- Email: [email protected]
The effects of thermal distortions on the diameter and cylindricity of dry drilled holes
International Journal of Machine Tools & Manufacture 41 (2001) 2261–2270
The effects of thermal distortions on the diameter and cylindricity of dry drilled holes Matthew Bono, Jun Ni
*
Department of Mechanical Engineering, University of Michigan, 1023 H.H. Dow Building, 2300 Hayward Street, Ann Arbor, MI 48109, USA Received 20 June 2000; accepted 26 March 2001
Abstract A model is developed to predict the effects of thermal distortion of the drill and workpiece on the diameter and cylindricity of dry drilled holes. Experiments using embedded thermocouples verify that the model predicts the flow of heat into the workpiece and into the drill reasonably well. The model predicts that thermal expansion of the drill is the dominant effect and leads to oversized holes with diameters that increase with depth. 2001 Elsevier Science Ltd. All rights reserved. Keywords: Dry drilling; Thermal distortion; Cylindricity; Hole quality; Metal cutting
1. Introduction The subject of dry drilling has received considerable attention recently, and it is quickly becoming a priority in many manufacturing industries. Many researchers are investigating tool geometries and coatings for performing dry drilling and near-dry drilling, but there is concern that the heat generated by the process can lead to thermal expansion of the drill and workpiece that will affect the size and quality of the holes. This study develops a model to predict the effects of thermal distortions on the diameter and cylindricity of dry drilled holes. Finite element models calculate the thermally distorted shapes of the drill and workpiece, which are used to calculate the diameter of the hole as a function of depth. The adverse effects of dry drilling are well known. Recently, Haan et al. [1] performed an experimental investigation of the role of cutting fluids in drilling. They found that dry drilled holes have a poorer surface finish than holes drilled with cutting fluid, and dry drilled holes have * Corresponding author. Fax: +1-734-936-0363. E-mail address: [email protected] (J. Ni).
0890-6955/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 8 9 0 - 6 9 5 5 ( 0 1 ) 0 0 0 4 7 - 5
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Nomenclature a aw b l h f q w Fc Ff,r Ft Fz kt kw lc q qfriction qshear q⬙drill q⬙wp R2 rinner router T V Vchip Vf
Rake angle Thermal permeability of workpiece material Friction angle Inclination angle Chip angle ⬇l Shear angle Angle between drill axis and the cutting edge Angular velocity of the drill Cutting force of the ECT acting parallel to tool velocity Frictional shearing force between chip and tool Force of the ECT acting perpendicular to the cutting edge and the tool velocity Thrust force of the ECT acting parallel to the drill axis Thermal conductivity of tool material Thermal conductivity of workpiece material Chip–tool contact length ⬇ (2)(uncut chip thickness) Rate of total heat generation for an ECT Rate of heat generation by friction for an ECT Rate of heat generation in shear for an ECT Heat flux load applied to each element of the drill Heat flux load applied to each element of the workpiece fraction of energy generated by friction on rake face that flows into chip Inner radius of the element Outer radius of the element Torque contributed by an ECT=(Fc)(radius) Cutting velocity of the ECT=(w)(radius) Chip velocity Feed velocity of the drill
a bell shape, with the minimum diameter at the top of the hole. Watanabe et al. [2] developed a model for predicting the effects of thermal distortions in low speed drilling. Their insightful analysis was similar to the current study, in that they predicted the thermal expansion of the workpiece and drill to obtain a rough calculation of the diameter of the drilled hole at different depths. The current study focuses on drilling at speeds of several thousand rpm and develops a model to predict the diameter of dry drilled holes as a function of depth. The objective is to determine the individual effects of thermal expansion of the workpiece and the drill and to predict the magnitudes of the diametral errors that are caused by thermal expansion.
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2. Predictive model 2.1. Geometry of the FEAs Two finite element models are used in this study. The first model consists of a two-dimensional, axisymmetric finite element model of a cylindrical workpiece, created with the commercial finite element code ABAQUS. The elements are of type CAX4T, which are four-node bilinear temperature and displacement elements. In the model, the drill machines a hole in the center of the workpiece, which induces thermal loads on the workpiece and raises the temperature. To represent the heat that flows into the workpiece during the drilling process, heat flux is applied to the elements located directly beneath the cutting edge of the drill. This heat raises the temperature of the workpiece material, and the resulting thermal deformations distort the shape of the workpiece, as shown in Fig. 1. The figure shows the shape that the workpiece assumes as a result of the thermal deformation. As the drill proceeds into the workpiece, elements are removed from the model, and heat flux is applied to the next row of elements. This process repeats until the drill has proceeded through the entire depth of the workpiece. All other surfaces of the workpiece are modeled as adiabatic. For each step of the analysis, the FEA computes the temperature field and the thermally distorted shape of the workpiece. The heat entering the workpiece causes it to expand radially, and the drill cuts the material when it is in this expanded configuration. Thus, when the workpiece cools back to room temperature, the diameter of the drilled hole shrinks as the workpiece contracts. Heat also flows into the drill during the drilling process. This heat raises the temperature of the drill and causes it to expand. Thus, the expansion of the drill and the expansion and subsequent contraction of the workpiece counteract each other to determine the final room temperature diameter of the drilled hole. Another finite element analysis calculates the diameter of the cutting edges of the hot drill as it progresses into the workpiece. This finite element model is illustrated in Fig. 2. This three-dimensional finite element model consists of eight-node coupled temperature and displacement elements of type C3D8T. The heat that enters the drill is modeled by applying heat flux to the elements on the rake face that correspond to the cutting edges of the drill. All other surfaces of the drill are adiabatic. The transient analyses of the drill and workpiece are used to calculate the room temperature shape of the drilled hole. As each layer of elements is removed from the FEM of the workpiece, the diameter of the cutting edges of the drill is calculated. The distorted configurations of the hot
Fig. 1.
Thermally distorted shape of the workpiece.
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Fig. 2. Finite element model of the drill and the heat flux loads.
drill and the hot workpiece are used to calculate the room temperature diameter of the drilled hole as a function of depth, thereby determining the cylindricity of the hole. 2.2. Calculating the heat flux loads In order to calculate the heat flux loads on each of the elements in the finite element models, the cutting edges of the drill are considered as a sequence of individual, elementary cutting tools (ECTs). Each ECT performs a simple metal cutting operation, so metal cutting theories can be used to evaluate the forces and heat transfer on each segment of the cutting edge. For each ECT, some of the heat generated on the shear plane flows into the workpiece, and some of the heat generated by friction on the rake face flows into the tool [3,4]. A model for calculating the heat partition on each ECT is developed in a previous study [5]. As described in this previous work, the heat flux load applied to each element of the FEA of the workpiece is given by: (1−qfriction/q)(Tw+FzVf) q⬙wp⫽ . p(r2outer−r2inner)
(1)
The fraction of the total heat dissipated by the ECT that is consumed by friction on the rake face is given by Eq. (2) through Eq. (5). qfriction Ff,rVchip ⫽ q Tw+FzVf
Vchip⫽V
cos l sin f cos h cos(f−a)
Fz+Fca Ft⫽ b
(2)
(3)
(4)
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(sin l−cos l sin a tan h)cos q a⬅ (sin l sin a tan h+cos l)cos l
b⬅
cos a tan h cos q (cos2 l−cos2 q)1/2 ⫹ (sin l sin a tan h+cos l)cos l cos l
Ff,r⫽
(cos a cos l)Ft+(sin a)Fc cos a cos l cos h+sin a(sin l sin h+sin a cos l cos h) 2
(5)
The drills used in this study have been ground to a prescribed geometry, so all of the cutting angles are known for each ECT. In addition, the thrust force and cutting force for each ECT are calculated from the total measured thrust and torque using the model created by Chandrasekharan and co-workers [6,7] and modified by Chen [8]. As described in the previous work [5], experiments have verified that this model correctly predicts the flow of heat into the workpiece. The flow of heat into the drill is calculated in a similar manner. The heat flux load applied to each element of the FEA of the drill is given by: (1−R2)(qfriction/q)(Tw+FzVf) q⬙drill⫽ . area of element
(6)
The partition of the energy generated by friction on the rake face between the chip and the tool is calculated using the model developed by Berliner and Krainov [9]. The fraction of this energy that is carried away by the chip is given by Eq. (7). Note that the current study is concerned with the fraction of this energy that flows into the tool, which is (1⫺R2).
冋
冉冊册
kt p R2⫽ 1⫹0.45 kw Pe
1/2 −1
Vchiplc Pe⫽ . aw
(7)
3. Experimental verification of the model In order to verify the accuracy of the model for the flow of heat into the drill, drilling tests are performed on a Mori Seiki TV-30 CNC drilling machine. Holes of diameter 9.92 mm are drilled with a HSS drill in a plate of aluminum 319 to a depth of 25 mm. The drills are standard single-cone twist drills, with a point angle of 125° and a helix angle of 39°. As the holes are drilled, a Kistler piezoelectric dynamometer measures the drilling thrust and torque. A type K thermocouple with a wire diameter of 127 µm is embedded in the drill to measure the transient temperature of a point near the cutting edge. Embedding thermocouples is a well
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established method of measuring drill temperatures [10]. The thermocouple is embedded in a slot that was ground into the drill point, as shown in Fig. 3. The thermocouple bead is located 0.8 mm from the cutting edge, 0.3 mm below the surface of the clearance face. The thermocouple wires run up the drill body in another slot, which was ground into the land of the drill. The thermocouple is held in place with high-temperature epoxy with a large thermal conductivity, which was designed for thermocouple applications. A slip ring transmits the thermocouple signal from the rotating drill to a personal computer, where the data is collected with an OMD-5508 TC board. The purpose of the thermocouple is to compare the experimentally measured drill temperatures with the temperatures predicted by the FEA. Thus, the model for the heat flow into the drill can be verified over a range of drilling speeds and feeds. The speeds range from 3000 to 7000 rpm, and the feeds range from 127 to 381 µm/rev. The predicted and measured temperature rises at the location of the thermocouple for each of the five drilling tests are plotted in Fig. 4. Fig. 4 shows that the model predicts the flow of heat into the drill reasonably well. In each case, both the predicted and measured temperatures increase continuously throughout the drilling process, and the measured temperatures immediately begin to decrease at the conclusion of the drilling process. The percentage errors between the predicted and measured temperature rises at the end of the drilling process for each of the experiments are summarized in Fig. 5. The maximum error occurs with a speed of 3000 rpm and a feed of 127 µm/rev. The accuracy of the predictive model increases with speed and feed, and for feeds of 381 µm/rev, the errors are each 4%. There are several possible causes of the discrepancies between the measured and predicted temperature rises for the smaller feedrates. For example, the model assumes that the face of the chip opposite the rake face is an adiabatic surface. For very thin chips, this assumption could result in an underprediction of the amount of heat that enters the chip and an overprediction of the amount of heat that enters the drill. Any number of other assumptions and simplifications made in the predictive model could cause the discrepancies between the measured and predicted temperatures. However, given all of the inherent complexities in predicting and measuring drill temperatures over a range of feeds and speeds, the predictive model is reasonably accurate. The previous experimental investigation of the flow of heat into the workpiece [5] and the current experiments have verified that the model predicts the flow of heat into the workpiece and into the drill reasonably well. Thus, the predicted heat fluxes can be used in the finite element models to determine the transient, thermally deformed shapes of the workpiece and drill and the resulting errors in the diameters of the drilled holes.
Fig. 3.
Thermocouple embedded in the drill point near the cutting edge.
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Fig. 4. Predicted and measured temperature rises for five different combinations of feed and speed.
Fig. 5. Percentage errors between the predicted and measured temperature rises at the end of the drilling process.
4. Results and discussion The model is used to predict the diametral errors encountered in dry drilling for speeds of 3000, 5000 and 7000 rpm, with feeds of 127, 254 and 381 µm/rev. Drilling tests are performed to measure the thrust force and torque for each of the nine combinations of feed and speed. The model predicts that when dry drilling aluminum 319 with a 9.92 mm HSS drill through a plate of thickness 29 mm, thermal expansion of the drill and workpiece produce diametral errors of ⬍30 µm. An example of the shape of the drilled hole wall at room temperature is plotted in Fig.
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Fig. 6.
M. Bono, J. Ni / International Journal of Machine Tools & Manufacture 41 (2001) 2261–2270
Predicted shape of the drilled hole at room temperature for a speed of 7000 rpm and a feed of 381 µm/rev.
6. This example is for a drilling speed of 7000 rpm and a feed of 381 µm/rev, but all of the predicted hole profiles have this same general shape. Recall that the final shape of the hole is determined by the contraction of the workpiece and the expansion of the drill. These independent effects are represented in the figure by the dotted line and the dashed line, respectively. The heavy dark line represents the final shape of the hole at room temperature. Several facts are apparent from Fig. 6. As expected, contraction of the workpiece tends to decrease the size of the hole, and expansion of the drill tends to increase the size of the hole. For these drilling conditions, the expansion of the drill is a more dominant factor than contraction of the workpiece. The entire hole is oversized, and the hole is smallest at the top and widens near the bottom. In this example, the maximum diameter is 25 µm larger than the minimum diameter. The predicted diametral errors for all of the data points are plotted in Fig. 7. Each bar on the chart corresponds to a different data point. The top of each bar represents the maximum diameter of the hole, and the bottom of the bar represents the minimum diameter of the hole. The vertical axis represents the deviation of the diameter from the nominal room temperature diameter of the drill, which is 9.922 mm. The model predicts that thermal distortions of the drill and workpiece lead to holes that are
Fig. 7.
Diametral deviations for all of the drilling tests, predicted from the measured drilling forces.
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oversized, and diametral errors range from 0 to 26 µm. Hole diameters vary through the depth of the part, and the diametral variations within individual holes range from 17 to 26 µm. The effects of feed and speed on diameter and cylindricity are quite complicated. Many competing effects determine the final diameter and shape of the hole, and changes in the feed and speed cause changes in many other parameters, including the feed velocity, the total drilling time, and the drilling forces. Recall that each of the predictions is based on measured drilling forces, and there is always some variation in the drilling forces for a set of drilling conditions. Thus, while these predictions estimate the magnitudes of the diametral errors, they are not intended to reveal the specific effects of feed and speed. However, for the range of conditions considered in this study, speed and feed appear to have only minor effects on the predicted maximum and minimum diameters of the drilled holes. The actual diameters of several of the drilled holes were measured with a coordinate measuring machine. The measured diameters are several hundred microns larger than the predicted diameters. The reason for the discrepancy between the measured and predicted diameters is that this predictive model considers only the diametral errors caused by thermal expansion effects. However, in reality, many other factors can contribute to the total diametral error. Some of these factors include whirling of the drill due to uneven lip height or asymmetric built up edge formation, wander of the drill point during initial entry into the workpiece, run out of the machine spindle, and vibration of the drill and the machine. The results of the predictions and experimental measurements indicate that only a small fraction of the total diametral error is caused by thermal distortion of the drill and the workpiece.
5. Conclusions A model has been developed to predict the effects of thermal distortion of the drill and workpiece on the diameter and cylindricity of dry drilled holes. Experiments verify that the model predicts the flow of heat into the workpiece and into the drill reasonably well. The study considers the quality of holes produced when drilling in a workpiece of aluminum 319, using a HSS drill of diameter 9.92 mm, with speeds ranging from 3000 to 7000 rpm, and with feeds ranging from 127 to 381 µm/rev. The model predicts that thermal distortions of the drill and workpiece lead to oversized holes, with diametral errors ranging up to 26 µm. The holes have a bell shape and are smaller at the top than near the bottom, and the diametral variations within individual holes range from 17 to 26 µm. CMM measurements of the dry drilled holes indicate that thermal distortions of the drill and workpiece account for only a fraction of the total diametral errors.
Acknowledgements This work was supported by the Engineering Research Program of the Office of Basic Energy Sciences at the Department of Energy, and by the Dry Machining of Aluminum Consortium through the National Center for Manufacturing Sciences.
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References [1] D.M. Haan, S.A. Batzer, W.W. Olson, J.W. Sutherland, An experimental study of cutting fluid effects in drilling, Journal of Materials Processing Technology 71 (1997) 305–313. [2] K. Watanabe, K. Yokoyama, R. Ichimiya, Thermal analyses of the drilling process, Bulletin of the Japan Society of Precision Engineering 11 (1977) 71–77. [3] M.C. Shaw, Metal Cutting Principles, Oxford University Press, Oxford, 1984. [4] D.A. Stephenson, J.S. Agapiou, Metal Cutting Theory and Practice, Marcel Dekker, New York, 1997. [5] M. Bono, Experimental and Analytical Issues in Drilling. Ph.D. Dissertation, University of Michigan, Ann Arbor, 2001. [6] V. Chandrasekharan, A Model to Predict the Three-dimensional Cutting Force System for Drilling with Arbitrary Point Geometry. Ph.D. Dissertation, University of Illinois at Urbana-Champaign, 1996. [7] V. Chandrasekharan, S.G. Kapoor, R.E. DeVor, A mechanistic model to predict the cutting force system for arbitrary drill point geometry, Journal of Manufacturing Science and Engineering 120 (1998) 563–570. [8] Y. Chen, Modeling for New Drilling Process Development. Ph.D. Dissertation, University of Michigan, Ann Arbor, 1999. [9] E.M. Berliner, V.P. Krainov, Analytic calculations of the temperature field and heat flows on the tool surface in metal cutting due to sliding friction, Wear 143 (1991) 379–395. [10] J.S. Agapiou, D.A. Stephenson, Analytical and experimental studies of drill temperatures, Journal of Engineering for Industry 116 (1994) 54–60.
The effects of thermal distortions on the diameter and cylindricity of dry drilled holes Matthew Bono, Jun Ni
*
Department of Mechanical Engineering, University of Michigan, 1023 H.H. Dow Building, 2300 Hayward Street, Ann Arbor, MI 48109, USA Received 20 June 2000; accepted 26 March 2001
Abstract A model is developed to predict the effects of thermal distortion of the drill and workpiece on the diameter and cylindricity of dry drilled holes. Experiments using embedded thermocouples verify that the model predicts the flow of heat into the workpiece and into the drill reasonably well. The model predicts that thermal expansion of the drill is the dominant effect and leads to oversized holes with diameters that increase with depth. 2001 Elsevier Science Ltd. All rights reserved. Keywords: Dry drilling; Thermal distortion; Cylindricity; Hole quality; Metal cutting
1. Introduction The subject of dry drilling has received considerable attention recently, and it is quickly becoming a priority in many manufacturing industries. Many researchers are investigating tool geometries and coatings for performing dry drilling and near-dry drilling, but there is concern that the heat generated by the process can lead to thermal expansion of the drill and workpiece that will affect the size and quality of the holes. This study develops a model to predict the effects of thermal distortions on the diameter and cylindricity of dry drilled holes. Finite element models calculate the thermally distorted shapes of the drill and workpiece, which are used to calculate the diameter of the hole as a function of depth. The adverse effects of dry drilling are well known. Recently, Haan et al. [1] performed an experimental investigation of the role of cutting fluids in drilling. They found that dry drilled holes have a poorer surface finish than holes drilled with cutting fluid, and dry drilled holes have * Corresponding author. Fax: +1-734-936-0363. E-mail address: [email protected] (J. Ni).
0890-6955/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 8 9 0 - 6 9 5 5 ( 0 1 ) 0 0 0 4 7 - 5
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Nomenclature a aw b l h f q w Fc Ff,r Ft Fz kt kw lc q qfriction qshear q⬙drill q⬙wp R2 rinner router T V Vchip Vf
Rake angle Thermal permeability of workpiece material Friction angle Inclination angle Chip angle ⬇l Shear angle Angle between drill axis and the cutting edge Angular velocity of the drill Cutting force of the ECT acting parallel to tool velocity Frictional shearing force between chip and tool Force of the ECT acting perpendicular to the cutting edge and the tool velocity Thrust force of the ECT acting parallel to the drill axis Thermal conductivity of tool material Thermal conductivity of workpiece material Chip–tool contact length ⬇ (2)(uncut chip thickness) Rate of total heat generation for an ECT Rate of heat generation by friction for an ECT Rate of heat generation in shear for an ECT Heat flux load applied to each element of the drill Heat flux load applied to each element of the workpiece fraction of energy generated by friction on rake face that flows into chip Inner radius of the element Outer radius of the element Torque contributed by an ECT=(Fc)(radius) Cutting velocity of the ECT=(w)(radius) Chip velocity Feed velocity of the drill
a bell shape, with the minimum diameter at the top of the hole. Watanabe et al. [2] developed a model for predicting the effects of thermal distortions in low speed drilling. Their insightful analysis was similar to the current study, in that they predicted the thermal expansion of the workpiece and drill to obtain a rough calculation of the diameter of the drilled hole at different depths. The current study focuses on drilling at speeds of several thousand rpm and develops a model to predict the diameter of dry drilled holes as a function of depth. The objective is to determine the individual effects of thermal expansion of the workpiece and the drill and to predict the magnitudes of the diametral errors that are caused by thermal expansion.
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2. Predictive model 2.1. Geometry of the FEAs Two finite element models are used in this study. The first model consists of a two-dimensional, axisymmetric finite element model of a cylindrical workpiece, created with the commercial finite element code ABAQUS. The elements are of type CAX4T, which are four-node bilinear temperature and displacement elements. In the model, the drill machines a hole in the center of the workpiece, which induces thermal loads on the workpiece and raises the temperature. To represent the heat that flows into the workpiece during the drilling process, heat flux is applied to the elements located directly beneath the cutting edge of the drill. This heat raises the temperature of the workpiece material, and the resulting thermal deformations distort the shape of the workpiece, as shown in Fig. 1. The figure shows the shape that the workpiece assumes as a result of the thermal deformation. As the drill proceeds into the workpiece, elements are removed from the model, and heat flux is applied to the next row of elements. This process repeats until the drill has proceeded through the entire depth of the workpiece. All other surfaces of the workpiece are modeled as adiabatic. For each step of the analysis, the FEA computes the temperature field and the thermally distorted shape of the workpiece. The heat entering the workpiece causes it to expand radially, and the drill cuts the material when it is in this expanded configuration. Thus, when the workpiece cools back to room temperature, the diameter of the drilled hole shrinks as the workpiece contracts. Heat also flows into the drill during the drilling process. This heat raises the temperature of the drill and causes it to expand. Thus, the expansion of the drill and the expansion and subsequent contraction of the workpiece counteract each other to determine the final room temperature diameter of the drilled hole. Another finite element analysis calculates the diameter of the cutting edges of the hot drill as it progresses into the workpiece. This finite element model is illustrated in Fig. 2. This three-dimensional finite element model consists of eight-node coupled temperature and displacement elements of type C3D8T. The heat that enters the drill is modeled by applying heat flux to the elements on the rake face that correspond to the cutting edges of the drill. All other surfaces of the drill are adiabatic. The transient analyses of the drill and workpiece are used to calculate the room temperature shape of the drilled hole. As each layer of elements is removed from the FEM of the workpiece, the diameter of the cutting edges of the drill is calculated. The distorted configurations of the hot
Fig. 1.
Thermally distorted shape of the workpiece.
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Fig. 2. Finite element model of the drill and the heat flux loads.
drill and the hot workpiece are used to calculate the room temperature diameter of the drilled hole as a function of depth, thereby determining the cylindricity of the hole. 2.2. Calculating the heat flux loads In order to calculate the heat flux loads on each of the elements in the finite element models, the cutting edges of the drill are considered as a sequence of individual, elementary cutting tools (ECTs). Each ECT performs a simple metal cutting operation, so metal cutting theories can be used to evaluate the forces and heat transfer on each segment of the cutting edge. For each ECT, some of the heat generated on the shear plane flows into the workpiece, and some of the heat generated by friction on the rake face flows into the tool [3,4]. A model for calculating the heat partition on each ECT is developed in a previous study [5]. As described in this previous work, the heat flux load applied to each element of the FEA of the workpiece is given by: (1−qfriction/q)(Tw+FzVf) q⬙wp⫽ . p(r2outer−r2inner)
(1)
The fraction of the total heat dissipated by the ECT that is consumed by friction on the rake face is given by Eq. (2) through Eq. (5). qfriction Ff,rVchip ⫽ q Tw+FzVf
Vchip⫽V
cos l sin f cos h cos(f−a)
Fz+Fca Ft⫽ b
(2)
(3)
(4)
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(sin l−cos l sin a tan h)cos q a⬅ (sin l sin a tan h+cos l)cos l
b⬅
cos a tan h cos q (cos2 l−cos2 q)1/2 ⫹ (sin l sin a tan h+cos l)cos l cos l
Ff,r⫽
(cos a cos l)Ft+(sin a)Fc cos a cos l cos h+sin a(sin l sin h+sin a cos l cos h) 2
(5)
The drills used in this study have been ground to a prescribed geometry, so all of the cutting angles are known for each ECT. In addition, the thrust force and cutting force for each ECT are calculated from the total measured thrust and torque using the model created by Chandrasekharan and co-workers [6,7] and modified by Chen [8]. As described in the previous work [5], experiments have verified that this model correctly predicts the flow of heat into the workpiece. The flow of heat into the drill is calculated in a similar manner. The heat flux load applied to each element of the FEA of the drill is given by: (1−R2)(qfriction/q)(Tw+FzVf) q⬙drill⫽ . area of element
(6)
The partition of the energy generated by friction on the rake face between the chip and the tool is calculated using the model developed by Berliner and Krainov [9]. The fraction of this energy that is carried away by the chip is given by Eq. (7). Note that the current study is concerned with the fraction of this energy that flows into the tool, which is (1⫺R2).
冋
冉冊册
kt p R2⫽ 1⫹0.45 kw Pe
1/2 −1
Vchiplc Pe⫽ . aw
(7)
3. Experimental verification of the model In order to verify the accuracy of the model for the flow of heat into the drill, drilling tests are performed on a Mori Seiki TV-30 CNC drilling machine. Holes of diameter 9.92 mm are drilled with a HSS drill in a plate of aluminum 319 to a depth of 25 mm. The drills are standard single-cone twist drills, with a point angle of 125° and a helix angle of 39°. As the holes are drilled, a Kistler piezoelectric dynamometer measures the drilling thrust and torque. A type K thermocouple with a wire diameter of 127 µm is embedded in the drill to measure the transient temperature of a point near the cutting edge. Embedding thermocouples is a well
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established method of measuring drill temperatures [10]. The thermocouple is embedded in a slot that was ground into the drill point, as shown in Fig. 3. The thermocouple bead is located 0.8 mm from the cutting edge, 0.3 mm below the surface of the clearance face. The thermocouple wires run up the drill body in another slot, which was ground into the land of the drill. The thermocouple is held in place with high-temperature epoxy with a large thermal conductivity, which was designed for thermocouple applications. A slip ring transmits the thermocouple signal from the rotating drill to a personal computer, where the data is collected with an OMD-5508 TC board. The purpose of the thermocouple is to compare the experimentally measured drill temperatures with the temperatures predicted by the FEA. Thus, the model for the heat flow into the drill can be verified over a range of drilling speeds and feeds. The speeds range from 3000 to 7000 rpm, and the feeds range from 127 to 381 µm/rev. The predicted and measured temperature rises at the location of the thermocouple for each of the five drilling tests are plotted in Fig. 4. Fig. 4 shows that the model predicts the flow of heat into the drill reasonably well. In each case, both the predicted and measured temperatures increase continuously throughout the drilling process, and the measured temperatures immediately begin to decrease at the conclusion of the drilling process. The percentage errors between the predicted and measured temperature rises at the end of the drilling process for each of the experiments are summarized in Fig. 5. The maximum error occurs with a speed of 3000 rpm and a feed of 127 µm/rev. The accuracy of the predictive model increases with speed and feed, and for feeds of 381 µm/rev, the errors are each 4%. There are several possible causes of the discrepancies between the measured and predicted temperature rises for the smaller feedrates. For example, the model assumes that the face of the chip opposite the rake face is an adiabatic surface. For very thin chips, this assumption could result in an underprediction of the amount of heat that enters the chip and an overprediction of the amount of heat that enters the drill. Any number of other assumptions and simplifications made in the predictive model could cause the discrepancies between the measured and predicted temperatures. However, given all of the inherent complexities in predicting and measuring drill temperatures over a range of feeds and speeds, the predictive model is reasonably accurate. The previous experimental investigation of the flow of heat into the workpiece [5] and the current experiments have verified that the model predicts the flow of heat into the workpiece and into the drill reasonably well. Thus, the predicted heat fluxes can be used in the finite element models to determine the transient, thermally deformed shapes of the workpiece and drill and the resulting errors in the diameters of the drilled holes.
Fig. 3.
Thermocouple embedded in the drill point near the cutting edge.
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Fig. 4. Predicted and measured temperature rises for five different combinations of feed and speed.
Fig. 5. Percentage errors between the predicted and measured temperature rises at the end of the drilling process.
4. Results and discussion The model is used to predict the diametral errors encountered in dry drilling for speeds of 3000, 5000 and 7000 rpm, with feeds of 127, 254 and 381 µm/rev. Drilling tests are performed to measure the thrust force and torque for each of the nine combinations of feed and speed. The model predicts that when dry drilling aluminum 319 with a 9.92 mm HSS drill through a plate of thickness 29 mm, thermal expansion of the drill and workpiece produce diametral errors of ⬍30 µm. An example of the shape of the drilled hole wall at room temperature is plotted in Fig.
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Fig. 6.
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Predicted shape of the drilled hole at room temperature for a speed of 7000 rpm and a feed of 381 µm/rev.
6. This example is for a drilling speed of 7000 rpm and a feed of 381 µm/rev, but all of the predicted hole profiles have this same general shape. Recall that the final shape of the hole is determined by the contraction of the workpiece and the expansion of the drill. These independent effects are represented in the figure by the dotted line and the dashed line, respectively. The heavy dark line represents the final shape of the hole at room temperature. Several facts are apparent from Fig. 6. As expected, contraction of the workpiece tends to decrease the size of the hole, and expansion of the drill tends to increase the size of the hole. For these drilling conditions, the expansion of the drill is a more dominant factor than contraction of the workpiece. The entire hole is oversized, and the hole is smallest at the top and widens near the bottom. In this example, the maximum diameter is 25 µm larger than the minimum diameter. The predicted diametral errors for all of the data points are plotted in Fig. 7. Each bar on the chart corresponds to a different data point. The top of each bar represents the maximum diameter of the hole, and the bottom of the bar represents the minimum diameter of the hole. The vertical axis represents the deviation of the diameter from the nominal room temperature diameter of the drill, which is 9.922 mm. The model predicts that thermal distortions of the drill and workpiece lead to holes that are
Fig. 7.
Diametral deviations for all of the drilling tests, predicted from the measured drilling forces.
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oversized, and diametral errors range from 0 to 26 µm. Hole diameters vary through the depth of the part, and the diametral variations within individual holes range from 17 to 26 µm. The effects of feed and speed on diameter and cylindricity are quite complicated. Many competing effects determine the final diameter and shape of the hole, and changes in the feed and speed cause changes in many other parameters, including the feed velocity, the total drilling time, and the drilling forces. Recall that each of the predictions is based on measured drilling forces, and there is always some variation in the drilling forces for a set of drilling conditions. Thus, while these predictions estimate the magnitudes of the diametral errors, they are not intended to reveal the specific effects of feed and speed. However, for the range of conditions considered in this study, speed and feed appear to have only minor effects on the predicted maximum and minimum diameters of the drilled holes. The actual diameters of several of the drilled holes were measured with a coordinate measuring machine. The measured diameters are several hundred microns larger than the predicted diameters. The reason for the discrepancy between the measured and predicted diameters is that this predictive model considers only the diametral errors caused by thermal expansion effects. However, in reality, many other factors can contribute to the total diametral error. Some of these factors include whirling of the drill due to uneven lip height or asymmetric built up edge formation, wander of the drill point during initial entry into the workpiece, run out of the machine spindle, and vibration of the drill and the machine. The results of the predictions and experimental measurements indicate that only a small fraction of the total diametral error is caused by thermal distortion of the drill and the workpiece.
5. Conclusions A model has been developed to predict the effects of thermal distortion of the drill and workpiece on the diameter and cylindricity of dry drilled holes. Experiments verify that the model predicts the flow of heat into the workpiece and into the drill reasonably well. The study considers the quality of holes produced when drilling in a workpiece of aluminum 319, using a HSS drill of diameter 9.92 mm, with speeds ranging from 3000 to 7000 rpm, and with feeds ranging from 127 to 381 µm/rev. The model predicts that thermal distortions of the drill and workpiece lead to oversized holes, with diametral errors ranging up to 26 µm. The holes have a bell shape and are smaller at the top than near the bottom, and the diametral variations within individual holes range from 17 to 26 µm. CMM measurements of the dry drilled holes indicate that thermal distortions of the drill and workpiece account for only a fraction of the total diametral errors.
Acknowledgements This work was supported by the Engineering Research Program of the Office of Basic Energy Sciences at the Department of Energy, and by the Dry Machining of Aluminum Consortium through the National Center for Manufacturing Sciences.
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