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The effects of process faults and misalignments on the cutting force system and hole quality in reaming
ARTICLE IN PRESS
International Journal of Machine Tools & Manufacture 46 (2006) 1281–1290 www.elsevier.com/locate/ijmactool
The effects of process faults and misalignments on the cutting force system and hole quality in reaming Onik Bhattacharyya, Martin B. Jun, Shiv G. Kapoor, Richard E. DeVor Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, IL 61801, USA Received 5 September 2005; received in revised form 28 October 2005; accepted 3 November 2005 Available online 20 December 2005
Abstract A chip thickness and cutting force model that considers the deflection of the tool and the regenerative effect resulting from the presence of process faults and misalignments has been developed for the reaming process. Through a series of experiments, the model has been calibrated and validated. The model predicts tool displacement, torque, thrust, X and Y forces, and the average radius of the reamed hole. The developed model is also shown to be capable of being used as a basis for the on-line detection of process faults present in the system. r 2005 Elsevier Ltd. All rights reserved. Keywords: Reaming; Process faults; Hole quality; Force model; Cutting force system; Misalignments
1. Introduction In reaming, when process faults and misalignments are present, due to the flexibility of the tool, the reamer has a tendency to deflect towards the initial hole axis as it passes through the hole. This deflection changes the value of the process fault parameters and introduces additional forces into the system that can influence the quality of the reamed hole. In order to accurately predict final hole quality, the influence of all these factors need to be better understood. In an earlier paper [1], a static force model was developed that accurately predicts torque and thrust in reaming in the presence of process faults. However, the tool was assumed rigid and the chip load model did not consider the effects of tool deflection and regeneration. Though this model is quite useful for torque and thrust predictions, in order to be able to predict X and Y forces and consequently hole quality, the effect of process faults on tool deflection and regeneration [2,3] of the chip load must also be taken into account. Therefore an objective of this research is to extend the model developed by Bhattacharyya et al. [1] and incorporate the effects of tool deflection and regeneration due to process faults. A further Corresponding author. Tel.: +1 217 333 3432.
E-mail address: [email protected] (S.G. Kapoor). 0890-6955/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2005.11.002
objective of this paper is to better understand the effects of process faults and misalignments on reamed hole quality. The contents of the paper are as follows. First, the nature of the tool deflections resulting from process faults and misalignments will be experimentally investigated. The next section describes the development of the extended chip load and force model that incorporates the effects of tool deflection and regeneration. This is followed by the model validation section that details the experiments conducted. Finally, a section on hole quality is presented where the experimental process for measuring the hole quality is first described followed by the use of the extended deflection and force model to predict hole quality. 2. Reaming process in the presence of process faults In reaming, the reamer will have a tendency to follow the initial hole. This causes deflection of the tool when process faults and/or misalignments are present. This also causes a change in the net runout characteristics and additional forces due to this deflection will act on the reamer as it passes through the hole. In order to observe the effects of reamer deflection, experiments were conducted using a Mori Seiki TV-30, a light milling, drilling, and tapping center. During these
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experiments tool deflections and process faults were measured using a C1-A Lion Precision capacitance sensor, with 500 mm range and 0.1 mm resolution. A 4-component Kistler dynamometer, which measures torque, thrust, X, and Y forces, was used to measure cutting forces. Fig. 1 shows the experimental setup used. The parallel offset runout, spindle tilt, parallel offset runout locating angle, and spindle tilt locating angle [1] were measured by the capacitance sensor to be 0.0376 mm, 0.081, 67.781, and 80.181, respectively. The feed and speed were 0.19 mm/rev and 19.79 m/s, respectively. There was no spindle/hole axis misalignment present during the test. Fig. 2 shows the force profile and the tool displacement from one of the experiments. The amplitude of the signal measured by the capacitance sensor prior to engagement, seen in the displacement profile in Fig. 2a, corresponds to the runout that the tool is experiencing at the point of
measurement. This runout occurs as a result of a contribution of the effect of four runout parameters: parallel offset runout, spindle tilt, and their respective locating angles [4]. From Fig. 2a it can also be seen that when the tool becomes engaged in the hole, the runout decreases significantly as seen by the decrease in the amplitude of the signal measured by the capacitance sensor. But the runout of the reamer during engagement is still significant, suggesting that this runout will have an effect on both the cutting forces and hole quality. Fig. 2b shows that during engagement/cutting, the X and Y forces are non-zero as expected due to the presence of net runout [1]. Fig. 2b also illustrates that after cutting is complete, while the tool is still rotating in the hole, the X and Y forces have non-zero magnitudes essentially identical to the X and Y forces during cutting. This indicates that the presence of a reaction force acting on the tool is the major component of the X and Y forces and emphasizes the need to take this phenomenon into account in the modeling of the reaming process.
3. Modified chip load and force model formulation It has been shown for related processes [4,5], the X and Y forces have a strong influence on final hole quality. Therefore, for accurate prediction of hole quality, the effects of tool deflection and regeneration must be incorporated due to their significant impact on the X and Y forces. Furthermore, X and Y forces have been shown to be useful in the on-line detection of process faults in tapping [6], suggesting that the same may be true for reaming. Therefore, the chip load model formulation of [1] should be extended to incorporate the effects of tool deflection and regeneration. In this section, the definition of process faults is given first. The tool deflection is then expressed as a function of the process faults present. The radius of rotation for each flute is modified to include this deflection, and the chip thickness taken by each flute is extended to consider the effect of regeneration. Finally, the formulation of cutting force model is presented.
0.15
Before Engagement
After Cutting
During Cutting
0.1 Tool Displacement (mm)
X and Y Forces (N) ; Thrust (N); Torque (N*cm)
Fig. 1. Experimental setup for tool displacement measurement.
0.05 0 0.05 0.1 0.15 0.2
(a)
4
6
8
10
12
14
Time (s)
16
18
20
22
200 Before Engagement
After Cutting
During Cutting
150
Torque
100 Thrust X & Y Forces
50
0
50
4
6
8
(b)
Fig. 2. Force and tool displacement profile.
10
12
14
Time (s)
16
18
20
22
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3.1. Definition of process fault system in reaming
1283
Y Direction of Rotation
In a fashion similar to Gupta et al. [4], the reamer in the presence of tool/spindle process faults is shown in Fig. 3, where e is the parallel offset runout, l is the parallel offset runout locating angle, a is the angle of spindle tilt, and ft is the spindle tilt locating angle that defines the plane of the spindle tilt. The total net runout rn and its locating angle fL are found from the process faults parameters as rn ¼ ½e2 þ z2 tan2 a þ 2ze tan a cos ft 1=2 ,
Initial
FmY.
Hole Center
Yoff
(1)
x
FmX
tan b þ ft fR , fL ¼ l þ ðL zÞ R where e sin ft fR ¼ tan1 , z tan a þ e cos ft
Fp
y
Fxc
(2) X off Fyc
(3) φ
and z is the distance along the reamer as shown in Fig. 3, R is the radius of the reamer, L is the projection length, and b is the helix angle. The stationary coordinate frame is represented by X–Y–Z, while the rotating frame is represented by x–y–z.
rn
Initial Hole
L
X
Fig. 4. Deflection forces on reamer in the presence of process faults.
3.2. Incorporation of tool deflection into the chip load model Fig. 4 shows the bottom face of the reamer in the presence of a net runout, rn, and axis misalignment in the X direction, Xoff, and the Y direction, Yoff. There are two separate forces at work that influence reamer deflection: forces acting on the reamer due to net runout, Fp, and forces acting on the reamer due to axis misalignment, FmX and FmY. The forces Fxc and Fyc represent the cutting forces in the x and y direction of the rotating frame. The amount of deflection of the reamer in the direction opposing the net runout is denoted by dl while the deflection opposing the
misalignment in the X and Y direction are denoted by dmX and dmY. The reaction force Fp acting on the tool during cutting acts in the direction opposing the net runout and therefore rotates with the tool, while the reaction forces FmX and FmY act in the directions opposing the misalignments with their directions remaining constant. These forces can be expressed by F p ¼ kdl ,
(4)
F mX ¼ kdmX ;
F mY ¼ kdmY ,
(5)
where k is the stiffness of the tool and is given by, 3EI , (6) L3 where E is defined as the Young’s modulus of elasticity and I is the reamer cross-sectional moment of inertia. The parameters dl, dmX, and dmY are defined as follows: k¼
SPINDLE AXIS
x φt
y z
Coordinate Systems λ
X
Y x ε
y α Z z X-Y-Z : Stationary frame x-y-z : Rotating frame
REAMER TOOL AXIS
dl ¼ rrn ;
0oro1,
dmX ¼ rX off ;
dmY ¼ rY off ;
(7) 0oro1,
where the parameter r is determined through experimental data. The procedure for determining this coefficient is discussed later in the paper. As a result of the tool deflection, dl , the effective radius at which flute j cuts is given by, Rc ðjÞ ¼ ½ðrn dl Þ2 þ R2 þ 2ðrn dl ÞR cosðfL þ ðj 1Þyp Þ1=2 ,
Fig. 3. Reamer in the presence of process faults.
(8)
ð9Þ
where R is the radius of the tool, yp is the pitch angle. The chip thickness taken by the jth flute at an angular position
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The total chip load, Ac, at time t is the summation of tc(j,t) over all flutes and is given by
yðtÞ due to the feeding of the tool is then given by tcm ðj; tÞ ¼ Rc ðjÞ ½Rh þ ðX off dmX Þ sin yðtÞ þ ðY off dmY Þ cos yðtÞ,
ð10Þ
Ac ¼
where Rh is the radius of the initial hole.
Due to the effect of process faults, the position of each flute is different at an arbitrary angular position of the reamer yðtÞ, and the jth flute may not necessarily remove the same amount of material as its predecessors, as shown in Fig. 5. It is important to note that the amount of material removed by the jth flute depends on the positions of the previous flutes at the same angular position. The jth flute not only removes the amount taken by the feeding of the tool (denoted as tcm ðj; tÞ in Fig. 5) but also removes the materials left by the previous flutes (denoted as tcm ðj; tÞ tcm ðj m; t mT Þ) due to process faults, where m goes from 1 to the number of flutes N f and T is the tooth passing period, assumed here to be constant. In order to determine the material left by the previous flutes and add it to the total chip thickness, two cases must be considered. For case 1, there is no material left by the previous flute, i.e., tcm ðj; tÞ tcm ðj m; t mTÞo0. However, for case 2, since the position of the previous flute is such that the radius of cut is smaller than that of the current flute, i.e., tcm ðj; tÞ tcm ðj m; t mT Þ40, additional chip thickness must be added. The total chip thickness taken by the jth flute must also include the materials left by the previous flutes and can be expressed as tc ðj; tÞ ¼ tcm ðj; tÞ þ Max½0; tcm ðj; tÞ tcm ðj 1; t TÞ N f 1 X
f t tc ðj; tÞ,
(13)
j¼1
3.3. Effect of regeneration on chip load model
þ
Nf X
Maxf0; Min½tcm ðj; tÞ tcm ðj ðm 1Þ;
m¼2
t ðm 1ÞTÞ; tcm ðj; tÞ tcm ðj m; t mTÞg, ð11Þ where tcm ðj m; t mTÞ is written as tcm ðj m; t mT Þ ¼ Rc ðj mÞ ½Rh ðt mTÞ þ X off sin yðtÞ þ Y off cos yðtÞ. ð12Þ
where ft varies due to the regeneration caused by the longitudinal vibration qz of the tool, and is expressed by ft ¼
fr þ qz ðtÞ qz ðt TÞ. Nf
For the longitudinal vibration, the tool is modeled as a continuous system fixed at one end and free at the other. The axial force (thrust) is assumed to act on the tool at the free end. The governing equation for the longitudinal vibration of the tool, modeled as a continuous system, is given by d2 q ¼ f z, (15) dz2 where fz represents the force in the z direction [7]. The governing equation for the longitudinal vibration is solved using the finite element method.
mq€ z þ cq_ z þ EAðzÞ
3.4. Extended cutting force model In the mechanistic approach to force modeling the normal and frictional forces, as defined by Chandrasekharan et al. [8], are proportional to the chip load, Ac, and are given by F n ¼ K n Ac ,
(16)
F f ¼ K f Ac ,
(17)
Kn and Kf are proportionality constants commonly referred to as the specific cutting energies that are estimated through model calibration. Assuming Stabler’s Rule and following the oblique model development in a fashion similar to Chandrasekharan [8], it is known that the magnitude of the threedimensional elemental oblique cutting forces, thrust Fth, tangential Ftan, and lateral force Flat can be written in terms of the magnitude of the friction Ff and normal Fn forces. These forces can then be transformed to the x and y rotating frame [1], defined in Fig. 3, denoted by Fxc and Fyc, illustrated in Initial hole wall
Initial hole wall
Tool axis Flute j-3
Tool axis Flute j-3
Flute j-2
tcm(j-1,t-T) Flute j-2
Feed per flute
tcm(j,t) - tcm(j-2,t-2T)
tcm(j,t) - tcm(j-1,t-T)
tcm(j,t) Flute j-1
Flute j-1
Flute j
Flute j
(a)
Chip load taken by flute j
(14)
(b)
Fig. 5. Illustration of chip load: (a) without; and (b) with the effect of process faults.
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Fig. 4. Incorporating the effect of tool deflection and regeneration, the total X and Y forces in global coordinate system can then be written as FX ¼
Nf X
½F xc cos yj ðtÞ F yc sin yj ðtÞ
Reamer
Lc
j¼1
þ F p cos yðtÞ þ F mX , FY ¼
Nf X
ð18Þ
Y
Capacitance Sensor
X
L
c
½F yc sin yj ðtÞ þ F xc cos yj ðtÞ
Z
j¼1
þ F p sin yðtÞ þ F mY ,
ð19Þ
where yj ðtÞ ¼ yðtÞ ðj 1Þyp .
Fp l
4. Model calibration and validation 4.1. Model calibration and parameter estimation
Fig. 6. Deflection magnitudes.
In the mechanistic modeling approach, the specific cutting energy coefficients, K n and K f , are dependent on the workpiece material, tool material, tool geometry, and machining conditions. The model was calibrated over a range of speed, 18.28–27.42 m/min, and a feed range of 0.18–0.23 mm/rev. The parallel offset runout and parallel offset runout locating angle present in the system were measured by the capacitance sensor to be 0.0011 mm and 73.41, respectively. The spindle tilt and spindle tilt locating angle were measured to be 0.00611 and 161.421, respectively. There was no axis misalignment present in the calibration experiments. A detailed description of the calibration procedure can be found in Chandrasekharan [9]. The capacitance sensor measurements were used in order to determine the proportionality coefficients detailed in Eqs. (7) and (8). As seen in Fig. 6 the deflection of the tool at the point of measurement of the capacitance sensor is denoted by dc . The deflection at the tool tip, dl , can be expressed in terms of dc by the following beam bending equation: dl ¼
2dc L3 . 2 Lc ð3L Lc Þ
(20)
Given the deflection at the tool tip the proportionality coefficient, r, was calculated using Eqs. (7) and (8) and was found to be equal to 0.9. 4.2. Model validation A series of experiments were conducted to validate the extended cutting force model using 11.1 mm diameter tools with 143.2 mm projection length, 6 flutes, 1.71 radial rake angle, 01 helix angle, 43.81 chamfer angle, and 1.5 mm chamfer length. The conditions under which the validation tests were run are given in Table 1. Process faults were measured using the capacitance sensor. The faults shown in Table 1 were induced intentionally in order to ascertain their effects on reaming process performance.
Table 2 shows the experimental forces from the validation experiments with the corresponding predictions using the previously developed static force model [1] and the extension of this model (referred to as ‘‘New’’ in the Table 2) discussed in this paper. The torque and thrust results shown in Table 2 are the steady state means. In order to calculate the mean values, 60 revolutions of data were averaged within the steady state range (full reamer immersion). Both the experimental and model-predicted mean X and Y forces along with the X and Y peak-to-valley (PV) are also shown in Table 2. The torque and thrust are predicted by both the static and the extended model with about the same average prediction error of 10%. However, as seen in Table 2, the static model consistently over predicts the peak-to-valley of the X and Y forces, most notably for Tests 4–6 where the net runout is significantly higher than for Tests 1–3. The extended model predicts the X and Y forces quite well, especially in Tests 4–6 where the process faults are higher. Table 3 shows the measured peak-to-valley of the tool displacement as result of process faults along with the corresponding extended model predictions. As seen in Table 3, model predictions, taking reamer deflection and regeneration effects into account, match experimental data well. The force and tool displacement profiles along with the corresponding model predictions for Tests 2 and 4 are shown in Figs. 7 and 8. As seen, the peak-to-valley value of the X and Y forces is considerably higher in magnitude for Test 4 (Fig. 8) than seen in Test 2 (Fig. 7). This is due to the fact that the net runout in Test 4 is higher that what was seen in Test 2, leading to higher deflection. The amount of deflection at the measurement point with the capacitive sensor is about 4 mm for Test 2, whereas the amount of deflection for Test 4 is about 65 mm, as shown in Fig. 8. In Test 2 (Fig. 7) there is a mean shift in the X and Y forces due to the effect of the misalignment as opposed to Test 4
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Table 1 Experimental conditions for model validation Test#
Feed (mm/rev)
Speed (m/min)
e (mm)
l (deg)
a (deg)
jt (deg)
rn (mm)
Xoff (mm)
Yoff (mm)
1 2 3 4 5 6
0.19 0.19 0.21 0.19 0.19 0.21
19.79 19.79 25.00 19.79 19.79 25.00
0.0231 0.0231 0.0231 0.0376 0.0376 0.0376
55.30 55.30 55.30 67.78 67.78 67.78
0.006 0.006 0.006 0.08 0.08 0.08
147.64 147.64 147.64 80.18 80.18 80.18
0.013 0.013 0.013 0.19 0.19 0.19
0.00 0.10 0.00 0.00 0.10 0.00
0.00 0.00 0.00 0.00 0.00 0.00
Table 2 Experimental torque, thrust, X and Y force results and corresponding model predictions Test
1 2 3 4 5 6
Torque [Ncm]
X [N]
Thrust [N]
X PV [N]
1 2 3 4 5 6
Y PV [N]
Exp
Static
New
Exp
Static
New
Exp
Static
New
Exp
Static
New
Exp
Static
New
Exp
Static
New
131 125 141 130 127 137
132 132 137 136 131 149
126 125 137 131 131 143
74.8 74.0 86.8 79.8 76.7 82.5
74.5 75.5 84.6 80.5 80.5 87.1
75.5 75.6 84.6 80.3 80.5 89.1
3.4 19.0 2.7 3.3 19.1 2.5
0 32.0 0 0 35.0 0
0 13.5 0 0 15.5 0
6.6 8.7 7.4 54.0 46.4 46.8
11.5 11.5 11.5 166 166 175
4.1 5.7 5.2 54.5 55.5 55.6
3.0 7.3 1.9 4.1 6.2 4.1
0 12.0 0 0 12.0 0
0 2.5 2.5 0 5.6 0
7.0 8.2 8.2 52.9 46.4 46.1
11.5 11.5 11.5 166 166 175
4.1 5.2 4.1 54.5 55.5 55.6
Table 3 Measured and predicted tool displacement peak-to-valley prior to and during engagement Test#
Y [N]
Tool displacement preengagement (mm)
Tool displacement during engagement (mm)
Experimental PV
Predicted PV
Experimental PV
Predicted PV
0.035 0.030 0.024 0.235 0.237 0.224
0.034 0.034 0.034 0.220 0.220 0.220
0.023 0.022 0.021 0.100 0.106 0.105
0.025 0.025 0.024 0.099 0.099 0.096
(Fig. 8) where there is no misalignment present. This is also seen in the displacement profile of Test 2 (Fig. 7) where the mean of the tool displacement shifts when the tool becomes engaged as opposed to Test 4 (Fig. 8). 5. Experimental assessment and model prediction of hole quality in reaming 5.1. Experimental assessment of hole quality The reamed holes that resulted from the model validation tests described in Table 2 were used to assess hole quality in reaming. A Keyence laser distance sensor with
0.01 mm resolution and a 20 mm spot size was used to measure the quality of the reamed holes. The x, y, and z stages of the laser distance sensor station have 50 mm of travel and a resolution of 100 nm. The workpieces used in the experimentation were cut in half and mounted on the station table. Fig. 9 shows a schematic of the top view of the workpiece after it was cut in half and mounted in preparation for hole quality measurements. As illustrated, at a particular depth along the hole axis, the laser scans a cross section of the hole, moving along the x-axis. Data were collected at 50 mm intervals along the x-axis. The cross sections measured lie in the x–z plane. After the scan is complete, the laser moves along the y-axis to a different depth of the hole and scans that cross section in a similar fashion. Using the top surface of the hole as a reference, the scans were taken at 3, 6, 9, and 12 mm depths along the hole axis. As seen in Fig. 9, the laser distance sensor was able to scan a portion of the reamed hole, approximately 601 sweep on each half of the hole, providing points in the x–y–z coordinate frame representing the surface of the hole. From the data gathered from each cross section, a regression analysis was done that fit the measured data to a circle. Using the center point of the fitted circle, the radius of each measured data point was calculated. Fig. 10 shows the variations of the hole radius within the scan area measured for Test 1, 2, 4, and 5. From the data gathered from each cross section, the average radius (the average radii for all the points measured by the laser distance sensor) and roundness
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120 Torque 100
120
Steady state forces
80 Thrust
60 40
X Force
20 Y Force
0 -20 15
1287
140
X and Y Forces (N); Thrust
X and Y Forces (N); Thrust (N); Torque (N*cm)
O. Bhattacharyya et al. / International Journal of Machine Tools & Manufacture 46 (2006) 1281–1290
15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9
80 60 40 20 0 -20 15
16
15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9
Time (s)
16
Time (s) 0.05
0.05 Engaged
0.04
0.04 0.03 0.02
Tool Displacement (mm)
Tool Displacement (mm)
Tool displacement
Pre-Engagement
0.01 0 -0.01 -0.02 7.5
(a)
8
8.5
9
0.02
Pre-Engagement Engaged
0.01 0 -0.01 -0.02 7.5
9.5
Time (s)
0.03
(b)
8
8.5
9
9.5
Time (s)
Fig. 7. Steady state forces and tool displacement for Test 2: (a) experimental; and (b) model predicted.
(the difference between the points with the maximum and minimum radius) were calculated. The average radius and roundness values for each cross section of the workpieces measured are given in Table 4. The result for Test 4 clearly shows the effect of the process faults. The average radius and the roundness are much greater than those seen for Tests 1 and 2. The presence of process faults increases the maximum radius of rotation, resulting in an enlarged hole dimension. Also, due to increase in the X and Y forces with higher process faults, there is an increase in the roundness from Test 1 to Test 4. It is interesting to note that the introduction of axis misalignment, though it slightly increases the average radius, seems to reduce the value of the roundness parameter. Test 1 and Test 2 have the same process fault conditions, the only difference being that Test 2 has an axis misalignment. As seen in Table 4, once axis misalignment is introduced the roundness improves. A similar phenomenon, at a much larger scale, is observed for Tests 5 and 6. This may be due to damping that occurs as a result of the constant force (Fmx) acting on the tool due to the misalignment in the X direction.
5.2. Model prediction of hole quality The average radius of the reamed hole can be predicted using the model by following the trajectory of the flute with the largest effective radius of rotation, Rcmax, which is determined from Eq. (9) as Rcmax ¼ max½Rc ðjÞ. As the tool traverses down the hole, the flute with the largest effective radius of rotation removes all the materials left uncut by the flute with smaller effective radii of rotation. The average radii of the hole predicted by the model are 5.557, 5.557, 5.571, and 5.571 mm for Test 1, 2, 4, and 5, respectively. Comparing with the average radii of the hole from experiments given in Table 4, the model predicts the average radius of the hole within 1–3 mm. As shown, the increase in the average radius due to the presence of process faults is well predicted by the model. The prediction results also show that the effect of process faults on the radius of the reamed hole is much greater than the effect of misalignments. This is because the presence of misalignments does not affect Rcmax. Hence, the model predictions are identical for Tests 1 and 2 and for Tests 3 and 4. This shows that reduction of process faults present
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160
160 Torque
N*cm)
140 120 100 80 60 40
X & Y Forces
20 0 -20 -40 13
140 120
Steady state forces
Thrust
X and Y Forces (N); Thrust
X and Y Forces (N); Thrust (N); Torque (N*cm)
1288
13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9
80 60 40 20 0 -20 -40
14
13
13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9
Pre-Engagement
Tool displacement
Tool Displacement (mm)
Tool Displacement (mm)
Pre-Engagement
0.1
0.1 Engaged
0.05 0 -0.05
Engaged
0.05 0 -0.05 -0.1
-0.1
6
(a)
14
Time (s)
Time (s)
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
Time (s)
6
7
(b)
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
7
Time (s)
Fig. 8. Steady state forces and tool displacement for Test 4: (a) experimental; and (b) model predicted.
Fig. 9. Schematic of the top view of the workpiece and the reamed hole.
in the reaming system is important for better control of the reamed hole dimensions. 6. Conclusions The following conclusions are drawn from this work: 1. The chip load formulation was modified in order to account for the reduction in the net runout due to the
tool deflection and to incorporate the regenerative effect due to the process faults and longitudinal vibrations of the tool. 2. The force and deflection model was validated via actual reaming experiments for cases with axis misalignment in the x-direction and for significant values of process faults. The model predicts the torque and thrust within an average error of 10% and the X and Y forces within 10 N. 3. A laser-based measurement system was used to assess the quality of the reamed holes resulting from the validation experiments. The presence of process faults increases the maximum radius of rotation, resulting in the hole radius being larger than the radius of the tool. Also, due to increase in the X and Y forces with higher process faults, the roundness of the hole deteriorates. The presence of axis misalignment, though slightly increasing the average radius, seems to dampen the tool vibration and improve the roundness. 4. The extended force model was used to predict the average radius of the reamed holes resulting from the validation experiments. The model is shown to predict the average radius of the hole within 1–3 mm.
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5.64 5.62
3 mm depth 6 mm depth 9 mm depth 12 mm depth
Test 1
Test 2 5.6
Radius (mm)
Radius (mm)
3 mm depth 6 mm depth 9 mm depth 12 mm depth
5.62
5.6 5.58 5.56
5.58 5.56
5.54
5.54
5.52
5.52
5.5 60
70
80
90
100
110
5.5 60
120
70
Angular Position (deg)
80
90
100
110
120
Angular Position (deg)
5.64
5.64
5.62
3 mm depth 6 mm depth 9 mm depth 12 mm depth
Test 4
5.62
3 mm depth 6 mm depth 9 mm depth 12 mm depth
Test 5
5.6
Radius (mm)
5.6
Radius (mm)
1289
5.58 5.56
5.58 5.56
5.54
5.54
5.52
5.52
5.5 60
70
80
90
100
110
120
5.5 60
70
Angular Position (deg)
80
90
100
110
120
Angular Position (deg)
Fig. 10. Radius of the hole vs. angular position. Table 4 Hole quality measurement results Tool radius: 5.5 mm
Depth (mm)
Average radius (mm)
Roundness (mm)
Test1
3 6 9 12 Average
5.557 5.557 5.560 5.558 5.558
0.052 0.040 0.040 0.046 0.044
Test 2
3 6 9 12 Average
5.558 5.559 5.566 5.556 5.559
0.053 0.039 0.034 0.031 0.039
Test 4
3 6 9 12 Average
5.588 5.573 5.561 5.571 5.573
0.128 0.100 0.097 0.091 0.104
3 6 9 12 Average
5.570 5.573 5.575 5.579 5.574
0.030 0.041 0.026 0.026 0.031
Test 5
5. Due to the accuracy with which X and Y forces are predicted, this model can be used as a basis for on-line detection of process faults and misalignments present in the system.
Acknowledgements The authors gratefully acknowledge the support of the University of Illinois at Urbana-Champaign Center for Machine Tool Systems Research and its member companies for their support and guidance of this research.
References [1] O. Bhattacharyya, S.G. Kapoor, R.E. DeVor, Mechanistic Model for the Reaming Process with Emphasis on Process Faults, to appear in International Journal of Machine Tools and Manufacture, in press. [2] K.A. Young, P.V. Bayly, J.E. Halley, dynamic simulation of reaming: theory, methods and application to the problem of lobed holes, in: Proceedings of the 1998 ASME International Mechanical Engineering Congress and Exposition, Anaheim, California, pp. 245–252, 15–20 Nov. 1998.
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[3] D.N. Dilley, P.V. Bayly, B.T. Whitehead, S.G. Calvert, An analytical study of the effect of process damping on reamer vibrations, Journal of Sound and Vibration 280 (2005) 997–1015. [4] K. Gupta, O.B. Ozdoganlar, S.G. Kapoor, R.E. DeVor, Modeling and prediction of hole profile in drilling, Part 1: modeling drill dynamics in the presence of drill alignment errors, Journal of Manufacturing Science and Engineering, Transactions of the ASME 125 (2003) 6–13. [5] A. Dogra, S.G. Kapoor, R.E. DeVor, Mechanistic Model for Tapping Process with Emphasis on Process Faults and Hole Geometry, Journal of Manufacturing Science and Engineering, Transactions of the ASME 124 (2002) 18–25.
[6] O. Mezentsev, R. Zhu, R.E. DeVor, S.G. Kapoor, Use of radial forces for fault detection in tapping, International Journal of Machine Tools and Manufacture 42 (2002) 478–488. [7] L. Merovitch, Elements of Vibration Analysis, McGraw-Hill, Singapore, 1986. [8] V. Chandrasekharan, A model to predict the three-dimensional cutting force system for drilling with arbitrary point geometry, Ph.D. Thesis, University of Illinois at Urbana-Champaign, Urbana, Illinois, 1996. [9] V. Chandrasekharan, S.G. Kapoor, R.E. DeVor, A calibration procedure for fundamental oblique cutting coefficients based on a three-dimensional mechanistic drilling force model, Transactions of the NAMRI/SME XXIV (1996) 39–44.
International Journal of Machine Tools & Manufacture 46 (2006) 1281–1290 www.elsevier.com/locate/ijmactool
The effects of process faults and misalignments on the cutting force system and hole quality in reaming Onik Bhattacharyya, Martin B. Jun, Shiv G. Kapoor, Richard E. DeVor Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, IL 61801, USA Received 5 September 2005; received in revised form 28 October 2005; accepted 3 November 2005 Available online 20 December 2005
Abstract A chip thickness and cutting force model that considers the deflection of the tool and the regenerative effect resulting from the presence of process faults and misalignments has been developed for the reaming process. Through a series of experiments, the model has been calibrated and validated. The model predicts tool displacement, torque, thrust, X and Y forces, and the average radius of the reamed hole. The developed model is also shown to be capable of being used as a basis for the on-line detection of process faults present in the system. r 2005 Elsevier Ltd. All rights reserved. Keywords: Reaming; Process faults; Hole quality; Force model; Cutting force system; Misalignments
1. Introduction In reaming, when process faults and misalignments are present, due to the flexibility of the tool, the reamer has a tendency to deflect towards the initial hole axis as it passes through the hole. This deflection changes the value of the process fault parameters and introduces additional forces into the system that can influence the quality of the reamed hole. In order to accurately predict final hole quality, the influence of all these factors need to be better understood. In an earlier paper [1], a static force model was developed that accurately predicts torque and thrust in reaming in the presence of process faults. However, the tool was assumed rigid and the chip load model did not consider the effects of tool deflection and regeneration. Though this model is quite useful for torque and thrust predictions, in order to be able to predict X and Y forces and consequently hole quality, the effect of process faults on tool deflection and regeneration [2,3] of the chip load must also be taken into account. Therefore an objective of this research is to extend the model developed by Bhattacharyya et al. [1] and incorporate the effects of tool deflection and regeneration due to process faults. A further Corresponding author. Tel.: +1 217 333 3432.
E-mail address: [email protected] (S.G. Kapoor). 0890-6955/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2005.11.002
objective of this paper is to better understand the effects of process faults and misalignments on reamed hole quality. The contents of the paper are as follows. First, the nature of the tool deflections resulting from process faults and misalignments will be experimentally investigated. The next section describes the development of the extended chip load and force model that incorporates the effects of tool deflection and regeneration. This is followed by the model validation section that details the experiments conducted. Finally, a section on hole quality is presented where the experimental process for measuring the hole quality is first described followed by the use of the extended deflection and force model to predict hole quality. 2. Reaming process in the presence of process faults In reaming, the reamer will have a tendency to follow the initial hole. This causes deflection of the tool when process faults and/or misalignments are present. This also causes a change in the net runout characteristics and additional forces due to this deflection will act on the reamer as it passes through the hole. In order to observe the effects of reamer deflection, experiments were conducted using a Mori Seiki TV-30, a light milling, drilling, and tapping center. During these
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experiments tool deflections and process faults were measured using a C1-A Lion Precision capacitance sensor, with 500 mm range and 0.1 mm resolution. A 4-component Kistler dynamometer, which measures torque, thrust, X, and Y forces, was used to measure cutting forces. Fig. 1 shows the experimental setup used. The parallel offset runout, spindle tilt, parallel offset runout locating angle, and spindle tilt locating angle [1] were measured by the capacitance sensor to be 0.0376 mm, 0.081, 67.781, and 80.181, respectively. The feed and speed were 0.19 mm/rev and 19.79 m/s, respectively. There was no spindle/hole axis misalignment present during the test. Fig. 2 shows the force profile and the tool displacement from one of the experiments. The amplitude of the signal measured by the capacitance sensor prior to engagement, seen in the displacement profile in Fig. 2a, corresponds to the runout that the tool is experiencing at the point of
measurement. This runout occurs as a result of a contribution of the effect of four runout parameters: parallel offset runout, spindle tilt, and their respective locating angles [4]. From Fig. 2a it can also be seen that when the tool becomes engaged in the hole, the runout decreases significantly as seen by the decrease in the amplitude of the signal measured by the capacitance sensor. But the runout of the reamer during engagement is still significant, suggesting that this runout will have an effect on both the cutting forces and hole quality. Fig. 2b shows that during engagement/cutting, the X and Y forces are non-zero as expected due to the presence of net runout [1]. Fig. 2b also illustrates that after cutting is complete, while the tool is still rotating in the hole, the X and Y forces have non-zero magnitudes essentially identical to the X and Y forces during cutting. This indicates that the presence of a reaction force acting on the tool is the major component of the X and Y forces and emphasizes the need to take this phenomenon into account in the modeling of the reaming process.
3. Modified chip load and force model formulation It has been shown for related processes [4,5], the X and Y forces have a strong influence on final hole quality. Therefore, for accurate prediction of hole quality, the effects of tool deflection and regeneration must be incorporated due to their significant impact on the X and Y forces. Furthermore, X and Y forces have been shown to be useful in the on-line detection of process faults in tapping [6], suggesting that the same may be true for reaming. Therefore, the chip load model formulation of [1] should be extended to incorporate the effects of tool deflection and regeneration. In this section, the definition of process faults is given first. The tool deflection is then expressed as a function of the process faults present. The radius of rotation for each flute is modified to include this deflection, and the chip thickness taken by each flute is extended to consider the effect of regeneration. Finally, the formulation of cutting force model is presented.
0.15
Before Engagement
After Cutting
During Cutting
0.1 Tool Displacement (mm)
X and Y Forces (N) ; Thrust (N); Torque (N*cm)
Fig. 1. Experimental setup for tool displacement measurement.
0.05 0 0.05 0.1 0.15 0.2
(a)
4
6
8
10
12
14
Time (s)
16
18
20
22
200 Before Engagement
After Cutting
During Cutting
150
Torque
100 Thrust X & Y Forces
50
0
50
4
6
8
(b)
Fig. 2. Force and tool displacement profile.
10
12
14
Time (s)
16
18
20
22
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3.1. Definition of process fault system in reaming
1283
Y Direction of Rotation
In a fashion similar to Gupta et al. [4], the reamer in the presence of tool/spindle process faults is shown in Fig. 3, where e is the parallel offset runout, l is the parallel offset runout locating angle, a is the angle of spindle tilt, and ft is the spindle tilt locating angle that defines the plane of the spindle tilt. The total net runout rn and its locating angle fL are found from the process faults parameters as rn ¼ ½e2 þ z2 tan2 a þ 2ze tan a cos ft 1=2 ,
Initial
FmY.
Hole Center
Yoff
(1)
x
FmX
tan b þ ft fR , fL ¼ l þ ðL zÞ R where e sin ft fR ¼ tan1 , z tan a þ e cos ft
Fp
y
Fxc
(2) X off Fyc
(3) φ
and z is the distance along the reamer as shown in Fig. 3, R is the radius of the reamer, L is the projection length, and b is the helix angle. The stationary coordinate frame is represented by X–Y–Z, while the rotating frame is represented by x–y–z.
rn
Initial Hole
L
X
Fig. 4. Deflection forces on reamer in the presence of process faults.
3.2. Incorporation of tool deflection into the chip load model Fig. 4 shows the bottom face of the reamer in the presence of a net runout, rn, and axis misalignment in the X direction, Xoff, and the Y direction, Yoff. There are two separate forces at work that influence reamer deflection: forces acting on the reamer due to net runout, Fp, and forces acting on the reamer due to axis misalignment, FmX and FmY. The forces Fxc and Fyc represent the cutting forces in the x and y direction of the rotating frame. The amount of deflection of the reamer in the direction opposing the net runout is denoted by dl while the deflection opposing the
misalignment in the X and Y direction are denoted by dmX and dmY. The reaction force Fp acting on the tool during cutting acts in the direction opposing the net runout and therefore rotates with the tool, while the reaction forces FmX and FmY act in the directions opposing the misalignments with their directions remaining constant. These forces can be expressed by F p ¼ kdl ,
(4)
F mX ¼ kdmX ;
F mY ¼ kdmY ,
(5)
where k is the stiffness of the tool and is given by, 3EI , (6) L3 where E is defined as the Young’s modulus of elasticity and I is the reamer cross-sectional moment of inertia. The parameters dl, dmX, and dmY are defined as follows: k¼
SPINDLE AXIS
x φt
y z
Coordinate Systems λ
X
Y x ε
y α Z z X-Y-Z : Stationary frame x-y-z : Rotating frame
REAMER TOOL AXIS
dl ¼ rrn ;
0oro1,
dmX ¼ rX off ;
dmY ¼ rY off ;
(7) 0oro1,
where the parameter r is determined through experimental data. The procedure for determining this coefficient is discussed later in the paper. As a result of the tool deflection, dl , the effective radius at which flute j cuts is given by, Rc ðjÞ ¼ ½ðrn dl Þ2 þ R2 þ 2ðrn dl ÞR cosðfL þ ðj 1Þyp Þ1=2 ,
Fig. 3. Reamer in the presence of process faults.
(8)
ð9Þ
where R is the radius of the tool, yp is the pitch angle. The chip thickness taken by the jth flute at an angular position
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The total chip load, Ac, at time t is the summation of tc(j,t) over all flutes and is given by
yðtÞ due to the feeding of the tool is then given by tcm ðj; tÞ ¼ Rc ðjÞ ½Rh þ ðX off dmX Þ sin yðtÞ þ ðY off dmY Þ cos yðtÞ,
ð10Þ
Ac ¼
where Rh is the radius of the initial hole.
Due to the effect of process faults, the position of each flute is different at an arbitrary angular position of the reamer yðtÞ, and the jth flute may not necessarily remove the same amount of material as its predecessors, as shown in Fig. 5. It is important to note that the amount of material removed by the jth flute depends on the positions of the previous flutes at the same angular position. The jth flute not only removes the amount taken by the feeding of the tool (denoted as tcm ðj; tÞ in Fig. 5) but also removes the materials left by the previous flutes (denoted as tcm ðj; tÞ tcm ðj m; t mT Þ) due to process faults, where m goes from 1 to the number of flutes N f and T is the tooth passing period, assumed here to be constant. In order to determine the material left by the previous flutes and add it to the total chip thickness, two cases must be considered. For case 1, there is no material left by the previous flute, i.e., tcm ðj; tÞ tcm ðj m; t mTÞo0. However, for case 2, since the position of the previous flute is such that the radius of cut is smaller than that of the current flute, i.e., tcm ðj; tÞ tcm ðj m; t mT Þ40, additional chip thickness must be added. The total chip thickness taken by the jth flute must also include the materials left by the previous flutes and can be expressed as tc ðj; tÞ ¼ tcm ðj; tÞ þ Max½0; tcm ðj; tÞ tcm ðj 1; t TÞ N f 1 X
f t tc ðj; tÞ,
(13)
j¼1
3.3. Effect of regeneration on chip load model
þ
Nf X
Maxf0; Min½tcm ðj; tÞ tcm ðj ðm 1Þ;
m¼2
t ðm 1ÞTÞ; tcm ðj; tÞ tcm ðj m; t mTÞg, ð11Þ where tcm ðj m; t mTÞ is written as tcm ðj m; t mT Þ ¼ Rc ðj mÞ ½Rh ðt mTÞ þ X off sin yðtÞ þ Y off cos yðtÞ. ð12Þ
where ft varies due to the regeneration caused by the longitudinal vibration qz of the tool, and is expressed by ft ¼
fr þ qz ðtÞ qz ðt TÞ. Nf
For the longitudinal vibration, the tool is modeled as a continuous system fixed at one end and free at the other. The axial force (thrust) is assumed to act on the tool at the free end. The governing equation for the longitudinal vibration of the tool, modeled as a continuous system, is given by d2 q ¼ f z, (15) dz2 where fz represents the force in the z direction [7]. The governing equation for the longitudinal vibration is solved using the finite element method.
mq€ z þ cq_ z þ EAðzÞ
3.4. Extended cutting force model In the mechanistic approach to force modeling the normal and frictional forces, as defined by Chandrasekharan et al. [8], are proportional to the chip load, Ac, and are given by F n ¼ K n Ac ,
(16)
F f ¼ K f Ac ,
(17)
Kn and Kf are proportionality constants commonly referred to as the specific cutting energies that are estimated through model calibration. Assuming Stabler’s Rule and following the oblique model development in a fashion similar to Chandrasekharan [8], it is known that the magnitude of the threedimensional elemental oblique cutting forces, thrust Fth, tangential Ftan, and lateral force Flat can be written in terms of the magnitude of the friction Ff and normal Fn forces. These forces can then be transformed to the x and y rotating frame [1], defined in Fig. 3, denoted by Fxc and Fyc, illustrated in Initial hole wall
Initial hole wall
Tool axis Flute j-3
Tool axis Flute j-3
Flute j-2
tcm(j-1,t-T) Flute j-2
Feed per flute
tcm(j,t) - tcm(j-2,t-2T)
tcm(j,t) - tcm(j-1,t-T)
tcm(j,t) Flute j-1
Flute j-1
Flute j
Flute j
(a)
Chip load taken by flute j
(14)
(b)
Fig. 5. Illustration of chip load: (a) without; and (b) with the effect of process faults.
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Fig. 4. Incorporating the effect of tool deflection and regeneration, the total X and Y forces in global coordinate system can then be written as FX ¼
Nf X
½F xc cos yj ðtÞ F yc sin yj ðtÞ
Reamer
Lc
j¼1
þ F p cos yðtÞ þ F mX , FY ¼
Nf X
ð18Þ
Y
Capacitance Sensor
X
L
c
½F yc sin yj ðtÞ þ F xc cos yj ðtÞ
Z
j¼1
þ F p sin yðtÞ þ F mY ,
ð19Þ
where yj ðtÞ ¼ yðtÞ ðj 1Þyp .
Fp l
4. Model calibration and validation 4.1. Model calibration and parameter estimation
Fig. 6. Deflection magnitudes.
In the mechanistic modeling approach, the specific cutting energy coefficients, K n and K f , are dependent on the workpiece material, tool material, tool geometry, and machining conditions. The model was calibrated over a range of speed, 18.28–27.42 m/min, and a feed range of 0.18–0.23 mm/rev. The parallel offset runout and parallel offset runout locating angle present in the system were measured by the capacitance sensor to be 0.0011 mm and 73.41, respectively. The spindle tilt and spindle tilt locating angle were measured to be 0.00611 and 161.421, respectively. There was no axis misalignment present in the calibration experiments. A detailed description of the calibration procedure can be found in Chandrasekharan [9]. The capacitance sensor measurements were used in order to determine the proportionality coefficients detailed in Eqs. (7) and (8). As seen in Fig. 6 the deflection of the tool at the point of measurement of the capacitance sensor is denoted by dc . The deflection at the tool tip, dl , can be expressed in terms of dc by the following beam bending equation: dl ¼
2dc L3 . 2 Lc ð3L Lc Þ
(20)
Given the deflection at the tool tip the proportionality coefficient, r, was calculated using Eqs. (7) and (8) and was found to be equal to 0.9. 4.2. Model validation A series of experiments were conducted to validate the extended cutting force model using 11.1 mm diameter tools with 143.2 mm projection length, 6 flutes, 1.71 radial rake angle, 01 helix angle, 43.81 chamfer angle, and 1.5 mm chamfer length. The conditions under which the validation tests were run are given in Table 1. Process faults were measured using the capacitance sensor. The faults shown in Table 1 were induced intentionally in order to ascertain their effects on reaming process performance.
Table 2 shows the experimental forces from the validation experiments with the corresponding predictions using the previously developed static force model [1] and the extension of this model (referred to as ‘‘New’’ in the Table 2) discussed in this paper. The torque and thrust results shown in Table 2 are the steady state means. In order to calculate the mean values, 60 revolutions of data were averaged within the steady state range (full reamer immersion). Both the experimental and model-predicted mean X and Y forces along with the X and Y peak-to-valley (PV) are also shown in Table 2. The torque and thrust are predicted by both the static and the extended model with about the same average prediction error of 10%. However, as seen in Table 2, the static model consistently over predicts the peak-to-valley of the X and Y forces, most notably for Tests 4–6 where the net runout is significantly higher than for Tests 1–3. The extended model predicts the X and Y forces quite well, especially in Tests 4–6 where the process faults are higher. Table 3 shows the measured peak-to-valley of the tool displacement as result of process faults along with the corresponding extended model predictions. As seen in Table 3, model predictions, taking reamer deflection and regeneration effects into account, match experimental data well. The force and tool displacement profiles along with the corresponding model predictions for Tests 2 and 4 are shown in Figs. 7 and 8. As seen, the peak-to-valley value of the X and Y forces is considerably higher in magnitude for Test 4 (Fig. 8) than seen in Test 2 (Fig. 7). This is due to the fact that the net runout in Test 4 is higher that what was seen in Test 2, leading to higher deflection. The amount of deflection at the measurement point with the capacitive sensor is about 4 mm for Test 2, whereas the amount of deflection for Test 4 is about 65 mm, as shown in Fig. 8. In Test 2 (Fig. 7) there is a mean shift in the X and Y forces due to the effect of the misalignment as opposed to Test 4
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Table 1 Experimental conditions for model validation Test#
Feed (mm/rev)
Speed (m/min)
e (mm)
l (deg)
a (deg)
jt (deg)
rn (mm)
Xoff (mm)
Yoff (mm)
1 2 3 4 5 6
0.19 0.19 0.21 0.19 0.19 0.21
19.79 19.79 25.00 19.79 19.79 25.00
0.0231 0.0231 0.0231 0.0376 0.0376 0.0376
55.30 55.30 55.30 67.78 67.78 67.78
0.006 0.006 0.006 0.08 0.08 0.08
147.64 147.64 147.64 80.18 80.18 80.18
0.013 0.013 0.013 0.19 0.19 0.19
0.00 0.10 0.00 0.00 0.10 0.00
0.00 0.00 0.00 0.00 0.00 0.00
Table 2 Experimental torque, thrust, X and Y force results and corresponding model predictions Test
1 2 3 4 5 6
Torque [Ncm]
X [N]
Thrust [N]
X PV [N]
1 2 3 4 5 6
Y PV [N]
Exp
Static
New
Exp
Static
New
Exp
Static
New
Exp
Static
New
Exp
Static
New
Exp
Static
New
131 125 141 130 127 137
132 132 137 136 131 149
126 125 137 131 131 143
74.8 74.0 86.8 79.8 76.7 82.5
74.5 75.5 84.6 80.5 80.5 87.1
75.5 75.6 84.6 80.3 80.5 89.1
3.4 19.0 2.7 3.3 19.1 2.5
0 32.0 0 0 35.0 0
0 13.5 0 0 15.5 0
6.6 8.7 7.4 54.0 46.4 46.8
11.5 11.5 11.5 166 166 175
4.1 5.7 5.2 54.5 55.5 55.6
3.0 7.3 1.9 4.1 6.2 4.1
0 12.0 0 0 12.0 0
0 2.5 2.5 0 5.6 0
7.0 8.2 8.2 52.9 46.4 46.1
11.5 11.5 11.5 166 166 175
4.1 5.2 4.1 54.5 55.5 55.6
Table 3 Measured and predicted tool displacement peak-to-valley prior to and during engagement Test#
Y [N]
Tool displacement preengagement (mm)
Tool displacement during engagement (mm)
Experimental PV
Predicted PV
Experimental PV
Predicted PV
0.035 0.030 0.024 0.235 0.237 0.224
0.034 0.034 0.034 0.220 0.220 0.220
0.023 0.022 0.021 0.100 0.106 0.105
0.025 0.025 0.024 0.099 0.099 0.096
(Fig. 8) where there is no misalignment present. This is also seen in the displacement profile of Test 2 (Fig. 7) where the mean of the tool displacement shifts when the tool becomes engaged as opposed to Test 4 (Fig. 8). 5. Experimental assessment and model prediction of hole quality in reaming 5.1. Experimental assessment of hole quality The reamed holes that resulted from the model validation tests described in Table 2 were used to assess hole quality in reaming. A Keyence laser distance sensor with
0.01 mm resolution and a 20 mm spot size was used to measure the quality of the reamed holes. The x, y, and z stages of the laser distance sensor station have 50 mm of travel and a resolution of 100 nm. The workpieces used in the experimentation were cut in half and mounted on the station table. Fig. 9 shows a schematic of the top view of the workpiece after it was cut in half and mounted in preparation for hole quality measurements. As illustrated, at a particular depth along the hole axis, the laser scans a cross section of the hole, moving along the x-axis. Data were collected at 50 mm intervals along the x-axis. The cross sections measured lie in the x–z plane. After the scan is complete, the laser moves along the y-axis to a different depth of the hole and scans that cross section in a similar fashion. Using the top surface of the hole as a reference, the scans were taken at 3, 6, 9, and 12 mm depths along the hole axis. As seen in Fig. 9, the laser distance sensor was able to scan a portion of the reamed hole, approximately 601 sweep on each half of the hole, providing points in the x–y–z coordinate frame representing the surface of the hole. From the data gathered from each cross section, a regression analysis was done that fit the measured data to a circle. Using the center point of the fitted circle, the radius of each measured data point was calculated. Fig. 10 shows the variations of the hole radius within the scan area measured for Test 1, 2, 4, and 5. From the data gathered from each cross section, the average radius (the average radii for all the points measured by the laser distance sensor) and roundness
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(N*cm)
120 Torque 100
120
Steady state forces
80 Thrust
60 40
X Force
20 Y Force
0 -20 15
1287
140
X and Y Forces (N); Thrust
X and Y Forces (N); Thrust (N); Torque (N*cm)
O. Bhattacharyya et al. / International Journal of Machine Tools & Manufacture 46 (2006) 1281–1290
15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9
80 60 40 20 0 -20 15
16
15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9
Time (s)
16
Time (s) 0.05
0.05 Engaged
0.04
0.04 0.03 0.02
Tool Displacement (mm)
Tool Displacement (mm)
Tool displacement
Pre-Engagement
0.01 0 -0.01 -0.02 7.5
(a)
8
8.5
9
0.02
Pre-Engagement Engaged
0.01 0 -0.01 -0.02 7.5
9.5
Time (s)
0.03
(b)
8
8.5
9
9.5
Time (s)
Fig. 7. Steady state forces and tool displacement for Test 2: (a) experimental; and (b) model predicted.
(the difference between the points with the maximum and minimum radius) were calculated. The average radius and roundness values for each cross section of the workpieces measured are given in Table 4. The result for Test 4 clearly shows the effect of the process faults. The average radius and the roundness are much greater than those seen for Tests 1 and 2. The presence of process faults increases the maximum radius of rotation, resulting in an enlarged hole dimension. Also, due to increase in the X and Y forces with higher process faults, there is an increase in the roundness from Test 1 to Test 4. It is interesting to note that the introduction of axis misalignment, though it slightly increases the average radius, seems to reduce the value of the roundness parameter. Test 1 and Test 2 have the same process fault conditions, the only difference being that Test 2 has an axis misalignment. As seen in Table 4, once axis misalignment is introduced the roundness improves. A similar phenomenon, at a much larger scale, is observed for Tests 5 and 6. This may be due to damping that occurs as a result of the constant force (Fmx) acting on the tool due to the misalignment in the X direction.
5.2. Model prediction of hole quality The average radius of the reamed hole can be predicted using the model by following the trajectory of the flute with the largest effective radius of rotation, Rcmax, which is determined from Eq. (9) as Rcmax ¼ max½Rc ðjÞ. As the tool traverses down the hole, the flute with the largest effective radius of rotation removes all the materials left uncut by the flute with smaller effective radii of rotation. The average radii of the hole predicted by the model are 5.557, 5.557, 5.571, and 5.571 mm for Test 1, 2, 4, and 5, respectively. Comparing with the average radii of the hole from experiments given in Table 4, the model predicts the average radius of the hole within 1–3 mm. As shown, the increase in the average radius due to the presence of process faults is well predicted by the model. The prediction results also show that the effect of process faults on the radius of the reamed hole is much greater than the effect of misalignments. This is because the presence of misalignments does not affect Rcmax. Hence, the model predictions are identical for Tests 1 and 2 and for Tests 3 and 4. This shows that reduction of process faults present
ARTICLE IN PRESS O. Bhattacharyya et al. / International Journal of Machine Tools & Manufacture 46 (2006) 1281–1290
160
160 Torque
N*cm)
140 120 100 80 60 40
X & Y Forces
20 0 -20 -40 13
140 120
Steady state forces
Thrust
X and Y Forces (N); Thrust
X and Y Forces (N); Thrust (N); Torque (N*cm)
1288
13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9
80 60 40 20 0 -20 -40
14
13
13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9
Pre-Engagement
Tool displacement
Tool Displacement (mm)
Tool Displacement (mm)
Pre-Engagement
0.1
0.1 Engaged
0.05 0 -0.05
Engaged
0.05 0 -0.05 -0.1
-0.1
6
(a)
14
Time (s)
Time (s)
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
Time (s)
6
7
(b)
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
7
Time (s)
Fig. 8. Steady state forces and tool displacement for Test 4: (a) experimental; and (b) model predicted.
Fig. 9. Schematic of the top view of the workpiece and the reamed hole.
in the reaming system is important for better control of the reamed hole dimensions. 6. Conclusions The following conclusions are drawn from this work: 1. The chip load formulation was modified in order to account for the reduction in the net runout due to the
tool deflection and to incorporate the regenerative effect due to the process faults and longitudinal vibrations of the tool. 2. The force and deflection model was validated via actual reaming experiments for cases with axis misalignment in the x-direction and for significant values of process faults. The model predicts the torque and thrust within an average error of 10% and the X and Y forces within 10 N. 3. A laser-based measurement system was used to assess the quality of the reamed holes resulting from the validation experiments. The presence of process faults increases the maximum radius of rotation, resulting in the hole radius being larger than the radius of the tool. Also, due to increase in the X and Y forces with higher process faults, the roundness of the hole deteriorates. The presence of axis misalignment, though slightly increasing the average radius, seems to dampen the tool vibration and improve the roundness. 4. The extended force model was used to predict the average radius of the reamed holes resulting from the validation experiments. The model is shown to predict the average radius of the hole within 1–3 mm.
ARTICLE IN PRESS O. Bhattacharyya et al. / International Journal of Machine Tools & Manufacture 46 (2006) 1281–1290 5.64
5.64 5.62
3 mm depth 6 mm depth 9 mm depth 12 mm depth
Test 1
Test 2 5.6
Radius (mm)
Radius (mm)
3 mm depth 6 mm depth 9 mm depth 12 mm depth
5.62
5.6 5.58 5.56
5.58 5.56
5.54
5.54
5.52
5.52
5.5 60
70
80
90
100
110
5.5 60
120
70
Angular Position (deg)
80
90
100
110
120
Angular Position (deg)
5.64
5.64
5.62
3 mm depth 6 mm depth 9 mm depth 12 mm depth
Test 4
5.62
3 mm depth 6 mm depth 9 mm depth 12 mm depth
Test 5
5.6
Radius (mm)
5.6
Radius (mm)
1289
5.58 5.56
5.58 5.56
5.54
5.54
5.52
5.52
5.5 60
70
80
90
100
110
120
5.5 60
70
Angular Position (deg)
80
90
100
110
120
Angular Position (deg)
Fig. 10. Radius of the hole vs. angular position. Table 4 Hole quality measurement results Tool radius: 5.5 mm
Depth (mm)
Average radius (mm)
Roundness (mm)
Test1
3 6 9 12 Average
5.557 5.557 5.560 5.558 5.558
0.052 0.040 0.040 0.046 0.044
Test 2
3 6 9 12 Average
5.558 5.559 5.566 5.556 5.559
0.053 0.039 0.034 0.031 0.039
Test 4
3 6 9 12 Average
5.588 5.573 5.561 5.571 5.573
0.128 0.100 0.097 0.091 0.104
3 6 9 12 Average
5.570 5.573 5.575 5.579 5.574
0.030 0.041 0.026 0.026 0.031
Test 5
5. Due to the accuracy with which X and Y forces are predicted, this model can be used as a basis for on-line detection of process faults and misalignments present in the system.
Acknowledgements The authors gratefully acknowledge the support of the University of Illinois at Urbana-Champaign Center for Machine Tool Systems Research and its member companies for their support and guidance of this research.
References [1] O. Bhattacharyya, S.G. Kapoor, R.E. DeVor, Mechanistic Model for the Reaming Process with Emphasis on Process Faults, to appear in International Journal of Machine Tools and Manufacture, in press. [2] K.A. Young, P.V. Bayly, J.E. Halley, dynamic simulation of reaming: theory, methods and application to the problem of lobed holes, in: Proceedings of the 1998 ASME International Mechanical Engineering Congress and Exposition, Anaheim, California, pp. 245–252, 15–20 Nov. 1998.
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[3] D.N. Dilley, P.V. Bayly, B.T. Whitehead, S.G. Calvert, An analytical study of the effect of process damping on reamer vibrations, Journal of Sound and Vibration 280 (2005) 997–1015. [4] K. Gupta, O.B. Ozdoganlar, S.G. Kapoor, R.E. DeVor, Modeling and prediction of hole profile in drilling, Part 1: modeling drill dynamics in the presence of drill alignment errors, Journal of Manufacturing Science and Engineering, Transactions of the ASME 125 (2003) 6–13. [5] A. Dogra, S.G. Kapoor, R.E. DeVor, Mechanistic Model for Tapping Process with Emphasis on Process Faults and Hole Geometry, Journal of Manufacturing Science and Engineering, Transactions of the ASME 124 (2002) 18–25.
[6] O. Mezentsev, R. Zhu, R.E. DeVor, S.G. Kapoor, Use of radial forces for fault detection in tapping, International Journal of Machine Tools and Manufacture 42 (2002) 478–488. [7] L. Merovitch, Elements of Vibration Analysis, McGraw-Hill, Singapore, 1986. [8] V. Chandrasekharan, A model to predict the three-dimensional cutting force system for drilling with arbitrary point geometry, Ph.D. Thesis, University of Illinois at Urbana-Champaign, Urbana, Illinois, 1996. [9] V. Chandrasekharan, S.G. Kapoor, R.E. DeVor, A calibration procedure for fundamental oblique cutting coefficients based on a three-dimensional mechanistic drilling force model, Transactions of the NAMRI/SME XXIV (1996) 39–44.