CN106685178B - Viscoelastic damping structure based on permanent magnet synchronous linear motor and application thereof - Google Patents

Viscoelastic damping structure based on permanent magnet synchronous linear motor and application thereof Download PDF

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CN106685178B
CN106685178B CN201710123761.XA CN201710123761A CN106685178B CN 106685178 B CN106685178 B CN 106685178B CN 201710123761 A CN201710123761 A CN 201710123761A CN 106685178 B CN106685178 B CN 106685178B
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permanent magnet
viscoelastic
linear motor
magnet synchronous
synchronous linear
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CN106685178A (en
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赵吉文
何中燕
董菲
王立俊
宋俊材
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Anhui University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K41/00—Propulsion systems in which a rigid body is moved along a path due to dynamo-electric interaction between the body and a magnetic field travelling along the path
    • H02K41/02—Linear motors; Sectional motors
    • H02K41/03—Synchronous motors; Motors moving step by step; Reluctance motors
    • H02K41/031—Synchronous motors; Motors moving step by step; Reluctance motors of the permanent magnet type
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K7/00—Arrangements for handling mechanical energy structurally associated with dynamo-electric machines, e.g. structural association with mechanical driving motors or auxiliary dynamo-electric machines

Abstract

The invention discloses a permanent magnet synchronous linear electricThe viscoelastic damping structure of the machine and application thereof are characterized in that: a viscoelastic damping strip is arranged on the back iron of the permanent magnet synchronous linear motor; a damping adjusting bolt with scales is arranged on the rotor and at a position corresponding to the viscoelastic damping strip; the bottom of the screw rod of the damping adjusting bolt is provided with a shearing area A' s Is a compact of the powder. The invention can reduce the thrust fluctuation of the permanent magnet synchronous linear motor, thereby improving the positioning precision of the permanent magnet synchronous linear motor and leading the permanent magnet synchronous linear motor to be widely applied in the precision machining technology.

Description

Viscoelastic damping structure based on permanent magnet synchronous linear motor and application thereof
Technical Field
The invention relates to the field of permanent magnet synchronous linear motors, in particular to a method for inhibiting thrust fluctuation of a permanent magnet synchronous linear motor by adopting viscoelastic damping.
Background
The permanent magnet synchronous linear motor (permanent magnet synchronous linear motor) has the advantages of simple structure, high thrust, low loss, high positioning precision and the like, and is widely applied to precision numerical control machine tools with less cutting force. However, due to the end effect and harmonic component generated by the on-off of the PMSLM stator, the PMSLM has the defect of large thrust fluctuation, and when high-precision machine tool machining is required, the thrust fluctuation causes the machining quality problems of workpiece surface scratches, unsatisfactory size and the like, and in addition, vibration and machine noise are caused to influence the positioning precision.
At present, scholars at home and abroad commonly inhibit thrust fluctuation from two angles: spatial harmonics and temporal harmonics. The space harmonic wave means that the internal structure of the motor is changed and optimized, for example, the thrust fluctuation is restrained by adopting methods of oblique poles, fractional slots, changing the arrangement mode of permanent magnets, magnetizing modes and the like; the time harmonic wave means that the input three-phase electricity is more approximate to sine by adopting a control strategy, for example, a feedforward compensator is designed according to the established mathematical model of thrust fluctuation, motor speed and position, and the thrust fluctuation is compensated under different motion speeds. Both of the above methods have respective drawbacks: the fractional slot reduces thrust fluctuation mainly by reducing tooth slot effect, the PMSLM effect of the iron-free core is not obvious, the arrangement mode of the permanent magnets is changed to determine optimal arrangement mainly by selecting pole arc coefficients, harmonic coefficients can be reduced, but the utilization rate of secondary poles is reduced, and the magnetizing mode is changed to enable the magnetic flux density to be close to sine, but the technical problem exists due to the magnetizing technology; while the feedforward compensation can only suppress the 5 th harmonic current and the 7 th harmonic current caused by the dead time of the inverter, the harmonic current suppression caused by other reasons is not obvious.
Disclosure of Invention
The invention provides a viscoelastic damping structure based on a permanent magnet synchronous linear motor and application thereof, which aim to solve the defect of large PMLSM thrust fluctuation in the prior art, so that the thrust fluctuation of the permanent magnet synchronous linear motor can be reduced, the positioning precision of the permanent magnet synchronous linear motor can be improved, and the permanent magnet synchronous linear motor can be widely applied to precision machining technology.
The invention adopts the following technical scheme for solving the technical problems:
the invention relates to a viscoelastic damping structure based on a permanent magnet synchronous linear motor, which comprises the following components: back iron, guide rail and active cell; the method is characterized in that a viscoelastic damping strip is arranged on the back iron of the permanent magnet synchronous linear motor; a damping adjusting bolt marked with scales is arranged on the rotor and at a position corresponding to the viscoelastic damping strip; the bottom of the screw rod of the damping adjusting bolt is provided with a contact area A s A' briquetting;
the pressing force generated by the pressing block acting on the viscoelastic damping strip forms a structure for inhibiting thrust fluctuation generated when the rotor moves on the guide rail.
The invention relates to a method for inhibiting thrust fluctuation of a permanent magnet synchronous linear motor based on viscoelastic damping, which is characterized by comprising the following steps:
step 1, representing the thrust F of the permanent magnet synchronous linear motor by using a formula (1):
Figure BDA0001237810150000021
in the formula (1), I is the current amplitude, N is the number of turns of the coil, L is the effective length of the coil, u 0 Is air permeability, m i Is the spatial frequency of the magnetic field, and has: m is m i = (2 i-1) pi/τ; i=1, 2 …; τ is the pole distance of the permanent magnet, M i Is a coefficient related to a spatial magnetic field, and has:
Figure BDA0001237810150000022
B r the residual magnetization intensity of the permanent magnet is p, and the width of the permanent magnet is p; delta is an air gap, h 1 Is the height of the permanent magnet, h 2 Is the coil height; omega is current frequency, t is time, X a1 And X a2 Representing the A-phase coefficient, X b1 And X b2 Representing B-phase coefficient, X c1 And X c2 Represents the C-phase coefficient, and has: x is X a1 ＝[cosm i d-cosm i (D-d)-1]、X a2 ＝[sinm i (D-d)-sinm i d-sinm i D]、/>
Figure BDA0001237810150000023
Figure BDA0001237810150000024
D is the width of one coil, and D is the width of a single-side coil; k (k) 1 And k 1 Represents the frequency coefficient, and has: />
Figure BDA0001237810150000025
Step 2, using the thrust F of the permanent magnet synchronous linear motor as excitation of the viscoelastic damper to obtain a calculation expression of the damping force F of the viscoelastic damper as shown in the formula (2):
Figure BDA0001237810150000026
in the formula (2), G 0 For the elastic coefficient of the viscoelastic damping strip, G 1 The damping coefficient of the viscoelastic damping strip; a is that s H' is the contact area between the pressing block and the viscoelastic damping strip in the viscoelastic damper, and is the thickness of the viscoelastic damping strip when being pressed; x is x 1a 、x 2a 、x 3a And x 4a Representing a damping force coefficient, x, generated by the A-phase thrust of the permanent magnet synchronous linear motor acting on the viscoelastic damping strip 1b 、x 2b 、x 3b 、x 4b Representing a damping force coefficient, x, generated by the B-phase thrust of the permanent magnet synchronous linear motor acting on the viscoelastic damping strip 1c 、x 2c 、x 3c 、x 4c The damping force coefficient generated by the C-phase thrust of the permanent magnet synchronous linear motor acting on the viscoelastic damping strip is represented, and the damping force coefficient comprises:
Figure BDA0001237810150000031
Figure BDA0001237810150000032
Figure BDA0001237810150000033
Figure BDA0001237810150000034
in the formulas (3) to (6), q is equal to a, b and c respectively;
step 3: order the
Figure BDA0001237810150000035
Is F i The thrust force F of the permanent magnet synchronous linear motor shown in the formula (7) after the action of the viscoelastic damper is obtained by adding the thrust force F and the viscoelastic damping force F 1 The expression:
Figure BDA0001237810150000036
step 4: in the same time period, respectively utilizing the formula (1) to make a graph of the thrust F of the permanent magnet synchronous linear motor before the action of the viscoelastic damper, and utilizing the formula (7) to make the thrust F of the permanent magnet synchronous linear motor after the action of the viscoelastic damper 1 Is used for adjusting the contact area A of a pressing block and a viscoelastic damping strip in the viscoelastic damper s And the thickness h' of the viscoelastic damping strip when being pressed, comparing the two thrust graphs, and when the thrust F 1 When the fluctuation of the curve is smaller than that of the F curve, the required contact area A is obtained s 'and thickness h';
step 5, selecting a viscoelastic damping strip meeting installation conditions and pasting the viscoelastic damping strip on the back iron of the permanent magnet synchronous linear motor;
step 6, damping adjusting bolts marked with scales are arranged on the rotor of the permanent magnet synchronous linear motor and at positions corresponding to the viscoelastic damping strips; the bottom of the damping adjusting bolt is provided with a contact area A s A' briquetting;
and 7, adjusting the tightness of the damping adjusting bolt to enable the thickness of the pressing block acting on the viscoelastic damping strip to be h' and generate a pressing force, so that thrust fluctuation generated when the mover moves on the guide rail is restrained.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention designs the viscoelastic damper to restrain thrust fluctuation by combining the structure and the motion characteristics of the permanent magnet synchronous linear motor, and the viscoelastic damping force generated by the viscoelastic damper is utilized to restrain thrust fluctuation generated during motor operation, so that the internal structure of the motor is not required to be changed, and the technical problems of high processing difficulty, unreasonable motor space use and the like caused by changing the structure of the motor are solved.
2. According to the invention, a technical means of restraining thrust fluctuation of the permanent magnet synchronous linear motor by using a viscoelastic damping force is adopted, the main frequency of the thrust fluctuation can be determined from the thrust expression of the permanent magnet synchronous linear motor represented by the formula (1), the thrust of the permanent magnet synchronous linear motor is used as excitation of the viscoelastic damper, the viscoelastic damping force under the excitation of the thrust is the same as the opposite frequency of the thrust direction of the permanent magnet synchronous linear motor, and the amplitude of a corresponding fluctuation frequency band can be reduced after the two are added, so that the purpose of restraining the thrust fluctuation is achieved.
3. According to the viscoelastic damper, the damping adjusting bolt is marked with scales, and the thickness h 'of the viscoelastic damper strip obtained in the step 4 can be accurately set to be h' according to the working thickness of the viscoelastic damper strip in specific implementation, so that the effect of inhibiting thrust fluctuation is more accurate and effective.
4. According to the characteristics of vibration reduction and buffering of the viscoelastic damping, the viscoelastic damper is designed and applied to the viscoelastic damper for inhibiting the thrust fluctuation of the permanent magnet synchronous linear motor, the thrust fluctuation can be effectively reduced, and compared with the prior art for inhibiting the thrust fluctuation through space harmonic wave and time harmonic wave angles, the novel concept for inhibiting the thrust fluctuation by externally installing a mechanical structure is further provided.
Drawings
FIG. 1 is a schematic diagram of a viscoelastic damping system in accordance with the present invention;
FIG. 2 is a schematic cross-sectional view of a viscoelastic damper in accordance with the present invention;
FIG. 3 is a schematic diagram of a PMSLM layer analysis model in the prior art;
FIG. 4 is a graph of PMSLM thrust in accordance with the present invention;
reference numerals in the drawings: 1 is a viscoelastic damping strip; 2 is a damping adjusting bolt; 3 is back iron; 4 is a guide rail; 5 is a rotor; 6 is a permanent magnet synchronous linear motor; v is the movement direction of the mover 5; 7 is a briquette.
Detailed Description
In this embodiment, as shown in fig. 1, a viscoelastic damping structure for suppressing thrust fluctuation of a permanent magnet synchronous linear motor, the permanent magnet synchronous linear motor 6 includes: back iron 3, guide rail 4 and mover 5; a viscoelastic damping strip 1 is arranged on a back iron 3 of a permanent magnet synchronous linear motor 6; a scale-marked resistor is arranged on the rotor 5 and at a position corresponding to the viscoelastic damping strip 1A damper adjusting bolt 2; the bottom of the screw rod of the damping adjusting bolt 2 is provided with a contact area A s A' briquette 7; a cross-sectional view of the viscoelastic damper is shown in fig. 2. The pressing force generated by the pressing block 7 acting on the viscoelastic damping strip 1 forms a structure for inhibiting thrust fluctuation generated when the rotor 5 moves on the guide rail 4.
In this embodiment, a method for suppressing thrust fluctuation of a permanent magnet synchronous linear motor based on viscoelastic damping is performed according to the following steps:
step 1, analyzing excitation action of a motor permanent magnet, and representing an equivalent magnetization space distribution function by using M (x):
Figure BDA0001237810150000051
in the formula (1), u 0 Is air permeability, B r Is the residual magnetization intensity of the permanent magnet, and tau is the polar distance; m is m i Is the spatial frequency of the magnetic field, and has: m is m i = (2 i-1) pi/τ; i=1, 2 …; p is the permanent magnet width.
The motor layer analysis is assumed as follows: neglecting the change of the magnetic field in the Z direction; the back ferromagnetic conductivity of the motor is infinite; the permanent magnets are uniformly magnetized. The motor layer analysis schematic diagram is shown in fig. 3, and poisson equations of an air gap area I and a permanent magnet area II are established according to maxwell equations:
Figure BDA0001237810150000052
in the formula (2), A I A II The vector magnetic potential of the air gap area and the permanent magnet area respectively has the boundary conditions that:
Figure BDA0001237810150000053
from the following components
Figure BDA0001237810150000054
Obtaining the y-axis magnetic flux density distribution function of the air gap areaBy1：
Figure BDA0001237810150000055
As shown in fig. 3, the induced electromotive force E of the motor a-phase winding a Can be characterized as:
Figure BDA0001237810150000056
in the formula (5), V is the motor movement speed.
The induced electromotive force E of the B phase and the C phase can be calculated by the same method b 、E c The induced electromotive force lags behind the A phase by 2 pi/3 and 4 pi/3 respectively.
Assuming that the initial phase angle of the a-phase current is zero, the three-phase symmetric sinusoidal ac current can be expressed as:
Figure BDA0001237810150000061
then by the formula
Figure BDA0001237810150000062
The thrust F of the permanent magnet synchronous linear motor (6) can be characterized: />
Figure BDA0001237810150000063
In the formula (7), I is the current amplitude, N is the number of turns of the coil, L is the effective length of the coil, M i Is a coefficient related to a spatial magnetic field, and has:
Figure BDA0001237810150000064
delta is an air gap, h 1 Is the height of the permanent magnet, h 2 Is the coil height; omega is current frequency, t is time, X a1 And X a2 Representing the A-phase coefficient, X b1 And X b2 Representing B-phase coefficient, X c1 And X c2 Represents the C-phase coefficient, and has:
X a1 ＝[cosm i d-cosm i (D-d)-1]、X a2 ＝[sinm i (D-d)-sinm i d-sinm i D]、
Figure BDA0001237810150000065
Figure BDA0001237810150000066
Figure BDA0001237810150000067
Figure BDA0001237810150000068
d is the width of one coil, and D is the width of a single-side coil;
k 1 and k 1 Represents the frequency coefficient, and has:
Figure BDA0001237810150000069
step 2, analyzing the viscoelastic damping force by adopting a Kelvin model, wherein the viscoelastic damping force can be expressed as follows under sine excitation of frequency omega':
Figure BDA00012378101500000610
in the formula (8), u is deformation quantity of viscoelastic damping under sine excitation,
Figure BDA0001237810150000071
is the derivative of the deformation u.
Since the thrust force F is obtained by adding sine and cosine functions in the form of the formula (7), the thrust force F of the permanent magnet synchronous linear motor 6 can be used as excitation of the viscoelastic damper, and the excitation frequency at this time is the current frequency ω, so as to obtain a calculation expression of the damping force F of the viscoelastic damper as shown in the formula (9):
Figure BDA0001237810150000072
in the formula (9), G 0 Elastic coefficient, G, of viscoelastic damping strip 1 1 Damping coefficient of the viscoelastic damping strip 1; a is that s The contact area between the pressing block 7 and the viscoelastic damping strip 1 in the viscoelastic damper is h' which is the thickness of the viscoelastic damping strip 1 when being pressed; x is x 1a 、x 2a 、x 3a And x 4a Representing damping force coefficient, x generated by A phase thrust of permanent magnet synchronous linear motor acting on viscoelastic damping strip 1b 、x 2b 、x 3b 、x 4b Represents the damping force coefficient, x, generated by the B phase thrust of the permanent magnet synchronous linear motor acting on the viscoelastic damping strip 1c 、x 2c 、x 3c 、x 4c The damping force coefficient generated by the C-phase thrust of the permanent magnet synchronous linear motor acting on the viscoelastic damping strip is shown as follows:
Figure BDA0001237810150000073
Figure BDA0001237810150000074
Figure BDA0001237810150000075
Figure BDA0001237810150000076
in the formulas (9) to (13), q is equal to a, b, c, respectively;
step 3: order the
Figure BDA0001237810150000077
Is F i The thrust force F and the viscoelastic damping force F are added to obtain permanent magnet synchronous linear electricity shown in the formula (14)Thrust force F of machine 6 after action of viscoelastic damper 1 The expression: />
Figure BDA0001237810150000081
Step 4: table 1 shows design parameters of a permanent magnet synchronous linear motor, wherein the motor is of a 7-stage 6-coil structure, and the viscoelastic damping strip is made of butyl rubber.
Table 1 design parameters of permanent magnet synchronous linear motor
Parameters (parameters) Numerical value/mm
Permanent magnet width P 15
Permanent magnet high h 1 3
Number of turns N of coil 100
Coil height h 2 5
Single side width d of coil 7
Coil width D 22
Polar distance τ 19
Air gap delta 2
The parameters shown in Table 1 and the relative properties of the viscoelastic damping material butyl rubber are adopted to respectively utilize the formula (7) to make a graph of the thrust F of the permanent magnet synchronous linear motor 6 before the action of the viscoelastic damper and the formula (14) to make the thrust F of the permanent magnet synchronous linear motor 6 after the action of the viscoelastic damper in the same time period by adopting an analytic method 1 Is used for adjusting the contact area A of the pressing block 7 and the viscoelastic damping strip 1 in the viscoelastic damper s And the thickness h' of the viscoelastic damping strip 1 when being pressed, and comparing the two thrust graphs, when the thrust F 1 When the curve fluctuation is significantly smaller than that of the F curve, the contact area A is obtained s ' and thickness h "are the desired values; the thrust curve is shown in FIG. 4
Step 5, selecting a viscoelastic damping strip 1 meeting installation conditions and adhering the viscoelastic damping strip to the back iron 3 of the permanent magnet synchronous linear motor 6;
step 6, damping adjusting bolts 2 marked with scales are arranged on the rotor 5 of the permanent magnet synchronous linear motor 6 and at positions corresponding to the viscoelastic damping strips 1; the bottom of the damping adjusting bolt 2 is provided with a contact area A s A' briquette 7;
and 7, adjusting the tightness of the damping adjusting bolt 2 to enable the thickness of the pressing block 7 acting on the viscoelastic damping strip 1 to be h' and generate a pressing force, so as to inhibit thrust fluctuation generated when the rotor 5 moves on the guide rail 4.

Claims (1)

1. A method of suppressing a viscoelastic damping structure based on a permanent magnet synchronous linear motor, the permanent magnet synchronous linear motor (6) comprising: a back iron (3), a guide rail (4) and a rotor (5); the method is characterized in that a viscoelastic damping strip (1) is arranged on a back iron (3) of the permanent magnet synchronous linear motor (6); on the mover (5) and at a position corresponding to the viscoelastic damping strip (1)A damping adjusting bolt (2) with scales is arranged on the damping adjusting bolt; the bottom of the screw rod of the damping adjusting bolt (2) is provided with a contact area A s A' briquette (7);
the pressing force generated by the pressing block (7) acting on the viscoelastic damping strip (1) forms a structure for inhibiting thrust fluctuation generated when the rotor (5) moves on the guide rail (4); the inhibition method comprises the following steps:
step 1, representing the thrust F of the permanent magnet synchronous linear motor (6) by using a formula (1):
Figure FDA0004167380870000011
in the formula (1), I is the current amplitude, N is the number of turns of the coil, L is the effective length of the coil, u 0 Is air permeability, m i Is the spatial frequency of the magnetic field, and has: m is m i = (2 i-1) pi tau; i=1, 2 …; τ is the pole distance of the permanent magnet, M i Is a coefficient related to a spatial magnetic field, and has:
Figure FDA0004167380870000012
B r the residual magnetization intensity of the permanent magnet is p, and the width of the permanent magnet is p; delta is an air gap, h 1 Is the height of the permanent magnet, h 2 Is the coil height; omega is current frequency, t is time, X a1 And X a2 Representing the A-phase coefficient, X b1 And X b2 Representing B-phase coefficient, X c1 And X c2 Represents the C-phase coefficient, and has: x is X a1 ＝[cosm i d-cosm i (D-d)-1]、X a2 ＝[sinm i (D-d)-sinm i d-sinm i D]、/>
Figure FDA0004167380870000013
Figure FDA0004167380870000014
D is the width of one coil, and D is the width of a single-side coil; k (k) 1 And k 1 Representing frequencyCoefficients, and has: />
Figure FDA0004167380870000015
Step 2, using the thrust F of the permanent magnet synchronous linear motor (6) as excitation of the viscoelastic damper to obtain a calculation expression of the damping force F of the viscoelastic damper shown in the formula (2):
Figure FDA0004167380870000021
/>
in the formula (2), G 0 Is the elastic coefficient, G, of the viscoelastic damping strip (1) 1 Is the damping coefficient of the viscoelastic damping strip (1); a is that s The contact area between the pressing block (7) and the viscoelastic damping strip (1) in the viscoelastic damper is h' which is the thickness of the viscoelastic damping strip (1) when being pressed; x is x 1a 、x 2a 、x 3a And x 4a Representing a damping force coefficient, x, generated by the A-phase thrust of the permanent magnet synchronous linear motor acting on the viscoelastic damping strip 1b 、x 2b 、x 3b 、x 4b Representing a damping force coefficient, x, generated by the B-phase thrust of the permanent magnet synchronous linear motor acting on the viscoelastic damping strip 1c 、x 2c 、x 3c 、x 4c The damping force coefficient generated by the C-phase thrust of the permanent magnet synchronous linear motor acting on the viscoelastic damping strip is represented, and the damping force coefficient comprises:
Figure FDA0004167380870000022
Figure FDA0004167380870000023
Figure FDA0004167380870000024
Figure FDA0004167380870000025
in the formulas (3) to (6), q is equal to a, b and c respectively;
step 3: order the
Figure FDA0004167380870000026
Is F i The thrust force F of the permanent magnet synchronous linear motor (6) shown in the formula (7) after the action of the viscoelastic damper is obtained by adding the thrust force F and the viscoelastic damping force F 1 The expression:
Figure FDA0004167380870000031
step 4: in the same time period, respectively utilizing the formula (1) to make a graph of the thrust F of the permanent magnet synchronous linear motor (6) before the action of the viscoelastic damper, and utilizing the formula (7) to make the thrust F of the permanent magnet synchronous linear motor (6) after the action of the viscoelastic damper 1 Is used for adjusting the contact area A of a pressing block (7) and a viscoelastic damping strip (1) in a viscoelastic damper s And the thickness h' of the viscoelastic damping strip (1) when being pressed, and comparing the two thrust graphs, when the thrust F 1 When the fluctuation of the curve is smaller than that of the F curve, the required contact area A is obtained s 'and thickness h';
step 5, selecting a viscoelastic damping strip (1) meeting installation conditions and adhering the viscoelastic damping strip to a back iron (3) of the permanent magnet synchronous linear motor (6);
step 6, damping adjusting bolts (2) marked with scales are arranged on the rotor (5) of the permanent magnet synchronous linear motor (6) and at positions corresponding to the viscoelastic damping strips (1); the bottom of the damping adjusting bolt (2) is provided with a contact area A s A' briquette (7);
and 7, adjusting the tightness of the damping adjusting bolt (2) to ensure that the thickness of the pressing block (7) acting on the viscoelastic damping strip (1) is h' and generate a pressing force, thereby inhibiting thrust fluctuation generated when the mover (5) moves on the guide rail (4).
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