Collaborative robot milling limit cutting depth prediction method based on response surface method

Abstract

The invention relates to a collaborative robot milling limit cutting depth prediction method based on a response surface method, which comprehensively considers three factors of cutter overhanging, feeding speed and main shaft inclination angle, and adopts the response surface method to design a collaborative robot milling test scheme. Furthermore, a regression prediction model is constructed according to the limit cutting depth test data under each test condition, the effectiveness of the model is verified through variance analysis, and the influence rule of different process parameters on the milling limit cutting depth of the collaborative robot is explored. Results show that the method can realize accurate prediction of the milling limit cutting depth of the collaborative robot under different working conditions. Compared with the prior art, the prediction method provided by the invention comprehensively considers the influence of various process parameters, and is simple in process, small in test amount and suitable for popularization and application.

Description

Technical Field

[0001] The present invention belongs to the field of robot processing, and particularly relates to a method for predicting the ultimate cutting depth of collaborative robot milling based on the response surface method. Background Art

[0002] Cracks in the runner of large Francis turbines have become a frequent problem in the hydropower industry, seriously threatening the safe and stable operation of hydropower units. Considering the restricted space between the maintenance passage and the runner blades, it is the best choice to use lightweight collaborative robots to mill the bevel and repair the cracks in the runner area by welding.

[0003] The weak rigidity of collaborative robots results in limited cutting depth, restricting the processing efficiency. Therefore, it is urgent to explore the influence law of different process parameters on the ultimate cutting depth, and optimize the process parameters based on this to increase the ultimate cutting depth. Existing methods mainly obtain a higher ultimate cutting depth by modeling the milling dynamics of the robot, then solving the stability lobe diagram, and optimizing the spindle speed accordingly. Although existing methods can accurately predict the ultimate cutting depth under specific working conditions (such as fixed tool overhang and spindle inclination angle), there are prominent problems such as complex theoretical modeling and single considered process parameters, making it difficult to apply to actual processing. Therefore, it is necessary to propose a method for predicting the ultimate cutting depth with a simple process and comprehensively considering the influence of multiple process parameters. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method for predicting the ultimate cutting depth of collaborative robot milling based on the response surface method, which can effectively predict the ultimate cutting depth of collaborative robot milling under the comprehensive influence of multiple process parameters, and provide theoretical guidance for the optimization of process parameters.

[0005] To solve the above technical problem, the technical solution adopted by the present invention is:

[0006] A method for predicting the ultimate cutting depth of collaborative robot milling based on the response surface method, the steps are as follows:

[0007] S1. Conduct a motion interference check between the collaborative robot and the runner to determine a suitable process parameter range, where the process parameter range includes the tool overhang and spindle inclination angle range;

[0008] S2. Based on the process parameter range determined in step S1, use the response surface method to design a collaborative robot milling test plan and determine the ultimate cutting depth under each test condition;

[0009] S3. Construct a regression prediction model of the ultimate cutting depth according to the test results of step S2, and then analyze the influence law of different process parameters on the ultimate cutting depth of collaborative robot milling.

[0010] Preferably, in S1, when performing motion interference inspection on the collaborative robot milling of the runner crack area, a suitable spindle inclination range is determined on the premise of ensuring no interference during the cutting process. According to the range of the spindle inclination, the appropriate length range of the tool overhang is calculated in combination with the motion interference inspection. The model representation of the tool overhang is determined as follows:

[0011]

[0012] Among them, L is the tool overhang, d is the vertical depth of the tool from the workpiece surface, and θ is the inclination angle of the spindle.

[0013] Preferably, in S2, to explore the interactive effects of different process parameters on the ultimate cutting depth in the collaborative robot milling process, a test plan is designed using the response surface method within the range of each process parameter determined in step S1. Considering three factors: tool overhang, feed rate, and spindle inclination angle, the ultimate cutting depth under each test condition is obtained through collaborative robot milling tests.

[0014] Preferably, during the collaborative robot milling test process, for each set of cutting tests, the ultimate cutting depth is determined by gradually increasing the axial cutting depth; the specific judgment criterion is: when the axial cutting depth exceeds a certain limit, the collaborative robot vibrates or the spindle overloads and stops, and this limit is the ultimate cutting depth.

[0015] Preferably, in S3, based on the ultimate cutting depth test data obtained in S2, a quadratic model is selected to construct a regression prediction model for the ultimate cutting depth. The quadratic model is expressed as follows:

[0016]

[0017] Among them, Y is the response variable, X1, X2,..., X k are input variables, β0 is the constant term, β i is the linear term coefficient, β ii is the quadratic term coefficient, β ij is the interaction term coefficient, and ε is the error term;

[0018] The adjusted index parameters are calculated through significance tests. The index parameters include goodness of fit, predicted goodness of fit, and p-value of the missing fit term. The appropriate model category is determined according to the magnitudes of each index parameter. The model categories include interaction regression model, quadratic polynomial regression model, and cubic term regression model; then the applicability of the prediction model is verified by analyzing the variance of the model and the P-values and F-values of each parameter in the model. 6. A method for predicting the ultimate cutting depth of a collaborative robot milling based on the response surface method according to claim 1, wherein: in S3, the relationship between the ultimate cutting depth of the collaborative robot milling constructed through statistical regression analysis and the tool overhang, feed rate, and spindle inclination angle is expressed as follows:

[0019] d lim = b0 + b1T + b2F + b3I + b4TI + b5IF + b6I 2 + b7F 2

[0020] where d lim is the limit cutting depth, and b0, b1, b2, b3, b4, b5, b6, b7 are constant coefficients; in addition, T, F, and I are the tool overhang, feed rate, and spindle inclination angle, respectively.

[0021] Preferably, in S1, through motion interference inspection, the appropriate tool overhang range is determined to be 35 to 60 mm, and the appropriate spindle inclination angle range is 0 to 30°; the feed rate range selected according to the tool and workpiece materials is 10 to 40 mm / s.

[0022] Preferably, the adjusted goodness of fit of the quadratic model is 0.9886, the predicted goodness of fit is 0.9365, and the p-value of the missing fit term is 0.0895. Then, the applicability of the model is evaluated through analysis of variance. The F-value of the prediction model is 154.87, and the P-value is less than 0.0001.

[0023] A collaborative robot milling limit cutting depth prediction system based on the response surface method. According to the described collaborative robot milling limit cutting depth prediction method based on the response surface method, the system includes:

[0024] Parameter setting module: used to carry out motion interference inspection between the collaborative robot and the runner, and determine the appropriate process parameter range, where the process parameter range includes the tool overhang and spindle inclination angle range;

[0025] Experimental plan design module: used to determine the process parameter range, design a collaborative robot milling experimental plan using the response surface method, and determine the limit cutting depth under each experimental condition;

[0026] Analysis module: used to construct a regression prediction model of the limit cutting depth based on the experimental results, and then analyze the influence law of different process parameters on the collaborative robot milling limit cutting depth.

[0027] A computer-readable storage medium with a computer program stored thereon. When the computer program is executed, it implements the collaborative robot milling limit cutting depth prediction method described in item.

[0028] The present invention can achieve the following beneficial effects:

[0029] In the present invention, since the response surface method is adopted to design the milling test scheme of the collaborative robot, an accurate prediction model of the critical depth of cut under the comprehensive influence of tool overhang, feed rate, and spindle inclination angle can be constructed with a small amount of test data. In addition, the process flow of this method is simple and does not require complex work such as dynamic modeling of the collaborative robot milling system, making it more suitable for popularization and application in actual machining. Brief Description of the Drawings

[0030] The present invention will be further described below with reference to the drawings and embodiments:

[0031] Figure 1 is the flow chart of the method according to the present invention;

[0032] Figure 2 is the interference check process diagram for determining the tool overhang range;

[0033] Figure 3 is the interference check process diagram for determining the spindle inclination angle range;

[0034] Figure 4 is the residual probability distribution diagram;

[0035] Figure 5 is the scatter plot of predicted value - experimental value;

[0036] Figure 6 is the influence diagram of tool overhang and feed rate on the critical depth of cut;

[0037] Figure 7 is the influence of spindle inclination angle and feed rate on the critical depth of cut. Detailed Embodiments

[0038] The preferred solution is as Figures 1 to 7 shown. A method for predicting the critical depth of cut in collaborative robot milling based on the response surface method, the steps are as follows:

[0039] (1) Conduct a motion interference check between the collaborative robot and the rotating wheel to determine the appropriate spindle inclination angle and tool overhang range;

[0040] (2) Based on the process parameter range determined in step (1), use the response surface method to design the milling test scheme of the collaborative robot and determine the critical depth of cut under each test condition;

[0041] (3) Construct a regression prediction model of the critical depth of cut according to the test results in step (2), and then analyze the influence law of different process parameters on the critical depth of cut in collaborative robot milling.

[0042] Further, in the step (1), motion interference inspection is carried out for the collaborative robot milling of the runner crack area. On the premise of ensuring no interference during the cutting process, a suitable spindle inclination range is determined. According to the range of the spindle inclination and combined with the interference inspection, a suitable length range of the tool overhang is calculated. The model representation of the tool overhang is determined as follows:

[0043]

[0044] Wherein, L is the tool overhang, d is the vertical depth of the tool from the workpiece surface, and θ is the inclination angle of the spindle.

[0045] Further, in the step (2), to explore the interactive influence of different process parameters on the limit cutting depth in the collaborative robot milling process, a test scheme is designed by the response surface method within the range of each process parameter determined in the step (1). Considering three factors of tool overhang, feed rate, and spindle inclination angle, the limit cutting depth under each test condition is obtained through the collaborative robot milling test;

[0046] Further, during the collaborative robot milling test process, for each group of cutting tests, the limit cutting depth is determined by gradually increasing the axial cutting depth. The specific judgment criterion is: when the axial cutting depth exceeds a certain limit, the collaborative robot vibrates or the spindle overloads and stops, and this limit is the limit cutting depth;

[0047] Further, in the step (3), based on the limit cutting depth test data obtained in the step (2), different model categories are selected (such as cross model, quadratic model, and cubic model). Taking the quadratic model as an example, the model is represented as follows:

[0048]

[0049] Wherein, Y is the response variable, X1, X2,..., X k are input variables, β0 is a constant term, β i is the coefficient of the linear term, β ii is the coefficient of the quadratic term, β ij is the coefficient of the interaction term, and ε is the error term. By performing a significance test, index parameters such as the adjusted goodness of fit, predicted goodness of fit, and p-value of the missing fitting term of each model are calculated, and a suitable model category is determined according to the magnitudes of these index parameters. Then, the applicability of the prediction model is verified by analyzing the P-value and F-value of the model and each parameter in the model through variance analysis;

[0050] Further, in the step (3), the relationship between the collaborative robot milling limit cutting depth and the tool overhang, feed rate, and spindle inclination angle constructed through statistical regression analysis is represented as follows:

[0051] d lim= b0 + b1T + b2F + b3I + b4TI + b5IF + b6I 2 + b7F 2 ;

[0052] where d lim is the limit cutting depth, and b0, b1, b2, b3, b4, b5, b6, b7 are constant coefficients. In addition, T, F, and I are the tool overhang, feed rate, and spindle inclination angle, respectively.

[0053] Example 1:

[0054] Refer to Figure 1 , which is a flow chart of a method for predicting the limit cutting depth of a collaborative robot milling based on the response surface method implemented according to the present invention, and includes the following steps:

[0055] (1) Interference check to determine the parameter range

[0056] Carry out kinematic interference check for the collaborative robot milling of the runner crack area, and determine the appropriate ranges of tool overhang and spindle inclination angle on the premise of ensuring no interference during the cutting process. The processes are shown in Figure 2 and Figure 3 . After the interference check, the appropriate range of tool overhang is determined to be 35 to 60 mm, and the appropriate range of spindle inclination angle is 0 to 30°. In addition, the preferred range of feed rate is 10 to 40 mm / s according to the tool and workpiece materials.

[0057] (2) Collaborative robot milling test

[0058] To explore the interactive effects of tool overhang, feed rate, and spindle inclination angle on the limit cutting depth during the collaborative robot milling process, within the ranges of each process parameter determined in step (1), use the response surface method to design a collaborative robot milling test plan and conduct the test.

[0059] During the collaborative robot milling test, for each set of cutting tests, determine the limit cutting depth by gradually increasing the axial cutting depth. The specific judgment criterion is: when the axial cutting depth exceeds a certain limit, the collaborative robot vibrates or the spindle overloads and stops, and this limit is the limit cutting depth.

[0060] (3) Limit cutting depth regression prediction and analysis

[0061] Based on the ultimate cutting depth test data obtained in step (2), different model categories (such as cross model, quadratic model, and cubic model) are selected. Through significance testing, index parameters such as the adjusted goodness of fit, predictive goodness of fit, and p-value of the missing fitting term of each model are calculated, and the appropriate model category is determined according to the magnitudes of these index parameters. Among them, the adjusted goodness of fit of the quadratic model is 0.9886, the predictive goodness of fit is 0.9365, and the p-value of the missing fitting term is 0.0895, which are all the largest compared to other models. Then, the applicability of the model is evaluated through analysis of variance. The F value of the prediction model is 154.87, and the P value is less than 0.0001, indicating that the model is significant. Therefore, the quadratic model is selected to fit the relationship between the ultimate cutting depth and the tool overhang, feed rate, and spindle inclination angle. The results are as follows:

[0062] d lim = b0 + b1T + b2F + b3I + b4TI + b5IF + + b6I 2 + b7F 2

[0063] Among them, d lim is the ultimate cutting depth, and T, F, and I are the tool overhang, feed rate, and spindle inclination angle respectively. The fitting results of the constant coefficients b0, b1, b2, b3, b4, b5, b6, and b7 are 2.77258, -0.019748, -0.042489, -0.050439, 0.00048, 0.000189, 0.000738, and 0.000304 respectively.

[0064] The effectiveness of the model is verified through the residual probability distribution diagram ( Figure 4 ) and the scatter diagram of predicted value - experimental value ( Figure 5 ). The residual points are roughly distributed along a straight line, and each predicted value - experimental value data point is basically distributed near the diagonal, indicating that the regression prediction model has a good fitting effect and high prediction accuracy.

[0065] Based on the constructed regression prediction model, analyze the influence laws of the tool overhang, feed rate, and spindle inclination angle on the ultimate cutting depth of collaborative robot milling. As Figure 6 shown, the ultimate cutting depth gradually decreases with the increase of the tool overhang and feed rate. In addition, the change rate of the ultimate cutting depth with the feed rate is closely related to the tool overhang, indicating that the interaction between the tool overhang and feed rate on the ultimate cutting depth is significant. As Figure 7 shown, the ultimate cutting depth gradually decreases with the increase of the spindle inclination angle, especially under the condition of a large feed rate, indicating that there is also a significant interaction between the spindle inclination angle and feed rate on the ultimate cutting depth.

[0066] The above embodiments are only the preferred technical solutions of the present invention and should not be regarded as limitations on the present invention. The protection scope of the present invention shall be the technical solutions recorded in the claims, including the equivalent replacement solutions of the technical features in the technical solutions recorded in the claims. That is, equivalent replacement improvements within this scope are also within the protection scope of the present invention.

Claims

1. A method for predicting the cutting depth limit of collaborative robot milling based on response surface methodology, characterized in that The following steps are involved: S1. Conduct motion interference inspection between the collaborative robot and the rotating wheel to determine the appropriate process parameter range, wherein the process parameter range includes tool overhang and spindle inclination range; S2. Based on the process parameter range determined in step S1, a collaborative robot milling test plan is designed using the response surface method to determine the limit cutting depth under each test condition; S3. According to the test results of step S2, a regression prediction model of the limit cutting depth is constructed, and then the influence of different process parameters on the limit cutting depth of collaborative robot milling is analyzed.

2. The method for predicting the limit cutting depth of collaborative robot milling based on response surface methodology according to claim 1, characterized in that: In S1, when the motion interference check is carried out for the collaborative robot milling processing in the crack area of ​​the runner, the appropriate spindle inclination range is determined under the premise of ensuring that there is no interference in the cutting process. The appropriate length range of the tool overhang is calculated based on the spindle inclination range combined with the motion interference check. The model for determining the tool overhang is expressed as follows: Where L is the tool overhang, d is the vertical depth between the tool and the workpiece surface, and θ is the inclination angle of the spindle.

3. The method for predicting the limit cutting depth of collaborative robot milling based on response surface methodology according to claim 2, characterized in that: In S2, in order to explore the interactive effects of different process parameters on the limit cutting depth of the collaborative robot milling process, the response surface method is used to design the test plan within the range of each process parameter determined in step S1, considering the three factors of tool overhang, feed speed and spindle inclination, and the limit cutting depth under each test condition is obtained through the collaborative robot milling test.

4. The method for predicting the limit cutting depth of collaborative robot milling based on response surface methodology according to claim 3 is characterized in that: During the collaborative robot milling test, for each set of cutting tests, the limit cutting depth was determined by gradually increasing the axial cutting depth; the specific judgment criteria were: when the axial cutting depth exceeded a certain limit, the collaborative robot would vibrate or the spindle would stop due to overload, and this limit was the limit cutting depth.

5. The method for predicting the limit cutting depth of collaborative robot milling based on response surface methodology according to claim 1, characterized in that: In S3, based on the limit cutting depth test data obtained in S2, a quadratic model is selected to construct a regression prediction model of the limit cutting depth. The quadratic model is expressed as follows: Among them, Y is the response variable, X1, X2, ..., X k is the input variable, β0 is the constant term, β i is the linear term coefficient, β ii is the quadratic term coefficient, β ij is the interaction term coefficient, ε is the error term; The index parameters were adjusted by calculating the significance test. The index parameters included goodness of fit, predicted goodness of fit and p-value of missing fit item. The appropriate model category was determined according to the size of each index parameter. The model categories included interactive regression model, quadratic polynomial regression model and cubic regression model. The model was evaluated by variance analysis and the P-value and F-value of each parameter in the model were used to verify the applicability of the prediction model.

6. The method for predicting the limit cutting depth of collaborative robot milling based on response surface methodology according to claim 1, characterized in that: In S3, the relationship between the collaborative robot milling limit cutting depth and the tool overhang, feed speed and spindle inclination angle constructed by statistical regression analysis is expressed as follows: <h2 style=";text-align:left;direction:ltr">d<h2 style=";text-align:left;direction:ltr"> lim <h2 style=";text-align:left;direction:ltr"> =b0+b1T+b2F+b3I+b4TI+b5IF++b6I<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +b7F<h2 style=";text-align:left;direction:ltr"> 2 Among them, d lim is the limiting cutting depth, b0, b1, b2, b3, b4, b5, b6 and b7 are constant coefficients; in addition, T, F and I are the tool overhang, feed speed and spindle inclination, respectively.

7. The method for predicting the limit cutting depth of collaborative robot milling based on response surface methodology according to claim 1, characterized in that: In S1, after motion interference check, it was determined that the appropriate tool overhang range was 35 to 60 mm, and the appropriate spindle inclination range was 0 to 30°; the feed speed range selected according to the tool and workpiece material was 10 to 40 mm / s.

8. The method for predicting the limit cutting depth of collaborative robot milling based on response surface methodology according to claim 5, characterized in that: The adjusted goodness of fit of the quadratic model was 0.9886, the predicted goodness of fit was 0.9365, and the p-value for the missing fit term was 0.0895. The applicability of the model was evaluated by analysis of variance, and the F-value of the prediction model was 154.87, and the P-value was less than 0.0001.

9. A collaborative robot milling limit cutting depth prediction system based on response surface methodology, characterized in that: According to a collaborative robot milling limit cutting depth prediction method based on response surface methodology according to any one of claims 1 to 8, the system comprises: Parameter setting module: used to carry out motion interference inspection between the collaborative robot and the rotating wheel, and determine the appropriate process parameter range, which includes the tool overhang and spindle inclination range; Experimental design module: used to determine the range of process parameters, design collaborative robot milling experimental plan using response surface methodology, and determine the limit cutting depth under various experimental conditions; Analysis module: used to build a regression prediction model of the limit cutting depth based on the test results, and then analyze the influence of different process parameters on the limit cutting depth of collaborative robot milling.

10. A computer-readable storage medium, characterized in that: A computer program is stored thereon, and when the computer program is executed, a collaborative robot milling limit cutting depth prediction method based on response surface method as described in any one of claims 1 to 8 is implemented.

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