Method for calculating processing parameters for residual stress control by parameter inversion

Abstract

The present invention belongs to the field of processing residual stress, and discloses a method for calculating processing parameters for residual stress control by parameter inversion. This method comprises: (a) extracting a characteristic index reflecting the residual stress distribution characteristic from a residual stress distribution curve; (b) respectively presetting initial values of processing parameters for residual stress control, calculating an initial value of the characteristic index, and drawing curves of the characteristic index over the respective processing parameters to obtain respective fitted curves; (c) respectively establishing a relation formula between respective characteristic index increment of the processing parameters and the fitting curve; and (d) assigning the values and performing inversion calculation to obtain the required processing parameters. The present invention is simple in operation, reduces the number of tests, lowers the production cost, improves the processing residual stress distribution of the workpiece and improves the anti-fatigue life of the components.

Claims

1. A method for calculating processing parameters for residual stress control by parameter inversion, comprising: (a) acquiring a residual stress distribution curve of a processed surface layer of a workpiece by a sensor, extracting a characteristic index Drs reflecting a residual stress distribution characteristic from the residual stress distribution curve and simultaneously acquiring a plurality of processing parameters A.sub.i (i=1, 2,3 . . . n) correlated to the characteristic index, where i is a serial number of the processing parameter and n is the total number of the processing parameters; (b) presetting initial values a.sub.10,a.sub.20, . . . ,a.sub.i0, . . . ,a.sub.n0 of the plurality of the processing parameters by a preprocessor, obtaining an initial value H (a.sub.10,a.sub.20, . . . ,a.sub.i0, . . . ,a.sub.n0) of the characteristic index Drs according to the initial values of the plurality of the processing parameters, and respectively fitting single-variable curves of each of the characteristic index over the respective processing parameters by the preprocessor to obtain respective fitted functions Drs(A.sub.i); (c) setting expected values of the characteristic index Drs according to actual needs and assigning characteristic index increments ΔDrs.sup.A.sup.i corresponds to each of the processing parameters A.sub.i by an assignment allocation unit; (d) transmitting the initial value H (H(a.sub.10, a.sub.20, . . . , a.sub.i0, . . . , a.sub.n0) of the characteristic index, the fitted function Drs(A.sub.i) of the characteristic index, the characteristic index Drs, and each of the characteristic index increments ΔDrs.sup.A.sup.i to a microprocessor through a input interface, the microprocessor obtaining respective characteristic index Drs corresponding to each of the processing parameters A.sub.i according to relation formulas (i), (ii) and (iii), combining the characteristic index Drs with the fitted function Drs(A.sub.i) to obtain the plurality of the processing parameters A.sub.i, and outputting the plurality of the processing parameters A.sub.i, wherein the relation formulas (i), (ii) and (iii) are $\begin{array}{cc}\Delta {\mathrm{Drs}}^{A_i}=\mathrm{Drs}\left(A_i\right)-H\left(a_{10},a_{20},\mathrm{.Math.},a_{i0},\mathrm{.Math.},a_{n0}\right)& \left(i\right)\\ \Delta \mathrm{Drs}=\underset{i=1}{\overset{n}{.Math.}}\Delta {\mathrm{Drs}}^{A_i}& \left(\mathrm{ii}\right)\\ \Delta \mathrm{Drs}=\mathrm{Drs}-H\left(a_{10},a_{20},\mathrm{.Math.},a_{i0},\mathrm{.Math.},a_{n0}\right);& \left(\mathrm{iii}\right)\end{array}$ (e) storing the plurality of the processing parameters A.sub.i output from the microprocessor to memory; (f) outputting the plurality of the processing parameters A.sub.i, in the memory to a control unit of a machine tool to control the machine tool to process the surface layer of the workpiece based on the processing parameters A.sub.i, so the processed surface layer of the workpiece has a needed residual stress.

2. The method of claim 1, wherein the characteristic index includes the maximum surface residual stress, the maximum residual compressive stress depth in the surface layer or the depth of the surface tensile stress layer.

3. The method of claim 1, wherein in the step (b), the processing parameters include cutting speed, feed rate, cutting depth, tool edge radius or tool rake angle.

4. The method of claim 1, wherein the initial value H(a.sub.10, a.sub.20, . . . , a.sub.i0, . . . , a.sub.n0) of the characteristic index is calculated by a residual stress analytical model or experimentally measured.

5. The method of claim 1, wherein in the step (b), the drawn curves of the characteristic index over the respective processing parameters A.sub.i are obtained by a processing residual stress theoretical model or experimental measurements.

6. The method of claim 2, wherein in the step (b), the processing parameters include cutting speed, feed rate, cutting depth, tool edge radius or tool rake angle.

7. The method of claim 2, wherein the initial value H(a.sub.10, a.sub.20, . . . , a.sub.i0, . . . , a.sub.n0) of the characteristic index is calculated by a residual stress analytical model or experimentally measured.

8. The method of claim 3, wherein the initial value H(a.sub.10, a.sub.20, . . . , a.sub.i0, . . . , a.sub.n0) of the characteristic index is calculated by a residual stress analytical model or experimentally measured.

9. The method of claim 2, wherein in the step (b), the drawn curves of the characteristic index over the respective processing parameters A.sub.i are obtained by a processing residual stress theoretical model or experimental measurements.

10. The method of claim 3, wherein in the step (b), the drawn curves of the characteristic index over the respective processing parameters A.sub.i are obtained by a processing residual stress theoretical model or experimental measurements.

11. The method of claim 4, wherein in the step (b), the drawn curves of the characteristic index over the respective processing parameters A.sub.i, are obtained by a processing residual stress theoretical model or experimental measurements.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a flowchart of a method for calculating processing parameters for residual stress control by parameter inversion according to preferred embodiments of the present invention.

(2) FIG. 2 is a distribution graph of residual stresses at different depths in the surface layer and a schematic diagram of a curve characteristic index Drs according to the preferred embodiments of the present invention.

(3) FIG. 3 is a distribution graph of residual stresses at different cutting speeds according to the preferred embodiments of the present invention.

(4) FIG. 4 is a distribution graph of residual stresses at different feed rates according to the preferred embodiments of the present invention.

(5) FIG. 5 is a distribution graph of the characteristic index over the cutting speed according to the preferred embodiments of the present invention.

(6) FIG. 6 is a distribution graph of the characteristic index over the feed rate according to the preferred embodiments of the present invention.

(7) FIG. 7 is a graph of Drs(V) and Drs(t.sub.c) of the residual stress over C.sub.1 according to the preferred embodiments of the present invention.

(8) FIG. 8 is a comparison diagram of a residual stress curve calculated at t.sub.c=0.207 mm and V=60 m/min according to the preferred embodiments of the present invention and a residual stress curve experimentally measured according to the method provided in the present invention.

(9) FIG. 9 is a comparison diagram of a residual stress curve calculated at t.sub.c=0.11 mm and V=29.42 m/min according to the preferred embodiments of the present invention and a residual stress curve experimentally measured according to the method provided in the present invention.

(10) FIG. 10 is a comparison diagram of a residual stress curve calculated at t.sub.c=0.172 mm and V=36.3 m/min according to the preferred embodiments of the present invention and a residual stress curve experimentally measured according to the method provided in the present invention.

(11) FIG. 11 is a comparison diagram of a residual stress curve calculated at t.sub.c=0.19 mm and V=40.7 m/min according to the preferred embodiments of the present invention and a residual stress curve experimentally measured according to the method provided in the present invention.

(12) FIG. 12 is a flowchart of a method for calculating processing parameters for residual stress control by parameter inversion according to preferred embodiments of controlling the residual stress of the cutting processing of the present invention.

DETAILED DESCRIPTION OF THE EMBODIMENTS

(13) For clear understanding of the objectives, features and advantages of the present invention, detailed description of the present invention will be given below in conjunction with accompanying drawings and specific embodiments. It should be noted that the embodiments described herein are only meant to explain the present invention, and not to limit the scope of the present invention.

(14) FIG. 1 is a flowchart of a method for calculating processing parameters for residual stress control by parameter inversion according to preferred embodiments of the present invention. According to FIG. 1, one can obtain the flowchart of this embodiment, as shown in FIG. 12. This method will be described below in conjunction with the example of residual stresses in the orthogonal cutting processing.

(15) (a) Acquiring a residual stress distribution of a processed surface layer of a workpiece by a sensor, drawing a curve of the variation of the residual stress to the depth to determine a characteristic index of a distribution curve of residual stresses. FIG. 2 is a distribution graph of residual stresses at different depths in the surface layer and a schematic diagram of a maximum residual compressive stress depth Drs according to the preferred embodiments of the present invention. In this example, only the maximum residual compressive stress depth Drs in the characteristic indexes of the residual stress distribution curve in the x direction is studied. By using a sensor to identify the cutting input parameters related to the maximum residual compressive stress depth Drs, the variation of the Drs could be studied through controlling the variables, which is measuring the variation of the Drs by the sensor when one of the cutting input parameter varies. In this embodiment, the related cutting input parameters are cutting speed V and the feed rate t.sub.c.

(16) (b) Reference values of the characteristic index of the residual stress distribution curve and processing parameters associated with it are set by the preprocessor. For the cutting processing, processing parameters affecting Drs include the cutting speed V and the feed rate t.sub.c. In a case of set reference values V.sub.0=60 m/min and t.sub.c0=0.11 mm/r, H(V.sub.0,t.sub.c0) is calculated by a residual stress analytical model for the orthogonal cutting processing as a reference value of Drs. Noted that the material assumed for the model is nickel-aluminum bronze alloy with elemental composition shown in Table 1, and other input variables in the model are shown in Table 2 and Table 3.

(17) TABLE-US-00001 TABLE 1 chemical composition of the nickel-aluminum bronze alloy Element Manga- Copper Aluminum Ferrum Nickel nese Carbon Symbol Cu Al Fe Ni Mn C Mass 77-82 8.5-10.0 2.0-6.0 3.0-6.0 0.8-2.5 ≤0.10 percent (%)

(18) TABLE-US-00002 TABLE 2 physical properties of the nickel-aluminum bronze alloy Specific linear Elasticity Yield heat Pois- expansion modulus stress capacity son's Density coefficient Melting E σ.sub.s c ratio ρ.sub.0 α.sub.0 point 110 300 419 0.327 7280 12*10.sup.−6 1060 (Gpa) (Mpa) (J/ (kg/m.sup.3) (/° C.) (° C.) (kg*° C.))

(19) TABLE-US-00003 TABLE 3 values of other input variables in the residual stress analytical model Friction Thermal coefficient of Cutting conductivity tool flank width Shear angle λ (W/ μ w (mm) φ (°) (mm° C.)) 0.22 5 22 0.03 Length of Cutting force in the Cutting force wear land of Rake cutting speed in the tool frank angle direction feed direction VB (mm) α (°) F.sub.c (N) F.sub.t (N) 0.04 17 1000 300

(20) A curve of residual stress distribution in the surface layer under the independent action of each processing parameter (such as cutting speed, feed rate, cutting depth and tool rake angle) is obtained by the processing residual stress theoretical model or experimental measurement, and a curve of the characteristic index over each processing parameter is fitted. FIG. 3 is a distribution graph of residual stresses at different cutting speeds according to the preferred embodiments of the present invention, and FIG. 4 is a distribution graph of residual stresses at different feed rates according to the preferred embodiments of the present invention.

(21) FIG. 5 is a distribution graph of the characteristic index over the cutting speed according to the preferred embodiments of the present invention, and FIG. 6 is a distribution graph of the characteristic index over the feed rate according to the preferred embodiments of the present invention. Drs in the residual stress curve is extracted, and the fitted curves for Drs to the cutting rate and the feed rate are respectively shown in FIG. 5 and FIG. 6, and their fitting functions are respectively Drs(V)=128e.sup.−0.04012*V+65.15e.sup.−0.002407*V and Drs(tc)=74.3e.sup.1.945*tc−50.43e.sup.−7.369*tc.

(22) (c) In an assignment allocation unit, it is mainly dealing with the allocation of the increment of the characteristic index Drs between ΔDrs.sup.V and ΔDrs.sup.tc, and creating an equation set regarding the relations between the increments. The effects of multiple processing parameters on the characteristic index of the residual stress curve are regarded to be linearly superimposed, and by taking the superimposed characteristic indexes of the residual stress curves and their increments as a parameter matrix M, establishing a system of linear equations expressing the relation among the characteristic indexes according to linear inversion equations: G.Math.M=F, where G represents a coefficient matrix, and F represents observation data (i.e., a constant term). Taking the cutting residual stress as an example, increments of Drs resulting from the cutting speed and the feed rate are respectively ΔDrs.sup.V=Drs(V)−H(V.sub.0,t.sub.c0) and ΔDrs.sub.tc=Drs(t.sub.c)−H(V.sub.0,t.sub.c0), and then the total increment (linear superposition) of Drs resulting from the cutting speed and the feed rate is ΔDrs=ΔDrs.sup.V+ΔDrs.sup.tc, where ΔDrs can also be expressed as ΔDrs=Drs−H(V.sub.0,t.sub.c0). Except the variable H(V.sub.0,t.sub.c0), other six variables ΔDrs.sup.V, ΔDrs.sup.tc, Drs(V), Drs(tc), ΔDrs and Drs in the above four formulas are regarded as parameters, and then the four formulas can be combined into a system of linear equations:

(23) $\begin{array}{cc}\begin{array}{cccccccc}\Delta \mathrm{Drs}& \Delta {\mathrm{Drs}}^{\mathrm{tc}}& \Delta {\mathrm{Drs}}^V& \mathrm{Drs}& \mathrm{Drs}\left(t_c\right)& \mathrm{Drs}\left(V\right)& H\left(t_{c0},V_0\right)& \mathrm{Constant}\mathrm{term}\\ 1& -1& -1& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& -1& 0& 1& 0\\ 0& 0& 1& 0& 0& -1& 1& 0\\ 1& 0& 0& -1& 0& 0& 1& 0\end{array}& \left(1\right)\end{array}$

(24) The above system of linear equations is expressed in a form of a matrix G.Math.M=F as follow:

(25) $\begin{array}{cc}\left(\begin{array}{ccccccc}1& -1& -1& 0& 0& 0& 0\\ 0& 1& 0& 0& -1& 0& 1\\ 0& 0& 1& 0& 0& -1& 1\\ 1& 0& 0& -1& 0& 0& 1\end{array}\right)\left(\begin{array}{c}\Delta \mathrm{Drs}\\ \Delta {\mathrm{Drs}}^{\mathrm{tc}}\\ \Delta {\mathrm{Drs}}^V\\ \mathrm{Drs}\\ \mathrm{Drs}\left(t_c\right)\\ \mathrm{Drs}\left(V\right)\\ H\left(t_{c0},V_0\right)\end{array}\right)=\left(\begin{array}{c}0\\ 0\\ 0\\ 0\end{array}\right)& \left(2\right)\end{array}$

(26) (d) The system of linear equations is solved in the microprocessor to obtain the cutting speed V and the feed rate t.sub.c corresponding to the characteristic index Drs. Since the number of equations in the system of linear equations (2) obtained in the previous step is 4 and the number of parameters is 6, the system of linear equations has infinitely many solutions. In order to obtain a unique solution, known conditions need to be added into the system of linear equations so that the number of equations is equal to the number of parameters. The additional known conditions are: (I) a specific value of the characteristic index of the required residual stress distribution curve, and (II) allocation of the specific value to different processing parameters. The additional known conditions must be such that the number of the above equations is equal to the number of parameters. Taking the cutting residual stress as an example, it is required that the maximum residual compressive stress depth in the surface layer after machining is Drs=C.sub.0; since Drs can be affected by the cutting speed and the feed rate at the same time, the increment of Drs resulting from the feed rate can be set as ΔDrs.sup.tc=C.sub.1 (or the increment of Drs resulting from the cutting speed can be set as ΔDrs.sup.V=C.sub.2). Thus, two known conditions are added into the system of linear equations (1):

(27) $\begin{array}{cc}\left(\begin{array}{cccccccc}\Delta \mathrm{Drs}& \Delta {\mathrm{Drs}}^{\mathrm{tc}}& \Delta {\mathrm{Drs}}^V& \mathrm{Drs}& \mathrm{Drs}\left(t_c\right)& \mathrm{Drs}\left(V\right)& H\left(t_{c0},V_0\right)& \mathrm{Constant}\mathrm{term}\\ 1& -1& -1& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& -1& 0& 1& 0\\ 0& 0& 1& 0& 0& -1& 1& 0\\ 1& 0& 0& -1& 0& 0& 1& 0\\ 0& 0& 0& 1& 0& 0& 0& C_0\\ 0& 1& 0& 0& 0& 0& 0& C_1\end{array}\right)& \left(3\right)\end{array}$

(28) The above system of linear equations is expressed in a form of a matrix G.Math.M=F as follow:

(29) $\begin{array}{cc}\left(\begin{array}{ccccccc}1& -1& -1& 0& 0& 0& 0\\ 0& 1& 0& 0& -1& 0& 1\\ 0& 0& 1& 0& 0& -1& 1\\ 1& 0& 0& -1& 0& 0& 1\\ 0& 0& 0& 1& 0& 0& 0\\ 0& 1& 0& 0& 0& 0& 0\end{array}\right)\left(\begin{array}{c}\Delta \mathrm{Drs}\\ \Delta {\mathrm{Drs}}^{\mathrm{tc}}\\ \Delta {\mathrm{Drs}}^V\\ \mathrm{Drs}\\ \mathrm{Drs}\left(t_c\right)\\ \mathrm{Drs}\left(V\right)\\ H\left(t_{c0},V_0\right)\end{array}\right)=\left(\begin{array}{c}0\\ 0\\ 0\\ 0\\ C_0\\ C_1\end{array}\right)& \left(4\right)\end{array}$

(30) The system of linear equations (4) has a unique solution and can be solved as follows:
Drs(t.sub.c)=H(t.sub.c0,V.sub.0)+C.sub.1
Drs(V)=C.sub.0−C.sub.1  (5)

(31) It can be seen that if C.sub.1 is regarded as a variable and Drs (V) and Drs (t.sub.c) are regarded as functions, their relationship can be represented by straight lines. FIG. 7 is a graph of Drs(V) and Drs (t.sub.c) of the residual stress over C.sub.1 according to the preferred embodiments of the present invention. As shown in FIG. 7, the dash and dot line perpendicular to the C.sub.1 axis respectively intersects function graph lines of Drs(V) and Drs (t.sub.c) at points A and B, indicating that when C.sub.0, C.sub.1 and H(V.sub.0,t.sub.c0) are determined, values of Drs(V) and Drs(t.sub.c) can be uniquely determined.

(32) Thus, according to the cutting conditions in step (b), it can be calculated that H(V.sub.0,t.sub.c0)=79 μm, and for the required Drs=C.sub.0, it is set that C.sub.0=100 μm. There are several situations in determination of C.sub.1:

(33) a) if ΔDrs is individually allocated to ΔDrs.sup.tc, ΔDrs.sup.tc=C.sub.1=21 μm, ΔDrs.sup.V=0 μm;

(34) b) if ΔDrs is individually allocated to ΔDrs.sup.V, ΔDrs.sup.tc=C.sub.1=0 μm, ΔDrs.sup.V=21 μm;

(35) c) if ΔDrs is equally allocated to ΔDrs.sup.tc and ΔDrs.sup.V, ΔDrs.sup.tc=C.sub.1=10.5 μm, ΔDrs.sup.V=10.5 μm; and

(36) d) if ΔDrs is randomly allocated to ΔDrs.sup.tc and ΔDrs.sup.V, for example, ΔDrs.sup.tc=C.sub.1=16 μm, then ΔDrs.sup.V=5 μm.

(37) The assignments of C.sub.1 in these four situations will result in the following results of Drs(V) and Drs(t.sub.c) in four situations:

(38) a) Drs(t.sub.c)=100 μm, Drs(V)=79 μm;

(39) b) Drs(t.sub.c)=79 μm, Drs(V)=100 μm;

(40) c) Drs(t.sub.c)=89.5 μm, Drs(V)=89.5 μm; and

(41) d) Drs(t.sub.c)=95 μm, Drs(V)=84 μm.

(42) Finally, values of t.sub.c and V in the four situations are calculated by the fitted formulas Drs(V)=128e.sup.−0.04012*V+65.15e.sup.−0.002407*V and Drs(t.sub.c)=74.3e.sup.1.945*tc−50.43e.sup.−7.369*tc in the step (b):

(43) a) t=0.207 mm, V=60 m/min;

(44) b) t.sub.c=0.11 mm, V=29.42 m/min;

(45) c) t=0.172 mm, V=36.3 m/min; and

(46) d) t.sub.c=0.19 mm, V=40.7 m/min.

(47) This is the final result obtained by using the set residual stress to calculate the processing parameters. In theory, the use of these calculated processing parameters during processing can achieve required processing residual stress distribution.

(48) (e) Storing the calculated cutting speed V and the feed rate t.sub.c to memory, so cutting speed V and the feed rate t.sub.c can be input to the machine tool when processing.

(49) (f) The cutting speed V and the feed rate t.sub.c are input to the control unit of the machine tool to drive the machine tool to process the cutting process.

(50) FIG. 8 is a comparison diagram of a residual stress curve calculated at t.sub.c=0.207 mm and V=60 m/min according to the preferred embodiments of the present invention and a residual stress curve experimentally measured according to the method provided in the present invention; FIG. 9 is a comparison diagram of a residual stress curve calculated at t.sub.c=0.11 mm and V=29.42 m/min according to the preferred embodiments of the present invention and a residual stress curve experimentally measured according to the method provided in the present invention; FIG. 10 is a comparison diagram of a residual stress curve calculated at t.sub.c=0.172 mm and V=36.3 m/min according to the preferred embodiments of the present invention and a residual stress curve experimentally measured according to the method provided in the present invention; and FIG. 11 is a comparison diagram of a residual stress curve calculated at t.sub.c=0.19 mm and V=40.7 m/min according to the preferred embodiments of the present invention and a residual stress curve experimentally measured according to the method provided in the present invention. The comparison of the residual stress curve calculated by plugging processing parameters into the residual stress analytical model and the residual stress curve experimentally measured according to the method provided in the present invention is shown in FIGS. 9, 10 and 11. It can be seen that the characteristic indexes Drs of the calculated and experimentally measured residual stress curves are substantially in the vicinity of the desired value of 100 μm, indicating that the proposed residual stress control method has a certain effect.

(51) The above is just described by taking the orthogonal cutting processing as an example, and the method of the present invention can be applicable to residual stress control of other processing methods such as forging, welding, laser processing, wire cutting, grinding, drilling, turning, milling, boring, shot peening and heat treatment.

(52) While particular embodiments of the present invention have been shown and described, it will be obvious to those skilled in the art that changes and modifications may be made without departing from the spirit and scope of the present invention.