CN113145907B - Optimal energy robot-based milling feeding direction optimization method - Google Patents

Optimal energy robot-based milling feeding direction optimization method Download PDF

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CN113145907B
CN113145907B CN202110480795.0A CN202110480795A CN113145907B CN 113145907 B CN113145907 B CN 113145907B CN 202110480795 A CN202110480795 A CN 202110480795A CN 113145907 B CN113145907 B CN 113145907B
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robot
milling
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CN113145907A (en
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彭芳瑜
肖名君
陈晨
闫蓉
唐小卫
胡华洲
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Huazhong University of Science and Technology
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23C—MILLING
    • B23C3/00—Milling particular work; Special milling operations; Machines therefor
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J11/00—Manipulators not otherwise provided for
    • B25J11/005—Manipulators for mechanical processing tasks
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/1605—Simulation of manipulator lay-out, design, modelling of manipulator
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1628—Programme controls characterised by the control loop
    • B25J9/1633—Programme controls characterised by the control loop compliant, force, torque control, e.g. combined with position control
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P70/00—Climate change mitigation technologies in the production process for final industrial or consumer products
    • Y02P70/10—Greenhouse gas [GHG] capture, material saving, heat recovery or other energy efficient measures, e.g. motor control, characterised by manufacturing processes, e.g. for rolling metal or metal working

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Abstract

The invention belongs to the technical field related to milling and discloses a milling and feeding direction optimization method based on an energy-optimal robot. The method comprises the following steps: s1, planning a machining track of a workpiece to be milled in a Cartesian space for the workpiece to be milled; s2, dividing the machining process of the workpiece to be milled into a tool drop stage, a milling stage and a tool lifting stage, constructing a dynamic model of the milling robot and a milling force model under a robot coordinate system, and solving and obtaining robot joint torque and joint speed corresponding to each stage; s3, constructing an energy consumption relational expression of each stage, constructing a total energy consumption optimization model of the whole machining process according to the energy consumption relational expression, and solving the corresponding feeding direction under the condition of minimum energy consumption to obtain the optimal feeding direction, so that the optimization of the feeding direction under the condition of optimal energy is realized. By the invention, energy consumption is reduced, processing cost is reduced, joint impact can be reduced, milling quality is improved, and service life of the robot is prolonged.

Description

Optimal energy robot-based milling feeding direction optimization method
Technical Field
The invention belongs to the technical field related to milling, and particularly relates to a milling feeding direction optimization method based on an energy-optimal robot.
Background
With the increase of the level of industrial automation, the manufacturing industry is becoming more and more automated and intelligent. The industrial robot plays an important role in the automatic and intelligent process of the manufacturing industry. Robots have begun to be widely used in the processing of various products, and particularly, the robots have great advantages in the processing of large and complex products. The robot milling processing is applied to production and manufacturing, including robot milling, robot polishing and the like, and because the joint rigidity of the robot is low, the influence of the processing track on the processing quality of the robot is larger than that of a machine tool.
Along with the wide application of industrial robots and the expansion of markets, the industrial robots consume most energy sources in the automatic and intelligent production processes, and the energy consumption is also a problem to be considered in the production process, because less energy consumption represents that the cost is reduced, the benefit is increased, and meanwhile, the energy-saving, emission reduction and environment protection are facilitated. In some scenes with special requirements on energy consumption, such as space or diving robots, energy optimization is especially important. In addition, the energy optimal performance and the impact performance are positively correlated, the impact of a motor and an actuator can be reduced by optimizing the energy, the service life of the robot is prolonged, and the milling processing quality of the robot can be improved by reducing the joint impact. In the chinese patent publication specification, application No.: CN 111037069A proposes an energy optimization method based on a welding gun rotation angle robot, which obtains a welding start point and end point welding gun rotation angle combination with minimum power consumption through a few tests, mainly performs energy optimization on a trajectory of a welding robot, and does not relate to energy optimization of a milling trajectory of a milling robot. The milling energy of the robot not only comprises the energy consumption of the robot body, but also needs to consider the energy consumption in the complex milling process, and is greatly different from the energy optimization of the welding robot trajectory planning. The research on the optimization of the energy consumption of the robot milling operation is less, and the feeding direction is generally given at will when the robot performs line cutting in the actual processing.
Disclosure of Invention
Aiming at the defects or the improvement requirements in the prior art, the invention provides an energy-optimal-robot-based milling and machining feeding direction optimization method, wherein a robot milling energy model is established, the robot milling and machining feeding direction is optimized according to the minimum energy, and the milling and machining from the feeding direction can reduce the energy consumption and the machining cost, reduce the joint impact, improve the milling quality and prolong the service life of the robot.
To achieve the above object, according to the present invention, there is provided an energy-optimized-based optimization method for a milling direction of a robot, the method comprising the steps of:
s1, setting cutting parameters corresponding to a workpiece to be milled for the workpiece to be milled, and planning a processing track of the workpiece to be milled in a Cartesian space according to the set cutting parameters;
s2, dividing the machining process of the workpiece to be milled into a tool drop stage, a milling stage and a tool lifting stage, constructing a dynamic model of the milling robot and a milling force model under a robot coordinate system, and solving and obtaining robot joint torque and joint speed corresponding to each stage;
and S3, constructing an energy consumption relational expression of each stage by utilizing the moment and the speed of the robot joint corresponding to each stage, constructing a total energy consumption optimization model of the whole machining process, and solving the corresponding feeding direction under the condition of minimum energy consumption to obtain the optimal feeding direction, thereby realizing the optimization of the feeding direction under the condition of optimal energy.
Further preferably, in step S3, the total energy consumption optimization model is established based on the following assumptions:
(a) Assuming that the milling process is continuous, there is no milling interruption;
(b) It is assumed that the frictional forces between the joints are negligible.
Further preferably, in step S3, the total energy consumption optimization model is performed according to the following relation:
minE＝Ed+Em+El
constraint conditions are as follows:
ql,min＜ql＜ql,max
Figure GDA0003805057550000031
Figure GDA0003805057550000032
|τl|＜|τl,max|
α∈[0，180°]
S(t)∈Srobot
wherein E is total energy consumption in the whole milling process, EdFor energy consumption during the knife-dropping process, EmFor energy consumption during milling, ElFor energy consumption in the process of lifting the cutter, qlThe joint angle of the ith joint, ql,min,ql,maxThe maximum value and the minimum value of the joint angle range of the ith joint respectively,
Figure GDA0003805057550000033
the joint angular velocity and the maximum value of the joint angular velocity of the ith joint are respectively,
Figure GDA0003805057550000034
the joint angular acceleration and the maximum value of the angular acceleration, tau, of the ith jointl,τl,maxThe joint moment and the maximum joint moment of the first joint are respectively, alpha is the line cutting feed direction, the range is 0 to 180 degrees, S (t) is the terminal coordinate of the cutter, SrobotIs a robot working space.
Further preferably, in step S2, the kinetic model is performed according to the following relation:
Figure GDA0003805057550000035
wherein, tau'i(t) joint drive moments for joint i at time t, i =1,2, \8230;, n, \8230j =1,2, \8230;, n, k =1,2, \8230;, n, m =6, b for 6-axis industrial robotsij(q) is the coefficient of the inertial term of the joint i, hijk(q) is the coefficient of the centrifugal force term of the joint i, gi(q) is the joint i gravity term, q is the joint angle matrix,
Figure GDA0003805057550000036
for the joint angular acceleration of joint j at time t,
Figure GDA0003805057550000037
respectively, the joints k and m areAnd (4) the joint angular velocity at the time t.
Further preferably, in step S2, the milling force model is performed according to the following relation:
τ”＝EJTF
wherein tau' is the joint moment providing the milling force,Ej is a velocity Jacobian matrix under the robot end coordinate system ECS, and F is a six-dimensional force and moment under the robot end coordinate system ECS.
Further preferably, in step S3, the energy consumption of each stage is calculated according to the following relation:
the energy consumption in the cutting stage is carried out according to the following relation:
Figure GDA0003805057550000041
the energy consumption in the milling stage is carried out according to the following relation:
Figure GDA0003805057550000042
the energy consumption in the cutting stage is carried out according to the following relational expression:
Figure GDA0003805057550000043
wherein N isd,Nm,NlRespectively the discrete time segments of the tool setting time, the milling time and the tool lifting time, L is the total number of joints of the robot, tau'l(n) is the joint drive moment, τ, of the joint at the nth moment "l(n) provides milling force joint moment for the joint l at the nth moment,
Figure GDA0003805057550000044
the angular velocity of the joint l at the nth time, n being the number of discrete time segments, Δ t being the discrete time interval.
Further preferably, in step S2, the robot joint torque corresponding to each stage is performed according to the following relation:
the joint moment in the milling stage is performed according to the following relation:
τ＝τ′+τ″
the joint moment calculation relational expressions of the cutter falling stage and the cutter lifting stage are the same, and the calculation is carried out according to the following relational expressions:
τ＝τ′
wherein, tau 'is joint driving moment, and tau' is joint moment providing milling force.
Further preferably, in step S2, when constructing the dynamic model of the milling robot, the cartesian space processing trajectory is first converted into a joint space trajectory in a robot coordinate system through inverse kinematics of the robot, and then B-spline curve interpolation is performed on the joint space trajectory to make the joint space trajectory smooth.
Further preferably, in step S2, the robot joint speed corresponding to each stage is obtained as follows:
obtaining a smooth joint space track after B spline interpolation, namely a joint angle value corresponding to the t moment, wherein the robot joint track is q (t) = (q)1(t),q2(t),q3(t),q4(t),q5(t),q6(t)), the joint velocity is the first derivative of the joint trajectory, i.e. the joint velocity is
Figure GDA0003805057550000051
Further preferably, in step S3, the corresponding feeding direction with the minimum energy consumption is solved according to the total energy consumption optimization model by using a genetic algorithm.
In general, compared with the prior art, the above technical solution conceived by the present invention has the following effects:
1. the milling process is divided into three stages, namely a tool lifting stage, a tool dropping stage and a milling stage, wherein the tool lifting stage and the tool dropping stage are energy consumption generated by a robot driving joint, and the milling stage is energy consumption generated by the robot driving joint and milling force supply in the milling process, namely the energy consumption brought by the robot driving joint and milling force supply in the robot milling process is comprehensively considered, so that the milling energy consumption of the robot can be accurately described and calculated;
2. the milling and feeding direction optimizing method based on the energy-optimal robot widens the milling and feeding track optimizing thought of the robot, considers the energy optimization except the time optimization, and performs milling and processing in the energy-optimal feeding direction, so that the energy can be saved, the joint impact can be reduced, the processing quality of the robot is improved, and the service life of the robot is prolonged;
3. the invention has stronger practicability in the actual production, the related equipment is simple, the data processing method is simple, and the invention is suitable for being used in the actual milling production process.
Drawings
FIG. 1 is a flow chart of a milling direction optimizing method based on an energy-optimized robot according to the present invention;
FIG. 2 is a tool coordinate system TCS lower blade infinitesimal milling model of the present invention;
FIG. 3 is a schematic representation of the transformation of edge infinitesimal milling forces to the center of the tool in the tool coordinate system TCS of the present invention, wherein (a) is a schematic representation of the radial, tangential, and normal milling forces on each tooth, and (b) is a schematic representation of the forces and moments acting on the center of the tool;
FIG. 4 is a schematic representation of the tool coordinate system TCS and the robot end coordinate system ECS of the present invention;
FIG. 5 is an algorithm flow diagram for solving the feed direction optimization by the genetic algorithm of the present invention;
FIG. 6 is a schematic diagram of the kinematic model of the ABB IRB6660 robot according to the preferred embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the respective embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
As shown in fig. 1, the present invention provides an energy-optimized-based method for optimizing a milling and machining direction of a robot, which optimizes the milling and machining direction of the robot from the perspective of energy minimization, thereby saving energy, improving machining quality and prolonging the service life of the robot. In the specific embodiment, the preferred embodiment is a 6-axis industrial robot ABB IRB6660-205/1.9 and a circular aluminum alloy with a 200mm diameter is milled by an end-mounted electric spindle, the speed, acceleration and moment constraints of the ABB IRB6660 robot in the preferred embodiment are shown in a table 1, D-H parameters are shown in a table 2, inertia parameters of each connecting rod are calculated by CAD/Preo software and are shown in a table 3, electric spindle parameters are shown in a table 4, processing parameters of the preferred embodiment are shown in a table 5, and the specific implementation steps are as follows:
s1, establishing a time parameter model of a circular aluminum alloy track with the diameter of 200mm milled by an industrial robot;
s2, transforming the milling force of the knife edge infinitesimal to the coordinate of the tail end of the robot through coordinate system transformation, and establishing a milling force model under the coordinate system of the tail end of the robot;
s3, establishing an ABB IRB6660-205/1.9 kinetic model of the milling robot based on a Lagrange kinetic equation;
s4, interpolating the space trajectory of the robot joint by adopting a B spline curve to determine a robot joint trajectory function;
and S5, as shown in the figure 5, establishing an energy-optimal-robot-based milling feeding direction optimization model, and solving by adopting a genetic algorithm.
TABLE 1 ABB IRB6660-205/1.9 robot velocity, acceleration and moment constraints
Figure GDA0003805057550000071
TABLE 2 ABB IRB6660-205/1.9 robot D-H parameters
Figure GDA0003805057550000072
TABLE 3 ABB IRB6660-205/1.9 robot Link inertia parameters
Figure GDA0003805057550000073
TABLE 4 electric spindle parameters
Figure GDA0003805057550000081
TABLE 5 simulation example parts and machining parameters
Figure GDA0003805057550000082
Further, step S1 specifically includes:
planning tool setting, milling and tool lifting tracks of a Cartesian space robot according to a circular aluminum alloy workpiece with the diameter of 200mm, and obtaining tool setting time t according to the length of the tracks and the feeding speeddMilling time tmAnd time t of lifting cutterlCombined with auxiliary time taThe method can obtain a robot milling track time parameter model:
tc＝ta+to＝ta+td+tm+tl
further, step S2 comprises the following substeps:
s21, establishing a tool coordinate system TCS lower cutting edge infinitesimal milling force model, wherein the milling force model is shown in figure 2, and tangential, radial and axial tangential force infinitesimals acting on the first cutting edge infinitesimal with the thickness dz on a cutter tooth j during actual milling of the robot can be expressed as follows:
Figure GDA0003805057550000083
in the formula (I), the compound is shown in the specification,Ktc,Krc,Kacare the tangential, radial and axial cutting force coefficients, h (phi), respectivelyjl) The thickness to be cut varies with the angular position of the cutting edge, and is a function of the angle of rotation of the cutting tooth, and can be approximated by h (phi)jl)＝f1sinφjl，f1For feed per tooth, f1And = f/NS, wherein f is a feeding speed in mm/min, N is the number of cutter teeth, and S is a spindle rotating speed in rpm. g (phi)jl) A function for determining the contact area, a unit step function, and g (phi) in the contact areajl) =1; outside the contact area, g (phi)jl)＝0。
S22 transforms the cutting edge infinitesimal milling forces to the center of the tool in the tool coordinate system TCS, as shown in fig. 3 (a) and (b), where an increased moment n is provided by the motorized spindle, the moment n being independent of the robot body, and the milling forces in the tool coordinate system TCS can be expressed as:
Figure GDA0003805057550000091
transformation matrix in equation
Figure GDA0003805057550000092
KcIs a cutting force coefficient matrix. Phi in matrix AjlRadial contact angle, κ axial contact angle.
By integrating in the axial direction and summing each tooth, the instantaneous milling forces acting on the entire milling cutter in the tool coordinate system TCS can be obtained:
Figure GDA0003805057550000093
in the formula, N is the number of cutter teeth, and M is the discrete number of the cutter edges along the cutter shaft direction.
S23, converting the milling into the ECS of the robot end coordinate system, and converting the conversion relation into a schematic diagram as shown in FIG. 4, wherein the conversion relation can be regarded as that the tool coordinate system TCS is along ZSTranslation L1To the intermediate coordinate System ICS, along YINegative squareTo move to L2Around XIThe axis rotates anticlockwise by 90 DEG around YIThe end coordinate system ECS is obtained after the shaft has been rotated 90 ° counter clockwise. The transformation matrix of the tool coordinate system TCS to the end coordinate system ECS can thus be expressed as:
Figure GDA0003805057550000094
the six-dimensional forces and moments of the end coordinate system ECS resulting from the milling forces are thus as follows:
Figure GDA0003805057550000101
in the processes of tool falling and tool lifting, no milling force exists, so that the force and the moment applied to the tail end of the robot are 0. The relationship between joint moment and tip force and moment can be represented by the jacobian matrix:
τ”＝EJTF
in the above formula, F is six-dimensional force and moment under the robot end coordinate system ECS,Ej is a velocity Jacobian matrix under the robot end coordinate system ECS.
Further preferably, step S3 is specifically:
since the ABB IRB6660 robot has a four-bar linkage, the robot is dynamically modeled using an extended linkage as follows, as shown in fig. 6, which gives a kinematic model of the ABB IRB6660, since LbAnd LcIs fixedly connected with LcIs regarded as LbAnd is referred to as a whole as
Figure GDA0003805057550000102
Order to
Figure GDA0003805057550000103
Will be provided with
Figure GDA0003805057550000104
And
Figure GDA0003805057550000105
as an extension link
Figure GDA0003805057550000106
Record as
Figure GDA0003805057550000107
The same notation is used for links without additional motors.
Neglecting the friction force among all joints, obtaining the generalized moment required by the i-th rod of the arm driven by the joint i driver based on the Lagrange's formula:
Figure GDA0003805057550000108
the first term in the formula is the inertial term of the robot, the second term is the centrifugal force term, and the third term is the gravity term. Coefficient of formula bij(q) is an element in the inertia term coefficient matrix B (q) (n × n).
Coefficient matrix of inertia terms
Figure GDA0003805057550000109
Since the ABB IRB6660 robot considers a four-bar linkage, B (q) (n × n) is an asymmetric matrix, resulting in a four-bar linkage
Figure GDA0003805057550000111
M in the above formulaijElements in an asymmetric matrix B (q) (n × n).
Coefficient hijkHaving the following relationship bij
Figure GDA0003805057550000112
Gravity term matrix
Figure GDA0003805057550000113
Wherein:
Figure GDA0003805057550000114
Figure GDA0003805057550000115
Figure GDA0003805057550000116
Figure GDA0003805057550000117
Figure GDA0003805057550000118
Figure GDA0003805057550000119
Figure GDA00038050575500001110
matrix operator:
Figure GDA00038050575500001111
in the formula
Figure GDA0003805057550000121
Generalized force (or moment), corner angle, angular velocity and angular acceleration of the ith joint, respectively;
Figure GDA0003805057550000122
and
Figure GDA0003805057550000123
respectively linear velocity Jacobian matrix and angular velocity Jacobian matrix, and respectively satisfy
Figure GDA0003805057550000124
And
Figure GDA0003805057550000125
is shown and
Figure GDA0003805057550000126
the + Z axis of (1) is the unit vector in the same direction; g0Is the gravitational acceleration vector in the base frame (g, if z is the vertical axis)0＝[00-g]T)；
Figure GDA0003805057550000127
Is a rod member
Figure GDA0003805057550000128
The mass of (c);
Figure GDA0003805057550000129
is a rod piece
Figure GDA00038050575500001210
The moment of inertia of;
Figure GDA00038050575500001211
is a rod piece
Figure GDA00038050575500001212
The product of inertia of;
Figure GDA00038050575500001213
is the centroid coordinate of the bar i in its bar coordinate system.
Joint moment of joint i during milling
Figure GDA00038050575500001214
Joint torque of joint i when tool is dropped and lifted
Figure GDA00038050575500001215
Further preferably, step S4 is specifically:
and setting the joint angle as a control vertex of the B spline curve, and calculating a basis function of the B spline curve through the known control vertex to finally obtain the B spline track.
By definition of B-spline curve:
Figure GDA00038050575500001216
wherein u (u ∈ [0,1 ]]) As nodes of B-spline function, di(i =1,2 \8230n) is the control vertex, k is the number of basis functions of the B-spline curve, Ni,k(u) (i =1,2 \8230n) is the basis function of a k-th order canonical B-spline curve, Ni,k(u) (i =1,2 \ 8230n) is calculated as follows:
Figure GDA00038050575500001217
as a further preference, step S5 comprises the steps of:
s51 to simplify the complexity of the model and ensure the accuracy of the model building, the preferred embodiment makes the following assumptions:
(1) Selecting an ABB IRB6660 six-axis industrial robot as a modeling object;
(2) Assuming that the milling process is continuous, no milling interruption occurs;
(3) The friction between joints is assumed to be negligible;
s52, establishing an energy-optimal-robot-based milling feeding direction optimization model. The energy consumption of the milling robot refers to the energy consumed in the process of executing given tool path milling by the mechanical arm, and the milling is started and finishedIs time-discrete into N Δ t, N · Δ t = tmAnd calculating the energy consumption of the robot milling operation under an ideal condition:
Figure GDA0003805057550000131
in the formula, tsAnd tfRespectively, the time when milling starts and the time when milling ends. P (t) is the power at which the robot operates, τlIs the joint moment of the joint l,
Figure GDA0003805057550000132
is the angular velocity of the joint l.
When the robot performs row cutting, the number of feeding directions is infinite, the energy consumed by different feeding directions is different for the same milling task, and the impact of the motor and the joint corresponding to the feeding direction with less energy is smaller. Based on total drive torque tau of robot jointlAnd joint angular velocity
Figure GDA0003805057550000133
The energy consumption of the three phases can be calculated separately:
the energy consumption of cutter falling:
Figure GDA0003805057550000134
milling energy consumption:
Figure GDA0003805057550000135
the energy consumption of cutter falling:
Figure GDA0003805057550000136
the energy optimization mathematical model is as follows:
minE＝Ed+Em+El
constraint conditions are as follows:
ql,min＜ql＜ql,max
Figure GDA0003805057550000141
Figure GDA0003805057550000142
|τl|＜|τl,max|
α∈[0，180°]
S(t)∈Srobot
s53 solves for the optimal feed direction. And calculating the milling feeding direction with the lowest energy consumption by means of an MATLAB genetic algorithm toolbox GA. In the genetic algorithm, the binary digit number of an individual is set to be 20 according to experience, the cross probability is set to be 0.9, the mutation probability is set to be 0.08, the variable dimension (population number) is 1, and the maximum genetic algebra is 100. The results of the simulation calculations for the preferred embodiment are obtained as follows:
table 6 simulation calculation results of the preferred embodiment
Figure GDA0003805057550000143
From the simulation calculation results of the preferred embodiment, for the same milling task, the maximum energy consumption and the minimum energy consumption have a certain difference in different feeding directions, and in the above four sets of simulation calculation results, the milling is performed in the energy optimal feeding direction, so that compared with the processing in the energy maximum feeding direction, the energy consumption can be respectively saved by 15.4%, 13.6%, 14.4% and 16.3%. Aiming at the milling tasks, different cutting parameters are adopted for milling, the minimum energy consumption feeding direction is concentrated at 0 degree or 5 degrees, the maximum energy consumption feeding direction is concentrated at 40 degrees to 60 degrees, the same milling task can be explained, and the minimum energy consumption feeding direction and the maximum energy consumption feeding direction can be concentrated in a certain direction interval under different cutting parameters. The invention aims to solve the minimum energy feeding direction by establishing an energy-optimal-based milling feeding direction optimization model of the robot, so that the energy is saved, the joint impact is reduced, the processing quality is improved, the service life of the robot is prolonged, and the method has important significance for the actual production process.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (9)

1. A milling machining feed direction optimization method based on an energy-optimized robot is characterized by comprising the following steps:
s1, setting cutting parameters corresponding to a workpiece to be milled for the workpiece to be milled, and planning a line cutting machining track of the workpiece to be milled in a Cartesian space according to the set cutting parameters;
s2, dividing the machining process of the workpiece to be milled into a tool drop stage, a milling stage and a tool lifting stage, constructing a dynamic model of the milling robot and a milling force model under a robot coordinate system, and solving and obtaining robot joint torque and joint speed corresponding to each stage;
s3, constructing an energy consumption relational expression of each stage by utilizing the moment and the speed of the robot joint corresponding to each stage, constructing a total energy consumption optimization model of the whole machining process according to the energy consumption relational expression, and solving a corresponding feeding direction under the condition of minimum energy consumption to obtain an optimal feeding direction so as to realize the optimization of the feeding direction under the condition of optimal energy;
the energy consumption of each stage is calculated according to the following relation:
the energy consumption in the cutting stage is carried out according to the following relational expression:
Figure FDA0003840962350000011
the energy consumption in the milling stage is carried out according to the following relation:
Figure FDA0003840962350000012
the energy consumption in the cutter lifting stage is carried out according to the following relational expression:
Figure FDA0003840962350000013
wherein N isd,Nm,NlRespectively representing the discrete time segments of the tool falling time, the milling time and the tool lifting time, wherein L represents the total number of the joints of the robot, tau'l(n) is the joint driving moment, tau, of the joint at the nth moment "l(n) provides the milling force joint moment for the joint l at the nth moment,
Figure FDA0003840962350000014
at the nth time the angular velocity of the joint i, n is the number of discrete time segments and Δ t is the discrete time interval.
2. The energy-optimized-robot-based optimization method for milling direction of feed as claimed in claim 1, wherein in step S3, the total energy consumption optimization model is established based on the following assumptions:
(a) Assuming that the milling process is continuous, without interruption;
(b) It is assumed that the frictional forces between the joints are negligible.
3. The energy-based optimization method for the milling direction of the robot in claim 1 or 2, wherein in step S3, the total energy consumption optimization model is performed according to the following relation:
minE＝Ed+Em+El
constraint conditions are as follows:
ql,min＜ql＜ql,max
Figure FDA0003840962350000021
Figure FDA0003840962350000022
|τl|＜|τl,max|
α∈[0，180°]
S(t)∈Srobot
wherein E is total energy consumption in the whole milling process, EdFor energy consumption during the cutting operation, EmFor energy consumption during milling, ElFor energy consumption in the process of lifting the cutter, qlIs the joint angle of the l-th joint, ql,min,ql,maxThe maximum value and the minimum value of the joint angle range of the ith joint are respectively,
Figure FDA0003840962350000023
the joint angular velocity and the maximum value of the joint angular velocity of the ith joint are respectively,
Figure FDA0003840962350000024
the joint angular acceleration and the maximum value of the angular acceleration, tau, of the ith jointl,τl,maxThe joint moment and the maximum joint moment of the first joint are respectively, alpha is the line cutting feed direction and ranges from 0 to 180 degrees, S (t) is the terminal coordinate of the cutter, and SrobotIs a robot working space.
4. The energy-optimized robot milling machining feed direction optimization method according to claim 1 or 2, characterized in that in step S2, the dynamic model is implemented according to the following relation:
Figure FDA0003840962350000031
wherein, tau'i(t) joint drive torque of joint i at time t, i =1,2, \8230;, n, j =1,2, \8230;, n, k =1,2, \8230;, n, m =1,2, \8230;, n =6, b for a 6-axis industrial robotij(q) is the coefficient of the inertia term of the joint i, hijk(q) is the coefficient of the centrifugal force term of the joint i, gi(q) is the joint i gravity term, q is the joint angle matrix,
Figure FDA0003840962350000032
the joint angular acceleration of the joint j at time t,
Figure FDA0003840962350000033
the joint angular velocities of joints k and m at time t, respectively.
5. The energy-based optimization method for the milling direction of the optimal robot in the claim 1 or 2, wherein in the step S2, the milling force model is performed according to the following relation:
τ”＝EJTF
wherein, tau' is the joint moment providing the milling force,Ej is a velocity Jacobian matrix under the robot end coordinate system ECS, and F is a six-dimensional force and moment under the robot end coordinate system ECS.
6. The energy-optimized robot milling machining feed direction optimization method according to claim 1 or 2, wherein in step S2, the robot joint moment corresponding to each stage is performed according to the following relation:
the joint moment in the milling stage is performed according to the following relation:
τ＝τ’+τ”
the joint moment calculation relational expressions of the cutter falling stage and the cutter lifting stage are the same, and the calculation is carried out according to the following relational expressions:
τ＝τ’
wherein tau 'is joint driving torque, and tau' is joint torque providing milling force.
7. The energy-optimized-robot-based milling machining feed direction optimization method according to claim 1 or 2, wherein in step S2, when a dynamic model of the milling robot is constructed, the cartesian-space machining trajectory is first converted into a joint space trajectory in a robot coordinate system through robot inverse kinematics, and then B-spline curve interpolation is performed on the joint space trajectory to smooth the joint space trajectory.
8. The energy-based optimization method for the milling direction of the robot in the optimal way according to claim 4, wherein in step S2, the joint speed of the robot corresponding to each stage is obtained according to the following mode:
obtaining a smooth joint space track after B spline interpolation, namely a joint angle value corresponding to the t moment, wherein the robot joint track is q (t) = (q)1(t),q2(t),q3(t),q4(t),q5(t),q6(t)), the joint velocity is the first derivative of the joint trajectory, i.e. the joint velocity is
Figure FDA0003840962350000041
q (t) is the joint angle at time t, q1(t) is the joint angle of the 1 st joint at time t, q2(t) is the joint angle of the 2 nd joint at time t, q3(t) is the joint angle of the 3 rd joint at time t, q4(t) is the joint angle of the 4 th joint at time t, q5(t) is the joint angle of the 4 th joint at time t, q6(t) is the joint angle of the 6 th joint at time t,
Figure FDA0003840962350000042
is the joint velocity at time t,
Figure FDA0003840962350000043
is the joint velocity of the 1 st joint at time t,
Figure FDA0003840962350000044
is the joint velocity of the 2 nd joint at time t,
Figure FDA0003840962350000045
is the joint velocity of the 3 rd joint at time t,
Figure FDA0003840962350000046
is the joint velocity of the 4 th joint at time t,
Figure FDA0003840962350000047
is the joint velocity of the 5 th joint at time t,
Figure FDA0003840962350000048
is the joint velocity of the 6 th joint at time t.
9. The energy-optimized-robot-based optimization method for milling direction of feeding as claimed in claim 1 or 2, wherein in step S3, the corresponding feeding direction with the minimum energy consumption is solved according to the total energy consumption optimization model by using genetic algorithm.
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