CN110703688B - Precision machining control method for large-sized cylindrical parts - Google Patents

Precision machining control method for large-sized cylindrical parts Download PDF

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CN110703688B
CN110703688B CN201911003412.XA CN201911003412A CN110703688B CN 110703688 B CN110703688 B CN 110703688B CN 201911003412 A CN201911003412 A CN 201911003412A CN 110703688 B CN110703688 B CN 110703688B
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angle
error
workpiece
theta
cylinder
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张蓉
陈雪林
任芝兰
唐田秋
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Hunan Institute of Technology
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    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/404—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by control arrangements for compensation, e.g. for backlash, overshoot, tool offset, tool wear, temperature, machine construction errors, load, inertia
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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Abstract

The invention discloses a precision machining control method for large cylindrical parts, which respectively compensates machining parameters and machining paths by considering angle errors, displacement errors and time differences caused by larger rotational inertia of an axle so as to improve the machining precision.

Description

Precision machining control method for large-sized cylindrical parts
The technical field is as follows:
the invention relates to a precision machining control method for large-sized cylinder parts, and belongs to the field of machining.
Technical background:
the large cylindrical parts (the length is more than 10 meters and the diameter is more than 5 meters) are used as key parts in the industries of aerospace, mining, rocket missile and oil gas transmission, and the processing precision requirement is high. The large cylindrical parts are difficult to accurately stop in machining due to the large weight and inertia of the large cylindrical parts, the original weight ratio of a machine tool is changed, and machining errors are caused. Meanwhile, machining errors are increased by vibration in machining, abrasion of a cutter and the like.
Specifically, the torsional response causes the problems of excessive cutting or insufficient cutting of the large-sized cylindrical part in the x direction, and the like, the axial surface of the cutter is not consistent with the radial direction of the large-sized cylindrical part, and the error in the x direction in the machining process is expanded to the machining surface of the whole part, so that the machining error of the size and the shape is caused.
The invention content is as follows:
in order to achieve the aim, the invention discloses a precision machining control method for large cylindrical parts, which respectively compensates machining parameters and a machining path by considering an angle error, a displacement error and a time difference caused by larger moment of inertia of an axle so as to improve the machining precision.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a precision machining control method for large cylindrical parts comprises the following steps:
step one, establishing a response model of the cylinder type part: wherein x-y-z is the ideal position of the workpiece after rotating an angle, wherein y is the axial direction of the workpiece, the z direction is the radial direction passing through the axis of the workpiece in the workpiece, the ideal z direction is the vertical direction, and x is the direction perpendicular to the y and z directions; x 'represents the axial direction of the workpiece after the cylindrical part responds to torsion, and y' represents the radial direction passing through the axis of the workpiece in the workpiece; z ' is a direction perpendicular to the y ' and x ';
at angular velocity of cylinder-like parts
Figure GDA0002527323030000011
The dynamic equation of the angular response after the rotation is subjected to the resisting moment is as follows:
Figure GDA0002527323030000012
wherein J0，
Figure GDA0002527323030000013
ct，
Figure GDA0002527323030000014
ktTheta and T are respectively the moment of inertia, angular acceleration, torsional damping coefficient, torsional angular velocity, torsional rigidity, torsional angle and received torque of the cylindrical part; in the rotation motion of the cylinder part, the rotation damping coefficient of the shaft is set as proportional torsion damping;
Figure GDA0002527323030000021
ct＝αJ0+βkt(4)
wherein m isiDenotes the mass per unit area of the cylindrical part, riThe distance from the center of mass of a unit area on the cylindrical part to the axis of the cylindrical part is represented, and the proportional torsional damping coefficient is as follows:
α＝100
β＝10-7
according to the torsion theory of the rod, the torque applied to the cylinder part is as follows:
Figure GDA0002527323030000022
wherein M ist，G，I0And l is the torque, shear modulus, polar inertia distance and axle length of the cylinder parts respectively;
the polar inertia distance of the section of the cylindrical part is as follows:
Figure GDA0002527323030000023
d represents the diameter of the cylinder type part;
the torsional rigidity of the cylinder part is as follows:
Figure GDA0002527323030000024
with the axle in the initial condition: t is 0 and theta is theta0，
Figure GDA0002527323030000025
Solving is carried out to obtain the response of the cylindrical parts, namely the error is thetaw(t)；
Step two, a processing parameter and processing path error compensation model
The machine tool bears the relative displacement and angle error of a cutter and a workpiece caused by cylindrical parts, and the effective compensation is carried out through the correction of processing parameters; and (3) compensating the processing parameters after the comprehensive error: the cutting depth, the feeding speed, the rotation angle of the chuck and the deflection motion angle of the main shaft of the machine tool in an x-z plane are respectively as follows:
Figure GDA0002527323030000031
ap，fzdepth of cut, feed rate, respectively; under the condition of not loading large-sized cylinder parts, the rotation angle of the input angle chuck set by the machine tool according to the requirement of processing workpieces, and the deflection motion angles of the main shaft of the machine tool in the x-z plane are respectively thetad，θt；apIndicating depth of cut, ξzRepresents the composite error in the z direction; f. ofz cIndicates the feed amount; thetad cRepresenting the angle of movement, theta, of the cylinder-like part after compensation for angular errors caused by angular movementdShowing the set angle of movement, ζ, of the cylinder partxzdThe angle error caused by the angle movement is represented and obtained by testing the angle difference between the angle position of a certain point of the cylinder part and the ideal angle position; thetat cRepresenting the angle of movement of the tool after compensation for angular errors due to time delay errors, thetatShowing the set angle of movement, ζ, of the toolxzThe angle error caused by the motion time delay error in the transmission process can be obtained by testing the time difference between the actual time and the ideal time of a certain point;
step three, in the machining path planning of the machine tool, the machining path of the original tool is set to be s (x)t，yt，zt，θt，θw) Wherein x istRepresenting the path of movement in the x-direction, y, over timetRepresenting the path of motion in the y-direction, z, over timetRepresenting the path of motion in the z-direction, theta, over timewThe rotating angle of the cylindrical part is shown to change along with time, and t is time; solving in the dynamic equation of the angular response of the cylinder type part at the initial condition: t is equal to 0, and t is equal to 0,
Figure GDA0002527323030000032
in the case, the torsional response of the large circular tube part is θ' (t), and the tool path needs to compensate the x-direction displacement, the z-direction displacement and the angle error in the x-z plane, and according to the geometrical relationship, the x-direction compensated displacement error Δ x, the z-direction compensated displacement error Δ z and the angle error θ (t) are respectively:
Δx＝sin(θw(t))rc(9)
Δz＝Δx sin(θw(t)) (10)
Figure GDA0002527323030000033
rcthe distance between the tool point and the axis of the cylinder part is shown;
therefore, the relative movement between the tool and the workpiece compensates the path of the tool (s') (x)t，yt，zt，θt，θw) Comprises the following steps:
s'(xt,yt,zt,θt,θw)＝s(xt+Δx,yt,zt+Δz,θt+θ'(t),θw) (12)
and machining the cylindrical part in the path compensated by the cutter.
The invention has the advantages that:
the invention takes a dynamic model in the cutting process as a basis, takes the angle error, the displacement error and the time difference caused by the larger moment of inertia of the axle into consideration, and respectively compensates the processing parameters and the processing path so as to improve the processing precision.
Description of the drawings:
FIG. 1 is a schematic diagram showing the central torsion angle response of a large-sized cylindrical part after the chuck stops rotating;
FIG. 2 is a schematic diagram of position and angle errors caused by rotational responses of cylinders during machining.
The specific implementation mode is as follows:
in order to illustrate the invention more specifically, the invention is illustrated by the following specific examples:
establishing an angle error model of torsional response of large-scale cylindrical parts
In the processing of large-scale drum type parts, because the carousel control drum type parts are rotatory fast, because drum type parts diameter exceeds 5 meters, and length exceeds 10 meters, its inertia is big, and it is difficult to in time pinpoint, is difficult to satisfy the requirement of quick accurate positioning, high-efficient precision finishing in the processing. And establishing a response model schematic diagram of the large-sized cylinder part, as shown in FIG. 1. Where x-y-z is the ideal position of the workpiece after it has been rotated through an angle, where y is the axial direction of the workpiece (cylinder-like part), the z-direction is the radial direction through the axis of the workpiece in the workpiece, ideally the z-direction is the vertical direction, and x is the direction perpendicular to the y and z-directions. x ', y ', z ' are axial directions of the cylindrical workpiece (axle) after the torsional response, and the radial directions passing through the workpiece axis in the workpiece are perpendicular to the y ' and z ' directions.
At angular velocity of cylinder-like parts
Figure GDA0002527323030000041
The dynamic equation of the angular response after the rotation is subjected to the resisting moment is as follows:
Figure GDA0002527323030000042
wherein J0，
Figure GDA0002527323030000043
ct，
Figure GDA0002527323030000044
ktAnd theta and T are respectively the moment of inertia, angular acceleration, torsional damping coefficient, torsional angular velocity, torsional rigidity, torsional angle and received torque of the cylindrical part. In the cylindrical rotary motion, the rotational damping coefficient of the shaft is set to proportional torsional damping.
Figure GDA0002527323030000045
ct＝αJ0+βkt(4)
According to Rao et al[16]The proportional torsional damping coefficient is:
α＝100
β＝10-7
according to the torsion theory of the rod, the torque is:
Figure GDA0002527323030000051
wherein M ist，G，I0And l is torque, shear modulus, polar moment of inertia, and axle length, respectively.
The polar inertia distance of the section of the cylindrical part is as follows:
Figure GDA0002527323030000052
the torsional stiffness of the axle is:
Figure GDA0002527323030000053
the method is characterized in that large cylindrical parts are used under the initial condition: t is 0 and theta is theta0，
Figure GDA0002527323030000054
Solving to obtain the response theta of the cylindrical partwAnd (t) is the angle error of the cylindrical part.
Processing parameter and processing path error compensation model
The machine tool can effectively compensate the relative displacement and angle error of the cutter and the workpiece caused by large cylindrical parts through the correction of machining parameters. And (3) compensating the processing parameters after the comprehensive error: the cutting depth, the feeding speed, the rotation angle of the chuck and the deflection motion angle of the main shaft of the machine tool in an x-z plane are respectively as follows:
Figure GDA0002527323030000055
ap,fzdepth of cut, feed rate (a) respectivelyp,fzThe optimized cutting depth and the optimized feeding speed can be respectively as follows: firstly, the relation between the surface quality (such as surface roughness) of a workpiece and cutting parameters is obtained through an orthogonal experiment, and the cutting parameters are matched according to the relation and the processing target of the surface quality). Under the condition of not loading large-sized cylinder parts, the rotation angle of the input angle chuck set by the machine tool according to the requirement of processing workpieces, and the deflection motion angles of the main shaft of the machine tool in the x-z plane are respectively thetad,θt。
The large-sized cylindrical parts have the problems of excessive cutting or insufficient cutting in the x direction caused by the torsional response, the axial surface of the cutter is not consistent with the radial direction of the large-sized cylindrical parts, and the error in the x direction in the machining process is expanded to the machining surface of the whole part, so that the machining error of the size and the shape is caused. The position and angle deviation error of the center of the large-sized cylinder part caused by the torsional response can change along with time after the initial cutting machining is enough, and can be compensated by the change along with time of the relative position and angle of the cutter and the workpiece, and the compensation can be realized by the machining path of the cutter. The displacement and angle errors caused by the large cylinder-like torsional response are shown in fig. 2.
In planning a machining path of a machine tool, a machining path of a tool is set to s (x)t,yt,zt,θt,θw) In the angular error model of the axle torsion response (i.e. the power equation of the angular response) the solution is found in the initial condition: t is equal to 0, and t is equal to 0,
Figure GDA0002527323030000061
the torsional response of the large circular tube part is theta' (t), the x-direction displacement, the z-direction displacement and the angle error in the x-z plane need to be compensated on the tool path, and the x-direction compensated displacement error, the y-direction compensated displacement error and the angle error are respectively as follows according to the geometrical relationship:
Δx＝sin(θw(t))rc(9)
Δz＝Δxsin(θw(t)) (10)
θ'(t)＝θw(t) (11)
therefore, the path s' (x, y, z, θ) after the compensation of the relative motion path of the tool and the workpiece is:
s'(xt,yt,zt,θt,θw)＝s(xt+Δx,yt,zt+Δz,θt+θ'(t),θw) (12)
the compensated cutter machining path is used for machining large-sized cylinder parts, and the requirement on machining precision can be met. The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and all simple modifications, changes and equivalent structural changes made to the above embodiment according to the technical spirit of the present invention still fall within the protection scope of the technical solution of the present invention.

Claims (1)

1. A precision machining control method for large cylindrical parts is characterized by comprising the following steps:
step one, establishing a response model of the cylinder type part: wherein x-y-z is the ideal position of the workpiece after rotating an angle, wherein y is the axial direction of the workpiece, the z direction is the radial direction passing through the axis of the workpiece in the workpiece, the ideal z direction is the vertical direction, and x is the direction perpendicular to the y and z directions; x 'represents the axial direction of the workpiece after the cylindrical part responds to torsion, and y' represents the radial direction passing through the axis of the workpiece in the workpiece; z ' is a direction perpendicular to the y ' and x ';
at angular velocity of cylinder-like parts
Figure FDA0002527323020000011
The dynamic equation of the angular response after the rotation is subjected to the resisting moment is as follows:
Figure FDA0002527323020000012
wherein J0，
Figure FDA0002527323020000013
Ct,
Figure FDA0002527323020000014
ktTheta and T are respectively the moment of inertia, angular acceleration, torsional damping coefficient, torsional angular velocity, torsional rigidity, torsional angle and received torque of the cylindrical part; in the rotation motion of the cylinder part, the rotation damping coefficient of the shaft is set as proportional torsion damping;
Figure FDA0002527323020000015
ct＝αJ0+βkt(4)
wherein m isiDenotes the mass per unit area of the cylindrical part, riThe distance from the center of mass of a unit area on the cylindrical part to the axis of the cylindrical part is represented, and the proportional torsional damping coefficient is as follows:
α＝100
β＝10-7
according to the torsion theory of the rod, the torque applied to the cylinder part is as follows:
Figure FDA0002527323020000016
wherein M ist，G，I0And l is the torque, shear modulus, polar inertia distance and axle length of the cylinder parts respectively;
the polar inertia distance of the section of the cylindrical part is as follows:
Figure FDA0002527323020000017
d represents the diameter of the cylinder type part;
the torsional rigidity of the cylinder part is as follows:
Figure FDA0002527323020000021
with the axle in the initial condition: t is 0 and theta is theta0，
Figure FDA0002527323020000022
Solving is carried out to obtain the response of the cylindrical parts, namely the error is thetaw(t)；
Step two, a processing parameter and processing path error compensation model
The machine tool bears the relative displacement and angle error of a cutter and a workpiece caused by cylindrical parts, and the effective compensation is carried out through the correction of processing parameters; and (3) compensating the processing parameters after the comprehensive error: the cutting depth, the feeding speed, the rotation angle of the chuck and the deflection motion angle of the main shaft of the machine tool in an x-z plane are respectively as follows:
Figure FDA0002527323020000023
ap,fzdepth of cut, feed rate, respectively; the rotation angle of the input angle chuck is set according to the requirement of a processing workpiece by a machine tool under the condition that large cylindrical parts are not loaded, and the main shaft of the machine tool is at xThe angle of the yaw motion in the z-plane is θd,θt；ap cIndicating depth of cut, ξzRepresents the composite error in the z direction; f. ofz cIndicates the feed amount; thetad cRepresenting the angle of movement, theta, of the cylinder-like part after compensation for angular errors caused by angular movementdShowing the set angle of movement, ζ, of the cylinder partxzdThe angle error caused by the angle movement is represented and obtained by testing the angle difference between the angle position of a certain point of the cylinder part and the ideal angle position; thetat cRepresenting the angle of movement of the tool after compensation for angular errors due to time delay errors, thetatShowing the set angle of movement, ζ, of the toolxzThe angle error caused by the motion time delay error in the transmission process can be obtained by testing the time difference between the actual time and the ideal time of a certain point;
step three, in the machining path planning of the machine tool, the machining path of the original tool is set to be s (x)t,yt,zt,θt,θw) Wherein x istRepresenting the path of movement in the x-direction, y, over timetRepresenting the path of motion in the y-direction, z, over timetRepresenting the path of motion in the z-direction, theta, over timewThe rotating angle of the cylindrical part is shown to change along with time, and t is time; solving in the dynamic equation of the angular response of the cylinder type part at the initial condition: t is equal to 0, and t is equal to 0,
Figure FDA0002527323020000031
in the case, the torsional response of the large circular tube part is θ '(t), and the x-direction displacement, the z-direction displacement and the angle error in the x-z plane need to be compensated on the tool path, and according to the geometrical relationship, the x-direction compensated displacement error Δ x, the z-direction compensated displacement error Δ z and the angle error θ' (t) are respectively:
Δx＝sin(θw(t))rc(9)
Δz＝Δxsin(θw(t))(10)
θ'(t)＝θw(t) (11)
rcthe distance between the tool point and the axis of the cylinder part is shown;
therefore, the relative movement between the tool and the workpiece compensates the path of the tool (s') (x)t,yt,zt,θt,θw) Comprises the following steps:
s'(xt,yt,zt,θt,θw)＝s(xt+Δx,yt,zt+Δz,θt+θ'(t),θw) (12)
and machining the cylindrical part in the path compensated by the cutter.
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