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Analysis of multi-axis milling in an anthropomorphic robot, using the design of experiments methodology
Journal of Materials Processing Technology 135 (2003) 235–241
Analysis of multi-axis milling in an anthropomorphic robot, using the design of experiments methodology J.F.C.P. Antunes Simo˜esb, T.J. Coolec, D.G. Cheshirea,*, Anto´nio R. Piresd a
School of Engineering and Advanced Technology, Staffordshire University, Stafford, UK b Escola Superior de Tecnologia, Instituto Polite´cnico de Setu´bal, Setu´bal, Portugal c Faculty of Technology, Buckinghamshire Chilterns University, Buckingham, UK d Escola Superior de Tecnologia, Instituto Polite´cnico de Setu´bal, Setu´bal, Portugal
Abstract Currently, the concept of advanced machining technologies (AMT) includes different processes such as high-speed machining, multi-axis machining, etc. The common characteristic between these technologies is that they aim to improve the cutting process. Research done in the past has mainly concentrated on metal machining. In this present research, efforts are made to apply these techniques to the ceramic industry. This work forms part of the ongoing research at Staffordshire University into the application of CNC machining techniques in the production of models and moulds, with regards to the production of tableware and sanitaryware items. This paper focuses on the analysis of multi-axis milling using an anthropomorphic robot to produce near net shape plaster parts. The robotic system was run based on a specific set-up that allows multi-axes toolpaths and avoids ‘‘Gimbal Lock’’ singularity. The milling tests were carried out on plaster using conventional cutting tools (slot-mills). The design of experiments (DoE) was implemented using factorial techniques. The surface quality and geometric accuracy of the plaster parts were the response variables used to characterise the part quality and test the levels of acceptability of lead/lag angle, feed-rate and robot arm-extension. A mathematical equation based on the geometric accuracy was developed and used to plot flatness contours. Through these plots it is easy to define other possible combinations of feed-rate and robot arm-extension that can be used. # 2002 Published by Elsevier Science B.V. Keywords: Multi-axis milling; Plaster; Robot
1. Introduction The plaster machining operation executed on a robot was a relatively unknown process before this research. The technical knowledge available before this work, regarding this process, was reduced to a few experiments and the initial studies conducted during the CRAFT project BE-S5-2523. Also, with the new aspect of the use of the robotic system, the machining of plaster was also a process not very well studied, including the tool wear occurring during plaster machining [1,2]. All the characteristics presented earlier illustrate the ‘‘lack of knowledge’’ conditions in the initial phase of this research, and indicate the necessity to initialise the research * Corresponding author. E-mail addresses: [email protected] (J.F.C.P. Antunes Simo˜es), [email protected] (T.J. Coole), [email protected] (D.G. Cheshire), [email protected] (A.R. Pires).
0924-0136/02/$ – see front matter # 2002 Published by Elsevier Science B.V. PII: S 0 9 2 4 - 0 1 3 6 ( 0 2 ) 0 0 9 0 8 - 1
predicting all the possible important process variables. In order to scan the more important variables involved with this machining operation the factorial design of experiment (DoE) methodology was used. With this factorial design and analysis approach it was possible to optimise the use of the experimental resources, during the study of the main variables effect. The work was divided into several phases, including the choice of variables and respective levels, selection of response variables, choice of experimental design, experimental work, and finally the statistical analysis of data. As a fundamental aspect of the factorial DoE methodology, the capability of the plaster machining operation executed on a robot was identified, as the problem to be analysed through this study. This process capability was considered in three basics aspects: the tool wear occurring on the cutting tools; the quality of the machined surface; the geometric accuracy of the parts. This specific paper presents the study made in respect of the following: (i) The quality of the machined
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surface—the evaluation of the quality in a surface machined with this process will assess the process capabilities to produce industrial products, in terms of surface roughness; (ii) the geometric accuracy of the parts—through the evaluation of the geometric accuracy achieved with this process, the capabilities of the process will be accessed to produce the necessary parts within the required tolerances. In the following section the independent variables (factors) and respective levels will be identified, and the characterisation of the response (dependent) variables will be carried out.
2. Experimental screening In the factorial DoE methodology the process variables are named ‘‘factors’’. For the screening design and analysis procedure 15 different factors were identified as being important in the plaster machining process using a robotic system. In the identification of factors all the possible variables that could influence the surface quality and the geometric accuracy of the end product were considered. For the purposes of this screening methodology, each factor was evaluated at two different levels. The two levels correspond to two different values/characteristics of the factor. The lowest and the maximum values are within the range of values in which the factor can work. In Table 1 the factors considered in this screening analysis procedure and their respective levels are listed.
Table 3 Scale for surface quality and geometric accuracy analysis Scale 1
2
3
4
5
6
Bad
Not acceptable
Acceptable with rework
Acceptable
Good
Excellent
Table 2 identifies the response variables used in the screening procedure, and shows the scale used in the evaluation of each one. The evaluation of the surface roughness generated during the machining was made visually using the scale presented in Table 3. Because of the surface softness of the plaster material, analysing the surface using traditional contact probes was not possible. The evaluation of surface flatness was made using the same scale as presented in Table 3. Figs. 1 and 2 show the graphical definitions of the flatness and roughness concepts, respectively. The flatness was evaluated through the measurement of the distance between two parallel planes that limited the top and the bottom levels of the machined surface. Through this concept the best
Table 1 Factors and levels in the screening process Factors
Step-over (mm) Step-down (mm) Tool flute angle (8) Feed-rate (m/min) Spindle-speed (rpm) Lead/lag angle (8) Cutting strategy Tool material Tool length (mm) Machining table Machining direction Block dimensions (mm) Machining time (min) Arm-extension (mm) Plaster material
Levels Low
High
2 2 30 2 5000 0 Conventional High-speed-steel 20 Horizontal Horizontal 100 50 800 (retracted) Molda 6
6 5 40 12 10 000 10 Climb Solid carbide 50 Vertical Vertical 800 150 2 000 (extended) Newcast 71
Fig. 1. Flatness definition.
Table 2 Response variables Response variables
Scales
Surface quality Geometric accuracy
Roughness analysis Flatness analysis
Fig. 2. Surface roughness definition,.
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Table 4 Experimental design Factors
Experiment number 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
(1) Lead/lag angle (2) Step-down (3) Flute angle (4) Feed-rate (5) Cutting strategy (6) Arm-extension (7) Block size (8) Tool material (9) Tool length (10) Machining table (11) Machine direction (12) Spindle-speed (13) Machining time (14) Step-over (15) Plaster material
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
surface flatness corresponds to the smallest distance between these planes. The surface roughness was evaluated through the visual analysis of the maximum roughness (RZ max). 2.1. Screening design Screening designs are specifically constructed to allow testing of the largest number of main effects with the least number of tests. The screening experimental design was carried out with the software ‘‘Statistica, version 5.1’’, using Plackett–Burman designs. The 16 experiments were established and a random sequence order was generated, as a way to minim‘ the possibility that some systematic changes in the dependent (response) variables over the consecutive runs could bias the results. Table 4 shows the design generated by the software for this screening procedure. In each experiment one of the two levels for the 15 different factors are identified through a 1 or a 1 value. The 1 corresponds to the lower level of the factor and the 1 to the higher level. The results obtained in the 16 experiments are presented in Table 5. 2.2. Screening analysis The screening analysis was made in order to evaluate the statistical ‘‘significance’’ of the selected 15 (independent variables) factors, in each of the two dependent (response) variables. The following two sections will present the analysis of the surface quality and geometric accuracy, respectively. The analysis was made initially through a Pareto chart of effects. The analysis was complemented using the ANOVA table in order to assess the statistical validity of the analysis. The graphical representation of the normal probability distribution of residuals was also
carried out in order to verify that the ANOVA requirements were met. 2.2.1. Surface quality analysis The Pareto chart for the surface roughness (see Fig. 3) shows that the more significant factors are lead/lag angle, feed-rate and the arm-extension. As was expected, lead/lag angle has the largest effect on surface quality. As can be seen in Fig. 3, the parameter value (effect) of the lead/lag angle factor is negative, thus the higher lead/lag angle values correspond to higher surface roughness, and consequently the worst surface quality. Table 6 presents the ANOVA table for the three factors selected previously through the Pareto chart analysis. As indicated by the asterisks (using the F ‘‘Fisher’’ test) all three factors are statistically significant. Table 5 Experimental results Experiment number
Surface roughness (16)
Surface flatness (16)
4 7 14 6 12 11 13 3 1 8 15 10 5 16 2 9
1.00 1.00 4.00 1.00 3.00 2.00 2.00 1.00 1.00 1.00 2.00 6.00 1.00 3.00 1.00 2.00
3.00 1.00 4.00 2.00 3.00 1.00 2.00 1.00 1.00 4.00 1.00 5.00 1.00 2.00 3.00 2.00
J.F.C.P. Antunes Simo˜ es et al. / Journal of Materials Processing Technology 135 (2003) 235–241
238
Fig. 3. Pareto chart (surface roughness).
Table 6 ANOVA table (surface roughness)a
Table 7 ANOVA table (surface flatness)
Factors
Factors
ANOVA—surface roughness (16) SS
(1) Lead/lag angle (4) Feed-rate (6) Arm-extension Error Total SS a
16.000 4.000 4.000 6.000 30.000
d.f. 1 1 1 12 15
MS 16.000 4.000 4.000 0.500
F a
32.000 8.000a 8.000a
(4) Feed-rate (6) Arm-extension Error Total SS a
ANOVA—surface flatness (16) SS
d.f.
MS
F
16.00000 4.00000 5.00000 25.00000
1 1 13 15
16.00000 4.00000 0.38462
55.46667a 10.40000a
F0:05;1;13 ¼ 4:67 (Fisher distribution).
F0:05;1;12 ¼ 4:75 (Fisher distribution).
2.2.2. Geometric accuracy analysis The Pareto chart for the surface flatness (see Fig. 4) shows that the more significant factors are feed-rate and the armextension. Feed-rate revealed the largest effect on the surface flatness. The effect of the feed-rate factor is negative,
thus lower surface flatness, and consequently worse geometric accuracy, corresponds to higher feed-rate values. Table 7 presents the ANOVA table for the two factors selected previously through the Pareto chart analysis. As indicated by the asterisks (using the F ‘‘Fisher’’ test), both factors are statistically significant.
Fig. 4. Pareto chart (surface flatness).
J.F.C.P. Antunes Simo˜ es et al. / Journal of Materials Processing Technology 135 (2003) 235–241
239
Fig. 5. Illustrating the loss of one degree of freedom: ‘‘Gimbal Lock’’.
3. 5-axis machining operations As a way to optimise the robotic systems capabilities, the use of 5-axis milling strategies was investigated. The six degrees of freedom of the robot used in this research [3,4] gave, in theory, the ability to use this equipment in advanced machining operations. During the initial experimental tests performed with the use of lead/lag (measured in the feed direction) and tilt angles (measured perpendicularly to the feed direction), a problem referenced as ‘‘Gimbal Lock’’ singularity was detected. This is a term derived from a mechanical problem that arises in the gimbal mechanism used to support a compass or gyroscope. This device generally consists on three concentric frames or rings, where under certain rotations a degree of freedom is lost; the mechanism is said to exhibit ‘‘Gimbal Lock’’. Supposing, for example, that the robot operator uses the above parameterisation to set up an arbitrary orientation. First, he/she applies a rotation about X, then another one about Y and finally a rotation about Z in order to move the cutting tool into a required orientation. Suppose further that during this process the robot operator specifies a rotation about Y of p/2. He/she will discover that the subsequent rotation about the Z-axis has an effect that is equivalent to rotating about the X-axis initially. The effect of the rotation about Y of p/2 is to rotate the X-axis to X0 , which is aligned with the Z-axis (see Fig. 5). Consequently any rotation about Z of y3 could have been achieved by a rotation about X of y1. Effectively, in this configuration with the X and the Zaxes aligned, it is impossible to rotate about the X-axis. In order to avoid the ‘‘Gimbal Lock’’ restriction, in the robot set-up for 5-axis machining a world co-ordinate system should be defined, which eliminates the successive 908 rotation characteristics in the 3-axis set-up methodology. To achieve this robot set-up specification the world coordinate can be, for example, a simple offset of the base co-ordinate system. In this case it will be important to adjust
the CAM software correctly for the tool orientation in relation to this world co-ordinate system. Using this approach it is possible to run a machining toolpath with the specification of positive lead/lag angles, and test the effect of this factor on the surface quality.
4. Surface quality and geometric accuracy modulation In order to detail precisely the influence of the lead/lag angle, a set of experiments to evaluate the effect of this factor on the surface roughness was established. Table 8 shows the values of the lead/lag angle tested, as well as the surface roughness obtained in each experiment. The values tested on the lead/lag angle were selected according to previous tests on 5-axis machining [5,6]. The results indicate that the lead/lag angle has a considerable effect on surface roughness. Lead/lag angles other than 08 produce machining surfaces with high roughness values. The effects of the feed-rate and arm-extension are discussed in the following section. The effect of both factors in the surface roughness is compounded by the effect of the same factors in the surface flatness. The results for feed-rate and arm-extension, obtained with the analysis of the surface flatness, can be used to estimate simultaneously the results for the analysis of the surface roughness. Table 8 Surface roughness versus lead/lag angle Lead/lag values (8)
Surface roughness (16)
0 þ1 þ3 þ5 þ10
6 2 1 1 1
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4.1. Mathematical modulation
Table 9 Experimental conditions and results
The analysis of the geometric accuracy of the plaster parts was based on two factors, the feed-rate and the arm-extension. These two factors were identified in the previous screening analysis as the most significant factors with regard to the geometric accuracy response variable. The final objective with this work is the specification of a mathematical equation to express the effects of feed-rate (F) and arm-extension (L) on the surface flatness (P) of a plaster block. The proposed relationship between the machining response (surface flatness) and the independent variables can be represented by the following function:
Trial number
Feed-rate, F (m/min)
Arm-extension, L (mm)
Surface flatness (16)
1 2 3 4 5 6 7 8
2 12 2 12 7 7 7 7
800 800 2000 2000 1400 1400 1400 1400
5 2 3 1 2 2 2 2
P ¼ f ðF; LÞ
(1)
The first order equation can be written as y ¼ b0 x0 þ b1 x1 þ b2 x2 þ b12 x1 x2 þ e
(2)
where y is the measured surface flatness (measured with the scale defined in Table 3); x0 ¼ 1 (dummy variable); x1 ; x2 , respectively, the feed-rate (m/min) and the arm-extension (mm), x1x2 the interaction between x1 and x2; e assumed to be a normally distributed uncorrelated random error with zero mean and constant variance; b0, b1, b2, b12 the model parameters. To develop the mathematical equation, a factorial design consisting of eight experiments was conducted. Four experiments constitute a 22 factorial design, with an added centre point repeated four times. The added centre points were used to estimate pure error. Table 9 shows the experimental cutting conditions together with the obtained surface flatness values. The ANOVA table for the two factors, feed-rate and arm-extension, indicated that both factors (feed-rate and
arm-extension) were statistically significant. This table also indicated that the effect of the interaction of the two factors is not statistically significant. The mathematical equation representing the first-order model for surface flatness, based on the eight experiments, is shown as follows: y ¼ 5:8750 0:2500x1 0:00125x2
(3)
where y is the estimate response for the surface flatness. Eq. (3) shows that the surface flatness decreases with the increase of feed-rate and arm-extension. This equation also shows that the feed-rate has the most dominant effect on the geometric accuracy. It was verified that using this equation the predicted values give a good estimation of the experimental results and the deviation between the two values can be accepted for the purpose of the surface flatness prediction. Eq. (3) was used to develop surface flatness contours in the feed-rate and arm-extension (see Fig. 6). These contours help to predict the geometric accuracy at any zone of the experimental domain.
Fig. 6. Surface flatness contours.
J.F.C.P. Antunes Simo˜ es et al. / Journal of Materials Processing Technology 135 (2003) 235–241
5. Conclusions The work presented in this paper characterises the capabilities of the robotic system to produce plaster moulds and models by milling operations. The experimental designs and the mathematical calculations were carried out with the software ‘‘Statistica, version 5.1’’. In the second section of this paper the screening method for the selection of the most important factors is presented. The experimental design was made according to the Plackett–Burman design. It was verified in this study that 1. Surface roughness—the most statistically significant factors to this response variable are lead/lag angle, feedrate and arm-extension. 2. Surface flatness—the most statistically significant factors identified to this response variable were the feed-rate and the arm-extension. In this paper the capabilities to perform 5-axis machining toolpaths was discussed. As was expected, this type of operations can be executed in the robotic system, giving an important technical advantage regarding the machining operations. Because of the controller system installed in this particular robot ‘‘Gimbal Lock’’ singularity was investigated and characterised. Based on this study another set-up strategy regarding the definition of the co-ordinate system during 5-axis milling operations was developed. This set-up strategy minimises the problems related to ‘‘Gimbal Lock’’ singularity. The surface quality and the geometric accuracy modulation on plaster parts was investigated. This work was carried out using the factorial ‘‘design and analysis of experiments’’ methodology. The results showed, in regard to the lead/lag angle, that the surface quality became unacceptable for angles other than 08. This problem can be explained by the specific movements in the robot displacement, generated by rotations in the robot joints, instead of the typical linear movements of the machining centres. It will be important to develop a further study to compare the results achieved in the machining of sculptured surfaces using slot-mill and the typical ball nose cutting tools.
241
The mathematical modulation of the geometric accuracy of the plaster parts was carried out in terms of feed-rate and arm-extension. The mathematical equation generated during this study was used to develop flatness contours in the feedrate and arm-extension, which can help to predict the geometric accuracy at any zone of the experimental domain.
Acknowledgements The authors wish to acknowledge Staffordshire University, and the Sandvik Portuguesa and Ceramic Product Development (CPD) for the use of equipment and resources during the period of this work. References [1] T.J. Coole, D.G. Cheshire, D.J. Newman, Excessive tool wear and moisture content of plaster in ceramic plaster machining, Brit. Ceram. Trans. Mag. 98 (3) (1999) 151–155. ISSN 0967-9782. [2] J.F.C.P. Antunes Simo˜ es, T.J. Coole, D.G. Cheshire, R.M.D. Mesquita, The analysis of tool wear in the machining of plaster material prototypes, in: Proceedings of the International Symposium on Automotive Technology and Automation (ISATA 2000), Advanced Manufacturing—Modular Manufacturing, Supplier Integration, Production Planning, Dublin, Ireland, 2000, pp. 149–156. ISBN 1902856-16-3. [3] T.J. Coole, D.G. Cheshire, R.M.D. Mesquita, J.F.C.P. Antunes Simo˜ es, Analysis of robot system capabilities in machining of full scale prototypes for sanitary ware industry, Brit. Ceram. Trans. Int. J. 99 (4) (2000) 175–178. ISSN 0967-9782. [4] J.F.C.P. Antunes Simo˜ es, T.J. Coole, D.G. Cheshire, R.M.D. Mesquita, Analysis of a robot system capabilities in the machining of full-scale prototypes, in: Proceedings of the International Symposium on Automotive Technology and Automation, Advanced Manufacturing in the Automotive Industry, Vienna, Austria, 1999, pp. 93–100. ISBN 1-902856-02-3. [5] Baptista, M.S.O. Rui, S. Antunes, C.P. Jose´ Filipe, 3- and 5-axis milling of sculptured surfaces, J. Mater. Process. Technol. 103 (3) (2000). ISSN 0924-0136. [6] Baptista, M.S.O. Rui, S. Antunes, C.P. Jose´ Filipe, The implementation and analysis of a 5-axis milling operation, in: Proceedings of the Fourth International Symposium on Product Development in Engineering Education (PDEE’98), Cologne, Germany, 1998. ISBN 300-003754-3.
Analysis of multi-axis milling in an anthropomorphic robot, using the design of experiments methodology J.F.C.P. Antunes Simo˜esb, T.J. Coolec, D.G. Cheshirea,*, Anto´nio R. Piresd a
School of Engineering and Advanced Technology, Staffordshire University, Stafford, UK b Escola Superior de Tecnologia, Instituto Polite´cnico de Setu´bal, Setu´bal, Portugal c Faculty of Technology, Buckinghamshire Chilterns University, Buckingham, UK d Escola Superior de Tecnologia, Instituto Polite´cnico de Setu´bal, Setu´bal, Portugal
Abstract Currently, the concept of advanced machining technologies (AMT) includes different processes such as high-speed machining, multi-axis machining, etc. The common characteristic between these technologies is that they aim to improve the cutting process. Research done in the past has mainly concentrated on metal machining. In this present research, efforts are made to apply these techniques to the ceramic industry. This work forms part of the ongoing research at Staffordshire University into the application of CNC machining techniques in the production of models and moulds, with regards to the production of tableware and sanitaryware items. This paper focuses on the analysis of multi-axis milling using an anthropomorphic robot to produce near net shape plaster parts. The robotic system was run based on a specific set-up that allows multi-axes toolpaths and avoids ‘‘Gimbal Lock’’ singularity. The milling tests were carried out on plaster using conventional cutting tools (slot-mills). The design of experiments (DoE) was implemented using factorial techniques. The surface quality and geometric accuracy of the plaster parts were the response variables used to characterise the part quality and test the levels of acceptability of lead/lag angle, feed-rate and robot arm-extension. A mathematical equation based on the geometric accuracy was developed and used to plot flatness contours. Through these plots it is easy to define other possible combinations of feed-rate and robot arm-extension that can be used. # 2002 Published by Elsevier Science B.V. Keywords: Multi-axis milling; Plaster; Robot
1. Introduction The plaster machining operation executed on a robot was a relatively unknown process before this research. The technical knowledge available before this work, regarding this process, was reduced to a few experiments and the initial studies conducted during the CRAFT project BE-S5-2523. Also, with the new aspect of the use of the robotic system, the machining of plaster was also a process not very well studied, including the tool wear occurring during plaster machining [1,2]. All the characteristics presented earlier illustrate the ‘‘lack of knowledge’’ conditions in the initial phase of this research, and indicate the necessity to initialise the research * Corresponding author. E-mail addresses: [email protected] (J.F.C.P. Antunes Simo˜es), [email protected] (T.J. Coole), [email protected] (D.G. Cheshire), [email protected] (A.R. Pires).
0924-0136/02/$ – see front matter # 2002 Published by Elsevier Science B.V. PII: S 0 9 2 4 - 0 1 3 6 ( 0 2 ) 0 0 9 0 8 - 1
predicting all the possible important process variables. In order to scan the more important variables involved with this machining operation the factorial design of experiment (DoE) methodology was used. With this factorial design and analysis approach it was possible to optimise the use of the experimental resources, during the study of the main variables effect. The work was divided into several phases, including the choice of variables and respective levels, selection of response variables, choice of experimental design, experimental work, and finally the statistical analysis of data. As a fundamental aspect of the factorial DoE methodology, the capability of the plaster machining operation executed on a robot was identified, as the problem to be analysed through this study. This process capability was considered in three basics aspects: the tool wear occurring on the cutting tools; the quality of the machined surface; the geometric accuracy of the parts. This specific paper presents the study made in respect of the following: (i) The quality of the machined
236
J.F.C.P. Antunes Simo˜ es et al. / Journal of Materials Processing Technology 135 (2003) 235–241
surface—the evaluation of the quality in a surface machined with this process will assess the process capabilities to produce industrial products, in terms of surface roughness; (ii) the geometric accuracy of the parts—through the evaluation of the geometric accuracy achieved with this process, the capabilities of the process will be accessed to produce the necessary parts within the required tolerances. In the following section the independent variables (factors) and respective levels will be identified, and the characterisation of the response (dependent) variables will be carried out.
2. Experimental screening In the factorial DoE methodology the process variables are named ‘‘factors’’. For the screening design and analysis procedure 15 different factors were identified as being important in the plaster machining process using a robotic system. In the identification of factors all the possible variables that could influence the surface quality and the geometric accuracy of the end product were considered. For the purposes of this screening methodology, each factor was evaluated at two different levels. The two levels correspond to two different values/characteristics of the factor. The lowest and the maximum values are within the range of values in which the factor can work. In Table 1 the factors considered in this screening analysis procedure and their respective levels are listed.
Table 3 Scale for surface quality and geometric accuracy analysis Scale 1
2
3
4
5
6
Bad
Not acceptable
Acceptable with rework
Acceptable
Good
Excellent
Table 2 identifies the response variables used in the screening procedure, and shows the scale used in the evaluation of each one. The evaluation of the surface roughness generated during the machining was made visually using the scale presented in Table 3. Because of the surface softness of the plaster material, analysing the surface using traditional contact probes was not possible. The evaluation of surface flatness was made using the same scale as presented in Table 3. Figs. 1 and 2 show the graphical definitions of the flatness and roughness concepts, respectively. The flatness was evaluated through the measurement of the distance between two parallel planes that limited the top and the bottom levels of the machined surface. Through this concept the best
Table 1 Factors and levels in the screening process Factors
Step-over (mm) Step-down (mm) Tool flute angle (8) Feed-rate (m/min) Spindle-speed (rpm) Lead/lag angle (8) Cutting strategy Tool material Tool length (mm) Machining table Machining direction Block dimensions (mm) Machining time (min) Arm-extension (mm) Plaster material
Levels Low
High
2 2 30 2 5000 0 Conventional High-speed-steel 20 Horizontal Horizontal 100 50 800 (retracted) Molda 6
6 5 40 12 10 000 10 Climb Solid carbide 50 Vertical Vertical 800 150 2 000 (extended) Newcast 71
Fig. 1. Flatness definition.
Table 2 Response variables Response variables
Scales
Surface quality Geometric accuracy
Roughness analysis Flatness analysis
Fig. 2. Surface roughness definition,.
J.F.C.P. Antunes Simo˜ es et al. / Journal of Materials Processing Technology 135 (2003) 235–241
237
Table 4 Experimental design Factors
Experiment number 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
(1) Lead/lag angle (2) Step-down (3) Flute angle (4) Feed-rate (5) Cutting strategy (6) Arm-extension (7) Block size (8) Tool material (9) Tool length (10) Machining table (11) Machine direction (12) Spindle-speed (13) Machining time (14) Step-over (15) Plaster material
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
surface flatness corresponds to the smallest distance between these planes. The surface roughness was evaluated through the visual analysis of the maximum roughness (RZ max). 2.1. Screening design Screening designs are specifically constructed to allow testing of the largest number of main effects with the least number of tests. The screening experimental design was carried out with the software ‘‘Statistica, version 5.1’’, using Plackett–Burman designs. The 16 experiments were established and a random sequence order was generated, as a way to minim‘ the possibility that some systematic changes in the dependent (response) variables over the consecutive runs could bias the results. Table 4 shows the design generated by the software for this screening procedure. In each experiment one of the two levels for the 15 different factors are identified through a 1 or a 1 value. The 1 corresponds to the lower level of the factor and the 1 to the higher level. The results obtained in the 16 experiments are presented in Table 5. 2.2. Screening analysis The screening analysis was made in order to evaluate the statistical ‘‘significance’’ of the selected 15 (independent variables) factors, in each of the two dependent (response) variables. The following two sections will present the analysis of the surface quality and geometric accuracy, respectively. The analysis was made initially through a Pareto chart of effects. The analysis was complemented using the ANOVA table in order to assess the statistical validity of the analysis. The graphical representation of the normal probability distribution of residuals was also
carried out in order to verify that the ANOVA requirements were met. 2.2.1. Surface quality analysis The Pareto chart for the surface roughness (see Fig. 3) shows that the more significant factors are lead/lag angle, feed-rate and the arm-extension. As was expected, lead/lag angle has the largest effect on surface quality. As can be seen in Fig. 3, the parameter value (effect) of the lead/lag angle factor is negative, thus the higher lead/lag angle values correspond to higher surface roughness, and consequently the worst surface quality. Table 6 presents the ANOVA table for the three factors selected previously through the Pareto chart analysis. As indicated by the asterisks (using the F ‘‘Fisher’’ test) all three factors are statistically significant. Table 5 Experimental results Experiment number
Surface roughness (16)
Surface flatness (16)
4 7 14 6 12 11 13 3 1 8 15 10 5 16 2 9
1.00 1.00 4.00 1.00 3.00 2.00 2.00 1.00 1.00 1.00 2.00 6.00 1.00 3.00 1.00 2.00
3.00 1.00 4.00 2.00 3.00 1.00 2.00 1.00 1.00 4.00 1.00 5.00 1.00 2.00 3.00 2.00
J.F.C.P. Antunes Simo˜ es et al. / Journal of Materials Processing Technology 135 (2003) 235–241
238
Fig. 3. Pareto chart (surface roughness).
Table 6 ANOVA table (surface roughness)a
Table 7 ANOVA table (surface flatness)
Factors
Factors
ANOVA—surface roughness (16) SS
(1) Lead/lag angle (4) Feed-rate (6) Arm-extension Error Total SS a
16.000 4.000 4.000 6.000 30.000
d.f. 1 1 1 12 15
MS 16.000 4.000 4.000 0.500
F a
32.000 8.000a 8.000a
(4) Feed-rate (6) Arm-extension Error Total SS a
ANOVA—surface flatness (16) SS
d.f.
MS
F
16.00000 4.00000 5.00000 25.00000
1 1 13 15
16.00000 4.00000 0.38462
55.46667a 10.40000a
F0:05;1;13 ¼ 4:67 (Fisher distribution).
F0:05;1;12 ¼ 4:75 (Fisher distribution).
2.2.2. Geometric accuracy analysis The Pareto chart for the surface flatness (see Fig. 4) shows that the more significant factors are feed-rate and the armextension. Feed-rate revealed the largest effect on the surface flatness. The effect of the feed-rate factor is negative,
thus lower surface flatness, and consequently worse geometric accuracy, corresponds to higher feed-rate values. Table 7 presents the ANOVA table for the two factors selected previously through the Pareto chart analysis. As indicated by the asterisks (using the F ‘‘Fisher’’ test), both factors are statistically significant.
Fig. 4. Pareto chart (surface flatness).
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Fig. 5. Illustrating the loss of one degree of freedom: ‘‘Gimbal Lock’’.
3. 5-axis machining operations As a way to optimise the robotic systems capabilities, the use of 5-axis milling strategies was investigated. The six degrees of freedom of the robot used in this research [3,4] gave, in theory, the ability to use this equipment in advanced machining operations. During the initial experimental tests performed with the use of lead/lag (measured in the feed direction) and tilt angles (measured perpendicularly to the feed direction), a problem referenced as ‘‘Gimbal Lock’’ singularity was detected. This is a term derived from a mechanical problem that arises in the gimbal mechanism used to support a compass or gyroscope. This device generally consists on three concentric frames or rings, where under certain rotations a degree of freedom is lost; the mechanism is said to exhibit ‘‘Gimbal Lock’’. Supposing, for example, that the robot operator uses the above parameterisation to set up an arbitrary orientation. First, he/she applies a rotation about X, then another one about Y and finally a rotation about Z in order to move the cutting tool into a required orientation. Suppose further that during this process the robot operator specifies a rotation about Y of p/2. He/she will discover that the subsequent rotation about the Z-axis has an effect that is equivalent to rotating about the X-axis initially. The effect of the rotation about Y of p/2 is to rotate the X-axis to X0 , which is aligned with the Z-axis (see Fig. 5). Consequently any rotation about Z of y3 could have been achieved by a rotation about X of y1. Effectively, in this configuration with the X and the Zaxes aligned, it is impossible to rotate about the X-axis. In order to avoid the ‘‘Gimbal Lock’’ restriction, in the robot set-up for 5-axis machining a world co-ordinate system should be defined, which eliminates the successive 908 rotation characteristics in the 3-axis set-up methodology. To achieve this robot set-up specification the world coordinate can be, for example, a simple offset of the base co-ordinate system. In this case it will be important to adjust
the CAM software correctly for the tool orientation in relation to this world co-ordinate system. Using this approach it is possible to run a machining toolpath with the specification of positive lead/lag angles, and test the effect of this factor on the surface quality.
4. Surface quality and geometric accuracy modulation In order to detail precisely the influence of the lead/lag angle, a set of experiments to evaluate the effect of this factor on the surface roughness was established. Table 8 shows the values of the lead/lag angle tested, as well as the surface roughness obtained in each experiment. The values tested on the lead/lag angle were selected according to previous tests on 5-axis machining [5,6]. The results indicate that the lead/lag angle has a considerable effect on surface roughness. Lead/lag angles other than 08 produce machining surfaces with high roughness values. The effects of the feed-rate and arm-extension are discussed in the following section. The effect of both factors in the surface roughness is compounded by the effect of the same factors in the surface flatness. The results for feed-rate and arm-extension, obtained with the analysis of the surface flatness, can be used to estimate simultaneously the results for the analysis of the surface roughness. Table 8 Surface roughness versus lead/lag angle Lead/lag values (8)
Surface roughness (16)
0 þ1 þ3 þ5 þ10
6 2 1 1 1
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4.1. Mathematical modulation
Table 9 Experimental conditions and results
The analysis of the geometric accuracy of the plaster parts was based on two factors, the feed-rate and the arm-extension. These two factors were identified in the previous screening analysis as the most significant factors with regard to the geometric accuracy response variable. The final objective with this work is the specification of a mathematical equation to express the effects of feed-rate (F) and arm-extension (L) on the surface flatness (P) of a plaster block. The proposed relationship between the machining response (surface flatness) and the independent variables can be represented by the following function:
Trial number
Feed-rate, F (m/min)
Arm-extension, L (mm)
Surface flatness (16)
1 2 3 4 5 6 7 8
2 12 2 12 7 7 7 7
800 800 2000 2000 1400 1400 1400 1400
5 2 3 1 2 2 2 2
P ¼ f ðF; LÞ
(1)
The first order equation can be written as y ¼ b0 x0 þ b1 x1 þ b2 x2 þ b12 x1 x2 þ e
(2)
where y is the measured surface flatness (measured with the scale defined in Table 3); x0 ¼ 1 (dummy variable); x1 ; x2 , respectively, the feed-rate (m/min) and the arm-extension (mm), x1x2 the interaction between x1 and x2; e assumed to be a normally distributed uncorrelated random error with zero mean and constant variance; b0, b1, b2, b12 the model parameters. To develop the mathematical equation, a factorial design consisting of eight experiments was conducted. Four experiments constitute a 22 factorial design, with an added centre point repeated four times. The added centre points were used to estimate pure error. Table 9 shows the experimental cutting conditions together with the obtained surface flatness values. The ANOVA table for the two factors, feed-rate and arm-extension, indicated that both factors (feed-rate and
arm-extension) were statistically significant. This table also indicated that the effect of the interaction of the two factors is not statistically significant. The mathematical equation representing the first-order model for surface flatness, based on the eight experiments, is shown as follows: y ¼ 5:8750 0:2500x1 0:00125x2
(3)
where y is the estimate response for the surface flatness. Eq. (3) shows that the surface flatness decreases with the increase of feed-rate and arm-extension. This equation also shows that the feed-rate has the most dominant effect on the geometric accuracy. It was verified that using this equation the predicted values give a good estimation of the experimental results and the deviation between the two values can be accepted for the purpose of the surface flatness prediction. Eq. (3) was used to develop surface flatness contours in the feed-rate and arm-extension (see Fig. 6). These contours help to predict the geometric accuracy at any zone of the experimental domain.
Fig. 6. Surface flatness contours.
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5. Conclusions The work presented in this paper characterises the capabilities of the robotic system to produce plaster moulds and models by milling operations. The experimental designs and the mathematical calculations were carried out with the software ‘‘Statistica, version 5.1’’. In the second section of this paper the screening method for the selection of the most important factors is presented. The experimental design was made according to the Plackett–Burman design. It was verified in this study that 1. Surface roughness—the most statistically significant factors to this response variable are lead/lag angle, feedrate and arm-extension. 2. Surface flatness—the most statistically significant factors identified to this response variable were the feed-rate and the arm-extension. In this paper the capabilities to perform 5-axis machining toolpaths was discussed. As was expected, this type of operations can be executed in the robotic system, giving an important technical advantage regarding the machining operations. Because of the controller system installed in this particular robot ‘‘Gimbal Lock’’ singularity was investigated and characterised. Based on this study another set-up strategy regarding the definition of the co-ordinate system during 5-axis milling operations was developed. This set-up strategy minimises the problems related to ‘‘Gimbal Lock’’ singularity. The surface quality and the geometric accuracy modulation on plaster parts was investigated. This work was carried out using the factorial ‘‘design and analysis of experiments’’ methodology. The results showed, in regard to the lead/lag angle, that the surface quality became unacceptable for angles other than 08. This problem can be explained by the specific movements in the robot displacement, generated by rotations in the robot joints, instead of the typical linear movements of the machining centres. It will be important to develop a further study to compare the results achieved in the machining of sculptured surfaces using slot-mill and the typical ball nose cutting tools.
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The mathematical modulation of the geometric accuracy of the plaster parts was carried out in terms of feed-rate and arm-extension. The mathematical equation generated during this study was used to develop flatness contours in the feedrate and arm-extension, which can help to predict the geometric accuracy at any zone of the experimental domain.
Acknowledgements The authors wish to acknowledge Staffordshire University, and the Sandvik Portuguesa and Ceramic Product Development (CPD) for the use of equipment and resources during the period of this work. References [1] T.J. Coole, D.G. Cheshire, D.J. Newman, Excessive tool wear and moisture content of plaster in ceramic plaster machining, Brit. Ceram. Trans. Mag. 98 (3) (1999) 151–155. ISSN 0967-9782. [2] J.F.C.P. Antunes Simo˜ es, T.J. Coole, D.G. Cheshire, R.M.D. Mesquita, The analysis of tool wear in the machining of plaster material prototypes, in: Proceedings of the International Symposium on Automotive Technology and Automation (ISATA 2000), Advanced Manufacturing—Modular Manufacturing, Supplier Integration, Production Planning, Dublin, Ireland, 2000, pp. 149–156. ISBN 1902856-16-3. [3] T.J. Coole, D.G. Cheshire, R.M.D. Mesquita, J.F.C.P. Antunes Simo˜ es, Analysis of robot system capabilities in machining of full scale prototypes for sanitary ware industry, Brit. Ceram. Trans. Int. J. 99 (4) (2000) 175–178. ISSN 0967-9782. [4] J.F.C.P. Antunes Simo˜ es, T.J. Coole, D.G. Cheshire, R.M.D. Mesquita, Analysis of a robot system capabilities in the machining of full-scale prototypes, in: Proceedings of the International Symposium on Automotive Technology and Automation, Advanced Manufacturing in the Automotive Industry, Vienna, Austria, 1999, pp. 93–100. ISBN 1-902856-02-3. [5] Baptista, M.S.O. Rui, S. Antunes, C.P. Jose´ Filipe, 3- and 5-axis milling of sculptured surfaces, J. Mater. Process. Technol. 103 (3) (2000). ISSN 0924-0136. [6] Baptista, M.S.O. Rui, S. Antunes, C.P. Jose´ Filipe, The implementation and analysis of a 5-axis milling operation, in: Proceedings of the Fourth International Symposium on Product Development in Engineering Education (PDEE’98), Cologne, Germany, 1998. ISBN 300-003754-3.