CN117724400A - Geometric error analysis and compensation method for five-axis denture processing center - Google Patents
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Abstract
The invention relates to a geometric error analysis and compensation method of a five-axis denture processing center, which comprises the following steps: according to the ideal kinematic positive solution model, calculating the position where the original G code wants to control the cutter to reach and the posture of the cutter at the position; according to the actual kinematic inverse model, under the condition of considering the geometric error of the five-axis false tooth processing center irrelevant to the position, when the cutter is controlled to reach the position and the preset cutter posture is presented on the position, the actual motion quantity array required by each axis of the five-axis false tooth processing center is deduced; finally, the numerical control instruction is rewritten by utilizing the deduced actual motion quantity of each shaft to realize the compensation of geometric errors irrelevant to the position, thereby greatly improving the cutting precision and the cutting quality.
Description
Technical Field
The invention relates to the technical field of five-axis denture processing centers, in particular to a geometric error analysis and compensation method of a five-axis denture processing center.
Background
The traditional false tooth manufacturing process can be completed through tens of procedures of six workshops such as mould taking, mould manufacturing, wax type design, gold turning treatment, porcelain feeding, porcelain turning, detection and the like. The processing efficiency is low, the cost is high, the manufacturing process is extremely complicated, the skill level requirement on technicians is high, and the whole repair process can be completed in nearly two weeks.
Therefore, when the computer aided design and manufacturing (CAD/CAM) technology is successfully applied to the denture processing field, the traditional denture manufacturing method is gradually replaced in the denture manufacturing field by virtue of the advantages of high efficiency, high speed, high quality, low skill level requirement of operators and the like. The CAD/CAM denture manufacturing technology replaces the traditional mould taking and model manufacturing steps by utilizing an optical scanning technology, and can directly scan the oral cavity of a patient to obtain a three-dimensional model in the oral cavity; CAD software can assist operators to complete the three-dimensional model design process of missing teeth, and replaces the traditional manual wax pattern design step; the CAM software analyzes and processes the artificial tooth three-dimensional model designed by the operator to generate a numerical control instruction file, and the numerical control artificial tooth processing center is utilized for processing, so that the traditional processing links such as turning gold, turning porcelain and the like are replaced.
As an industrial master, the accuracy of machine tool operation directly affects the accuracy of machined parts. The machine tool is limited by the manufacturing level, and geometric errors can be generated in the manufacturing, assembling and clamping processes; the machine tool is subjected to thermal errors caused by internal and external heat sources in the running process; cutting force, gravity and the like in the processing process can also cause force errors of a process system; the numerical control system can introduce control errors in servo, driving and other links; in addition, the factors such as vibration and environment lead to very complex error sources of the machine tool, so that in order to solve the technical problems, a person skilled in the art needs to design a geometric error analysis and compensation method of the five-axis denture processing center.
Disclosure of Invention
Aiming at the defects, the invention aims to provide a geometric error analysis and compensation method of a five-axis denture processing center, which greatly improves cutting precision and cutting quality.
The invention provides the following technical scheme:
a geometric error analysis and compensation method for a five-axis denture processing center, the method comprising the steps of:
first, character string information in a G code file is converted into floating point type digital information and stored in an array of motion amounts of corresponding axes (S X 、S Y 、S Z 、θ A 、θ B ) In (a) and (b);
according to the ideal kinematic positive solution model in the formula (1), calculating the position where the original G code wants to control the tool to reach and the tool posture at the position;
(1)
Wherein P (a, b, c) and O (O (1), O (2), O (3)) represent the position and orientation of the tool relative to the workpiece coordinate system; θ A 、θ B 、θ X 、θ Y θ Z The motion amount of each axis of the five-axis denture processing center;
then according to the actual kinematic inverse model of formulas (2), (3) and (4), under the condition of considering the geometric error of the five-axis denture processing center irrelevant to the position, when the cutter is controlled to reach the position and the preset cutter posture is presented on the position, the actual motion quantity array required by each axis of the five-axis denture processing center is deduced (S * X 、S * Y 、S * Z 、θ * A 、θ * B ）；
(2)
(3)
(4)
Finally, the numerical control instruction is rewritten to realize the compensation of the geometric error irrelevant to the position by utilizing the deduced actual motion quantity of each axis.
As a preferred technical scheme of the geometric error analysis and compensation method of the five-axis denture processing center, the module of the geometric error analysis and compensation method comprises the following steps:
the G code information reading module is used for converting character string information in the G code file into floating point type digital information and storing the floating point type digital information into an array of motion quantity of a corresponding shaft;
the ideal kinematic correct solution module is used for solving the ideal pose of the cutter at each approximation point in each planned processing path in the G code through the ideal kinematic correct solution;
the actual kinematic inverse solution module reversely obtains the actual motion quantity of each axis required by reaching the ideal pose at each approaching point on the originally planned processing track through the actual kinematic inverse solution;
and the numerical control instruction writing module is used for re-writing the information into a numerical control instruction file and finishing the final file output.
As a preferable technical scheme of the geometric error analysis and compensation method of the five-axis denture processing center, when the denture processing center is used for processing a complex curved surface, a G01 straight line adding instruction is generally utilized in a numerical control instruction to guide the denture processing center to move a section of micro line segment to fit the complex curved surface structure;
specifically, a position D of the start point of the straight-line adding instruction is established 1 （a 1 ,b 1 ,c 1 ) Location D of termination point 2 （a 2 ,b 2 ,c 2 ），S 1 To increase the linear movement rate, t 1 To perform the time interval required for the addition operation, t 2 To increase the acceleration time of the movement;
adding a linear span:(5)
Discharging acceleration and deceleration, and calculating to obtain theoretical increment step number:
(6)
In fact, considering the inertia effect of the tool, the acceleration section and the deceleration section should be respectively established before and after the addition line, the actual addition step number is larger than the theoretical addition step number, and the actual addition step number F can be obtained by the following formula:
(7)
Wherein S is 2 Acceleration time t for adding linear adding motion 2 Acceleration and deceleration at time F S2 The step number for adding the acceleration and deceleration section of the movement;
a certain adding point D can be resolved according to the acceleration and deceleration characteristics i (i=1 to n), and the span between the point and the first addition point is
(8)
Determining an addition point D i Position by adding the starting point D of the straight line 1 （a 1 ,b 1 ,c 1 ) And add point D i Calculation of components in a spatial coordinate system to obtain D i （a i ,b i ,c i ）;
(9)
Wherein,；/>；/>；
resolving to obtain position coordinates D of each added point i And solving the actual motion quantity required by each axis of the machining center corresponding to each adding point through an actual kinematic inverse model.
As a preferable technical scheme of the geometric error analysis and compensation method of the five-axis denture processing center, the motion quantity of each axis is compensated and analyzed, character type numbers read from a numerical control instruction file are required to be converted into floating point type numerical value variables, and the floating point type numerical value variables are stored in a storage space corresponding to the motion axis.
As a preferable technical scheme of the geometric error analysis and compensation method of the five-axis denture processing center, the specific steps of the compensation analysis of the motion quantity of each axis comprise the following steps:
s1, opening an original numerical control instruction file by utilizing a fopen instruction in Matlab;
s2, reading the content of the next row in the file through the fgets function;
s3, sequentially searching the XYZAB and the FTMGS in the read content by utilizing a strfind function, and recording the positions of the characters.
As a preferable technical scheme of the geometric error analysis and compensation method of the five-axis denture processing center,
if any one of the five characters of XYZAB is searched in the read content, defining the state as 'detected', recording the position of the character appearing first in the five characters, and defining a character string formed by all characters positioned before the character as 'first character';
if any one of the five characters "XYZAB" is not detected in the read content, the read content is entirely defined as "first character".
As a preferable technical scheme of the geometric error analysis and compensation method of the five-axis denture processing center,
if the state is 'detected', recording the position of the last character appearing in the five characters of 'XYZAB', searching the first character appearing behind the position in the characters of 'FTMGS', recording the position of the first character, and defining the character string formed by all characters behind the position as 'tail character';
if the search result is null, adding a null character to the whole content read by the fgets function, recording the position of the null character, and defining the null character as a tail character.
As a preferable technical scheme of the geometric error analysis and compensation method of the five-axis denture processing center, the str2double function is utilized to convert the characters between the positions of the characters of XYZAB and the recorded positions into floating point type values, and the floating point type values are stored in the strain amount.
The beneficial effects of the invention are as follows: calculating the position where the original G code wants to control the cutter to reach and the cutter posture at the position according to an ideal kinematic positive solution model, deducing the actual movement quantity required by each axis of the five-axis denture processing center when the cutter reaches the position and presents the preset cutter posture at the position under the condition of considering the geometric errors of the five-axis denture processing center irrelevant to the position according to an actual kinematic solution model, and finally, re-compiling a numerical control instruction by utilizing the deduced movement quantity of each axis to realize the compensation of the geometric errors irrelevant to the position, thereby greatly improving the cutting precision and the cutting quality; the curved surface of the false tooth is convenient to grind by the cutter through the straight line adding instruction, the accuracy is improved, and the computing capacity of the five-axis false tooth processing center controller is reduced by properly adding the time interval required by executing the adding operation and the method for reducing the adding points, so that the hardware cost is reduced.
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The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate the invention and together with the embodiments of the invention, serve to explain the invention. In the drawings:
FIG. 1 is a flow chart of a geometric error analysis and compensation method for a five-axis denture processing center;
FIG. 2 is fitting data before compensation;
fig. 3 is the compensated fitting data.
Detailed Description
The conception, specific structure, and technical effects produced by the present invention will be clearly and completely described below with reference to the embodiments and the drawings to fully understand the objects, aspects, and effects of the present invention. It should be noted that, the embodiments and features in the embodiments in the present application may be combined with each other without conflict. It should be noted that, unless otherwise specified, when a feature is referred to as being "fixed" or "connected" to another feature, it may be directly or indirectly fixed or connected to the other feature.
Referring to fig. 1, a geometric error analysis and compensation method for a five-axis denture processing center, the method comprises the following steps:
a geometric error analysis and compensation method for a five-axis denture processing center, the method comprising the steps of:
first, character string information in a G code file is converted into floating point type digital information and stored in an array of motion amounts of corresponding axes (S X 、S Y 、S Z 、θ A 、θ B ) In (a) and (b);
according to the ideal kinematic positive solution model in the formula (1), calculating the position where the original G code wants to control the tool to reach and the tool posture at the position;
(1)
Wherein P (a, b, c) and O (O (1), O (2), O (3)) represent the position and orientation of the tool relative to the workpiece coordinate system; θ A 、θ B 、θ X 、θ Y θ Z The motion amount of each axis of the five-axis denture processing center;
then according to the actual kinematic inverse model of formulas (2), (3) and (4), under the condition of considering the geometric error of the five-axis denture processing center irrelevant to the position, when the cutter is controlled to reach the position and the preset cutter posture is presented on the position, the actual motion quantity array required by each axis of the five-axis denture processing center is deduced (S * X 、S * Y 、S * Z 、θ * A 、θ * B ）；
(2)
(3)
(4)
Finally, the numerical control instruction is rewritten to realize the compensation of the geometric error irrelevant to the position by utilizing the deduced motion quantity of each axis.
The module of the geometric error analysis and compensation method comprises the following steps: the G code information reading module is used for converting character string information in the G code file into floating point type digital information and storing the floating point type digital information into an array of motion quantity of a corresponding shaft; the ideal kinematic correct solution module is used for solving the ideal pose of the cutter at each approximation point in each planned processing path in the G code through the ideal kinematic correct solution; the actual kinematic inverse solution module reversely obtains the actual motion quantity of each axis required by reaching the ideal pose at each approaching point on the originally planned processing track through the actual kinematic inverse solution; and the numerical control instruction writing module is used for re-writing the information into a numerical control instruction file and finishing the final file output.
When the denture processing center is used for processing a complex curved surface, a G01 straight line is generally utilized in a numerical control instruction to guide the denture processing center to move a section of micro line segment to fit the complex curved surface structure; specifically, a position D of the start point of the straight-line adding instruction is established 1 （a 1 ,b 1 ,c 1 ) Location D of termination point 2 （a 2 ,b 2 ,c 2 ），S 1 To increase the linear movement rate, t 1 To perform the time interval required for the addition operation, t 2 To increase the acceleration time of the movement;
adding a span in a straight line:(5)
Discharging acceleration and deceleration, and calculating to obtain theoretical increment step number:
(6)
In fact, considering the inertia effect of the tool, the acceleration section and the deceleration section should be respectively established before and after the addition line, the actual addition step number is larger than the theoretical addition step number, and the actual addition step number F can be obtained by the following formula:
(7)
Wherein S is 2 Acceleration time t for adding linear adding motion 2 Acceleration and deceleration at time F S 2 is the number of adding steps of the acceleration and deceleration section of the adding movement;
a certain adding point D can be resolved according to the acceleration and deceleration characteristics i (i=1 to n), and the span between the point and the first addition point is
(8)
Determining an addition point D i Position by adding the starting point D of the straight line 1 （a 1 ,b 1 ,c 1 ) And add point D i Calculation of components in a spatial coordinate system to obtain D i （a i ,b i ,c i ）;
(9)
Wherein,；/>；/>；
resolving to obtain position coordinates D of each added point i And solving the actual motion quantity required by each axis of the machining center corresponding to each adding point through an actual kinematic inverse model. The curved surface of the false tooth is ground by the cutter through the straight line adding instruction, the accuracy is improved, the calculation capacity of the five-axis false tooth processing center controller is reduced through properly adding the time interval required by executing the adding calculation and the method of reducing the adding points, and the reduction is carried outHardware cost.
As a preferable technical scheme of the geometric error analysis and compensation method of the five-axis denture processing center, the motion quantity of each axis is compensated and analyzed, character type numbers read from a numerical control instruction file are required to be converted into floating point type numerical value variables, and the floating point type numerical value variables are stored in a storage space corresponding to the motion axis.
As a preferable technical scheme of the geometric error analysis and compensation method of the five-axis denture processing center, the specific steps of the compensation analysis of the motion quantity of each axis comprise the following steps:
s1, opening an original numerical control instruction file by utilizing a fopen instruction in Matlab;
s2, reading the content of the next row in the file through the fgets function;
s3, sequentially searching the XYZAB and the FTMGS in the read content by utilizing a strfind function, and recording the positions of the characters.
As a preferable technical scheme of the geometric error analysis and compensation method of the five-axis denture processing center,
if any one of the five characters of XYZAB is searched in the read content, defining the state as 'detected', recording the position of the character appearing first in the five characters, and defining a character string formed by all characters positioned before the character as 'first character';
if any one of the five characters "XYZAB" is not detected in the read content, the read content is entirely defined as "first character".
As a preferable technical scheme of the geometric error analysis and compensation method of the five-axis denture processing center,
if the state is 'detected', recording the position of the last character appearing in the five characters of 'XYZAB', searching the first character appearing behind the position in the characters of 'FTMGS', recording the position of the first character, and defining the character string formed by all characters behind the position as 'tail character';
if the search result is null, adding a null character to the whole content read by the fgets function, recording the position of the null character, and defining the null character as a tail character.
The str2double function is used to convert the characters between the positions of the several characters of XYZAB and the recorded positions into floating point values and store the floating point values into the corresponding dependent variables.
To verify that the proposed off-line compensation method was theoretically effective, the machining process was simulated using Vericut software, which simulates cutting a standard test dental model on a denture blank. The three-dimensional model of the denture processing center is imported into software, and each axis rotates around the origin or moves along the coordinate axis direction through the function of configuring the model so as to simulate each position independent geometric error item. And then the initial position and cutter parameters of each shaft are regulated, a blank model and a design model (namely an ideal part model) are imported, and finally a G code file before compensation is imported for simulation processing. After the simulation is finished, the difference between the simulation processing result and the design is analyzed by using the self-contained 'automatic comparison' function of Vericut, and the processing effect is confirmed, as shown in figure 2. And finally, replacing the compensated G code file, and repeating the steps, wherein the compensated processing effect is shown in figure 3.
As can be seen from simulation results, the average error before compensation is-0.0128, the average error after compensation is-0.003, the error before compensation is 84.1026% is within +/-0.05, the error after compensation is 94.488% is within +/-0.05, the number of the errors after compensation and the magnitude of the error values are improved greatly, and the geometric error analysis and compensation method of the five-axis denture processing center is effective.
The foregoing description is only a preferred embodiment of the present invention, and the present invention is not limited thereto, but it is to be understood that modifications and equivalents of some of the technical features described in the foregoing embodiments may be made by those skilled in the art, although the present invention has been described in detail with reference to the foregoing embodiments. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (7)
1. A geometric error analysis and compensation method for a five-axis denture processing center, the method comprising the steps of:
first, character string information in a G code file is converted into floating point type digital information and stored in an array of motion amounts of corresponding axes (S X 、S Y 、S Z 、θ A 、θ B ) In (a) and (b);
according to the ideal kinematic positive solution model in the formula (1), calculating the position where the original G code wants to control the tool to reach and the tool posture at the position;
formula (1);
wherein P (a, b, c) and O (O (1), O (2), O (3)) represent the position and orientation of the tool relative to the workpiece coordinate system; θ A 、θ B 、θ X 、θ Y θ Z The motion amount of each axis of the five-axis denture processing center;
then according to the actual kinematic inverse model of formulas (2), (3) and (4), under the condition of considering the geometric error of the five-axis denture processing center irrelevant to the position, when the cutter is controlled to reach the position and the preset cutter posture is presented on the position, the actual motion quantity array required by each axis of the five-axis denture processing center is deduced (S * X 、S * Y 、S * Z 、θ * A 、θ * B ）；
Formula (2);
formula (3);
formula (4);
finally, the actual motion quantity of each axis is deduced (S * X 、S * Y 、S * Z 、θ * A 、θ * B ) Re-writing numerical control instructions to achieve compensation of position-independent geometric errors;
when the denture processing center is used for processing a complex curved surface, the G01 straight line adding instruction is utilized in the numerical control instruction to guide the denture processing center to move a section of micro line segment to fit the complex curved surface structure.
2. The geometric error analysis and compensation method of a five-axis denture processing center according to claim 1, wherein,
position D of the starting point of the build-up line add instruction 1 （a 1 ,b 1 ,c 1 ) Location D of termination point 2 （a 2 ,b 2 ,c 2 ），S 1 To increase the linear movement rate, t 1 To perform the time interval required for the addition operation, t 2 To increase the acceleration time of the movement;
adding a span in a straight line:formula (5);
discharging acceleration and deceleration, and calculating to obtain theoretical increment step number:
formula (6);
in fact, considering the inertia effect of the tool, the acceleration section and the deceleration section should be respectively established before and after the addition line, the actual addition step number is larger than the theoretical addition step number, and the actual addition step number F can be obtained by the following formula:
formula (7);
wherein S is 2 Acceleration time t for adding linear adding motion 2 Acceleration and deceleration at time F S2 The step number for adding the acceleration and deceleration section of the movement;
a certain adding point D can be resolved according to the acceleration and deceleration characteristics i (i=1 to n), and the span between the point and the first addition point is
Formula (8);
determining an addition point D i Position by adding the starting point D of the straight line 1 （a 1 ,b 1 ,c 1 ) And add point D i Calculation of components in a spatial coordinate system to obtain D i （a i ,b i ,c i ）;
Formula (9);
wherein,；/>；/>；
resolving to obtain position coordinates D of each added point i And solving the actual motion quantity required by each axis of the machining center corresponding to each adding point through an actual kinematic inverse model.
3. The geometric error analysis and compensation method of a five-axis denture processing center according to claim 1, wherein the module of the geometric error analysis and compensation method comprises:
the G code information reading module is used for converting character string information in the G code file into floating point type digital information and storing the floating point type digital information into an array of motion quantity of a corresponding shaft;
the ideal kinematic correct solution module is used for solving the ideal pose of the cutter at each approximation point in each planned processing path in the G code through the ideal kinematic correct solution;
the actual kinematic inverse solution module reversely obtains the actual motion quantity of each axis required by reaching the ideal pose at each approaching point on the originally planned processing track through the actual kinematic inverse solution;
and the numerical control instruction writing module is used for re-writing the information into a numerical control instruction file and finishing the final file output.
4. The geometric error analysis and compensation method of a five-axis denture processing center according to claim 1, wherein the specific step of converting character string information in the G code file into floating point type digital information comprises the steps of:
s1, opening an original numerical control instruction file by utilizing a fopen instruction in Matlab;
s2, reading the content of the next row in the file through the fgets function;
s3, sequentially searching the XYZAB and the FTMGS in the read content by utilizing a strfind function, and recording the positions of the characters.
5. The geometric error analysis and compensation method of a five-axis denture processing center according to claim 4,
if any one of the five characters of XYZAB is searched in the read content, defining the state as 'detected', recording the position of the character appearing first in the five characters, and defining a character string formed by all characters positioned before the character as 'first character';
if any one of the five characters "XYZAB" is not detected in the read content, the read content is entirely defined as "first character".
6. The geometric error analysis and compensation method of a five-axis denture processing center according to claim 5, wherein,
if the state is 'detected', recording the position of the last character appearing in the five characters of 'XYZAB', searching the first character appearing behind the position in the characters of 'FTMGS', recording the position of the first character, and defining the character string formed by all characters behind the position as 'tail character';
if the search result is null, adding a null character to the whole content read by the fgets function, recording the position of the null character, and defining the null character as a tail character.
7. The geometric error analysis and compensation method of a five-axis denture processing center according to claim 6, wherein the character between the position of the several characters "XYZAB" and the recorded position is converted into a floating point value by using str2double function, and stored in the strain amount.
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