CN113997157A - Multi-surface common-body optical curved surface polishing machine tool and method based on macro-micro composite driving - Google Patents
Multi-surface common-body optical curved surface polishing machine tool and method based on macro-micro composite driving Download PDFInfo
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- CN113997157A CN113997157A CN202111329611.7A CN202111329611A CN113997157A CN 113997157 A CN113997157 A CN 113997157A CN 202111329611 A CN202111329611 A CN 202111329611A CN 113997157 A CN113997157 A CN 113997157A
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B24—GRINDING; POLISHING
- B24B—MACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
- B24B13/00—Machines or devices designed for grinding or polishing optical surfaces on lenses or surfaces of similar shape on other work; Accessories therefor
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B24—GRINDING; POLISHING
- B24B—MACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
- B24B1/00—Processes of grinding or polishing; Use of auxiliary equipment in connection with such processes
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B24—GRINDING; POLISHING
- B24B—MACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
- B24B13/00—Machines or devices designed for grinding or polishing optical surfaces on lenses or surfaces of similar shape on other work; Accessories therefor
- B24B13/0031—Machines having several working posts; Feeding and manipulating devices
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Abstract
The invention discloses a polyhedral common optical curved surface polishing machine tool based on macro-micro compound drive and a method thereof, wherein the machine tool comprises a machine tool body base, an X-direction macro-micro compound drive feeding mechanism, a Y-direction feeding mechanism and a Z-direction feeding mechanism; the X-direction macro-micro compound driving feeding mechanism is fixed on the bed base, a part to be machined is arranged on the X-direction macro-micro compound driving feeding mechanism, and the X-direction macro-micro compound driving feeding mechanism drives the part to be machined to move left and right along the X-axis direction; the Z-direction feeding mechanism is fixed on the bed body base and positioned behind the X-direction macro-micro composite driving feeding mechanism, the Y-direction feeding mechanism is fixed on the Z-direction feeding mechanism, and the Z-direction feeding mechanism drives the Y-direction feeding mechanism to move up and down along the Z-axis direction; the Y-direction feeding mechanism is used for installing the polishing tool head, drives the polishing tool head to perform front-back feeding motion, up-down pitching motion and left-right swinging motion along the Y-axis direction, and is matched with the X-direction macro-micro composite driving feeding mechanism to realize polishing of the part to be processed.
Description
Technical Field
The invention belongs to the technical field of machining, and particularly relates to a multi-surface co-body optical curved surface polishing machine tool based on macro-micro composite driving and a control method thereof.
Background
The large-visual-field and high-resolution photoelectric observing and aiming system is an eye of various physical space-time sensing equipment, is a core point for technical change breakthrough in the fields of national defense safety, space detection, high and new technology and the like, and the manufacturing technology of the system is highly valued by various countries. The off-axis free curved surface is a revolutionary technology which breaks through the short action distance of a multiband photoelectric observing and aiming system and realizes common caliber, light weight and small size.
The existing photoelectric sight system mostly adopts split design and manufacture of an off-axis free-form surface optical system, but the split structure has the problems of complex structure, difficult assembly and adjustment, poor stability and the like, and the common manufacture opens up a new way for solving the problem. However, the current co-body manufacturing research is still in a primary stage, a relevant theoretical support and a perfect process implementation scheme are lacked, and the whole manufacturing links (design, processing, measurement, evaluation and application) are difficult. More and more researchers are looking to solve the problem of ultra-precision machining of split structures of off-axis free optical systems by means of the emerging method of co-body fabrication.
On the other hand, due to nonlinear factors such as guide rail friction and the mass limit of the large-stroke motion platform, the positioning accuracy and the control bandwidth of the existing single-stage driving motion platform reach a certain threshold value, and the high-accuracy requirement is not easily met.
Disclosure of Invention
The invention aims to provide a polyhedral common body optical curved surface polishing machine tool based on macro-micro compound driving and a control method thereof, so as to solve the problems in the background technology.
In order to achieve the above purpose, the present invention provides the following technical solutions, in combination with the accompanying drawings:
a multi-surface common-body optical curved surface polishing machine tool based on macro-micro compound driving comprises a machine tool body base 1, an X-direction macro-micro compound driving feeding mechanism 2, a Y-direction feeding mechanism 3 and a Z-direction feeding mechanism 4; the X-direction macro and micro compound driving feeding mechanism 2 is fixed on the lathe bed base 1, the part 6 to be machined is arranged on the X-direction macro and micro compound driving feeding mechanism 2, and the X-direction macro and micro compound driving feeding mechanism 2 drives the part 6 to be machined to move left and right along the X-axis direction; the Z-direction feeding mechanism 4 is fixed on the lathe bed base 1 and is positioned behind the X-direction macro-micro composite driving feeding mechanism 2, the Y-direction feeding mechanism 3 is fixed on the Z-direction feeding mechanism 4, and the Z-direction feeding mechanism 4 drives the Y-direction feeding mechanism 3 to move up and down along the Z-axis direction; the Y-direction feeding mechanism 3 is used for installing the polishing tool head 50, driving the polishing tool head to perform front-back feeding motion, up-down pitching motion and left-right swinging motion along the Y-axis direction, and matching with the X-direction macro-micro composite driving feeding mechanism 2, realizing polishing processing of the part 6 to be processed;
the X-direction macro and micro compound driving feeding mechanism 2 comprises an X-direction feeding mechanism base 9, a macro motion platform 25, an X-direction macro motion mechanism, a micro motion platform 11, an X-direction micro motion mechanism 26, a rotating platform 12 and a clamp platform 13; the X-direction feeding mechanism base 9 is fixed on the machine tool base 1, the X-direction macro motion mechanism is fixed on the X-direction feeding mechanism base 9, the macro motion platform 25 is installed on the X-direction macro motion mechanism, and the macro motion platform 25 moves left and right relative to the machine tool base 1 along the X-axis direction under the drive of the X-direction macro motion mechanism; the X-direction micro-motion mechanism 26 is arranged on the macro-motion platform 25, the micro-motion platform 11 is arranged on the X-direction micro-motion mechanism 26, and the micro-motion platform 11 is driven by the X-direction micro-motion mechanism 26 to move left and right relative to the macro-motion platform 25 along the X-axis direction; the rotary table 12 is mounted on the micro-motion stage 11, and the clamp table 13 is mounted on the rotary table 12 and rotated by the rotary table 12.
The X-direction macro motion mechanism comprises a linear motor 24, a macro motion air floatation guide rail 19, a macro motion sliding frame and a macro motion grating ruler 23; a macro motion air floatation guide rail 19 supporting block 10 is fixed on the X-direction feeding mechanism base 9; the macro motion sliding frame is connected on the macro motion air floatation guide rail 19 in a sliding way; the linear motor 24 is arranged below the macro motion air floatation guide rail 19 and used for driving the macro motion sliding frame to slide along the macro motion air floatation guide rail 19; the macro movement grating ruler 23 is arranged on the front side of the macro movement air floatation guide rail 19; the macro motion platform 25 is fixed on the macro motion sliding frame.
The macro motion sliding frame comprises a sliding frame 16, a long sliding groove rod 17 and a short sliding groove rod 18; a long sliding chute rod 17 is fixed on the upper end surface of the sliding frame 16, and the long sliding chute rod 17 is provided with an air floatation supporting pad 14 through a sliding chute; short chute rods 18 are fixed at the front side and the rear side of the sliding frame 16, and the short chute rods 18 are provided with air floatation guide pads 8 through chutes; an air film is formed between the air floatation supporting pad 14 and the air floatation guiding pad 8 and the macro motion air floatation guide rail 19 at the same time, so that the macro motion sliding frame can slide on the macro motion air floatation guide rail 19 without friction; the macro motion platform 25 is fixed on the long chute bar 17 on the upper end surface of the sliding frame 16.
The X-direction micro-motion mechanism 26 comprises a micro-motion grating ruler 29, a piezoelectric ceramic driver 31, an X-direction micro-motion slide carriage 32, an X-direction micro-motion slide block 33, an X-direction micro-motion guide rail 34 and a micro-motion guide rail base; the X-direction micro-motion guide rail 34 is fixed on a micro-motion guide rail base which is fixed on the macro-motion platform 25; the micro-motion grating ruler 29 is fixed on one side of the X-direction micro-motion guide rail 34; an X-direction micro-motion sliding block 33 is connected to an X-direction micro-motion guide rail 34 in a sliding mode, an X-direction micro-motion slide carriage 32 is fixed to the X-direction micro-motion sliding block 33, one end of a piezoelectric ceramic driver 31 is fixed to the X-direction micro-motion slide carriage 32, the other end of the piezoelectric ceramic driver 31 is connected with a macro-motion platform 25 through a coupling connection block 28, the X-direction micro-motion sliding block 33 is driven to slide along the X-direction micro-motion guide rail 34 by controlling deformation of the piezoelectric ceramic driver 28, and then the micro-motion sliding block moves relative to the macro-motion platform 25.
The Y-direction feeding mechanism 3 comprises a servo motor 47, a polishing tool head connecting mechanism 45, a cylindrical shell 46 and three parallel driving mechanisms; the servo motor 47 is connected to the rear end face of the polishing tool head connecting mechanism 45, and the polishing tool head connecting mechanism 45 is used for connecting the polishing tool head 50 and driving the polishing tool head 50 to work through the servo motor 47; the three parallel driving mechanisms are uniformly distributed in the cylindrical shell 46 along the circumferential direction and are respectively fixed on the inner surface of the cylindrical shell 46; the three parallel driving mechanisms are respectively hinged with the polishing tool head connecting mechanism 45; the three parallel drive mechanisms work in cooperation to drive the polishing tool head 50 to perform a feed-forward motion, a pitch-up motion, a pitch-down motion, and a yaw-left motion along the Y-axis direction.
The parallel driving mechanism comprises a connecting block 35, a universal hinge 36, a plate type connecting rod piece 37, a parallel mechanism sliding plate 38, a Y-direction lead screw nut pair 39, a Y-direction feeding guide rail 40, a parallel mechanism base 41, a parallel mechanism sliding block 42 and a parallel mechanism servo motor 43; the parallel mechanism base 41 is fixed on the inner surface of the cylindrical shell 46, the output end of the parallel mechanism servo motor 43 is connected with the Y-direction lead screw nut pair 39, and the Y-direction lead screw nut pair 39 is fixed on the parallel mechanism base 41 and provides Y-direction feeding motion; the Y-direction feeding guide rail 40 is fixed on the parallel mechanism base 41, the parallel mechanism sliding block 42 is connected to the Y-direction feeding guide rail 40 in a sliding mode, the parallel mechanism sliding plate 38 is fixed at the top of the parallel mechanism sliding block 42, the parallel mechanism sliding plate 38 is connected with the Y-direction lead screw nut pair 39, the parallel mechanism sliding plate 38 is hinged to one end of the plate type connecting rod piece 37, the other end of the plate type connecting rod piece 37 is connected with the universal hinge 36 through threads, and the other end of the universal hinge 36 is connected with the polishing tool head 50 through the connecting block 35.
The Z-direction feeding mechanism 4 comprises a Z-direction servo motor 51, a Z-direction lead screw nut pair 52, a Z-direction feeding motion table 53, a Z-direction upright 54 and a cross beam 55; two Z-direction upright posts 54 are symmetrically and fixedly connected to the bed base 1, a Z-direction feeding moving table 53 is installed on the Z-direction upright posts 54, an output shaft of a Z-direction servo motor 51 is connected with a Z-direction lead screw nut pair 52, and the Z-direction lead screw nut pair 52 is connected with the Z-direction feeding moving table 53; the beam 55 is connected between the two Z-direction feeding motion tables 53, and the beam 55 is used for mounting the Y-direction feeding mechanism 3; the Z-direction feeding motion table 53 is controlled by a Z-direction servo motor 51, and the beam 55 is synchronously driven to move up and down along the Z-axis direction.
The Z-direction feed motion table 53 includes a Z-direction guide rail base 56, a cross ball guide rail 57, and a Z-direction slide plate 58; the Z-direction rail base 56 is connected to the inside of the Z-direction column 54, the cross ball rail 57 is fixed to the Z-direction rail base 56, the Z-direction slide plate 58 is slidably connected to the cross ball rail 57, and the Z-direction slide plate 58 is connected to the Z-direction screw nut pair 52 at the same time.
The invention also provides a control method of the polyhedral co-body optical curved surface polishing machine tool based on macro-micro composite driving, and the processing control process mainly comprises the following steps:
(1) and measuring the part to be processed by a high-precision three-coordinate measuring machine to obtain relevant information of the part, such as the curvature radius, the surface roughness, the surface shape and the like of the free-form surface.
(2) And according to the obtained part information, obtaining a measurement model through a curved surface reconstruction technology, and simultaneously generating the track information of the machining tool on corresponding simulation software through the designed model. And then, judging according to the shape characteristics of the theoretical model, and carrying out model matching on the measurement model and the design model.
(3) And selecting proper machining parameters such as the size of the polishing tool head (the shape of the tool head, the surface curvature and the like), the rotating speed of the spindle, the machining allowance, motor parameters and the like according to the obtained part information and the planned machining track, and determining the machining allowance and the machining process.
(4) And (3) performing machining simulation according to the machining parameters selected in the previous step, judging whether interference collision occurs or not, and returning to the step (2) to reselect for model design if interference exists.
(5) And if collision interference does not exist, performing related numerical control programming, determining the tool track, further generating a corresponding numerical control code of the track, inputting the numerical control code into the numerical control machine tool, and preparing for actual processing.
(6) And clamping the part to be processed on a fixture table 13 of the Y-direction feeding mechanism 3, checking the machine tool, starting the machine tool after confirming no error, resetting and basically operating the machine tool, and confirming that the machine tool can normally operate again.
(7) And (4) aligning the cutter, aligning the starting point to the starting point of the program, and aligning the reference of the cutter.
(8) And starting the machine tool to polish the parts. During the machining process, the measuring instrument related to the system measures the position of the tool in real time and performs tool compensation. A control method with self-adaption capability is added in a NURBS curve interpolation algorithm, the NURBS curve interpolation can improve the processing performance, and the processing impact caused by the non-ideal ACC/DEC molded lines is eliminated.
(9) And after the machining is finished, measuring the machined part by using a related measuring instrument, and if the precision requirement is met, withdrawing the tool by using the system to finish the machining. And if the precision requirement is not met, returning to the flow (8).
The control method of the polyhedral co-body optical curved surface polishing machine tool based on macro-micro composite driving comprises a self-adaptive real-time NURBS curve interpolation algorithm, and comprises the following specific contents:
one NURBS curve P (u) can be defined as formula (1)
Wherein, the k-order B-spline basis function { NiK (u) } recursion is defined as the following formula (2)
The node vector U obtained by the Risselford method is as follows (3)
Interpolation preprocessing
NURBS curve interpolation expressions are relatively complex, which can reduce interpolation efficiency. To avoid this problem, NURBS curves are usually represented in matrix form. Rational fraction of NURBS curve is represented by the following formula (4)
Wherein, a3、a2、a1、a0Is the coefficient of the node parameter in the molecule, b3、b2、b1、b0Is the coefficient of the node parameter in the denominator. A new variable t is defined as equation (5)
Wherein k is the order of NURBS curve, and k is less than or equal to i is less than or equal to n + 1. From the specific expression of the 'i-2' segment in the NURBS curve in equations (4) and (5), the following equation (6) can be written
Wherein the content of the first and second substances,
③ parameter densification
Now, define U 00, and calculating U by the following formula (8)1，U2
A simplified iterative interpolation algorithm for Adams differential equation is as in equation (9)
Obtaining a corresponding estimate of the current interpolation point, as in equation (10)
The corresponding interpolation estimation step can be written as equation (11)
Self-adaptive feed speed control
Since the interpolation is performed at equal intervals, the control of the feed speed can be converted into the control of the step size. In the following, the constraints on step size are in two aspects, chord error and normal acceleration. Determination of feed rate constrained by chord length error: the expression for the chord length error can be described in equation (12) below,
the feed step limited by the chord length error can be provided by equation (13) below
The determination of the feed speed is constrained by the normal acceleration, assuming the maximum allowable normal acceleration is amax, the feed step constrained by the normal acceleration can be expressed as equation (14)
The maximum step length allowed in the machining process is Li0. The minimum of the three lengths can be used as the current feed step size, and the error between the estimated step size and the expected step size can be represented by the relative error deltaiIs expressed as formula (15)
If the estimated value of the interpolation point exceeds the allowable range, the correction should be made by equation (16) until the error is within the allowable range.
Therefore, the self-adaptive adjustment of the feeding step length can be realized through the constraint of chord length error and normal acceleration.
Compared with the prior art, the invention has the following beneficial effects:
1. the invention designs a macro-micro composite driving system which comprises a macro-motion platform, a micro-motion platform, a macro-micro driver and the like, wherein compared with the traditional 'motor + guide rail' driving, the macro-micro composite driving platform has higher dynamic precision and stability.
2. The invention designs a set of feeding system (Y-direction feeding mechanism) of a polishing tool head, three parallel driving mechanisms comprise a universal hinge, a plate type connecting rod piece, a Y-direction feeding guide rail and a servo motor, the feeding system is different from a common mode of directly driving in a mode of 'motor + guide rail', but the three parallel driving mechanisms are connected to the polishing tool head in parallel by utilizing a parallel structure, and the large-angle stepless deflection of the tool head is realized by controlling the rotating speed of the servo motor, so that the working requirement of the feeding system is met. Compared with the traditional structure, the parallel mechanism has the advantages of difficult dynamic error, higher precision, small motion inertia, high mechanism rigidity, stable structure, thermal symmetry structural design, small thermal deformation and the like.
3. The invention designs a Z-direction feeding mechanism with a gantry structure, adopts a double-crossed roller guide rail to form a moving platform so as to provide feeding motion, and improves the motion precision and the motion stability in the Z-axis direction.
Drawings
Fig. 1 is a schematic view of the overall structure of a multi-surface co-body optical curved surface polishing machine tool based on macro-micro composite driving.
Fig. 2 is a schematic structural diagram of an X-direction macro-micro compound driving feeding mechanism according to the present invention.
Fig. 3 is a rear view of the X-direction macro-micro compound driving feeding mechanism of the present invention.
Fig. 4 is a schematic structural diagram of a carriage in the X-direction macro-micro compound driving feeding mechanism of the invention.
Fig. 5 is an exploded schematic view of the structures of the platforms in the X-direction macro-micro compound driving feeding mechanism.
Fig. 6 is an exploded schematic view of a micro-motion mechanism in the X-direction macro-micro compound driving feeding mechanism according to the present invention.
Fig. 7 is a structural cross-sectional view of a micro-motion mechanism in the X-direction macro-micro compound driving feeding mechanism according to the invention.
Fig. 8 is a schematic structural diagram of an independent parallel mechanism in the Y-direction feeding mechanism according to the present invention.
Fig. 9 is a schematic structural view of the Y-direction feeding mechanism according to the present invention.
Fig. 10 is an exploded view of a tool head structure of the Y-direction feeding mechanism according to the present invention.
FIG. 11 is a schematic structural view of a Z-direction feeding mechanism according to the present invention.
FIG. 12 is a side cross-sectional view of the Z-feed mechanism of the present invention.
Fig. 13 is a schematic structural view of a feeding motion table in the Z-direction feeding mechanism according to the present invention.
FIG. 14 is a control flow chart of the present invention.
In the figure:
1. a machine tool body base, 2, an X-direction macro and micro compound driving feeding mechanism, 3, a Y-direction feeding mechanism, 4, a Z-direction feeding mechanism, 5, an X-axis positioning table, 6, a part to be processed, 8, an air floating guide pad, 9, an X-direction feeding mechanism base, 10, a supporting block, 11, a micro motion platform, 12, a rotating table, 13, a clamp table, 14, an air floating supporting pad, 15, a clamping element, 16, a sliding frame, 17, a long sliding groove rod, 18, a short sliding groove rod, 19, a macro motion air floating guide rail, 20, a limit switch, 21, a first screw connecting hole, 22, a counter, 23, a macro motion grating ruler, 24, a linear motor, 25, a macro motion platform, 26, an X-direction micro motion mechanism, 27, a groove, 28, a coupling connecting block, 29, a micro motion grating ruler, 30, a second screw connecting hole, 31, a piezoelectric ceramic driver, 32, an X-direction micro motion slide carriage, 33, 34, an X-direction micro motion guide rail, 35. connecting block, 36 universal hinge, 37 plate type connecting rod piece, 38 parallel mechanism sliding plate, 39Y direction lead screw nut pair, 40Y direction feeding guide rail, 41 parallel mechanism base, 42 parallel mechanism sliding block, 43 parallel mechanism servo motor, 44 plum blossom coupling, 45 polishing tool head connecting piece, 46 cylindrical shell, 47 servo motor, 48 servo motor shaft, 49 elastic pin coupling, 50 polishing tool head, 51Z direction servo motor, 52Z direction lead screw nut pair, 53.Z direction feeding motion platform, 54Z direction upright post, 55 cross beam, 56.Z direction guide rail base, 57 cross ball guide rail, 58.Z direction sliding plate
Detailed Description
The technical solution of the present patent will be described in further detail with reference to the following embodiments.
Reference will now be made in detail to embodiments of the present patent, examples of which are illustrated in the accompanying drawings. The described embodiments are only some, but not all embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Examples
In this embodiment, as shown in fig. 1, a polishing machine tool based on macro-micro compound drive for a polyhedral common optical curved surface includes a bed base 1, an X-direction macro-micro compound drive feeding mechanism 2, a Y-direction feeding mechanism 3, a Z-direction feeding mechanism 4, an X-axis positioning table 5, a part to be processed 6, an outer protective cover (not shown in the figure), and the like. The X-axis positioning table 5 is positioned on the lathe bed base 1 and is integrated with the lathe bed base 1; the X-direction macro and micro compound driving feeding mechanism 2 is fixed on the X-axis positioning table 5, the part 6 to be machined is arranged on the X-direction macro and micro compound driving feeding mechanism 2, and the X-direction macro and micro compound driving feeding mechanism 2 drives the part 6 to be machined to move left and right along the X-axis direction; the Z-direction feeding mechanism 4 is fixed on the lathe bed base 1 and is positioned behind the X-direction macro-micro composite driving feeding mechanism 2, the Y-direction feeding mechanism 3 is fixed on the Z-direction feeding mechanism 4, and the Z-direction feeding mechanism 4 drives the Y-direction feeding mechanism 3 to move up and down along the Z-axis direction; the Y-direction feeding mechanism 3 is used for installing the polishing tool head 50, driving the polishing tool head to perform front-back feeding motion, up-down pitching motion and left-right swinging motion along the Y-axis direction, and matching with the X-direction macro-micro composite driving feeding mechanism 2, the polishing processing of the part 6 to be processed is realized.
As shown in fig. 2 to 7, the X-direction macro and micro compound drive feeding mechanism 2 includes an X-direction feeding mechanism base 9, a macro motion platform 25, an X-direction macro motion mechanism, a micro motion platform 11, an X-direction micro motion mechanism 26, a rotary table 12, and a clamp table 13; the X-direction feeding mechanism base 9 is fixed on an X-axis positioning table 5 of the machine tool base 1 through a first screw connecting hole 21, the X-direction macro motion mechanism is fixed on the X-direction feeding mechanism base 9, the macro motion platform 25 is installed on the X-direction macro motion mechanism, and the macro motion platform 25 moves left and right relative to the machine tool base 1 along the X-axis direction under the drive of the X-direction macro motion mechanism; the X-direction micro-motion mechanism 26 is arranged on the macro-motion platform 25, the micro-motion platform 11 is arranged on the X-direction micro-motion mechanism 26, and the micro-motion platform 11 is driven by the X-direction micro-motion mechanism 26 to move left and right relative to the macro-motion platform 25 along the X-axis direction; the rotary stage 12 is mounted on the micro-motion stage 11, and the jig stage 13 is mounted on the rotary stage 12 and rotated about the Z-axis by the rotary stage 12.
As shown in fig. 2 and 3, the X-direction macro movement mechanism includes a linear motor 24, a macro movement air floating guide rail 19, a macro movement sliding frame, a macro movement grating ruler 23, and a support block 10; two sides of the macro motion air floatation guide rail 19 are respectively connected to the X-direction feeding mechanism base 9 through supporting blocks 10 in a threaded manner; the macro motion sliding frame is connected on the macro motion air floatation guide rail 19 in a sliding way; the linear motor 24 is arranged below the macro motion air floatation guide rail 19 and used for driving the macro motion sliding frame to slide along the macro motion air floatation guide rail 19, and the translational degree of freedom in the X direction is provided by providing the speed of the voltage control platform moving in the X direction with different frequencies; the macro movement grating ruler 23 is arranged on the front side of the macro movement air floatation guide rail 19, and the reader 22 is arranged on the macro movement grating ruler 23 and used for detecting and reading the movement speed of the X-direction feeding mechanism 2 in real time; the macro motion platform 25 is fixed on the macro motion sliding frame, the limit switches 20 are arranged on two sides of the macro motion air floatation guide rail 19 and are respectively provided with the limit switches 20, the limit switches 20 are used for limiting the position of the macro motion platform 25 in the X-axis direction, and when the movement of the macro motion platform 25 in the X-axis direction exceeds the limit position, the limit switches 20 trigger to stop the current action.
As shown in fig. 4, the macro motion carriage comprises a carriage 16, a long chute bar 17, a short chute bar 18; a long sliding chute rod 17 is fixed on the upper end surface of the sliding frame 16, and the long sliding chute rod 17 is provided with an air floatation supporting pad 14 through a sliding chute; short chute rods 18 are fixed at the front side and the rear side of the sliding frame 16, and the short chute rods 18 are provided with air floatation guide pads 8 through chutes; a layer of thin air film with uniform thickness is formed between the air floatation supporting pad 14 and the air floatation guiding pad 8 and the macro motion air floatation guide rail 19 at the same time, so that the macro motion sliding frame can slide on the macro motion air floatation guide rail 19 without friction; the long chute bar 17 on the upper end of the carriage 16 is used to fix the macro motion platform 25.
As shown in fig. 5, an X-direction micro-motion mechanism 26 is installed in the groove 27 on the upper end surface of the macro-motion platform 25 through a threaded connection, the X-direction micro-motion mechanism 26 is connected with the micro-motion platform 11 through a second screw connection hole 30, and the micro-motion platform 11 is connected with the rotary table 12 through a threaded connection, so that the degree of freedom of rotation around the C axis is provided. A clamping table 13 is screwed onto the rotary table 12, and four clamping elements 15 are arranged laterally on the clamping table 13 for clamping the part 6 to be machined placed thereon.
As shown in fig. 6 and 7, the X-direction micro-motion mechanism 26 includes a micro-motion grating scale 29, a second screw connection hole 30, a piezoelectric ceramic driver 31, an X-direction micro-motion slide carriage 32, an X-direction micro-motion slider 33, an X-direction micro-motion guide rail 34, and a micro-motion guide rail base. The X-direction micro-motion guide rail 34 is fixed on a micro-motion guide rail base which is fixed in the groove 27 on the upper end surface of the macro-motion platform 25; the micro-motion grating ruler 29 is fixed on one side of the X-direction micro-motion guide rail 34 through threaded connection and is used for detecting the motion speed of the X-direction micro-motion mechanism in real time; an X-direction micro-motion sliding block 33 is connected to an X-direction micro-motion guide rail 34 in a sliding mode, an X-direction micro-motion slide carriage 32 is fixed to the X-direction micro-motion sliding block 33, one end of a piezoelectric ceramic driver 31 is fixed to the X-direction micro-motion slide carriage 32, the other end of the piezoelectric ceramic driver 31 is connected with a macro-motion platform 25 through a coupling connection block 28, the X-direction micro-motion sliding block 33 is driven to slide along the X-direction micro-motion guide rail 34 by controlling deformation of the piezoelectric ceramic driver 28, and then the micro-motion sliding block moves relative to the macro-motion platform 25.
As shown in fig. 9, the Y-direction feeding mechanism 3 includes a servo motor 47, a polishing tool head connecting mechanism 45, a cylindrical housing 46, and three parallel driving mechanisms; the servo motor 47 is connected to the rear end face of the polishing tool head connecting mechanism 45, and the polishing tool head connecting mechanism 45 is used for connecting the polishing tool head 50 and driving the polishing tool head 50 to work through the servo motor 47; the three parallel driving mechanisms are uniformly distributed in the cylindrical shell 46 along the circumferential direction and are respectively fixed on the inner surface of the cylindrical shell 46 through threaded connection; the three parallel driving mechanisms are respectively hinged with the polishing tool head connecting mechanism 45; the three parallel drive mechanisms work in cooperation to drive the polishing tool head 50 to perform a feed-forward motion, a pitch-up motion, a pitch-down motion, and a yaw-left motion along the Y-axis direction.
As shown in fig. 8, the parallel driving mechanism includes a connecting block 35, a universal hinge 36, a plate-type connecting rod 37, a parallel mechanism sliding plate 38, a Y-direction screw nut pair 39, a Y-direction feeding guide rail 40, a parallel mechanism base 41, a parallel mechanism sliding block 42, and a parallel mechanism servo motor 43; the parallel mechanism base 41 is fixed on the inner surface of the cylindrical shell 46, the output end of the parallel mechanism servo motor 43 is connected with the Y-direction lead screw nut pair 39, and the Y-direction lead screw nut pair 39 is fixed on the parallel mechanism base 41 and provides Y-direction feeding motion; the Y-direction feeding guide rail 40 is fixed on the parallel mechanism base 41, the parallel mechanism sliding block 42 is connected to the Y-direction feeding guide rail 40 in a sliding mode, the parallel mechanism sliding plate 38 is fixed at the top of the parallel mechanism sliding block 42, the parallel mechanism sliding plate 38 is connected with the Y-direction lead screw nut pair 39, the parallel mechanism sliding plate 38 is hinged to one end of the plate type connecting rod piece 37, the other end of the plate type connecting rod piece 37 is connected with the universal hinge 36 through threads, and the other end of the universal hinge 36 is connected with the polishing tool head 50 through the connecting block 35.
When the servo motors 43 of the three independent parallel driving mechanisms are controlled to work synchronously, the polishing tool head 50 can be driven to translate along the Y axis; when the three servo motors 43 work asynchronously, a certain displacement difference is generated in the Y-axis direction of the slide plate 38 of the parallel mechanism, and under the combined action of the plate type connecting rod piece 37 and the universal hinge 36, one end of the tool head is tilted, so that 6 degrees of freedom are provided in total.
As shown in fig. 10, the servo motor 47 is provided with a servo motor shaft 48 and an elastic pin coupling 49, the servo motor shaft 48 is connected to the tool head servo motor 47 through the elastic pin coupling 49, and the servo motor shaft 48 passes through the polishing tool head connecting mechanism 45 and is connected to the polishing tool head 50.
As shown in fig. 11 and 12, the Z-direction feeding mechanism 4 includes a Z-direction servo motor 51, a Z-direction lead screw nut pair 52, a Z-direction feeding motion table 53, a Z-direction upright 54 and a cross beam 55; two Z-direction upright posts 54 are symmetrically and fixedly connected to the bed base 1, a Z-direction feeding moving table 53 is installed on the Z-direction upright posts 54, an output shaft of a Z-direction servo motor 51 is connected with a Z-direction lead screw nut pair 52, and the Z-direction lead screw nut pair 52 is connected with the Z-direction feeding moving table 53; the beam 55 is connected between the two Z-direction feeding motion tables 53 through threads to form a gantry structure, and the beam 55 is used for installing the Y-direction feeding mechanism 3; the Z-direction feeding motion table 53 is controlled by a Z-direction servo motor 51, and the beam 55 is synchronously driven to move up and down along the Z-axis direction.
As shown in fig. 13, the Z-feed moving stage 53 includes a Z-guide base 56, a cross ball guide 57, and a Z-slide plate 58. The Z-direction guide rail base 56 is screwed to the inside of the Z-direction column 54, the cross ball guide 57 is fixed to the Z-direction guide rail base 56, the Z-direction slide plate 58 is slidably connected to the cross ball guide 57, and the Z-direction slide plate 58 is connected to the Z-direction screw nut pair 52.
The invention also provides a control method of the polyhedral co-body optical curved surface polishing machine tool based on macro-micro composite driving, and the processing control process mainly comprises the following steps:
(1) and measuring the part to be processed by a high-precision three-coordinate measuring machine to obtain relevant information of the part, such as the curvature radius, the surface roughness, the surface shape and the like of the free-form surface.
(2) And generating the processing cutter track information on corresponding simulation software according to the obtained part information. And determining a tool feeding route after planning by a NURBS curve interpolation technology with a real-time self-adaptive function.
(3) And selecting proper machining parameters such as the size of the polishing tool head (the shape of the tool head, the surface curvature and the like), the rotating speed of the spindle, the machining allowance, motor parameters and the like according to the obtained part information and the planned machining track.
(4) And (4) performing machining simulation according to the machining parameters selected in the previous step, judging whether interference collision occurs or not, and returning to the step (3) to reselect the machining parameters if interference exists.
(5) And if collision interference does not exist, performing related numerical control programming, determining the tool track, further generating a corresponding numerical control code of the track, inputting the numerical control code into the numerical control machine tool, and preparing for actual processing.
(6) And clamping the part to be processed on a fixture table 13 of the Y-direction feeding mechanism 3, checking the machine tool, starting the machine tool after confirming no error, resetting and basically operating the machine tool, and confirming that the machine tool can normally operate again.
(7) And (4) aligning the cutter, aligning the starting point to the starting point of the program, and aligning the reference of the cutter.
(8) And starting the machine tool to polish the parts. During the machining process, the measuring instrument related to the system measures the position of the tool in real time and performs tool compensation. A control method with self-adaption capability is added in a NURBS curve interpolation algorithm, the NURBS curve interpolation can improve the processing performance, and the processing impact caused by the non-ideal ACC/DEC molded lines is eliminated.
(9) And after the machining is finished, measuring the machined part by using a related measuring instrument, and if the precision requirement is met, withdrawing the tool by using the system to finish the machining. And if the precision requirement is not met, returning to the flow (8).
The control method of the polyhedral co-body optical curved surface polishing machine tool based on macro-micro composite driving comprises a self-adaptive real-time NURBS curve interpolation algorithm, and comprises the following specific contents:
a NURBS curve P (u) can be defined as formula (1)
Wherein, the k-order B-spline basis function { NiK (u) } recursion is defined as the following formula (2)
The node vector U obtained by the Risselford method is as follows (3)
Interpolation pretreatment
NURBS curve interpolation expressions are relatively complex, which can significantly reduce interpolation efficiency. To avoid this problem, NURBS curves are usually represented in matrix form. Rational fraction of NURBS curve is represented by the following formula (4)
Wherein, a3、a2、a1、a0Is the coefficient of the node parameter in the molecule, b3、b2、b1、b0Is the coefficient of the node parameter in the denominator. A new variable t is defined as equation (5)
Wherein k is the order of NURBS curve, and k is less than or equal to i is less than or equal to n + 1. In this example, k is 3, and a specific expression of the segment 'i-2' in the NURBS curve according to equations (4) and (5) can be written as the following equation (6)
Wherein the content of the first and second substances,
(ii) parameter densification
Now, define U 00, and calculating U by the following formula (8)1，U2
A simplified iterative interpolation algorithm for Adams differential equation is as in equation (9)
Obtaining a corresponding estimate of the current interpolation point, as in equation (10)
The corresponding interpolation estimation step can be written as equation (11)
-self-adaptive feed speed control
Since the interpolation is performed at equal intervals, the control of the feed speed can be converted into the control of the step size. In the following, the constraints on step size are in two aspects, chord error and normal acceleration. Determination of feed rate constrained by chord length error: the expression for the chord length error can be described in equation (12) below,
the feed step limited by the chord length error can be provided by equation (13) below
The determination of the feed speed is constrained by the normal acceleration, assuming the maximum allowable normal acceleration is amax, the feed step constrained by the normal acceleration can be expressed as equation (14)
The maximum step length allowed in the machining process is Li0. The minimum of the three lengths can be used as the current feed step size, and the error between the estimated step size and the expected step size can be represented by the relative error deltaiIs expressed as formula (15)
If the estimated value of the interpolation point exceeds the allowable range, the correction should be made by equation (16) until the error is within the allowable range.
Therefore, the self-adaptive adjustment of the feeding step length can be realized through the constraint of chord length error and normal acceleration.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications and substitutions should be considered to be within the scope of the present invention and not to affect the effect of the practice of the invention and the utility of the patent.
Claims (10)
1. A multi-surface common-body optical curved surface polishing machine tool based on macro-micro compound driving is characterized by comprising a machine tool body base (1), an X-direction macro-micro compound driving feeding mechanism (2), a Y-direction feeding mechanism (3) and a Z-direction feeding mechanism (4); the X-direction macro and micro compound driving feeding mechanism (2) is fixed on the bed base (1), a part (6) to be machined is arranged on the X-direction macro and micro compound driving feeding mechanism (2), and the X-direction macro and micro compound driving feeding mechanism (2) drives the part (6) to be machined to move left and right along the X-axis direction; the Z-direction feeding mechanism (4) is fixed on the lathe bed base (1) and is positioned behind the X-direction macro-micro composite driving feeding mechanism (2), the Y-direction feeding mechanism (3) is fixed on the Z-direction feeding mechanism (4), and the Z-direction feeding mechanism (4) drives the Y-direction feeding mechanism (3) to move up and down along the Z-axis direction; the Y-direction feeding mechanism (3) is used for installing the polishing tool head (50), driving the polishing tool head to perform front-back feeding motion, up-down pitching motion and left-right swinging motion along the Y-axis direction, and matching with the X-direction macro-micro composite driving feeding mechanism (2), the polishing processing of the part (6) to be processed is realized;
the X-direction macro and micro compound driving feeding mechanism (2) comprises an X-direction feeding mechanism base (9), a macro motion platform (25), an X-direction macro motion mechanism, a micro motion platform (11), an X-direction micro motion mechanism (26), a rotating table (12) and a clamp table (13); an X-direction feeding mechanism base (9) is fixed on the machine tool base (1), an X-direction macro motion mechanism is fixed on the X-direction feeding mechanism base (9), a macro motion platform (25) is installed on the X-direction macro motion mechanism, and the macro motion platform (25) moves left and right along the X-axis direction relative to the machine tool base 1 under the drive of the X-direction macro motion mechanism; the X-direction micro-motion mechanism (26) is arranged on the macro-motion platform (25), the micro-motion platform (11) is arranged on the X-direction micro-motion mechanism (26), and the micro-motion platform (11) is driven by the X-direction micro-motion mechanism (26) to move left and right along the X-axis direction relative to the macro-motion platform (25); the rotating platform (12) is arranged on the micro-motion platform (11), and the clamp platform (13) is arranged on the rotating platform (12) and driven by the rotating platform (12) to rotate.
2. The multi-surface co-body optical curved surface polishing machine tool based on macro and micro compound drive as claimed in claim 1, wherein the X-direction macro motion mechanism comprises a linear motor (24), a macro motion air floating guide rail (19), a macro motion sliding frame, a macro motion grating ruler (23); a supporting block 10 of a macro motion air floatation guide rail (19) is fixed on the X-direction feeding mechanism base (9); the macro motion sliding frame is connected on a macro motion air floatation guide rail (19) in a sliding manner; the linear motor (24) is arranged below the macro motion air floatation guide rail (19) and is used for driving the macro motion sliding frame to slide along the macro motion air floatation guide rail (19); the macro motion grating ruler (23) is arranged on the front side of the macro motion air floatation guide rail (19); the macro motion platform (25) is fixed on the macro motion sliding frame.
3. The multi-surface co-body optical curved surface polishing machine tool based on macro and micro compound driving as claimed in claim 2, characterized in that the macro motion sliding frame comprises a sliding frame (16), a long sliding groove rod (17), a short sliding groove rod (18); a long sliding chute rod (17) is fixed on the upper end surface of the sliding frame (16), and an air floatation support pad (14) is arranged on the long sliding chute rod (17) through a sliding chute; short chute rods (18) are fixed on the front side and the rear side of the sliding frame (16), and air floatation guide pads (8) are installed on the short chute rods (18) through sliding chutes; an air film is formed between the air floatation supporting pad (14) and the air floatation guiding pad (8) and the macro motion air floatation guide rail (19) at the same time, so that the macro motion sliding frame can slide on the macro motion air floatation guide rail (19) without friction; the macro motion platform (25) is fixed on a long sliding groove rod (17) on the upper end surface of the sliding frame (16).
4. The polyhedral co-body optical curved surface polishing machine tool based on macro and micro compound drive as claimed in claim 1, wherein the X-direction micro movement mechanism (26) comprises a micro movement grating ruler (29), a piezoelectric ceramic driver (31), an X-direction micro movement slide carriage (32), an X-direction micro movement slide block (33), an X-direction micro movement guide rail (34), a micro movement guide rail base; the X-direction micro-motion guide rail (34) is fixed on a micro-motion guide rail base, and the micro-motion guide rail base is fixed on the macro-motion platform (25); the micro-motion grating ruler (29) is fixed on one side of the X-direction micro-motion guide rail (34); x is to micromotion slider (33) sliding connection on X is to micromotion guide rail (34), X is fixed on X is to micromotion slider (33) to micromotion carriage apron (32), piezoceramics driver (31) one end is fixed on X is to micromotion carriage apron (32), the macrostep motion platform (25) are connected through coupling connecting block (28) to piezoceramics driver (31) other end, the deformation through control piezoceramics driver 28 drives X and slides along X to micromotion guide rail (34) to micromotion slider (33), and then moves macro motion platform (25) relatively.
5. The macro and micro compound drive-based polyhedral common body optical curved surface polishing machine tool as claimed in claim 1, wherein the Y-direction feeding mechanism (3) comprises a servo motor (47), a polishing tool head connecting mechanism (45), a cylindrical shell (46), three parallel driving mechanisms; the servo motor (47) is connected to the rear end face of the polishing tool head connecting mechanism (45), and the polishing tool head connecting mechanism (45) is used for connecting the polishing tool head (50) and driving the polishing tool head (50) to work through the servo motor (47); the three parallel driving mechanisms are uniformly distributed in the cylindrical shell (46) along the circumferential direction and are respectively fixed on the inner surface of the cylindrical shell (46); the three parallel driving mechanisms are respectively hinged with a polishing tool head connecting mechanism (45); the three parallel driving mechanisms work cooperatively to drive the polishing tool head (50) to perform forward and backward feeding movement, up and down pitching movement and left and right swinging movement along the Y-axis direction.
6. The multi-surface co-body optical curved surface polishing machine tool based on the macro-micro compound drive as claimed in claim 5, wherein the parallel drive mechanism comprises a connecting block (35), a universal hinge (36), a plate type connecting rod piece (37), a parallel mechanism sliding plate (38), a Y-direction lead screw nut pair (39), a Y-direction feeding guide rail (40), a parallel mechanism base (41), a parallel mechanism sliding block (42) and a parallel mechanism servo motor (43); the parallel mechanism base (41) is fixed on the inner surface of the cylindrical shell (46), the output end of a parallel mechanism servo motor (43) is connected with a Y-direction lead screw nut pair (39), and the Y-direction lead screw nut pair (39) is fixed on the parallel mechanism base (41) and provides Y-direction feeding motion; the Y-direction feeding guide rail (40) is fixed on the parallel mechanism base (41), the parallel mechanism sliding block (42) is connected to the Y-direction feeding guide rail (40) in a sliding mode, the parallel mechanism sliding plate (38) is fixed to the top of the parallel mechanism sliding block (42), the parallel mechanism sliding plate (38) is connected with the Y-direction lead screw nut pair (39), the parallel mechanism sliding plate (38) is hinged to one end of the plate type connecting rod piece (37), the other end of the plate type connecting rod piece (37) is connected with the universal hinge (36) through threads, and the other end of the universal hinge (36) is connected with the polishing tool head (50) through the connecting block (35).
7. The micro-macro composite drive-based polyhedral common body optical curved surface polishing machine tool as claimed in claim 1, wherein the Z-direction feed mechanism (4) comprises a Z-direction servo motor (51), a Z-direction lead screw nut pair (52), a Z-direction feed motion table (53), a Z-direction upright post (54) and a cross beam (55); two Z-direction vertical columns (54) are symmetrically and fixedly connected to a bed base (1), a Z-direction feeding moving table (53) is installed on the Z-direction vertical columns (54), an output shaft of a Z-direction servo motor (51) is connected with a Z-direction lead screw nut pair (52), and the Z-direction lead screw nut pair (52) is connected with the Z-direction feeding moving table (53); the cross beam (55) is connected between the two Z-direction feeding motion tables (53), and the cross beam (55) is used for mounting the Y-direction feeding mechanism (3); a Z-direction feeding motion table (53) is controlled by a Z-direction servo motor (51), and a beam (55) is synchronously driven to move up and down along the Z-axis direction.
8. The polyhedral common body optical curved surface polishing machine tool based on the macro-micro compound drive as claimed in claim 7, wherein the Z-direction feed motion table (53) comprises a Z-direction guide rail base (56), a crossed ball guide rail (57) and a Z-direction sliding plate (58); the Z-direction guide rail base (56) is connected to the inner side of the Z-direction upright post (54), the crossed ball guide rail (57) is fixed on the Z-direction guide rail base (56), the Z-direction sliding plate (58) is connected on the crossed ball guide rail (57) in a sliding mode, and the Z-direction sliding plate (58) is connected with the Z-direction screw nut pair (52) at the same time.
9. The method for controlling the polyhedral common body optical curved surface polishing machine tool based on the macro-micro compound driving as claimed in claim 1, which comprises the following steps:
step 1, measuring a part to be processed by a high-precision three-coordinate measuring machine to obtain relevant information of the part;
step 2, obtaining a measurement model through a curved surface reconstruction technology according to the obtained part information, and generating machining cutter track information on corresponding simulation software through a designed model; then judging according to the shape characteristics of the theoretical model, and carrying out model matching on the measurement model and the design model;
step 3, selecting proper machining parameters according to the obtained part information and the planned machining track, and determining machining allowance and machining process;
step 4, according to the processing parameters selected in the previous step, processing simulation is carried out, whether interference collision occurs or not is judged, if interference exists, the step/2 is returned to, and model design is carried out again;
step 5, if collision interference does not exist, carrying out numerical control programming, determining the tool track, further generating a corresponding numerical control code of the track, inputting the numerical control code into a numerical control machine tool, and preparing for actual processing;
step 6, clamping the part to be machined on a fixture table of the Y-direction feeding mechanism, checking the machine tool, starting the machine tool after confirming that no error exists, resetting and basically operating the machine tool, and confirming that the machine tool can normally operate again;
step 7, tool setting, namely, aligning the starting point to the starting position of the program and aligning the reference of the tool;
step 8, starting the machine tool, and polishing the parts; in the machining process, a measuring instrument is used for measuring the position of the cutter in real time and compensating the cutter; adding a self-adaptive real-time NURBS curve interpolation algorithm in the NURBS curve interpolation algorithm;
step 9, after the machining is finished, measuring the machined part by using a related measuring instrument, and if the precision requirement is met, withdrawing the system to finish the machining; and if the accuracy requirement is not met, returning to the step 8.
10. The method according to claim 9, wherein in step 8, the adaptive real-time NURBS curve interpolation algorithm is specifically:
one NURBS curve p (u) can be defined as follows:
wherein, the k-order B-spline basis function { NiK (u) } recursion is defined as follows:
the node vector U, which can be obtained according to the riesen verdet method, is as follows:
interpolation preprocessing
NURBS curve interpolation expressions are relatively complex, which can significantly reduce interpolation efficiency. To avoid this problem, NURBS curves are usually represented in matrix form. The rational formula of the NURBS curve is represented as follows:
wherein, a3、a2、a1、a0Is the coefficient of the node parameter in the molecule, b3、b2、b1、b0Is the coefficient of the node parameter in the denominator; a new variable t is defined as:
wherein k is the order of the NURBS curve, and k is not less than i not more than n + 1; the specific expression for the 'i-2' segment in the NURBS curve can be written as:
wherein the content of the first and second substances,
③ parameter densification
Definition of U00 and calculating U by the following formula1，U2
The simplified iterative interpolation algorithm for the adatans differential equation is as follows:
the corresponding estimate of the current interpolation point is obtained as follows:
the corresponding interpolation estimation step size can be written as:
self-adaptive feed speed control
Because the interpolation is performed in equal periods, the control of the feeding speed can be converted into the control of the step length; the constraints on step size are in two respects, chord error and normal acceleration; determination of feed rate constrained by chord length error: the expression for the chord length error is:
the feed step limited by the chord length error can be provided by
The determination of the feed speed is constrained by the normal acceleration: assuming that the maximum allowable normal acceleration is amax, the feed step constrained by the normal acceleration can be expressed as:
the maximum step length allowed in the machining process is Li0(ii) a The minimum of the three lengths can be used as the current feed step size, and the error between the estimated step size and the expected step size can be represented by the relative error deltaiTo show that:
if the estimated value of the interpolation point exceeds the allowable range, the correction is carried out by the following formula until the error is within the allowable range;
therefore, the self-adaptive adjustment of the feeding step length can be realized through the constraint of chord length error and normal acceleration.
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