CN108563852B - Method for calculating spraying thickness accumulation rate based on spherical coordinate system - Google Patents
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Abstract
The invention discloses a method for calculating the cumulative rate of spraying thickness based on a spherical coordinate system, which is characterized by comprising the following steps: s1, establishing a function expression of the spray gun coating material flow rate model under a spray gun spherical coordinate system; s2, establishing a relation between a paint accumulation rate model and a spray gun paint supply flow rate model at any point on the free curved surface under a spherical coordinate system; s3, determining each parameter or coefficient to be determined in the function of the spray gun paint flow rate, and calculating the spray gun paint flow rate; and S4, calculating the paint accumulation rate according to the paint supply flow rate of the spray gun. The invention can be widely applied to the spraying operation of various spraying robots with complex free-form surfaces, has more intuitive expression and simpler calculation, and can lay a good foundation for subsequent trajectory planning and accumulated thickness simulation; the robot spraying device can provide theoretical and algorithmic basis for realizing automatic spraying off-line programming and simulation of the robot, and is beneficial to improving the spraying quality of workpieces.
Description
Technical Field
The invention belongs to the field of automatic spraying of robots, and particularly relates to a method for calculating a spraying thickness accumulation rate based on a spherical coordinate system.
Background
The spraying robot is based on the robot technology and combines advanced coating equipment developed by a spraying process, can finish the spraying operation of different workpieces through programming, ensures the consistency of the spraying quality, can reduce the loss of paint, greatly improves the spraying efficiency and the spraying quality, reduces the spraying production cost, can adapt to various complex spraying environments, eliminates the damage to the body of a worker caused by the traditional spraying operation, and is widely used for the spraying operation of products such as automobiles, electrical appliances, furniture and the like.
In the spraying production of the robot, a spraying thickness accumulated rate model of any point on a workpiece has a decisive influence on the spraying effect of the whole workpiece, and is a premise and a key point of spraying track planning and spraying simulation research, so that the establishment of an accurate spray gun spraying accumulated rate model which accords with the actual spraying is very important.
At present, spray gun spraying thickness accumulation models are mainly divided into two types: one is an infinite range model, such as gaussian distribution and cauchy distribution models, which are only suitable for spraying a spray gun perpendicular to the surface of a workpiece to be sprayed and are rarely used in practical application. And the model firstly assumes a mathematical expression of the model according to the actual spraying condition, and then combines experimental data to perform fitting approximation on the mathematical expression to obtain a final spraying model, so that the spraying operation can be better met under the condition of meeting the error requirement. However, the models are sprayed to a plane based on a spray gun, when the models are popularized to free-form surface spraying, approximation and introduction of a complex algorithm are needed, and the calculation and implementation are not simple, convenient and intuitive.
Disclosure of Invention
Aiming at least one of the defects or the improvement requirements in the prior art, the invention provides the method for calculating the spraying thickness accumulation rate based on the spherical coordinate system, the model has stronger spraying universality on complex parts, more intuitive expression and simpler calculation, and can lay a good foundation for subsequent trajectory planning and accumulated thickness simulation.
To achieve the above object, according to one aspect of the present invention, there is provided a method for calculating a cumulative rate of spray coating thickness based on a spherical coordinate system, comprising: the method comprises the following steps:
s1, establishing a function expression of the spray gun coating material flow rate model under a spray gun spherical coordinate system;
s2, establishing a relation between a paint accumulation rate model and a spray gun paint supply flow rate model at any point on the free curved surface under a spherical coordinate system;
s3, determining each parameter or coefficient to be determined in the function of the spray gun paint flow rate, and calculating the spray gun paint flow rate;
and S4, calculating the paint accumulation rate according to the paint supply flow rate of the spray gun.
Preferably, the step S1 includes the steps of:
s1.1, establishing a spherical coordinate system by taking a point O at the center of an outlet of a spray gun as an origin, and expressing any point P in space as
Is the coordinate of the point P under a spherical coordinate system, wherein r is the radial distance between the original point and the point P, theta is the included angle between the connecting line from the original point to the point P and the Z axis,
is an included angle between a projection line of a connecting line from an original point to a point P on an XY plane and an X axis;
s1.2, the function of the spray gun coating supply flow rate is recorded as
The volume of the sprayed material sprayed by the spray gun in a unit solid angle per unit time is represented as follows:
where dV denotes volume infinitesimal, d Ω denotes cube-corner infinitesimal, and dt denotes time infinitesimal.
Preferably, the step S2 includes the steps of:
the surface of a workpiece to be sprayed is a free curved surface and is marked as S, a spraying substance with volume dV covers the curved surface S within a time interval dt and a solid angle infinitesimal d omega, a corresponding area infinitesimal is marked as dA, and the thickness growth rate on the spraying surface is as follows:
combining equation (1) yields:
wherein r is the distance from the center point O of the spray gun to the center point P of the area infinitesimal dA,
is a radial unit vector of the spherical coordinate system,
is the normal vector for area infinitesimal dA.
Preferably, the step S3 includes the steps of:
assuming that the shape of the material sprayed by the spray gun is a spherical center angle body, the symmetry of the spherical center angle body can be known,
only with respect to theta, and, in addition,
satisfies the following conditions:
wherein f is0Is the maximum paint flow rate of the spray gun, e.f0Representing the spray gun at the maximum spray angle thetamaxThe coating feed rate;
the spray gun coating material supply flow rate function is expressed in terms of undetermined parameters or coefficients as:
wherein a and b are undetermined coefficients, f0Is a parameter to be determined;
as can be seen from equations (2) and (4), the thickness growth rate on the sprayed surface can be expressed as:
spraying the spray gun to the known free-form surface in unit time, and measuring a series of known points on the free-form surface
The thickness of the coating is recorded
i is a serial number, and calculating
Length of corresponding vector under spray gun spherical coordinate system
And direction
On a free-form surface
Normal vector of (C)
As can be seen from equation (2):
combining the results measured by the spraying experiment and the calculated values with the formula (6) to obtain the target
Fitting is carried out, and the value of each undetermined parameter or coefficient can be determined.
Preferably, in the spraying production process, assuming that the coating is sprayed out from one point of a spray gun nozzle in a radial shape, the surface of the workpiece to be sprayed is a plane and is marked as S', the central line of the spray gun is always vertical to the surface of the workpiece, and all parameters of the spray gun are adjusted to be the same as those in the actual spraying process for spraying;
because the center line of the spray gun is always vertical to the surface of the workpiece, namely,
equation (2) can be simplified as:
the relation between the spherical coordinate system and the Cartesian coordinate system is established, the spraying experiment is measured based on the Cartesian coordinate system, and then the coordinates and the corresponding spraying thickness of the spray gun in the spherical coordinate system are deduced:
establishing a spray gun spherical coordinate system at a spray gun central point O, recording the distance from the point O to a plane S ' as h, taking the intersection point of a spray gun outlet central line and a spraying plane as an original point, recording as O ', taking the spraying plane as XO ' Y, establishing a Cartesian coordinate system, wherein the expression of any point P in the space in the Cartesian coordinate system is P (x, Y, z), and the (x, Y, z) is the coordinate of P in the Cartesian coordinate system, and the coordinate transformation relation between the two coordinate systems is as follows:
through the spraying experiment, the coordinate values of a series of points on the spraying plane under the Cartesian coordinate system are measured and recorded as
And the thickness of the spray at these points, noted
By using the formula (8), the coordinates of the series of points in the gun spherical coordinate system can be obtained
And corresponding thickness of the spray
Fitting the formula (5) to finally obtain coefficients a and b and a parameter f0The value of (c).
Preferably, the spray gun coating material supply flow rate function is expressed in a polynomial manner as follows:
carrying out subsequent corresponding calculation instead of the formula (4); wherein i is a serial number, n is a serial number, and c is a parameter.
The above-described preferred features may be combined with each other as long as they do not conflict with each other.
Generally, compared with the prior art, the above technical solution conceived by the present invention has the following beneficial effects:
1) the method for calculating the cumulative rate of the spraying thickness based on the spherical coordinate system can be widely applied to spraying operation of spraying robots for various complex free-form surfaces, is more intuitive in expression and simpler in calculation, and can lay a good foundation for subsequent trajectory planning and cumulative thickness simulation;
2) the robot spraying device can provide theoretical and algorithmic basis for realizing automatic spraying off-line programming and simulation of the robot, and is beneficial to improving the spraying quality of workpieces.
Drawings
FIG. 1 is a schematic flow chart of a method for calculating the cumulative velocity of spray coating thickness based on a spherical coordinate system according to the present invention;
FIG. 2 is a schematic view of the coordinates of a spray gun sphere;
FIG. 3 is a schematic diagram of free-form surface spraying in a spherical coordinate system of a spray gun;
FIG. 4 is a schematic diagram of a model of the cumulative rate of thickness of a planar spray.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other. The present invention will be described in further detail with reference to specific embodiments.
As a preferred embodiment of the present invention, as shown in fig. 1, the present invention provides a method for calculating a cumulative velocity of a sprayed thickness based on a spherical coordinate system, which is characterized in that: the method comprises the following steps:
s1, establishing a function expression of the spray gun coating material flow rate model under a spray gun spherical coordinate system;
s2, establishing a relation between a paint accumulation rate model and a spray gun paint supply flow rate model at any point on the free curved surface under a spherical coordinate system;
s3, determining each parameter or coefficient to be determined in the function of the spray gun paint flow rate, and calculating the spray gun paint flow rate;
and S4, calculating the paint accumulation rate according to the paint supply flow rate of the spray gun.
In the step S1, in the process of establishing a function expression of the spray gun paint flow rate model in the spray gun spherical coordinate system, the method includes the following steps:
s1.1, as shown in FIG. 2, adopting the definition of a spherical coordinate system in ISO 80000-2:2009, establishing the spherical coordinate system by taking the center O point of the outlet of the spray gun as an origin, and expressing any point P in the space as being expressed in the spherical coordinate system
Is the coordinate of the point P under a spherical coordinate system, wherein r is the radial distance between the original point and the point P, theta is the included angle between the connecting line from the original point to the point P and the Z axis,
is an included angle between a projection line of a connecting line from an original point to a point P on an XY plane and an X axis;
s1.2, the function of the spray gun coating supply flow rate is recorded as
The volume of the sprayed material sprayed by the spray gun in a unit solid angle per unit time is represented as follows:
where dV denotes volume infinitesimal, d Ω denotes cube-corner infinitesimal, and dt denotes time infinitesimal.
In the step S2, the process of establishing the relationship between the paint accumulation rate model and the spray gun paint supply flow rate model at any point on the free-form surface in the spherical coordinate system includes the following steps:
the surface of a workpiece to be sprayed is a free curved surface and is marked as S, a spraying substance with volume dV covers the curved surface S within a time interval dt and a solid angle infinitesimal d omega, a corresponding area infinitesimal is marked as dA, and the thickness growth rate on the spraying surface is as follows:
combining equation (1) yields:
wherein r is the distance from the center point O of the spray gun to the center point P of the area infinitesimal dA,
is a radial unit vector of the spherical coordinate system,
is the normal vector for area infinitesimal dA.
In the step S3, the process of determining each parameter or coefficient to be determined in the function of the supply flow rate of the spray gun paint, and calculating the supply flow rate of the spray gun paint includes the following steps:
assuming that the shape of the material ejected from the spray gun is a spherical central angle body (spherical sector), the symmetry of the spherical central angle body can be known,
only with respect to theta, and, in addition,
must satisfy:
wherein f is0Is the maximum paint flow rate of the spray gun, e.f0Representing the spray gun at the maximum spray angle thetamaxThe coating feed rate, which is typically near zero.
The present invention assumes that the spray gun coating supply flow rate function is expressed as a function of the undetermined parameter or coefficient:
wherein a and b are undetermined coefficients, f0Is a parameter to be determined;
it can also be assumed that
In other forms, such as polynomial expressions:
carrying out subsequent corresponding calculation instead of the formula (4); wherein i is a serial number, n is a serial number, and c is a parameter.
As can be seen from equations (2) and (4), the thickness growth rate on the sprayed surface can be expressed as:
to calculate the spray rate function, parameters or coefficients in the functional expression are determined, which may be determined by experimental data.
Spraying the spray gun to the known free-form surface in unit time, and measuring a series of known points on the free-form surface
The thickness of the coating is recorded
i is a serial number, and calculating
Length of corresponding vector under spray gun spherical coordinate system
And direction
On a free-form surface
Normal vector of (C)
As can be seen from equation (2):
combining the results measured by the spraying experiment and the calculated values with the formula (6) to obtain the target
Fitting is carried out, and the value of each undetermined parameter or coefficient can be determined.
In the spraying production process, assuming that the coating is sprayed out from one point of a spray gun nozzle in a radial shape, the surface of a workpiece to be sprayed is a plane and is marked as S', and the central line of the spray gun is always vertical to the surface of the workpiece; adjusting various parameters of the spray gun to the same parameters as those in the actual spraying process for spraying, wherein the spraying flow of the spray gun is 84ml/s, and the spraying opening angle of the spray gun is 60 degrees (the maximum spraying angle theta is selected)max) The spraying distance of the spray gun is 250mm, and the moving spraying speed of the spray gun is 120 mm/s.
Because the center line of the spray gun is always vertical to the surface of the workpiece, namely,
equation (2) can be simplified as:
coordinate value of spraying point under spherical coordinate system
The coordinate value of the spraying point under the spray gun spherical coordinate system can be deduced according to the relation between the Cartesian coordinate system and the spraying plane. The measurement of the spray results in the spray experiments is also based on a cartesian coordinate system.
Establishing a spray gun spherical coordinate system at a spray gun central point O, recording the distance from the point O to a plane S ' as h, taking the intersection point of a spray gun outlet central line and a spraying plane as an original point, recording as O ', taking the spraying plane as XO ' Y, establishing a Cartesian coordinate system, wherein the expression of any point P in the space in the Cartesian coordinate system is P (x, Y, z), and the (x, Y, z) is the coordinate of P in the Cartesian coordinate system, and the coordinate transformation relation between the two coordinate systems is as follows:
through the spraying experiment, the coordinate values of a series of points on the spraying plane under the Cartesian coordinate system are measured and recorded as
And the thickness of the spray at these points, noted
By using the formula (8), the coordinates of the series of points in the gun spherical coordinate system can be obtained
And corresponding thickness of the spray
Fitting the formula (5) to finally obtain coefficients a and b and a parameter f0The value of (c):
f0＝40.0,a＝0.8,b＝7.26,
by substituting equation (7), the thickness growth rate on the sprayed surface is:
the method for calculating the cumulative rate of the spraying thickness based on the spherical coordinate system can be widely applied to spraying operation of spraying robots for various complex free-form surfaces, is more intuitive in expression and simpler in calculation, and can lay a good foundation for subsequent trajectory planning and cumulative thickness simulation; the robot spraying device can provide theoretical and algorithmic basis for realizing automatic spraying off-line programming and simulation of the robot, and is beneficial to improving the spraying quality of workpieces.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (4)
1. A method for calculating the cumulative velocity of spraying thickness based on a spherical coordinate system is characterized in that: the method comprises the following steps:
s1, establishing a function expression of the spray gun coating material flow rate model under a spray gun spherical coordinate system;
s2, establishing a relation between a paint accumulation rate model and a spray gun paint supply flow rate model at any point on the free curved surface under a spherical coordinate system;
s3, determining each parameter or coefficient to be determined in the function of the spray gun paint flow rate, and calculating the spray gun paint flow rate;
s4, calculating the paint accumulation rate according to the paint supply flow rate of the spray gun;
the step S1 includes the steps of:
s1.1, establishing a spherical coordinate system by taking a point O at the center of an outlet of a spray gun as an origin, and expressing any point P in space as
Is the coordinate of the point P under a spherical coordinate system, wherein r is the radial distance between the original point and the point P, theta is the included angle between the connecting line from the original point to the point P and the Z axis,
is an included angle between a projection line of a connecting line from an original point to a point P on an XY plane and an X axis;
s1.2, the function of the spray gun coating supply flow rate is recorded as
The volume of the sprayed material sprayed by the spray gun in a unit solid angle per unit time is represented as follows:
wherein dV represents a volume infinitesimal, d Ω represents a solid angle infinitesimal, and dt represents a time infinitesimal;
the step S2 includes the steps of:
the surface of a workpiece to be sprayed is a free curved surface and is marked as S, a spraying substance with volume dV covers the curved surface S within a time interval dt and a solid angle infinitesimal d omega, a corresponding area infinitesimal is marked as dA, and the thickness growth rate on the spraying surface is as follows:
combining equation (1) yields:
wherein r is the distance from the center point O of the spray gun to the center point P of the area infinitesimal dA,
is a radial unit vector of the spherical coordinate system,
is the normal vector for area infinitesimal dA.
2. The method for calculating the cumulative velocity of sprayed thickness based on the spherical coordinate system as claimed in claim 1, wherein: the step S3 includes the steps of:
assuming that the shape of the material sprayed by the spray gun is a spherical center angle body, the symmetry of the spherical center angle body can be known,
only with respect to theta, and, in addition,
satisfies the following conditions:
wherein f is0Is the maximum paint flow rate of the spray gun, e.f0Representing the spray gun at the maximum spray angle thetamaxThe coating feed rate;
the spray gun coating material supply flow rate function is expressed in terms of undetermined parameters or coefficients as:
wherein a and b are undetermined coefficients, f0Is a parameter to be determined;
as can be seen from equations (2) and (4), the thickness growth rate on the sprayed surface can be expressed as:
spraying the spray gun to the known free-form surface in unit time, and measuring a series of known points on the free-form surface
The thickness of the coating is recorded
i is a serial number of the series,and calculate
Length of corresponding vector under spray gun spherical coordinate system
And direction
On a free-form surface
Normal vector of (C)
As can be seen from equation (2):
combining the results measured by the spraying experiment and the calculated values with the formula (6) to obtain the target
Fitting is carried out, and the value of each undetermined parameter or coefficient can be determined.
3. The method for calculating the cumulative velocity of sprayed thickness based on the spherical coordinate system as set forth in claim 2, wherein: in the spraying production process, assuming that the coating is sprayed out from one point of a spray gun nozzle in a radial shape, the surface of a workpiece to be sprayed is a plane and is marked as S', the central line of the spray gun is always vertical to the surface of the workpiece, and all parameters of the spray gun are adjusted to be the same as those in the actual spraying process for spraying;
because the center line of the spray gun is always vertical to the surface of the workpiece, namely,
equation (2) can be simplified as:
the relation between the spherical coordinate system and the Cartesian coordinate system is established, the spraying experiment is measured based on the Cartesian coordinate system, and then the coordinates and the corresponding spraying thickness of the spray gun in the spherical coordinate system are deduced:
establishing a spray gun spherical coordinate system at a spray gun central point O, recording the distance from the point O to a plane S ' as h, taking the intersection point of a spray gun outlet central line and a spraying plane as an original point, recording as O ', taking the spraying plane as XO ' Y, establishing a Cartesian coordinate system, wherein the expression of any point P in the space in the Cartesian coordinate system is P (x, Y, z), and the (x, Y, z) is the coordinate of P in the Cartesian coordinate system, and the coordinate transformation relation between the two coordinate systems is as follows:
through a spraying experiment, coordinate values of a series of points on a spraying plane under a Cartesian coordinate system are measured and recorded as { P }i C(xi，yi，zi) And the thickness of the spray at these points, noted
By using the formula (8), the coordinates of the series of points in the gun spherical coordinate system can be obtained
And corresponding thickness of the spray
Fitting the formula (5) to finally obtain coefficients a and b and a parameter f0The value of (c).
4. The method for calculating the cumulative rate of sprayed thickness based on the spherical coordinate system as set forth in claim 2 or 3, wherein: the spray gun coating supply flow rate function is expressed in a polynomial manner as follows:
carrying out subsequent corresponding calculation instead of the formula (4); wherein i is a serial number, n is a serial number, and c is a parameter.
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| CN109543267B (en) * | 2018-11-13 | 2023-05-26 | 福州大学 | Image processing-based artwork surface spraying simulation and optimization method |
| CN112387552B (en) * | 2020-11-05 | 2022-05-17 | 大连交通大学 | Method for self-adjusting spraying parameters of putty coating robot |
| CN112570229A (en) * | 2020-12-08 | 2021-03-30 | 江苏科技大学 | Spraying method for multiple types of car lamps |
| CN112722322B (en) * | 2020-12-25 | 2023-12-15 | 中国航空工业集团公司沈阳飞机设计研究所 | Accurate reproduction method and system for airplane horizontal measurement points |
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