CN112643486B - Abrasive belt wear prediction method in complex curved surface workpiece grinding process - Google Patents
Abrasive belt wear prediction method in complex curved surface workpiece grinding process Download PDFInfo
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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
- B24B21/00—Machines or devices using grinding or polishing belts; 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
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Abstract
The invention relates to a method for predicting abrasive belt abrasion in a complex curved surface workpiece grinding process, and belongs to the technical field of precision machining. Determining the change rule of the abrasive belt wear coefficient along with factors such as grinding parameters, grinding duration and the like through a calibration experiment; the shape and pressure distribution of a contact area in the process of grinding a complex curved surface workpiece by a grinding wheel are obtained by establishing an elastic grinding contact model; and constructing a contact area swept body according to the change of the contact area with time under a local coordinate system, and providing a prediction method of the non-uniform change of the abrasive belt wear coefficient by depending on the contact area swept body. The method solves the problem that the traditional method can not predict the non-uniform abrasion of the abrasive belt, can realize the change prediction of the abrasion coefficient distribution in the abrasive belt grinding process of the complex curved surface, and has the characteristics of high calculation efficiency, good prediction precision and wide application range.
Description
Technical Field
The invention belongs to the technical field of precision machining, and relates to a method for predicting abrasive belt wear in a complex curved surface grinding process.
Background
In the belt grinding process, the abrasive grains of the belt are gradually worn along with the increase of the grinding time. Belt wear has a very important effect on material removal efficiency and workpiece surface quality. When the abrasive belt is abraded to a certain degree, the material removal efficiency is rapidly reduced, so that the allowance cannot be effectively removed, and due to the fact that the friction coefficient is increased, the grinding resistance is increased, a large amount of grinding heat is generated, and accordingly the surface of a workpiece is burnt. Therefore, forecasting the abrasion change of the abrasive belt before actual grinding has important significance for improving the geometric accuracy and the surface quality of the workpiece.
When a complex curved surface workpiece is ground by an abrasive belt, the abrasion degree of the abrasive belt is not uniformly distributed, the abrasion degree of each part is influenced by various factors such as contact pressure, the linear velocity of the abrasive belt, the geometric scale of the surface of the workpiece and the like, and the change trend of the non-uniform abrasion of the abrasive belt cannot be predicted by the traditional method.
Disclosure of Invention
Technical problem to be solved
The invention provides a prediction method of uneven abrasive belt abrasion, aiming at the abrasive belt abrasion problem in the complex curved surface grinding process. The method is characterized in that the uneven abrasion of the abrasive belt in the grinding process of the complex curved surface workpiece is forecasted through an abrasion experiment under multiple factors and by combining the analysis of the abrasive belt grinding contact state.
Technical scheme
A method for predicting abrasive belt abrasion in a complex curved surface workpiece grinding process is characterized by comprising the following steps:
step 1: establishing a contact area swept volume and calculating a pressure profile
Establishing a local coordinate system attached to a grinding contact point, calculating the shape of a contact area of the abrasive belt wheel and a workpiece under the local coordinate system, constructing a contact area swept body according to the change of the shape of the contact area along with grinding time, and simultaneously calculating the contact pressure distribution P (x, y) at each grinding contact point:
the contact region boundary expression is:
in the formula: a and b are respectively the length of a long axle shaft and a short axle shaft of the oval contact area; the contact pressure distribution P (x, y) at each contact point is:
in the formula: p 0 Is the maximum pressure in the contact area;
step 2: calculating relevant parameters of abrasive belt infinitesimal in grinding process
Dividing the swept volume of the contact area by using an x plane, and dividing the swept volume of the contact area at discrete time t according to the infinitesimal of the swept volume of the contact area obtained by the division i Calculating abrasive belt infinitesimalIncluding the length of operation t per unit length w And the average pressure P ave
In the formula: t is t w The unit length working time of the abrasive belt infinitesimal between two adjacent discrete moments is represented by delta t, the discrete moment interval is represented by L, the length of a contact area on the abrasive belt infinitesimal is represented by L, and the abrasive belt perimeter is represented by L;
in the formula: p is ave The average pressure of the abrasive belt infinitesimal between two adjacent discrete moments is shown, F is the contact pressure, and x is the distance between the abrasive belt infinitesimal and the abrasive belt infinitesimal in the circle where the contact point is;
and step 3: calculating the wear coefficient of abrasive belt infinitesimal
The abrasion degree of the abrasive belt is defined as an abrasion coefficient K t Quantification, obtaining K by calibration experiments t And t w And P ave The relationship between:
in the formula: k t Is the wear coefficient of the abrasive belt, b 1 A base number, b 1 The calculation method comprises the following steps:
b 1 ＝-1.692P ave +0.8888
according to the coefficient of wear K t Calculating the wear coefficient of each circle of abrasive belt infinitesimal according to the change rule:
in the formula: k tn Is [ t ] n ,t n+1 ) The abrasion coefficient of the abrasive belt infinitesimal in the time period,
the abrasive belt is composed of abrasive belt elements at t 0 Initial wear coefficient at time, b 1,i Is [ t ] i ,t i+1 ) B within time 1 Value, t w,i Is [ t ] i ,t i+1 ) T within time w The value is obtained.
Advantageous effects
According to the abrasive belt abrasion prediction method in the complex curved surface workpiece grinding process, by means of grinding experiments under multiple factors and combination of analysis of the contact state of complex curved surface abrasive belt grinding, the problem that the uneven abrasion of the abrasive belt cannot be predicted by a traditional method is solved, the change prediction of the abrasion coefficient distribution in the complex curved surface abrasive belt grinding process can be realized, and the abrasive belt abrasion prediction method has the characteristics of high calculation efficiency, good prediction precision and wide application range.
Drawings
Fig. 1 local coordinate system creation for belt grinding
Figure 2 elliptical contact area for belt grinding
FIG. 3 construction of a contact area swept volume
FIG. 4 abrasive belt infinitesimal correlation parameter calculation
FIG. 5 shows the change of material removal rate with grinding time under different contact pressures
FIG. 6 shows the change of the wear coefficient with grinding time under different contact pressures
FIG. 7 is a graph showing the change rule of the wear coefficient with the working time per unit length under different contact pressures
FIG. 8 shows a fitted curve of the change in wear coefficient under different contact pressures
FIG. 9 dependence of the base of the exponential function on the contact pressure
FIG. 10 distribution of wear coefficients before and after belt grinding
Detailed Description
The invention will now be further described with reference to the following examples and drawings:
the invention provides a prediction method for uneven abrasive belt wear. Determining the change rule of the abrasive belt wear coefficient along with factors such as grinding parameters, grinding duration and the like through a calibration experiment; the shape and pressure distribution of a contact area in the process of grinding a complex curved surface workpiece by a grinding wheel are obtained by establishing an elastic grinding contact model; and constructing a contact area swept body according to the change of the contact area with time under a local coordinate system, and providing a prediction method of the non-uniform change of the abrasive belt wear coefficient by depending on the contact area swept body. The details are as follows:
the method comprises the following steps: defining wear coefficient
In order to predict the wear of the sanding belt, it is first necessary to quantify the degree of wear of the sanding belt. The invention adopts the wear coefficient K t Characterizing the degree of wear of the sanding belt, K t Is an interval (0, 1)]The variables in (c). When the abrasive belt is worn uniformly, the abrasive belt can be worn by one K t Represents; when the abrasive belt is worn unevenly, the abrasive belt can be divided into a plurality of circles of abrasive belt infinitesimal along the width direction of the abrasive belt, and the wear coefficient of each circle of abrasive belt infinitesimal can use one K t Shows the wear coefficient K of each circle of abrasive belt infinitesimal after grinding t The distribution represents a non-uniform wear of the sanding belt.
When a metal material is ground by using a certain type of abrasive belt, the removal depth of the material per unit time is defined as the material removal rate r (in mm/s). The factors influencing the material removal rate r are numerous, and the contact pressure P and the linear velocity v of the abrasive belt are assumed s When the parameters are determined, the material removal rate of the new abrasive belt is r 0 The abrasive belt after the time of t is used for grinding the same material under the same parameters, and the material removal rate is r t Then define r t And r 0 The ratio of (A) to (B) is the wear factor K of the belt at that time t Namely:
coefficient of wear K t Is a physical quantity representing the wear degree of the abrasive belt, and K is a function which is monotonically decreased along with the time t and the material removal rate r is a function because the abrasive belt is continuously worn in the using process t Is a (0, 1)]A number between, and K t And decreases as time t increases.
The abrasive belt wheel used for belt grinding is generally a cylinder made of rubber, the rubber has large elasticity, and the surface of the workpiece is generally not a plane, which causes the abrasion rate of the abrasive belt to be inconsistent in the width direction of the abrasive belt. In order to represent the non-uniform abrasion of the abrasive belt in the grinding process, the abrasive belt is dispersed into a plurality of infinitesimal with extremely small width along the width direction of the abrasive belt, the circumference of each circle of abrasive belt infinitesimal is the same as the circumference of the original abrasive belt, and because the linear speed of the abrasive belt is far greater than the grinding feeding speed, the abrasion coefficients of all points on the same circle of abrasive belt infinitesimal are considered to be the same at any moment, and the abrasion coefficients of the different circles of abrasive belt infinitesimal are not related to each other. The wear coefficient of each part of the new abrasive belt is 1, the wear coefficient of each circle of abrasive belt infinitesimal is different after the abrasive belt is used, and the non-uniform wear of the abrasive belt is predicted, namely the wear coefficient change of each circle of abrasive belt infinitesimal in the grinding process is predicted.
To determine the belt parameters at given parameters (contact pressure P, belt linear velocity v) s ) The material removal rate r of a certain material is ground, and a calibration experiment can be carried out on a standard test piece prepared from the material under the grinding parameters, wherein the specific experiment method comprises the following steps:
preparing a standard test piece by using the same material as a workpiece, wherein the cross section of the test piece is a square with the side length D, and the constant contact pressure F and the linear velocity v of the abrasive belt are realized s And (3) enabling the test piece to be in contact with the abrasive belt for delta t time, and keeping the contact pressure unchanged in the grinding process, so that the contact pressure is always P. Calculating the material removal rate r according to the height variation delta H of the test piece in delta t time, wherein the calculation formula is as follows:
when Δ t is a small value, the material removal rate r obtained by the calibration experiment can be considered as the material removal rate of the abrasive belt grinding the material under the grinding parameter in the current state.
It is clear that the material removal rate r obtained from calibration experiments with new and old belt differs even if all grinding parameters remain the same. In order to obtain the material removal rates of the abrasive belts with different wear degrees, new abrasive belts can be continuously worn under different grinding parameter combinations, the abrasive belts are subjected to calibration experiments at intervals, and the change rule of the abrasive belt wear coefficient along with the grinding parameters and the grinding duration is obtained according to the material removal rate change calibrated under the same grinding parameters.
Step two: establishing a wear coefficient change model
Defining the length of operation t per unit length of the belt or belt elements w Will t w As coefficient of wear K t And calibrating K under various grinding parameter combinations through the grinding experiment of the standard test piece t With t w And establishing a wear coefficient change model according to the change rule.
Step three: establishing elastic grinding contact model
And establishing an elastic grinding contact model of the abrasive belt grinding of the complex curved surface workpiece based on a Hertz contact equation, and calculating the contact area shape and the contact pressure distribution of the abrasive belt wheel and the workpiece under the action of normal contact force according to the elastic grinding contact model.
Step four: predicting abrasive belt wear coefficient distribution variation
And establishing a local coordinate system attached to the grinding contact point, and constructing a contact area swept body according to the change of the contact area in the local coordinate system along with time. A prediction method for abrasive belt wear coefficient distribution change is provided on the basis of a wear coefficient change model and an elastic grinding contact model by relying on a contact area swept body.
The specific implementation steps of the prediction method obtained by the derivation are as follows:
the method comprises the following steps:
Step1：
for complex curved surface grinding, a tangent point of a workpiece and an abrasive belt wheel is defined as a contact point when the contact force is 0, the position of the contact point on the abrasive belt wheel is unchanged, and the contact points on the surface of the workpiece are integrated into a grinding path. In order to study the wear variations in the grinding process at various points, it is first necessary to establish a local coordinate system in the grinding curve of the belt.
Local coordinate system: in the process of grinding a curved surface workpiece by using a cylindrical abrasive belt wheel, a local coordinate system is established by taking a contact point on the abrasive belt wheel as an original point and taking a tangent plane of the surface of the abrasive belt wheel at the contact point as an x-y plane, the x axis of the local coordinate system is axially parallel to the abrasive belt wheel, the forward direction of the x axis points to the right side of the advancing direction of the abrasive belt wheel, and the forward direction of the y axis points to the front of the abrasive belt wheel relative to the feeding of the workpiece.
When the abrasive belt wheel is fed along the grinding path, the x-axis of the local coordinate system is always kept parallel to the main normal direction of the grinding path, and the y-axis is always parallel to the tangential direction of the grinding path, as shown in fig. 1.
Step2：
After the local coordinate system is established, the normal grinding force F n The contact area of the abrasive belt and the workpiece surface is a typical ellipse according to the Hertz contact equation, and the contact pressure distribution of the abrasive belt and the workpiece surface is semi-ellipsoidal as shown in figure 2.
The boundary formula of the elliptical contact area according to the hertzian contact equation is:
in the formula: a b is the length of the half shaft of the long shaft and the half shaft of the short shaft of the contact ellipse respectively, and the solving formula is respectively as follows:
f is the normal contact force between the abrasive belt wheel and the surface of the workpiece;
is the relative modulus of the abrasive belt wheel and the workpiece, E 1 V and v 1 Respectively representing Young's modulus and Poisson's ratio, E of the abrasive belt wheel material 2 V and v 2 Respectively representing the Young modulus and the Poisson ratio of the workpiece material; a and B are relative curvatures of contact points, and the calculation formula is as follows:
in the formula R 1 ' and R 1 "represents the maximum and minimum radii of curvature, R, of the abrasive belt wheel at the point of contact 2 ' and R 2 "represents the maximum and minimum curvature radius of the workpiece surface at the contact point, α is the included angle between the abrasive belt wheel and the main direction of the workpiece surface at the contact point, and the solving formula of other relevant parameters is:
in the above formula,. kappa. 2 Is the ratio of the major and minor semi-axes, epsilon (kappa) 2 ) Is the second type of elliptic integral.
The pressure intensity P distribution of the workpiece and the abrasive belt in the elliptical contact area is as follows:
in the formula P 0 Is the maximum pressure in the contact area, the position of the maximum pressure is located at the center point of the elliptical contact area, P 0 The calculation formula of (2) is as follows:
Step3：
because the main curvatures of the complex curved surface are different, the shape of the contact area under the local coordinate system changes along with the relative motion of the abrasive belt wheel and the workpiece, in order to express the change more intuitively, the invention adds a time axis t axis on the basis of a two-dimensional local coordinate system, so that the contact areas at different moments form a swept body in an xyt three-dimensional coordinate system, which is called as a contact area swept body, as shown in fig. 3. And the t axis of the swept body of the contact area corresponds to the grinding time, and the zero point of the t axis is the time for starting grinding. If the contact area swept volume is intersected by a plane perpendicular to the t-axis (referred to as the t-plane), the resulting elliptical cross-section is the shape of the contact area at that instant in time in the local coordinate system. The pressure values at various points within the swept volume of the contact area can be calculated from the elastic grinding contact model in step 2.
Step two:
Step1：
the contact area swept volume is segmented in an xyt three-dimensional coordinate system using several parallel planes perpendicular to the x-axis (called the x-plane). On each t plane, a two-dimensional area sandwiched by two adjacent x planes is a part of a circle of abrasive belt microelements in the current contact area; in the whole swept volume of the contact area, the three-dimensional area sandwiched by two adjacent x planes is the swept volume formed by the part of the abrasive belt infinitesimal in the contact area, which is called as the swept volume infinitesimal.
Fig. 4 shows two adjacent x-planes, where the swept volume microelements are cut off from the swept volume in the contact area, and because the contact state at each contact point is different, the length and pressure distribution of the swept volume microelements on each t-plane are also different. If a point is arbitrarily chosen on the sanding belt infinitesimal, the pressure applied to the point every time the point passes through the contact area changes at any time. Because the feeding speed is slow and the linear speed of the abrasive belt is high, the average pressure of the swept volume infinitesimal on each t plane can be used for representing the pressure of each point on the corresponding abrasive belt infinitesimal when passing through the current contact area.
Step2：
In order to characterize the actual service life of the sanding belt, the working time per unit length of the sanding belt needs to be calculated. The unit length of abrasive belt is a physical quantity for representing the continuous service time of each point on abrasive belt, and t is used in the invention w Expressed in units of s.
Assuming that several discrete time points t are taken during grinding i ，[t i ,t i+1 ) Working time t per unit length of abrasive belt infinitesimal in certain circle in time period w,i The calculation method comprises the following steps:
in the formula:
l-the circumference of the abrasive belt;
Δt——[t i ,t i+1 ) A time interval;
l i ——t i the length of the contact area on the sanding belt infinitesimal at the moment.
Suppose that the distance between a certain circle of abrasive belt infinitesimal and the circle of abrasive belt infinitesimal where the contact point is located is x Then t is i Length l of contact area on abrasive belt infinitesimal at moment i Comprises the following steps:
furthermore, the average pressure P of the contact area on the abrasive belt element needs to be calculated ave,i ：
In the above formula a i ,b i Is t i And (3) calculating the long half shaft and the short half shaft of the contact area of the abrasive belt wheel and the workpiece according to corresponding formulas in the step one.
Step three:
according to the second step, a plurality of discrete time t i Working time t of abrasive belt infinitesimal unit length is calculated w,i And the average pressure P ave,i At two adjacent discrete times [ t ] i ,t i+1 ) It is assumed that neither the contact area nor the degree of abrasive wear of the belt elements has changed.
Wear coefficient K of abrasive belt t Representing the abrasion degree of each circle of abrasive belt infinitesimal, and determining the abrasion coefficient K of the abrasive belt t As the length of unit length of the operating time t w The exponential function of (c):
base number b in the above formula 1 Is a variable, the mean contact pressure P to which the abrasive belt is subjected ave,i The specific relation between the two needs to be calibrated by experiments, and the specific experimental steps are as follows:
at a suitable belt line speed (e.g. v) s 15m/s) was calibrated for belt wear coefficient as a function of contact pressure and grinding duration, and the experimental design is shown in table 1. In table 1, the 2 nd and 3 rd columns are grinding parameters in the wear process, the 4 th and 5 th columns are grinding parameters of the material removal rate calibration experiment, and the change rules of the calibrated material removal rate and the wear coefficient are shown in fig. 5 and 6. The properties of the test pieces and abrasive belt portions used in the example experiments were as follows:
test piece: materials: steel No. 45; side length of the cross section: d is 7 mm.
Sanding belt: abrasive grain material: white corundum; abrasive belt granularity: 150 #; width of abrasive belt: w is 25 mm; the circumference of the abrasive belt is as follows: l1510 mm.
Calculating K according to the calibration experiment result t The method comprises the following steps: defining the removal depth of the material in unit time as the material removal rate r (unit mm/s), and assuming the contact pressure P and the linear velocity v of the abrasive belt s When the parameters are determined, the material removal rate of the new abrasive belt is r 0 The abrasive belt after the time of t is used for grinding the same material under the same parameters, and the material removal rate is r t Then define r t And r 0 The ratio of (A) to (B) is the wear factor K of the belt at that time t Namely:
according to the size of the test piece and the length of the abrasive belt adopted in the experiment shown in FIG. 5, the abrasive belt wear coefficient K under different contact pressures can be calculated t And the unit length of the abrasive belt is the working time t w FIG. 7 shows the relationship of (1).
According to the distribution rule of the five groups of experimental data in FIG. 7, exponential functions can be adopted for fitting respectively, and the base number b of the exponential functions 1 Decreases with increasing contact pressure P, so that again a linear velocity v of the belt is obtained s B at 15m/s 1 The change rule with P is shown in FIG. 8 and FIG. 9. B in FIG. 9 1 The relationship with P substantially conforms to a linear function within a certain range, and can be fitted as follows:
b 1 ＝-1.692P+0.8888 (16)
obtain b 1 After the change rule along with P, suppose the abrasive belt infinitesimal is t 0 Initial wear coefficient at time of day of
[t i ,t i+1 ) The average pressure in the time period is P ave,i Then at [ t n ,t n+1 ) Wear coefficient of abrasive belt infinitesimal in time period
Comprises the following steps:
in the examples given in the present invention, b in the above formula 1,i Is to be [ t ] i ,t i+1 ) Average pressure P over a period of time ave,i Substituting the result obtained by the formula (16):
b 1,i ＝-1.692P ave,i +0.8888 (18)
according to the steps, the wear coefficient change of each circle of abrasive belt infinitesimal at any time can be calculated, and the wear coefficient distribution before and after the abrasive belt grinds the workpiece is shown in figure 10.
TABLE 1 calibration experiment of material removal rate under different grinding parameter combinations
Claims (1)
1. A method for predicting abrasive belt abrasion in a complex curved surface workpiece grinding process is characterized by comprising the following steps:
step 1: establishing a contact area swept volume and calculating a pressure profile
Establishing a local coordinate system attached to a grinding contact point, calculating the shape of a contact area of the abrasive belt wheel and a workpiece under the local coordinate system, constructing a contact area swept body according to the change of the shape of the contact area along with grinding time, and simultaneously calculating the contact pressure distribution P (x, y) at each grinding contact point:
the contact region boundary expression is:
in the formula: a and b are respectively the length of a long axle shaft and a short axle shaft of the oval contact area; the contact pressure distribution P (x, y) at each contact point is:
in the formula: p 0 Maximum pressure at the contact area;
step 2: calculating relevant parameters of abrasive belt infinitesimal in grinding process
Contact area sweep divided by x-planeAccording to the contact area swept volume infinitesimal obtained by division, at discrete time t i Calculating relevant parameters of abrasive belt infinitesimal including unit length working time t w And the average pressure P ave ：
In the formula: t is t w The unit length working time of the abrasive belt infinitesimal between two adjacent discrete moments is represented by delta t, the discrete moment interval is represented by L, the length of a contact area on the abrasive belt infinitesimal is represented by L, and the abrasive belt perimeter is represented by L;
in the formula: p ave The average pressure of the abrasive belt infinitesimal between two adjacent discrete moments is shown, F is the contact pressure, and x is the distance between the abrasive belt infinitesimal and the abrasive belt infinitesimal in the circle where the contact point is;
and step 3: calculating the wear coefficient of abrasive belt infinitesimal
The abrasion degree of the abrasive belt is defined as an abrasion coefficient K t Quantification, obtaining K by calibration experiments t And t w And P ave The relationship between:
in the formula: k t Is the wear coefficient of the abrasive belt, b 1 A base number, b 1 The calculation method comprises the following steps:
b 1 ＝-1.692P ave +0.8888
according to the coefficient of wear K t Calculating the wear coefficient of each circle of abrasive belt infinitesimal according to the change rule:
in the formula:
is [ t ] n ,t n+1 ) The abrasion coefficient of the abrasive belt infinitesimal in the time period,
the abrasive belt is composed of abrasive belt elements at t 0 Initial wear coefficient at time, b 1,i Is [ t ] i ,t i+1 ) B within time 1 Value, t w,i Is [ t ] i ,t i+1 ) T within time w The value is obtained.
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