coil +2d coil (T-1)]
Wherein: l (L) total Is the total length of the i-th layer coil, where i=1, 2, … L;
s45, calculating the coil volume V coil ：
S46, calculating the coil mass m coil ：
m coil ＝ρη pack V coil
Wherein: ρ is the density of copper wire, η pack Copper filling rate;
s47, calculating coil heat consumption Q:
wherein: r is coil resistance, S is copper wire sectional area, ρ r Is the resistivity of the copper wire;
s48, setting boundary condition one of the geometric dimensions of the Lorentz force actuator:
wherein: t is t coil Is the coil thickness; w (w) coil Is the width of a single-side coil; l (L) coil A coil length; w (W) coil Coil width; d, d 1 Is the distance between the permanent magnets on one side;
s49, setting a boundary condition II of the geometric dimension of the Lorentz force actuator:
wherein: x is x 1 、x 2 、x 3 The outer envelope of the lorentz force actuator is thick, wide and long.
In order to achieve the above object, in a second aspect, the present invention provides a lorentz force actuator, which is obtained by adopting the design method of the lorentz force actuator in the first aspect.
In general, through the above technical solutions conceived by the present invention, the following beneficial effects can be obtained:
firstly, establishing a Lorentz force actuator initialization model based on design indexes of the Lorentz force actuator; based on the initialization model, analyzing the relationship between the rotor, the stator and the air gap magnetic induction intensity in the Lorentz force actuator; further, analyzing the geometric parameters of the permanent magnet and the relation between the length of the air gap and the magnetic induction intensity of the air gap, and providing a rapid calculation method of the magnetic induction intensity of the air gap so as to rapidly determine the optimization direction of the geometric parameters of the permanent magnet and the length of the air gap; finally, a Lorentz force actuator parameterized model is constructed, and permanent magnet structures and coil parameters are optimally designed by taking the principle of maximizing the output force of the actuator and simultaneously minimizing the coil quality and heat consumption and taking the outer envelope size of the actuator as constraint conditions. The design method disclosed by the invention can realize maximum output force of the actuator, and meanwhile, the coil quality and heat consumption are minimum, and the method is efficient and accurate.
Drawings
FIG. 1 is a flow chart of steps in a method of designing a Lorentz force actuator according to an embodiment of the present invention;
FIG. 2 is a front view of the structure of a Lorentz force actuator according to an embodiment of the invention;
FIG. 3 is a schematic diagram of the parameters of a coil in a Lorentz force actuator according to an embodiment of the invention;
FIG. 4 is a front triaxial view of a Lorentz force actuator according to an embodiment of the present invention;
FIG. 5 is a diagram of D in a Lorentz force actuator according to an embodiment of the invention 1 /D 2 A position diagram;
FIG. 6 is a diagram of D in a Lorentz force actuator according to an embodiment of the invention 1 And D 2 A relation diagram of magnetic induction intensity;
FIG. 7 is a graph showing the comparison between the calculation and simulation results of the magnetic induction intensity formula in the Lorentz force actuator according to the embodiment of the invention;
FIG. 8 is a graph of magnetic induction intensity versus length and width of a permanent magnet in a Lorentz force actuator according to an embodiment of the present invention;
FIG. 9 is a graph of magnetic induction intensity versus permanent magnet thickness and air gap length for a Lorentz force actuator according to an embodiment of the present invention;
FIG. 10 is a graph of Lorentz force versus number of coil turns, air gap length for a Lorentz force actuator according to an embodiment of the present invention;
FIG. 11 is a graph of coil mass versus coil number of turns and air gap length for a Lorentz force actuator of an embodiment of the invention;
FIG. 12 is a graph of coil heat loss versus coil number of turns and air gap length for a Lorentz force actuator of an embodiment of the invention;
fig. 13 is a graph comparing simulation results and experimental results in the lorentz force actuator of the embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
In the present invention, the terms "first," "second," and the like in the description and in the drawings, if any, are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order.
As shown in FIG. 1, by adopting the design method of the Lorentz force actuator provided by the invention, the maximum output of the actuator can be realized, and the coil quality and the heat consumption are minimum. In order to pursue high thrust, the conventional lorentz force actuator often needs to sacrifice the overall size, heat consumption and the like of the actuator. It should be noted that the design of the lorentz force actuator is guided by the requirements. Taking a Lorentz force actuator which is designed based on the efficient method and is put into engineering application as an example, the design index requirements in the step 1 are as follows; thrust constant: k (K) F =18 (±10%) N/a; output force interval of actuator: 0.1N-50N; actuator travel d 2 ≤3mm。
And 2, establishing an original structure of the Lorentz force actuator, wherein the Lorentz force actuator constructed in the 2 is composed of two groups of bar-shaped permanent magnets with opposite magnetic poles, a rectangular-like hollow coil and two magnetic yokes. Given the object material properties, the initial structure output lorentz force satisfies the following condition: f=2n coil B s Il≥K F I, wherein: F. n (N) coil 、B s 、I、l、K F The magnetic flux is respectively corresponding to Lorentz force, turns of the coil, air gap magnetic induction intensity, coil current, effective length of each turn of coil and thrust constant.The schematic diagrams are shown in figures 2, 3 and 4, wherein the yoke material is DT4C, the permanent magnet material is NdFe50, and the remanence B thereof r 1.4T. Based on the structure, 3D parameterized simulation analysis is carried out in ANSYS to obtain a parameter D 1 ，D 2 With air gap magnetic induction intensity (B) s ) And (3) completing step 3. Wherein D is 1 、D 2 The position diagram is shown in fig. 5, and the relation between the position diagram and the magnetic induction intensity of the air gap is shown in fig. 6. In this embodiment, the coil portion is defined as a stator, and the permanent magnet portion is defined as a mover. As can be seen from the analysis of fig. 6, the air gap induction is maximized when the coil is positioned at the geometric center with respect to the magnetic field.
In step 4, the enhancement effect of the yoke on the magnetic circuit is considered, and the air gap magnetic induction intensity (B s ) Is calculated according to the formula:
the formula air gap magnetic induction intensity B s Pairs of calculated results and ANSYS simulation results are shown in fig. 7. From the comparison result, the validity of the provided calculation formula is verified. Therefore, according to the formula, the length l of the permanent magnet can be analyzed by MATLAB software m Width w m With air gap magnetic induction intensity B s The method comprises the steps of carrying out a first treatment on the surface of the Thickness t of permanent magnet m Air gap length s and air gap magnetic induction intensity B s Is a relationship of (3). The analysis results are shown in fig. 8 and 9, respectively. As can be seen from fig. 8 and 9, the geometry of the permanent magnet increases and the air gap induction increases, and the relationship between the air gap induction and the air gap length s concludes the opposite. The direction of optimization is therefore to maximize the permanent magnet geometry, minimize the air gap length, while taking into account the geometric boundary conditions and position constraints in step 5.
After the steps 1 to 4 are completed, a lorentz force actuator parameterized model can be further established, a foundation is provided for subsequent optimization, and the step 5 comprises the following steps:
50, calculate the number of turns N of the coil coil ：
Wherein: F. b (B) s The Lorentz force, the air gap magnetic induction intensity, the coil current and the effective length of each turn of coil are respectively corresponding to I, l;
51, calculating the number of winding layers L of the coil:
wherein: d, d 2 For actuator travel, c is the thickness of the coil housing, d coil The diameter of the copper wire;
52, calculating the number of turns T of each layer of the coil:
53, calculate the length l of each turn of coil ij ：
Wherein: l (L) ij Represents the j-th turn coil length of the i-th layer, where i=1, 2, … L, j=1, 2, … T; p and q are the hollow length and width dimensions of the coil respectively;
54, calculating the total length l of the single-layer coil total ：
l total ＝l i1 +l i2 +l i3 …l iT ＝2T [p+q+4d coil +2d coil (T-1)] (5)
Wherein: l (L) total Is the total length of the i-th layer coil, where i=1, 2, … L;
55, calculate coil volume V coil ：
56, calculating coil mass m coil ：
m coil ＝ρη pack V coil (7)
Wherein: ρ is the density of copper wire, η pack Copper filling rate;
57, coil heat loss Q:
wherein: r is coil resistance, S is copper wire sectional area, ρ r Is the resistivity of the copper wire;
58, setting a boundary condition one of the geometric dimensions of the Lorentz force actuator according to the internal geometric position relation of the Lorentz force actuator:
wherein: t is t coil Is the coil thickness; w (w) coil Is the width of a single-side coil; l (L) coil A coil length; w (W) coil Coil width; d, d 1 Is the distance between the permanent magnets on one side;
59, setting a boundary condition II of the geometric dimension of the lorentz force actuator according to the maximum dimension of the lorentz force actuator:
wherein: x is x 1 、x 2 、x 3 The outer envelope of the lorentz force actuator is thick, wide and long.
Equations (1) to (10) are lorentz force actuator parameterized models.
Based on the Lorentz force actuator parameterized model, the actuator multi-objective optimization model in the step 6 is established, and the actuator multi-objective optimization model comprises the following steps:
based on the parameterized model established in step 5,with maximum air gap induction B s Minimizing coil mass m coil And the heat consumption Q is taken as an optimization target, and the following multi-target optimization model is established:
further, based on the multi-objective optimization model, the lorentz force F and the coil mass m can be obtained coil And heat loss Q and number of turns N coil Relationship of air gap length s. The results are shown in fig. 10, 11 and 12, respectively.
Based on the analysis results of the steps 3 and 4, according to the model and the analysis results established in the steps 5 and 6, utilizing a MATLAB optimization tool box to develop permanent magnet structure optimization design and coil parameter design, and iteratively completing the steps 7 to 10. The parameters of the actuators before and after optimization are shown in Table 1:
table 1 before and after optimization of the actuator parameter table
| Parameters (parameters) | Unit (B) | Initial value | Optimizing results | |
| l m ×w m ×t m | mm | 35×15×5 | 47×19×6 | |
| d 2 | mm | 2 | 2 | |
| s | mm | 13 | 12 | |
| p× | mm | 14×8 | 20×10 | |
| d coil | mm | 0.332 | 0.344 | |
| | mm | 2 | 2 | |
| I | A | 1 | 1 | |
| N coil | -- | 667 | 503 | |
| w coil | mm | 16 | 13 | |
| l coil | mm | 46 | 46 | |
| W coil | mm | 40 | 36 | |
| K F | N/A | 17.9 | 18.3 | |
| m coil | g | 36.72 | 35.05 | |
| Q | w | 11.85 | 9.58 |
Step 11: from the optimized results, the thrust constant K F =18.3n/a > 18N/a, while coil mass m coil The heat consumption Q is smaller than the initial value. In addition, as can be seen from fig. 13, the simulation and test results are well matched, the consistency is high, and the fact that the lorentz force actuator output thrust linearity realized based on the design method is high is explained. Finally, fitting the experimental result data to obtain an actual thrust constant K F =17.85N/a satisfies the 18 (±10%) N/a requirement.
It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (7)
1. The design method of the Lorentz force actuator is characterized by comprising the following steps of:
s1, acquiring design indexes of a Lorentz force actuator, and establishing an initialization model of the Lorentz force actuator;
s2, based on the Lorentz force actuator initialization model, determining the air gap magnetic induction intensity B through simulation s When maximizing, distance D from stator to magnetic field center in Lorentz force actuator along Lorentz force direction 1 And distance D from stator to magnetic field center along magnetic field vector direction 2 Is the optimum value of (2);
s3, analyzing the length l of the permanent magnet m Width w m Thickness t m And air gap length s and air gap magnetic induction intensity B s To determine the air gap induction B s Length of permanent magnet at maximum l m Width w m Thickness t m And the direction of optimization of the air gap length s;
s4, constructing a Lorentz force actuator parameterized model, wherein the Lorentz force actuator parameterized model comprises coil mass m coil And the coil heat loss Q, and boundary conditions of the geometric dimensions of the Lorentz force actuator;
s5, to maximize the air gap magnetic induction intensity B s Minimizing coil mass m coil And taking the coil heat consumption Q as an optimization target, and solving the Lorentz force actuator parameterized model in combination with the optimization direction determined in the step S3, so as to determine the optimal value of each parameter of the Lorentz force actuator.
2. The method for designing a lorentz force actuator according to claim 1, wherein in S1, when the lorentz force actuator initialization model is established, the following should be satisfied:
F＝2N coil B s Il≥K F I
in the middle of：F、N coil 、B s 、I、l、K F The magnetic flux is respectively corresponding to Lorentz force, turns of the coil, air gap magnetic induction intensity, coil current, effective length of each turn of coil and thrust constant.
3. The method for designing a lorentz force actuator according to claim 1, characterized in that in S2, the distance D from the stator to the center of the magnetic field in the lorentz force direction in the lorentz force actuator is analyzed by performing 3D parametric simulation analysis in ANSYS 1 Distance D between stator and magnetic field center along magnetic field vector direction 2 With air gap magnetic induction intensity B s To determine the air gap induction B s D when maximized 1 And D 2 Is set to the optimum value of (2).
4. The method for designing a lorentz force actuator according to claim 1, wherein in S3, the length l of the permanent magnet is resolved by the following formula m Width w m Thickness t m And air gap length s and air gap magnetic induction intensity B s Is the relation of:
wherein: b (B) r Residual magnetism for the permanent magnet material; k is the equivalent thickening coefficient of the permanent magnet under the condition of considering the reinforcing effect of the magnetic yoke on the magnetic circuit.
5. The method for designing a lorentz force actuator according to claim 4, characterized in that in S3, the permanent magnet length l is set to satisfy the boundary condition of the lorentz force actuator geometry m Width w m Thickness t m And the air gap length s is optimized in the following direction: maximizing permanent magnet length l m Width w m Thickness t m The air gap length s is minimized.
6. The method for designing a lorentz force actuator according to claim 1, characterized in that S4 comprises:
s40, calculating the number of turns N of the coil coil ：
Wherein: F. b (B) s The Lorentz force, the air gap magnetic induction intensity, the coil current and the effective length of each turn of coil are respectively corresponding to I, l;
s41, calculating the winding layer number L of the coil:
wherein: d, d 2 For actuator travel, c is the thickness of the coil housing, d coil The diameter of the copper wire;
s42, calculating the number of turns T of each layer of the coil:
s43, calculating the length l of each turn of the coil ij ：
Wherein: l (L) ij Represents the j-th turn coil length of the i-th layer, where i=1, 2, … L, j=1, 2, … T; p and q are the hollow length and width dimensions of the coil respectively;
s44, calculating the total length l of the single-layer coil total ：
l total ＝l i1 +l i2 +l i3 …l iT ＝2T[p+q+4d coil +2d coil (T-1)]
Wherein: l (L) total Is the total length of the i-th layer coil, wherein i=1,2,…L；
S45, calculating the coil volume V coil ：
S46, calculating the coil mass m coil ：
m coil ＝ρη pack V coil
Wherein: ρ is the density of copper wire, η pack Copper filling rate;
s47, calculating coil heat consumption Q:
Wherein: r is coil resistance, S is copper wire sectional area, ρ r Is the resistivity of the copper wire;
s48, setting boundary condition one of the geometric dimensions of the Lorentz force actuator:
wherein: t is t coil Is the coil thickness; w (w) coil Is the width of a single-side coil; l (L) coil A coil length; w (W) coil Coil width; d, d 1 Is the distance between the permanent magnets on one side;
s49, setting a boundary condition II of the geometric dimension of the Lorentz force actuator:
wherein: x is x 1 、x 2 、x 3 Outer envelope for lorentz force actuatorThick, wide, long dimensions.
7. A lorentz force actuator, characterized in that it is obtained by the design method of a lorentz force actuator according to any one of claims 1 to 6.
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