DOI 10.1007/s00170-003-1825-5 O R I G I N A L A R T I C L E
Chyn-Shu Deng · Jih-Hua Chin
Hole roundness in deep-hole drilling as analysed by Taguchi methods
Received: 27 March 2003 / Accepted: 10 June 2003 / Published online: 25 August 2004 Springer-Verlag London Limited 2004
Abstract This work investigates the roundness of holes by ap-plication of Taguchi methods to BTA deep-hole drilling with reference to process factors. Taguchi methods and statistical techniques are used in experimental layout, in the analysis of each control factor, and in prediction of the optimum setting for control factors. A set of confirmatory tests is then conducted to verify the estimated response. Influences of the control factors are discussed, and the levels of factors that produce holes of de-sired roundness with sufficient robustness are presented. Keywords BTA deep-hole drilling· Control factor · Roundness· Taguchi methods
Nomenclature
d Tool diameter, mm Shaft length, mm ∆z Feed rate, mm/rev n Rotational speed, rpm R Roundness error of hole, mm DF Degree of freedom SS Sum of squares F Fisher statistic V Mean square Percent contribution
1 Introduction
Deep-hole drilling is a complex machining process in which the ratio of hole depth to hole diameter exceeds 10. Hence the stiff-C.-S. Deng · J.-H. Chin
Department of Mechanical Engineering, National Chiao Tung University, Hsinchu, Taiwan, R.O.C. C.-S. Deng
Department of Mechanical Engineering, National Lien-Ho Institute of Technology, Miaoli, Taiwan, R.O.C.
ness of the tool shaft is weakened by its own length, which makes the tool shaft susceptible to deflection and thus causes inaccura-cies in the machined hole, affecting the roughness of the surface and the roundness of the hole. Often, the user must adjust various machining conditions to obtain a hole of high quality. It is al-ways desirable to configure suitable machining conditions to get optimised machining quality.
The quality of machining in deep-hole drilling has been studied under various machining conditions [1–5]. These stud-ies employed the one-variable-at-a-time technique, which is time consuming and incapable of yielding conclusions that are asso-ciated with a statistical level of confidence [6]. It is desirable to select a combination of optimum machining conditions to pro-duce holes of good quality. The Taguchi method is used here to study the multi-variable process and to serve the purpose of con-dition optimisation. This method is economical because fewer experiments are needed than required by the one-variable-at-a-time method; moreover, the conclusions can be associated with a statistical level of confidence [7, 8].
This work investigates the roundness of holes by application of Taguchi methods to BTA deep-hole drilling with reference to process factors. The machining conditions tool diameter, shaft length, feed rate and rotational speed influence the roundness of holes in deep-hole drilling. Five control factors were used in a modified L8 orthogonal array design. The signal-to-noise (S/N) ratios are derived from the lower-the-better roundness error because to obtain optimal machining quality, the minimum roundness error of a hole is desired. Therefore, the lower-the-better roundness error should be selected. An analysis of vari-ance (ANOVA) was performed to determine the effect of the control factors. The optimal level combination of control factors was selected from high S/N ratios. The final step is to predict and verify the quality characteristic.
2 Experimental technique
A series of experiments were performed on a retrofitted machine (Fig. 1) which can perform BTA deep-hole drilling to examine
Fig. 1. BTA drilling system
the dynamic effects of a long tool shaft on the roundness of a drilled hole. The machine has an external cutting fluid supply and internal chip transport. The tool head is screwed onto the tool shaft, and cutting fluid is supplied through the space between the tool shaft and the machined hole and then removed along with the chips through the tool shaft. The cross section of the tool shaft is round.
The workpiece material was AISI 1045 steel with dimen-sions ofφ 50 ×300 mm. The workpiece was drilled to a depth of 220 mm and cut into four equal pieces (about 50 mm long) after the drilling test.
An analysis of BTA drilling showed that the machining con-ditions tool diameter, shaft length, feed rate and rotational speed affect the quality of the hole profile. A tool of large diameter is screwed onto a shaft of large diameter (Appendix A), which cre-ates larger stiffness of shaft than a smaller tool diameter. The shaft length dimension corresponds to the tool diameter dimen-sion (Appendix A), but two-shaft lengths (1200 and 1600 mm)
Fig. 2. Roundness error of hole: 0.0075 mm. Tool diameter: 18.91 mm, shaft
length: 1600 mm, feed rate: 0.10 mm, rotational speed: 855 rpm, hole depth: 50 mm
were used to relate the shaft length to the hole quality charac-teristics. A higher feed rate or rotational speed creates a higher machining rate but degrades the quality of the hole profile [1]. After all the trials are completed, the roundness of the hole is measured along its length (50, 100, 150 and 200 mm). The in-strument for measuring roundness is the Mitutoyo (RA-2 type), which utilises the least square circle method (LSC) to express the hole profile. Figure 2 shows a sample of the roundness error of the hole.
3 Taguchi experiment: design and analysis
3.1 Orthogonal array experiment
Classical experimental design methods are time consuming. Many experiments must be performed when the number of con-trol factors is high. Taguchi methods [7] use a special design of orthogonal arrays to study the entire factor space with only a small number of experiments. Table 1 lists the five control fac-tors (four machining facfac-tors and one noise factor) and the two selected levels analysed in this study. The levels were assigned randomly and the limits used were determined from preliminary experiments. Table 2 specifies the experimental layout: 1 and 2 refer to the levels 1 and 2 of each control factor, respectively. A basic L8 orthogonal array can be established for use in this experimental analysis [7]. Furthermore, a two-level outer array was used to study the effect of the day-to-day variation (noise) of the BTA drilling process and to provide an independent esti-mate of experimental error in the testing of the main effects. Each experimental trial involved four-measurement data at each noise level. The roundness of the hole in the workpiece was meas-ured at depths of 50, 100, 150 and 200 mm. Table 3 lists the
Table 1. Control factors and levels for the BTA drilling experiment
Symbol Control factor Level 1 Level 2
A Tool diameter, d (mm) 18.91 26.40
B Shaft length, (mm) 1200 1600
C Feed rate,∆z (mm/rev) 0.05 0.10
D Rotational speed, n (rpm) 390 855
Table 2. Experimental layout
Trial no. Control factor Noise N
A B C D I II 1 1 1 1 1 ∗ ∗ ∗ ∗ ∗ ∗ 2 1 1 1 2 ∗ ∗ ∗ ∗ ∗ ∗ 3 1 2 2 1 ∗ ∗ ∗ ∗ ∗ ∗ 4 1 2 2 2 ∗ ∗ ∗ ∗ ∗ ∗ 5 2 1 2 1 ∗ ∗ ∗ ∗ ∗ ∗ 6 2 1 2 2 ∗ ∗ ∗ ∗ ∗ ∗ 7 2 2 1 1 ∗ ∗ ∗ ∗ ∗ ∗ 8 2 2 1 2 ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ Measurement data
data collected on two consecutive days. The table shows that the roundness errors on the two days differ slightly for a given level of control factor; the difference is due to experimental variation associated with dynamic effects in the BTA drilling process. 3.2 Signal-to-noise ratios
The Taguchi method uses the signal-to-noise (S/N) ratio instead of the average to convert the trial result data into a value for the characteristic in the optimum setting analysis. The S/N ratio re-flects both the average and the variation of the quality character-istic. The S/N ratio for the lower-the-better quality characteristic on the roundness error of the hole must be taken, because to ob-tain optimal machining quality the minimum roundness error of hole is desired. Therefore, the lower-the-better roundness error should be selected. The η value of the S/N ratio is calculated according to [7] η = −10 log10 1 r r i=1 y2i , (1)
Table 3. Roundness error of hole of BTA drilling for different day
Trial no. Factor and column no. Day Roundness error, R (mm)
A B C D 50 mm 100 mm 150 mm 200 mm 1 1 1 1 1 Day 1 0.0016 0.0015 0.0013 0.0014 Day 2 0.0018 0.0016 0.0015 0.0015 2 1 1 1 2 Day 1 0.0026 0.0025 0.0023 0.0022 Day 2 0.0025 0.0024 0.0022 0.0020 3 1 2 2 1 Day 1 0.0035 0.0033 0.0030 0.0031 Day 2 0.0036 0.0035 0.0032 0.0032 4 1 2 2 2 Day 1 0.0075 0.0069 0.0060 0.0060 Day 2 0.0071 0.0068 0.0065 0.0063 5 2 1 2 1 Day 1 0.0022 0.0020 0.0020 0.0018 Day 2 0.0020 0.0019 0.0017 0.0016 6 2 1 2 2 Day 1 0.0033 0.0034 0.0030 0.0029 Day 2 0.0035 0.0033 0.0034 0.0031 7 2 2 1 1 Day 1 0.0016 0.0015 0.0015 0.0014 Day 2 0.0019 0.0018 0.0016 0.0015 8 2 2 1 2 Day 1 0.0022 0.0020 0.0019 0.0016 Day 2 0.0020 0.0019 0.0019 0.0017
Table 4. Roundness error S/N ratios
Trial no. Control factor S/N ratios (dB)
A B C D Day 1 Day 2 1 1 1 1 1 η11= 56.75 η21= 55.89 2 1 1 1 2 η12= 52.38 η22= 52.83 3 1 2 2 1 η13= 49.81 η23= 49.42 4 1 2 2 2 η14= 43.68 η24= 43.50 5 2 1 2 1 η15= 53.96 η25= 54.86 6 2 1 2 2 η16= 50.01 η26= 49.56 7 2 2 1 1 η17= 56.47 η27= 55.35 8 2 2 1 2 η18= 54.26 η28= 54.53
Whereηij is theη value of each experiment, i = day of experiments, j =
trial no.
where r is the number of measurements made on the workpiece (in this study, r= 4) and yi is the measured roundness error
value. Based on the roundness error value in Table 3 and using Eq. 1, the S/N ratios are calculated and shown in Table 4; the table shows that a small roundness error creates a high S/N ratio and vice versa. For example, trial 4 in Table 3 had the largest roundness error on both days, which corresponded to the small-est S/N ratio in Table 4.
The influence of each control factor ( A, B, C, D and N) on the roundness error was analysed from the S/N ratio response table, which expresses the S/N ratio at each level of control factor. The control factor influence is determined by its level dif-ference values. A bigger control factor level difdif-ference means a greater influence on the roundness error of the hole. The in-fluence of level k of factor P and the level difference between level 1 and level 2 of factor P can be calculated as follows: Level kP=
ηPk
8 (2)
where level kP is the influence of level k (k= 1, 2) of factor P
(P= A, B, C, D and N) and ηPkis theη value of level k of
fac-tor P. Based on theη value in Table 4 and using Eqs. 2 and 3, the influence of all control factors and level differences can be calculated as shown in Table 5. The control factor influence hi-erarchy is C (feed rate), D (rotational speed), A (tool diameter) and B (shaft length). The control factor N (noise) has a weak in-fluence on the S/N ratio in BTA drilling. Furthermore, the feed rate is the most influential process factor since it has the highest level of difference among all control factors.
Response graphs more clearly plot the influence of each con-trol factor. A response graph shows the change of the S/N ratio when the control factor is changed from level 1 to level 2. The slope of the line determines the power of the control factor in-fluence. Figure 3 displays response graphs for all control factors of the BTA drilling process. The control factor settings that yield the best-quality characteristic can be determined from these re-sponse graphs. By selecting those factors with higher S/N ratio values, the best hole roundness from BTA drilling is achieved at:
• Tool diameter d = 26.40 mm, • Shaft length = 1200 mm,
Table 5. S/N ratio response table for roundness error
Symbol Control factor S/N ratio (dB) Level difference Level 1 Level 2 (dB)
A Tool diameter 50.53 53.63 3.10
B Shaft length 53.28 50.88 2.40
C Feed rate 54.81 49.35 5.46
D Rotational speed 54.06 50.09 3.97
N Day of the week (noise) 52.17 51.99 0.18
Fig. 3. Response graphs for hole roundness error
• Feed rate ∆z = 0.05 mm/rev, • Rotational speed n = 390 rpm, • Day 1 machining.
3.3 Analysis of variance
The purpose of the analysis of variance (ANOVA) is to determine the control factor that significantly affects the quality characteris-tic. Besides the significance of control factors, the significance of their interactions on the roundness error of the hole was studied as well. The interactions among control factors were between: • Tool diameter and noise (A × N ),
• Shaft length and noise (B × N ), • Feed rate and noise (C × N ), • Rotational speed and noise (D × N ).
The percentage contribution of each process factor in the total sum of squares can be used to evaluate the importance of the process factor change on the performance characteristic. Additionally, the F value, named after Fisher [9], can be used to determine which process factors significantly affect the per-formance characteristic. Usually the change in the process factor significantly affects the performance characteristic when F is large.
The ANOVA is used to analyse the experimental data as fol-lows [10]: SST= η2 ij− ηij 2 16 (4) SSP= η2 pk 2 8 − ηij2 16 (5) SSE= SST− SSP (6) VP= SSP DFP (7) FP= VP Ve (8) P= SSP− DFPVe SST , (9) where SSTis the total sum of squares; SSPis the sum of squares of factor P (P= A, B, C, D, N, A × N, B × N, C × N and D × N); SSEis the sum of squares of error;ηij is theη value of each experiment (i= 1 to 2, j = 1 to 8), as shown in Table 4; nPk is
theη value of level k (k = 1, 2) of factor P; DFPis the number of degrees of freedom of factor P; VPis the mean square of fac-tor P; FPis the F value of factor P; Veis the variance of pooled error (i.e., summed error); andPis the percentage contribution of factor P.
Based on the S/N ratio values (Table 4) and using Eqs. 4–9, the ANOVA for the roundness error of the holes can be calcu-lated as shown in Table 6. An estimate of the sum of squares for the pooled error can be obtained by pooling the sum of squares of factors with the lowest sum of squares – noise, inter-actions among the control factors, and error. The pooled error has
Table 6. ANOVA for roundness error (S/N analysis)
Factor Degrees of Sum of Mean square F value Contribution
( p) freedom (DFP) squares (SSP) (VP) (FP) (P) A 1 38.2542 38.2542 33.7249 14.50% B 1 23.0880 23.0880 21.9537 8.58% C 1 119.1372 119.1372 105.0315 46.09% D 1 63.0436 63.0436 55.5793 24.18% N 1 0.1190∗ A× N 1 0.0210∗ B× N 1 0.1332∗ C× N 1 0.0812∗ D× N 1 0.1521∗ Error 6 11.9709∗
Pooled error Eq. 11 (12.4774) (1.1343) (17.0146) (6.65%)
Total 15 256.0004 256.0004 100%
∗Indicates the sum of squares added together to estimate the pooled error sum of squares in parentheses.
11 degrees of freedom and a sum of squares of 12.4774, as indi-cated in parentheses. Hence the pooled error variance is 1.1343. The F value can be found using the ratio of mean square of a fac-tor to variance of pooled error. It can be seen from the F value result that the significant factors are the control factors in the order C (feed rate), D (rotational speed), A (tool diameter) and B (shaft length). Furthermore, the feed rate is the most significant drilling process since it contributes a greater percentage than all the other control factors. The conclusions in Tables 5 and 6 are consistent with the multiple performance characteristics.
3.4 Determination of optimal machining conditions
Tables 5 and 6 show that control factors have different influ-ences upon hole roundness in the BTA drilling process. Optimal machining conditions in terms of these control factors can be very easily determined from the S/N ratio response graphs in Fig. 3. Best hole roundness values are obtained at higher S/N ra-tios. Table 7 presents optimal machining conditions for a drilling workpiece. It is obvious that the noise has only weak influence on the machining quality, which shows the robustness of the BTA drilling process.
Equation 10 determines the S/N ratio at optimal settings of the main control factors. We can derive the expression for round-ness error Eq. 11 from Eq. 1 and calculate the roundround-ness error (Rcal) at optimal machining conditions:
ηcal = ¯η + ¯A2− ¯η +¯B1− ¯η +¯C1− ¯η +¯D1− ¯η = ¯A2+ ¯B1+ ¯C1+ ¯D1− 3¯η = 53.63 + 53.28 + 54.81 + 54.06 − 3 × 52.08 = 59.54 , (10) Rcal= 10−ηcal/20= 10−59.54/20= 0.0011 mm , (11)
whereηcal is the S/N ratio at optimal machining conditions, ¯η
is the average S/N ratio of all control factors, ¯A2is the average
Table 7. Optimal settings of control factors
Control factor Notation Setting
Tool diameter, d (mm) A2 26.40
Shaft length, (mm) B1 1200
Feed rate,∆z (mm/rev) C1 0.05
Rotational speed, n (rpm) D1 390
Day of the week (noise) N1 Day 1
S/N ratio when factor A (tool diameter) is at level 2, ¯B1 is the average S/N ratio when factor B (shaft length) is at level 1, ¯C1is the average S/N ratio when factor C (feed rate) is at level 1, and ¯D1is the average S/N ratio when factor D (rotational speed) is at level 1. Comparing Eq. 10 with Table 4, and Eq. 11 with Table 3 reveals that the optimal combination of A2B1C1D1N1 yielded the highest S/N ratio and the best hole quality.
3.5 Confirmatory test
A confirmatory test was performed after the optimal control fac-tor settings were determined. The confirmafac-tory test is a repetition of the experiment in BTA machining with the control factors set at optimal settings to achieve the predicted quality characteris-tics. Two trials at the optimal control factor settings were made in the confirmation test. The results of the confirmatory test are pre-sented in Table 8. The table shows that S/N ratios of 57.36 and 57.70 dB correspond to average roundness errors of 0.0014 and 0.0013 mm, respectively. Furthermore, the CI value of 5%
confi-Table 8. Confirmatory test results
Trial Roundness error, R (mm) Average roundness S/N ratios no. 50 mm 100 mm 150 mm 200 mm error Rver(mm) ηver(dB)
1 0.0015 0.0014 0.0012 0.0013 0.0014 57.36 2 0.0014 0.0013 0.0013 0.0012 0.0013 57.70
Table 9. Compare confirmatory test results and calculated value
Trial no. Confirmatory test results Calculated values Difference
Rver(mm) ηver(dB) Rcal(mm) ηcal(dB) |Rver− Rcal| |ηver− ηcal|
1 0.0014 57.36 0.0011 59.54 0.0003 2.18
2 0.0013 57.70 0.0011 59.54 0.0002 1.84
dence band with the confirmatory test trial number is calculated according to [7] CI= F0.05;1;ve× Ve× 1 neff+ 1 nver = 4.84 × 1.1343 × 5 8+ 1 2 = 2.49 (12) neff= ntol 1+ v= 8 1+ 4= 8 5, (13)
where F0.05;1;ve is the F value for 95% confidence [10],ve is
the degrees of freedom for pooled error, Ve is the variance of
pooled error, ntol is the total trial number,v is the total main
factor degrees of freedom, and nveris the confirmatory test trial
number. Table 9 shows some differences between the values ob-tained in the confirmatory test (Table 8) and the calculated values (Eq. 10) of the S/N ratios, but differences of 2.18 and 1.84 dB are under a 5% confidence band value of 2.49 dB, and thus at a 95% confidence level. Hence the optimal control factor settings were confirmed and further experiments could be performed or response roundness methods applied.
3.6 Discussion
In the factor space explored, the feed rate is the most significant process variable affecting hole roundness. The lower feed rate of 0.05 mm/rev was preferred to the higher feed rate of 0.1 mm/rev. A higher feed rate creates a larger chip and the tool bears a greater cutting force [11], producing a larger deflection of the tool shaft than that obtained at a lower feed rate. High rotational speed in-creases productivity; however, a low rotational speed of 390 rpm was preferred in the experiments because the tool shaft produces vibrations at higher speeds [1]. The tool diameter of 26.40 mm was preferred over the smaller diameter of 18.91 mm because the tool shaft with the larger diameter is stiffer than the one with the smaller diameter [12]. The 1200-mm-long shaft was preferred to the 1600-mm-long shaft because a shorter shaft is stiffer [12] and thus produces a smaller deflection.
4 Conclusions
Hole roundness in BTA deep-hole drilling was analysed by Taguchi methods. The hierarchy of process variables affecting roundness was established, and optimal cutting conditions for obtaining a hole with the desired roundness with a minimal num-ber of experimental runs were determined. Optimal cutting con-ditions were confirmed with a verification experiment.
The response table of the S/N ratios and the ANOVA analy-sis for all five control factors shows a very strong influence of feed rate (C), a strong influence of rotational speed (D) and tool diameter ( A), a moderate influence of shaft length (B) and no or little influence of noise (N) on the roundness of the hole formed in BTA drilling. The optimal control settings of A2B1C1D1N1 were found to yield the highest S/N ratios and optimal hole quality. At these optimal settings, the confirmatory test returned a roundness error within the 95% confidence interval.
Verifying sufficient roundness is especially important in two situations: when the machining phase represents an important portion of the production cost of a product and when a small number of very expensive workpieces are being machined. This study contributes to research in BTA drilling and describes a ro-bust approach to this process which offers a basis for further cost-effective machining processes.
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Appendix A
1. Lathe
SAN SHING SK26120 HEAVY-DUTY PRECISION LATHE BTA drilling system (Fig. 1)
2. BTA drilling
(a) Tool head: SANDVIK 420.6 series (b) Tool shaft
Type: SANDVIK 420.5-800-2
• Tool head: 18.91 mm, internal and external diameters of tool shaft: 11.5 and 17 mm, respectively; shaft length: 1600 mm
• Tool head: 26.40 mm; internal and external diameters of tool shaft: 14 and 22 mm, respectively; shaft length: 2600 mm Material: JIS SNCM 21 Density: 7860 kg/m3 Young’s modulus E: 206× 109Pa 3. Cutting fluid Type: R32 Densityf: 871 kg/m3
