CN109240269B - A Dynamic Performance Analysis Method for Parallel Mechanisms - Google Patents
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Abstract
本发明公开了一种用于并联机构的动态性能分析方法，属于机电一体化技术领域。该方法首先在关节空间建立并联机构的动力学模型，计算驱动轴的最大负载惯量；建立并联机构驱动轴的双惯量控制系统，获得角速度传递关系与角度位置传递关系；进一步为双惯量控制系统选择合适的总体阻尼比，并确定速度环控制器及位置环控制器的控制参数；最后计算双惯量控制系统第一、第二阻尼比的变化及第一、第二固有频率的变化，用于解释并联机构的动态性能变化。本发明为分析并联机构这一复杂机电一体化装备的动态性能提供了有效的工具。
The invention discloses a dynamic performance analysis method for a parallel mechanism, which belongs to the technical field of electromechanical integration. This method firstly establishes the dynamic model of the parallel mechanism in the joint space, and calculates the maximum load inertia of the drive shaft; establishes the double inertia control system of the parallel mechanism drive shaft, and obtains the angular velocity transfer relationship and the angular position transfer relationship; further, it is selected for the double inertia control system. Appropriate overall damping ratio, and determine the control parameters of the speed loop controller and the position loop controller; finally calculate the changes of the first and second damping ratios and the changes of the first and second natural frequencies of the dual inertia control system, which are used to explain Dynamic performance changes of parallel mechanisms. The invention provides an effective tool for analyzing the dynamic performance of the complex mechanical and electrical integration equipment of the parallel mechanism.
Description
Technical Field
The invention belongs to the technical field of mechanical and electrical integration, and particularly relates to a dynamic performance analysis problem of a parallel mechanism which is a complex mechanical and electrical integration device.
Background
Compared with the traditional series mechanism, the parallel mechanism has higher rigidity-mass ratio and better acceleration capability in theory, so the parallel mechanism has better dynamic performance potential. In the last two decades, a large number of industrial applications based on parallel mechanisms have been developed in succession, in particular some mechatronics equipment oriented to high-speed application scenarios, such as parallel spindle heads, motion simulators and pick-up robots. However, due to the characteristic of the complex multi-closed-loop structure of the parallel mechanism, the dynamic performance of the parallel mechanism also has the time-varying characteristic, and is difficult to guarantee in practical application. Therefore, in order to further improve the dynamic performance of the parallel mechanism, it is first necessary to deeply analyze the dynamic performance change of the parallel mechanism, and a dynamic performance analysis method for the parallel mechanism is provided.
The dynamic performance of the parallel mechanism is greatly influenced by the performance of a joint space servo system of the parallel mechanism, and the characteristics of the servo system are mainly influenced by load inertia. In most existing methods for analyzing the dynamic performance of the serial mechanism, a joint space servo system is equivalent to a servo motor model, the inertia of the servo motor model is fixed, and the load inertia only serves as external interference to enter the servo system and cannot cause excessive influence on the stability and performance of the servo system. However, for the parallel mechanism, due to the time-varying dynamic load characteristic, the load inertia of the joint space servo system also has a time-varying characteristic, and in the motion process, the time-varying load inertia can cause a large influence on the performance of the closed-loop system, so that the dynamic performance of the parallel mechanism is changed, and therefore, the traditional dynamic performance analysis method based on the servo motor model is not suitable for the parallel mechanism.
Disclosure of Invention
1. A dynamic performance analysis method for a parallel mechanism is characterized by comprising the following steps:
1) establishing a dynamic model of the parallel mechanism in a joint space:
in the formula, τmIs the driving moment of the parallel mechanism, M is an inertia matrix, C is a centrifugal force/Coriolis force matrix, G is a gravity matrix,
and
the angular acceleration and the angular velocity of the drive shaft servo motor are respectively;
singular value decomposition is carried out on the inertia matrix M to obtain the maximum singular value JL，JLThe maximum load inertia of the driving shaft;
2) establishing a double-inertia control system of the driving shaft of the parallel mechanism to obtain an angular velocity transfer relation:
in the formula, ωaActual angular velocity, ω, of load inertiarAt a desired angular velocity, KpvAnd TivProportional gain of speed loop controllerWith integral time coefficient, JmFor driving the inertia of the servo motor, KtIs the moment coefficient, s is the Laplace operator, ωnAnd omegacRespectively an antiresonance frequency and a resonance frequency, omeganAnd omegacThe calculation method comprises the following steps:
in the formula, ksIn order to control the connection rigidity of the system by double inertia,
is the inertia ratio;
based on the angular velocity transfer relationship, further obtaining an angular position transfer relationship:
in the formula, thetaaIs the actual angle of inertia of the load, θrAt a desired angle, KppIs the proportional gain of the position loop controller;
3) and when the rotation angle α of the parallel mechanism is equal to β and equal to 0, the original pose of the parallel mechanism is taken, α and β are euler angles, and further, the total damping ratio zeta is selected for the double-inertia control system, wherein the zeta meets the constraint relation:
determining a proportional gain K of the speed loop controller after the overall damping ratio ζ is determinedpvIntegral time coefficient TivAnd proportional gain K of position loop controllerpp：
Kpv＝Jm(2ζ1ω1+2ζ2ω2)
In the formula, ζ1、ζ2First damping ratio and second damping ratio, omega, for a dual inertia control system1、ω2The first natural frequency and the second natural frequency of the double-inertia control system;
5) calculating a new first damping ratio, a new second damping ratio, a new first natural frequency and a new second natural frequency of the parallel mechanism driving shaft double-inertia control system at different poses:
in the formula, ζn1For a new first damping ratio, ζn2Is the new second damping ratio, ωn1Is a new first natural frequency, ωn2Is a new second natural frequency, t1、t2、t3And t4Is the root of the characteristic equation Δ, and Δ is:
using ζn1、ζn2、ωn1、ωn2Relative ζ1、ζ2、ω1、ω2The change of the parallel mechanism explains the change of the dynamic performance of the parallel mechanism, and finally the analysis of the dynamic performance of the parallel mechanism is completed.
Hair brushIn step 3) of the above process, ζ1、ζ2、ω1、ω2And KppIs determined according to the following steps:
1) determining Zeta according to the determined overall damping ratio Zeta of the dual inertia control system1、ζ2Comprises the following steps:
ζ1＝ζ2＝ζ
2) further calculate ω1And omega2Comprises the following steps:
3) writing out an open-loop transfer function G of a dual-inertia control systempComprises the following steps:
according to GpDetermining proportional gain K of position loop controller by using root track methodpp。
The invention provides a dynamic performance analysis method for a parallel mechanism, which has the following advantages and prominent technical effects: the invention provides a widely effective dynamic performance analysis method aiming at the problem that the dynamic performance time-varying characteristic of the parallel mechanism cannot be fully reflected by using the traditional dynamic performance analysis method of the series mechanism and combining the characteristics of the parallel mechanism, which is lack of an effective method for analyzing the dynamic performance of the parallel mechanism at present, has important significance for deeply understanding and explaining the change of the dynamic performance of the parallel mechanism in the motion process, is an important basis for further improving the dynamic performance of the parallel mechanism, and provides an effective tool for analyzing the dynamic performance of the parallel mechanism, namely a complex electromechanical integrated device.
Drawings
Fig. 1 is a typical parallel mechanism.
FIG. 2 is a flow chart of a method for dynamic performance analysis of a parallel mechanism according to the present invention.
Fig. 3 is a speed response error of a parallel mechanism obtained by using the invention.
Fig. 4 shows a parallel mechanism position response error obtained by using the present invention.
In fig. 1: 1-a first slide block; 2-a second slide block; 3-a third slide block; 4-terminal moving platform; 5-a first bar; 6-a second bar; 7-third bar.
Detailed Description
Firstly, establishing a dynamic model of a parallel mechanism in a joint space, and calculating the maximum load inertia of a driving shaft; establishing a double-inertia control system of a driving shaft of the parallel mechanism to obtain an angular speed transfer relation and an angular position transfer relation; further selecting a proper total damping ratio for the double-inertia control system, and determining control parameters of a speed ring controller and a position ring controller; and finally, calculating the change of the first damping ratio and the second damping ratio of the double-inertia control system and the change of the first natural frequency and the second natural frequency, and explaining the change of the dynamic performance of the parallel mechanism.
The invention is described in further detail below with reference to the figures and the embodiments.
Fig. 1 shows a typical three-degree-of-freedom parallel mechanism, where the parallel mechanism drives a terminal moving platform 4 to move through the movement of a first slider 1, a second slider 2, and a third slider 3, the first slider 1, the second slider 2, and the third slider 3 are driven by corresponding servo motors, the moving platform 4 is connected with the first slider 1 through a first rod 5, the moving platform 4 is connected with the second slider 2 through a second rod 6, the moving platform 4 is connected with the third slider 3 through a third rod 7, a shaft of the slider 1 is a first driving shaft, a shaft of the slider 2 is a second driving shaft, and a shaft of the slider 3 is a third driving shaft.
FIG. 2 is a flow chart of a method for analyzing dynamic performance of a parallel mechanism according to the present invention. The proposed method for analyzing the dynamic performance of the parallel mechanism is applied to the parallel mechanism, and the method comprises the following specific steps:
1) firstly, a dynamic model of the parallel mechanism is established in a joint space as follows:
in the formula, τmRepresenting the driving moment of the parallel mechanism, M is an inertia matrix, C is a centrifugal force/Coriolis force matrix, G is a gravity matrix,
and
the angular acceleration and the angular velocity of the drive shaft servo motor are respectively;
2) the inertia matrix M is further represented as:
in the formula, PhIs ball screw lead, MsInertia matrix, M, for driving the sliders for parallel mechanismspIs an inertia matrix of a movable platform of a parallel mechanism terminal, MliIs an inertia matrix of the rods of the parallel mechanism, GaIs a transmission matrix between the speed of the driving shaft of the parallel mechanism and the speed of the terminal moving platform, JivωThe transmission matrix is the transmission matrix between the speed of the terminal moving platform of the parallel mechanism and the speed of the rod piece;
3) at the corner α e [ -2 π/92 π/9 of the parallel mechanism]rad，β∈[-2π/9 2π/9]In the rad range, α and β are Euler angles, singular value decomposition is carried out on the inertia matrix M to obtain the maximum load inertia J of the driving shaftLThe variation range of (A) is as follows:
0.0085kg·m2≤JL≤0.0432kg·m2(3)
4) establishing a double-inertia control system of the driving shaft of the parallel mechanism to obtain an angular velocity transfer relation:
in the formula, ωaActual angular velocity, ω, of load inertiarAt a desired angular velocity, KpvAnd TivProportional gain and integral time coefficient, J, respectively, of the speed loop controllermThe inertia of the servo motor of the driving shaft is 0.0103 kg.m2，KtThe moment coefficient is 1.4 N.m/A, s is Laplace operator, omeganAnd omegacRespectively an antiresonance frequency and a resonance frequency, omeganAnd omegacThe calculation method comprises the following steps:
in the formula, ksThe connecting rigidity of the double-inertia control system is 1200 N.m/rad,
is the inertia ratio;
based on the angular velocity transfer relationship, further obtaining an angular position transfer relationship:
in the formula, thetaaIs the actual angle of inertia of the load, θrAt a desired angle, KppIs the proportional gain of the position loop controller;
5) when the rotating angle α is selected to be β is selected to be 0, the original pose of the parallel mechanism is selected, and the maximum load inertia at the moment is 0.0085 kg-m2The inertia ratio R is 0.8252, and the overall damping ratio ζ of the available dual inertia control system needs to satisfy the relationship:
combining the constraint condition, selecting an overall damping ratio zeta of 0.4 for the double-inertia control system;
6) let first damping ratio ζ of double inertia control system1Zeta second damping ratio2Comprises the following steps:
ζ1＝ζ2＝ζ＝0.4 (7)
further obtaining the first natural frequency omega of the double inertia control system1And a second natural frequency omega2Comprises the following steps:
in the formula, ωnTaking the value of 375.7646 rad/s;
7) according to ζ1、ζ2、ω1And omega2Obtaining the proportional gain K of the speed ring controller of the parallel mechanism driving shaft double-inertia control systempvAnd integral time coefficient TivComprises the following steps:
Kpv＝Jm(2ζ1ω1+2ζ2ω2)＝7.3847 (10)
8) writing out an open-loop transfer function G of a dual-inertia control systempComprises the following steps:
obtaining proportional gain K of position loop controller by root track methodpp＝60；
9) The parallel mechanism is respectively in an original pose, a middle pose and an edge pose, and the maximum load inertia and the corresponding inertia ratio of a driving shaft of the parallel mechanism at the moment are as follows:
in the formula, JL1、JL2And JL3The maximum load inertia R of the driving shaft when the parallel mechanism is in the original pose, the middle pose and the edge pose respectively1、R2And R3Respectively corresponding inertia ratios;
based on the established double-inertia control system and the obtained control parameters, under the condition that the speed input signal is sin (2 pi t) rad/s and the position input signal is sin (2 pi t) rad, speed and position response results of the parallel mechanism under three poses are obtained, response errors are shown in fig. 3 and fig. 4, the abscissa of fig. 3 and fig. 4 represents a time change range, the unit is s, and the ordinate represents the speed response error and the position response error respectively, and the unit is rad/s and rad; curve R in fig. 31、R2And R3Respectively representing the speed response errors of the parallel mechanism under the original pose, the middle pose and the edge pose, and a curve R in figure 41、R2And R3Respectively representing the position response errors of the parallel mechanism under the original pose, the middle pose and the edge pose. It is clear from the two figures that the speed and position response errors of the parallel mechanism appear in the obvious vibration situation at the initial stage of the movement, and the curve R3Is most obvious, curve R1The vibration of the parallel mechanism is the weakest, which shows that the dynamic performance of the parallel mechanism changes correspondingly along with the change of the pose of the parallel mechanism;
10) in order to explain the change of the dynamic performance of the parallel mechanism, after the pose of the parallel mechanism is changed from the original pose to the middle pose and the edge pose, calculating a new first damping ratio, a new second damping ratio, a new first natural frequency and a new second natural frequency of a parallel mechanism driving shaft double-inertia control system;
when the parallel mechanism changes from the original pose to the intermediate pose, the calculation result is as follows:
in the formula, ζn1(1)、ζn2(1)、ω1(1)、ω2(1)Respectively, a new first damping ratio, a new second damping ratio, a new first natural frequency and a new second natural frequency of the double-inertia control system when the parallel mechanism is in the middle pose;
when the parallel mechanism changes from the original pose to the edge pose, the calculation result is as follows:
in the formula, ζn1(2)、ζn2(2)、ω1(2)、ω2(2)Respectively, a new first damping ratio, a new second damping ratio, a new first natural frequency and a new second natural frequency of the double-inertia control system when the parallel mechanism is in the edge pose;
comparing the results of the equations (14), (15) and (7), (8) and (9), it can be clearly seen that when the parallel mechanism changes from the original pose to the middle pose and the edge pose, the first damping ratio, the second damping ratio, the first natural frequency and the second natural frequency of the driving shaft dual inertia control system change, and further cause the dynamic performance change shown in fig. 3 and 4, therefore, by using the proposed method, the reason for the change of the dynamic performance of the parallel mechanism can be better explained, and an effective tool is provided for the analysis of the dynamic performance of the parallel mechanism.
Claims (2)
1. A dynamic performance analysis method for a parallel mechanism is characterized by comprising the following steps:
1) establishing a dynamic model of the parallel mechanism in a joint space:
in the formula, τmIs the driving moment of the parallel mechanism, M is an inertia matrix, C is a centrifugal force/Coriolis force matrix, G is a gravity matrix,
and
the angular acceleration and the angular velocity of the drive shaft servo motor are respectively;
representing the pose of the parallel mechanism by Euler angles α and β, designating the variation range of α and β, and further performing singular value decomposition on the inertia matrix M to obtain the maximum singular value JLRange of variation of (1), JLThe variation range of (a) is the variation range of the maximum load inertia of the drive shaft;
2) establishing a double-inertia control system of the driving shaft of the parallel mechanism to obtain an angular velocity transfer relation:
in the formula, ωaActual angular velocity, ω, of load inertiarAt a desired angular velocity, KpvAnd TivProportional gain and integral time coefficient, J, respectively, of the speed loop controllermFor driving the inertia of the servo motor, KtIs the moment coefficient, s is the Laplace operator, ωnAnd omegacRespectively an antiresonance frequency and a resonance frequency, omeganAnd omegacThe calculation method comprises the following steps:
in the formula, ksIn order to control the connection rigidity of the system by double inertia,
is the inertia ratio;
based on the angular velocity transfer relationship, further obtaining an angular position transfer relationship:
in the formula, thetaaIs the actual angle of inertia of the load, θrAt a desired angle, KppIs the proportional gain of the position loop controller;
3) and when α is β is 0, the total damping ratio zeta is further selected for the double-inertia control system, and meets the constraint relation:
determining a proportional gain K of the speed loop controller after the overall damping ratio ζ is determinedpvIntegral time coefficient TivAnd proportional gain K of position loop controllerpp：
Kpv＝Jm(2ζ1ω1+2ζ2ω2)
In the formula, ζ1、ζ2First damping ratio and second damping ratio, omega, for a dual inertia control system1、ω2The first natural frequency and the second natural frequency of the double-inertia control system;
5) calculating a new first damping ratio, a new second damping ratio, a new first natural frequency and a new second natural frequency of the parallel mechanism driving shaft double-inertia control system at different poses:
in the formula, ζn1For a new first damping ratio, ζn2Is the new second damping ratio, ωn1Is a new first natural frequency, ωn2Is a new second natural frequency, t1、t2、t3And t4Is the root of the characteristic equation Δ, and Δ is:
using ζn1、ζn2、ωn1、ωn2Relative ζ1、ζ2、ω1、ω2The change of the parallel mechanism explains the change of the dynamic performance of the parallel mechanism, and finally the analysis of the dynamic performance of the parallel mechanism is completed.
2. The method according to claim 1, wherein ζ in step 3) is set to zero1、ζ2、ω1、ω2And KppIs determined according to the following steps:
(1) determining Zeta according to the determined overall damping ratio Zeta of the dual inertia control system1、ζ2Comprises the following steps:
ζ1＝ζ2＝ζ
(2) further calculate ω1And omega2Comprises the following steps:
(3) writing out an open-loop transfer function G of a dual-inertia control systempComprises the following steps:
according to GpDetermining proportional gain K of position loop controller by using root track methodpp。
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2012056045A (en) * | 2010-09-10 | 2012-03-22 | Nagoya Institute Of Technology | Force-sensation-presentation manipulator having five axes |
| CN102662327A (en) * | 2012-05-18 | 2012-09-12 | 哈尔滨工业大学 | Design method for resolving modal space controller of hydraulic drive six-degree-of-freedom parallel mechanism |
| CN102729249A (en) * | 2012-06-19 | 2012-10-17 | 哈尔滨工业大学 | Parameter optimization method for six-degree of freedom parallel mechanism for modal space control |
| CN108527365A (en) * | 2018-03-21 | 2018-09-14 | 清华大学 | A kind of high speed parallel robot drive system parameters optimized Selection method |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2012056045A (en) * | 2010-09-10 | 2012-03-22 | Nagoya Institute Of Technology | Force-sensation-presentation manipulator having five axes |
| CN102662327A (en) * | 2012-05-18 | 2012-09-12 | 哈尔滨工业大学 | Design method for resolving modal space controller of hydraulic drive six-degree-of-freedom parallel mechanism |
| CN102729249A (en) * | 2012-06-19 | 2012-10-17 | 哈尔滨工业大学 | Parameter optimization method for six-degree of freedom parallel mechanism for modal space control |
| CN108527365A (en) * | 2018-03-21 | 2018-09-14 | 清华大学 | A kind of high speed parallel robot drive system parameters optimized Selection method |
Non-Patent Citations (1)
| Title |
|---|
| 3-PRS并联机器人惯量耦合特性研究;王冬,等;《力学学报》;20160731;第48卷(第4期);804-812 * |
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