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Thermal modeling and optimization of interrupted grinding
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CIRP-1816; No. of Pages 4 CIRP Annals - Manufacturing Technology xxx (2018) xxx–xxx
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CIRP Annals - Manufacturing Technology jou rnal homep age : ht t p: // ees .e lse vi er . com /ci r p/ def a ult . asp
Thermal modeling and optimization of interrupted grinding Changsheng Guo (2)*, Yan Chen United Technologies Research Center, East Hartford, CT, USA
A R T I C L E I N F O
A B S T R A C T
Keywords: Grinding Temperature Modeling
Finishing parts such as blade tips of assembled engine rotors is an interrupted grinding process. Thermal issues such as burn often become more prominent for interrupted grinding because of the low thermal capacity during the entry and the exit of each interruption. This paper presents models to calculate the transient and steady state temperatures for interrupted grinding. The developed models are then used to investigate the influence of grinding process parameters and cooling on the transient temperature rise. The model results can be used to develop new grinding cycles with variable work speed to increase material removal rate while maintaining temperature below burn limit. © 2018 Published by Elsevier Ltd on behalf of CIRP.
1. Introduction
2. Thermal model for interrupted grinding
Finishing of parts such as blade tips of assembled compressor or turbine rotors is an interrupted grinding process. Thermal damage, which is often the main factor affecting workpiece quality and limiting the grinding production rates, becomes especially important for interrupted grinding because of the unfavourable thermal conditions caused by the low thermal capacity and variable cooling during the exit of each interruption. Extensive research work has been published to investigate the grinding thermal problems for both straight and cylindrical surface grinding [1–4]. Malkin and Guo presented detailed review of grinding thermal research [4]. Thermal analyses of grinding processes are usually based upon the application of the moving heat source theory [4]. A critical parameter needed for calculating the workpiece temperature response is the energy partition to the workpiece, which is the fraction of the total grinding energy transported to the workpiece as heat at the grinding zone. The energy partition depends on the type of grinding, the grinding wheel and workpiece materials, coolant type, and the operating conditions. Extensive research has also been done on cooling effectiveness and energy partition in grinding [4–9]. Energy partition for regular grinding with conventional abrasive wheels is typically in the range of 60–70%, and 3–5% for creep–feed grinding [4]. Grinding with super abrasive wheels has found to have lower energy partition of 20–25% due to the higher thermal conductivity of both CBN and diamond abrasives. Thermal models in the literature that produce a quasi–steady state temperature distribution are insufficient for interrupted grinding. The objective of this paper is to develop transient thermal models to understand the underlying factors which affect the grinding temperature rises in interrupted grinding and develop process optimization strategies to increase removal rate.
For external cylindrical grinding as shown in Fig. 1a, the temperature will reach a quasi–steady state after the grinding wheel has travelled a distance greater than 5 times of the wheelworkpiece contact length which is typically a few millimetres. The maximum quasi–steady state temperature at the grinding zone um can be readily calculated using the following equation [4]:
* Corresponding author. E-mail address: [email protected] (C. Guo).
um ¼
1:128qw a1=2 a1=4 de kvw 1=2
1=4
¼
1:128qw ðlc =2Þ kPe 0:5
ð1Þ
where de [m] is the equivalent diameter, a [m] is the wheel depth of cut, vw [m/s] is the work speed, k [W/m K] and a [m2/s] are the thermal conductivityand thermal diffusivityof the workpiece respectively, Pe is the Peclet number defined as Pevwlc/4a and qw [W/m2] is the heat flux to the workpiece which can be calculated using the grinding power per unit width of grinding P0, the wheel-workpiece contact length lc and the energy partition to the workpiece e as follows: 0
qw ¼ e
P lc
ð2Þ
The above thermal model has been experimentally verified successfully applied to optimize and control grinding processes to increase productivity while avoiding thermal damage to the workpiece [10–13]. For interrupted grinding as illustrated in Fig. 1b, however, the thermal quasi–steady state as described above may not be reached. The short workpiece such as a blade tip starts exiting the grinding zone before a quasi–steady state temperature can be reached. For example, the width of a blade tip for high compressor stages or turbine of modern jet engines might be only 1–2 mm which is close to the wheel-workpiece contact length at small depths of cut 0.025 mm. Hence, a transient thermal situation may prevail during each of the interrupt grinding where the workpiece is
https://doi.org/10.1016/j.cirp.2018.04.083 0007-8506/© 2018 Published by Elsevier Ltd on behalf of CIRP.
Please cite this article in press as: Guo C, Chen Y. Thermal modeling and optimization of interrupted grinding. CIRP Annals Manufacturing Technology (2018), https://doi.org/10.1016/j.cirp.2018.04.083
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Fig. 4. Illustration of heat conduction during entry and exit.
Fig. 1. Illustration of interrupted grinding.
heated up during grinding and then cooled down after it exits the grinding zone. For analysing the thermal situation of interrupted grinding, a transient thermal model is needed to account for all the factors that contribute to the transient behaviour of the thermal problem. First, the heat flux to the workpiece is a variable for interrupted grinding (Fig. 2). The variation of the heat flux qw will depend on the grinding condition. If a smaller wheel grinds a relatively thicker blade (Case I in Fig. 3) at a smaller depth of cut, the heat flux goes up gradually when the blade tip enters the grinding zone. It reaches a constant value during grinding the middle portion of the blade tip. The heat flux starts to decrease when the blade tip starts exiting from the grinding zone. For Case II, the full depth of cut will not be reached because of the larger grinding wheel, larger depth of cut and the relatively thinner blade tip. The grinding wheel starts exiting the grinding zone before the full depth of cut is reached.
not all, of the grinding cycle for some of the interrupted grinding cases. It should be noted that the effect of the workpiece geometry on the grinding heat transfer will become even more pronounced for workpiece materials with higher thermal conductivity. For the thermal problem described above, obtaining a closed form solution for the transient temperature distribution was not successful. In this paper, a finite difference method under MATLAB is used to calculate the transient temperature distribution. First, a full model containing all the blades was established. It was verified that there is no temperature difference among blades during and after grinding. However, the full model is very computational intensive in order to keep track the temperature distribution history of all the blades. A simplified model with one blade is used in this paper. Fig. 5 shows the model setup and the boundary conditions. There are 3 regions R1, R2, R3 during each workpiece revolution. Region R1 is the grinding region during which grinding heat flux calculated using Eq. (2) is applied at the top. Within Region R2, cooling is applied at portion of the top surface outside the grinding zone and the side surfaces. The bottom of the blade is set at a constant temperature of 20 because it is far from the top surface. There is no heating and only air cooling when the blade is in Region R3.
Fig. 2. Thermal model of interrupted grinding.
Fig. 5. Thermal model.
For calculating the heat flux at the grinding zone with Eq. (2), the grinding power per unit width P0 is calculated using the following grinding power model [16]: P
Fig. 3. Heating and cooling during interrupted grinding.
Secondly, the cooling can occur at both the top and the side surfaces of the blade as illustrated in Fig. 2. Cooling starts before the blade enters the grinding zone and it can also continue for a short time after it exists from the grinding zone. The region of cooling as illustrated in Fig. 2 depends on the cooling condition and the nozzle setup condition [14,15]. The cooling variation within each workpiece revolution is also illustrated in Fig. 3. Finally, the workpiece geometry is another contributor to the transient behaviour. For continuous cylindrical grinding, the heat into the workpiece can conduct into the workpiece in all directions as illustrated in Fig. 4b. For interrupted grinding, however, the workpiece is not available for heat conduction during both entry and exit as shown in Fig. 4a and c. This entry and exit situation occupies most, if
0
¼ uch ðavw Þ þ mpa Aðade Þ
0:5
vs þ F 0 pl vs
ð3Þ
where pa is the average contact pressure at the wheel-workpiece contact, which is proportional to the curvature difference as discussed in Ref. [16]. The model coefficients for the nickel alloy IN100 were obtained as: specific chip formation energy uch = 17.6 J/ mm3, coefficient of friction m = 0.27, plowing force per unit width Fpl = 0.42 N/mm, wheel wear flat area A = 0.01, and the constant for contact pressure p0 = 3.02 106 MPa mm [16]. The energy partition to the workpiece can vary with grinding conditions. In this paper, e = 25% is used for grinding Ni alloy with plated CBN wheels [17]. 3. Results and discussions In this section, model results for grinding a part resembling a rotor with a number of blades are presented to discuss the influence of grinding process parameters on the temperature rises. The blade is made of a nickel super alloy (IN100) with the following properties: thermal conductivity k = 11.4 W/(m K), specific heat cp = 435 J/(kg K), density r = 8000 kg/m3, and yield strength s s = 1100 MPa. Wheel diameter ds = 200 mm, diameter at the blade tip dw=500 mm, wheel speed vs = 60 m/s will be used for the examples below unless they are specified.
Please cite this article in press as: Guo C, Chen Y. Thermal modeling and optimization of interrupted grinding. CIRP Annals Manufacturing Technology (2018), https://doi.org/10.1016/j.cirp.2018.04.083
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3.1. An example An example is shown in Fig. 6 for grinding a blade tip under the following grinding condition: blade tip diameter dw = 500 mm, tip width t = 3 mm, work speed vw = 0.2 m/s, wheel diameter ds = 200 mm, wheel speed vs = 60 m/s, and depth of cut a = 0.05 mm. The convective heat transfer coefficient is set to 0 (dry grinding). The maximum temperature rises for the first 5 revolutions and the 1st revolution are shown in Fig. 6a and b. The temperature rises sharply when the blade starts entering the grinding zone. It reaches a “quasi–steady” value of 620 when the wheel is grinding the middle portion of the blade during the 1st workpiece revolution. This is comparable to the value calculated with Eq. (1) which is 624 . The temperature rises above this value when the wheel starts exiting from the workpiece. The maximum temperature reaches 646 . Because of no cooling to cool down the workpiece bulk, the maximum temperature keeps going up and reaches 760 at the end of the 5th revolution. Fig. 6c shows a contour of the temperature distribution of the blade tip to a depth of 0.6 mm near the end of the 1st revolution (Time = 0.028 s). It can be seen that the heat only reaches a shallow depth into the blade due to the low thermal conductivity.
Fig. 7. Influence of works peed on maximum temperature (computed).
3.3. Influence of cooling Fig. 8 shows the influence of cooling on maximum temperature rises. The figure shows the maximum temperature for the 1st and the 5th workpiece revolution under the same grinding condition as in Fig. 6. Three convective cooling coefficients (h = 1000, 4000, and 8000 W/(m2 K)) were applied on the top surface outside the grinding zone and the side surfaces when the blade is within Region R2 (Figs. 2 and 5). Result for the dry grinding case (h = 0) is also included for comparison. First, the cooling suppresses the additional temperature rise during the exit. At h = 8000 W/(m2 K), there is no additional temperature rise at the exit. Secondly, cooling reduces the bulk temperature of the part. The part has lower temperature when it comes into the grinding zone for the next revolution. With h = 8000 W/(m2 K), the maximum surface temperature is only 10 when it comes into grinding for the 5th revolution. It is 68 if h = 1000 W/(m2 K), and 115 if no cooling (Fig. 6). Fig. 8c plots the maximum temperature versus the blade length (depth) near the end of the 5th revolution. Nozzle setup is important to cooling on the side surfaces especially during exit.
Fig. 6. An example of temperature variation (computed). Fig. 8. Influence of cooling on maximum temperature (computed).
3.2. Influence of work speed and depth of cut 3.4. Influence of wheel diameter Under the same specific removal rate, the work speed and depth of cut can have different influence on the temperature rise. Fig. 7 shows the maximum temperature versus time for the 1st workpiece revolution under 3 work speeds and depths of cut while keeping a constant specific removal rate q0 = avw = 0.1 mm3/ (mm s). The maximum temperature reaches 688 C for work speed vw = 0.1 m/s, it drops to 645 C at vw = 0.2 m/s, and further down to 631 C at vw = 0.3 m/s. The temperature reduction is not linear with the increase of work speed. Optimization can be done to obtain the optimum work speed for a given grinding situation.
Grinding wheel diameter has influence on the wheel-workpiece contact length lc, the grinding power, and the heat flux at the grinding zone. Larger wheel diameter leads to longer wheelworkpiece contact and longer duration of grinding. It increases the grinding power (Eq. (3)) but reduces the heat flux. An example of the wheel diameter influence on maximum temperature is shown in Fig. 9. The maximum temperature is plotted for 3 wheel diameters. Other grinding conditions are the same as example in Fig. 6. Larger grinding wheel reduces the temperature. It should be
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less thermally conductive materials such as nickel alloys. The high thermal concentration near the surface is one of the reasons why it is difficult to manage the thermal problem for grinding nickel alloys. 4. Conclusions
Fig. 9. Influence of wheel diameter on maximum temperature (computed).
noted that larger wheel makes it more challenging to apply coolant to the grinding zone which can be more important for some grinding situation. 3.5. Influence of workpiece thermal property Thermal property can have significant influence on grinding temperature. An example is shown in Fig. 10 to compare two materials. Thermal conductivity k = 11.4 W/(m K) represents nickel alloys and k = 60.5 W/(m K) represents carbon steels. In this example, the same grinding power calculated with Eq. (3) and the same energy partition of 25% are used even though the power will can be much lower for grinding carbon steels as compared to grinding nickel alloys [18]. It can be seen that the maximum temperature rise is much slower for workpiece with higher thermal conductivity. With the higher thermal conductivity case (k = 60.5 W/(m K)), the temperature has not reached a quasi–steady state for the tip width of t = 3 mm before the workpiece exiting from the grinding zone. The additional temperature rises are also higher for the highly thermal conductive materials. Thermal conductivity has a big influence on the depth of thermal penetration into the workpiece as shown in Fig. 10b. Higher thermal conductivity leads to deeper thermal penetration while heat is concentrated near the surface layer for
Fig. 10. Influence of thermal property on maximum workpiece temperature (computed).
A transient thermal model is developed for interrupted grinding. The model accounts for the 3 factors that distinguish interrupted grinding from continuous OD plunge grinding: the variable heat flux, the variable cooling, and the reduced thermal capacity of the workpiece during entry and exit. The model results show the following main findings: 1. Interrupt grinding leads to higher temperature than continuous OD plunge grinding under the same grinding condition. Temperature rises higher during exit. 2. Higher work speeds lead to less difference in temperatures between continuous plunge OD grinding and interrupted grinding. 3. Cooling from the side surfaces becomes critical to suppress temperature for interrupted grinding especially for slow work speed. Cooling is very important to keep lower temperature by cooling the bulk. 4. Higher workpiece thermal conductivity and lower work speeds lead to higher additional temperature rises for interrupted grinding during exit. The quasi–steady state temperature model of Eq. (1) should not be used under this condition.
References [1] Shaw MC (1990) A Simplified Approach to Workpiece Temperature in Fine Grinding. Annals of the CIRP 39(1):345–349. [2] Rowe WB, Black SCE, Mills B, Qi HS, Morgan MN (2005) Experimental Investigation of Heat Transfer in Grinding. Annals of the CIRP 44(1):329–332. [3] Guo C, Malkin S (1994) Analytical and Experimental Investigation of Burn-out in Creep-feed Grinding. Annals of the CIRP 43(1):283–286. [4] Malkin S, Guo C (2007) Thermal Analysis of Grinding. Annals of the CIRP 56 (2):760–782. [5] Jin T, Stephenson DJ (2008) A Study of the Convection Heat Transfer Coefficients of Grinding Fluids. Annals of the CIRP 57(1):367–370. [6] Jin T, Stephenson DJ, Xie GZ, Sheng XM (2011) Investigation on Cooling Efficiency of Grinding Fluids in Deep Grinding. Annals of the CIRP 60 (1):343–346. [7] Zheng HW, Gao H (1994) A General Thermal Model for Grinding with Slotted or Segmented Wheel. Annals of the CIRP 43(1):287–290. [8] Rowe WB, Pettit JA, Boyle A, Moruzzi JL (1988) Avoidance of Thermal Damage in Grinding and Prediction of the Damage Threshold. Annals of the CIRP 37 (1):327–330. [9] Oliveira JF, Silva EJ, Coelho RT, Brozek L, Bottene LC, Marcos GP (2015) Dry Grinding Process with Workpiece Precooling. Annals of the CIRP 64(1):329– 332. [10] Xiao G, Malkin S (1996) On-line Optimization for Internal Plunge Grinding. Annals of the CIRP 45(1):287–290. [11] Krajnik P, Drazumeric R, Badger J, Hashimoto F (2014) Cycle Optimization in Cam-lobe Grinding for High Productivity. Annals of the CIRP 63(1):333. [12] Sridharan U, Bedekar V, Kolarits FM (2017) A Functional Approach to Integrating Grinding Temperature Modeling and Barkhausen Noise Analysis for Prediction of Surface Integrity in Bearing Steels. Annals of the CIRP 66(1):333–336. [13] Krajnik P, Drazumeric R, Badger J (2013) Optimization of Peripheral Non-round Cylindrical Grinding via an Adaptable Constant-temperature Process. Annals of the CIRP 62(1):347–350. [14] Guo C, Malkin S (1992) Analysis of Fluid Flow in Grinding. ASME Journal of Engineering for Industry 114:427–434. [15] Engineer F, Guo C, Malkin S (1992) Experimental Investigation of Fluid Flow in Grinding. ASME Journal of Engineering for Industry 114:61–66. [16] Guo C, Shi Z, Attia H, McIntosh D (2007) Power and Wheel Wear for Grinding Nickel Alloy with Plated CBN Wheels. Annals of the CIRP 56(1):343–346. [17] Kohli S, Guo C, Malkin S (1993) Energy Partition to the Workpiece for Grinding with Aluminium Oxide and CBN Abrasive Wheels. ASME Journal of Engineering for Industry 117:160–168. [18] Shi Z (2004) Grinding with Electroplated Cubic Boron Nitride (CBN) Wheels. Ph.D. Thesis, University of Massachusetts, Amherst.
Please cite this article in press as: Guo C, Chen Y. Thermal modeling and optimization of interrupted grinding. CIRP Annals Manufacturing Technology (2018), https://doi.org/10.1016/j.cirp.2018.04.083
CIRP-1816; No. of Pages 4 CIRP Annals - Manufacturing Technology xxx (2018) xxx–xxx
Contents lists available at ScienceDirect
CIRP Annals - Manufacturing Technology jou rnal homep age : ht t p: // ees .e lse vi er . com /ci r p/ def a ult . asp
Thermal modeling and optimization of interrupted grinding Changsheng Guo (2)*, Yan Chen United Technologies Research Center, East Hartford, CT, USA
A R T I C L E I N F O
A B S T R A C T
Keywords: Grinding Temperature Modeling
Finishing parts such as blade tips of assembled engine rotors is an interrupted grinding process. Thermal issues such as burn often become more prominent for interrupted grinding because of the low thermal capacity during the entry and the exit of each interruption. This paper presents models to calculate the transient and steady state temperatures for interrupted grinding. The developed models are then used to investigate the influence of grinding process parameters and cooling on the transient temperature rise. The model results can be used to develop new grinding cycles with variable work speed to increase material removal rate while maintaining temperature below burn limit. © 2018 Published by Elsevier Ltd on behalf of CIRP.
1. Introduction
2. Thermal model for interrupted grinding
Finishing of parts such as blade tips of assembled compressor or turbine rotors is an interrupted grinding process. Thermal damage, which is often the main factor affecting workpiece quality and limiting the grinding production rates, becomes especially important for interrupted grinding because of the unfavourable thermal conditions caused by the low thermal capacity and variable cooling during the exit of each interruption. Extensive research work has been published to investigate the grinding thermal problems for both straight and cylindrical surface grinding [1–4]. Malkin and Guo presented detailed review of grinding thermal research [4]. Thermal analyses of grinding processes are usually based upon the application of the moving heat source theory [4]. A critical parameter needed for calculating the workpiece temperature response is the energy partition to the workpiece, which is the fraction of the total grinding energy transported to the workpiece as heat at the grinding zone. The energy partition depends on the type of grinding, the grinding wheel and workpiece materials, coolant type, and the operating conditions. Extensive research has also been done on cooling effectiveness and energy partition in grinding [4–9]. Energy partition for regular grinding with conventional abrasive wheels is typically in the range of 60–70%, and 3–5% for creep–feed grinding [4]. Grinding with super abrasive wheels has found to have lower energy partition of 20–25% due to the higher thermal conductivity of both CBN and diamond abrasives. Thermal models in the literature that produce a quasi–steady state temperature distribution are insufficient for interrupted grinding. The objective of this paper is to develop transient thermal models to understand the underlying factors which affect the grinding temperature rises in interrupted grinding and develop process optimization strategies to increase removal rate.
For external cylindrical grinding as shown in Fig. 1a, the temperature will reach a quasi–steady state after the grinding wheel has travelled a distance greater than 5 times of the wheelworkpiece contact length which is typically a few millimetres. The maximum quasi–steady state temperature at the grinding zone um can be readily calculated using the following equation [4]:
* Corresponding author. E-mail address: [email protected] (C. Guo).
um ¼
1:128qw a1=2 a1=4 de kvw 1=2
1=4
¼
1:128qw ðlc =2Þ kPe 0:5
ð1Þ
where de [m] is the equivalent diameter, a [m] is the wheel depth of cut, vw [m/s] is the work speed, k [W/m K] and a [m2/s] are the thermal conductivityand thermal diffusivityof the workpiece respectively, Pe is the Peclet number defined as Pevwlc/4a and qw [W/m2] is the heat flux to the workpiece which can be calculated using the grinding power per unit width of grinding P0, the wheel-workpiece contact length lc and the energy partition to the workpiece e as follows: 0
qw ¼ e
P lc
ð2Þ
The above thermal model has been experimentally verified successfully applied to optimize and control grinding processes to increase productivity while avoiding thermal damage to the workpiece [10–13]. For interrupted grinding as illustrated in Fig. 1b, however, the thermal quasi–steady state as described above may not be reached. The short workpiece such as a blade tip starts exiting the grinding zone before a quasi–steady state temperature can be reached. For example, the width of a blade tip for high compressor stages or turbine of modern jet engines might be only 1–2 mm which is close to the wheel-workpiece contact length at small depths of cut 0.025 mm. Hence, a transient thermal situation may prevail during each of the interrupt grinding where the workpiece is
https://doi.org/10.1016/j.cirp.2018.04.083 0007-8506/© 2018 Published by Elsevier Ltd on behalf of CIRP.
Please cite this article in press as: Guo C, Chen Y. Thermal modeling and optimization of interrupted grinding. CIRP Annals Manufacturing Technology (2018), https://doi.org/10.1016/j.cirp.2018.04.083
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Fig. 4. Illustration of heat conduction during entry and exit.
Fig. 1. Illustration of interrupted grinding.
heated up during grinding and then cooled down after it exits the grinding zone. For analysing the thermal situation of interrupted grinding, a transient thermal model is needed to account for all the factors that contribute to the transient behaviour of the thermal problem. First, the heat flux to the workpiece is a variable for interrupted grinding (Fig. 2). The variation of the heat flux qw will depend on the grinding condition. If a smaller wheel grinds a relatively thicker blade (Case I in Fig. 3) at a smaller depth of cut, the heat flux goes up gradually when the blade tip enters the grinding zone. It reaches a constant value during grinding the middle portion of the blade tip. The heat flux starts to decrease when the blade tip starts exiting from the grinding zone. For Case II, the full depth of cut will not be reached because of the larger grinding wheel, larger depth of cut and the relatively thinner blade tip. The grinding wheel starts exiting the grinding zone before the full depth of cut is reached.
not all, of the grinding cycle for some of the interrupted grinding cases. It should be noted that the effect of the workpiece geometry on the grinding heat transfer will become even more pronounced for workpiece materials with higher thermal conductivity. For the thermal problem described above, obtaining a closed form solution for the transient temperature distribution was not successful. In this paper, a finite difference method under MATLAB is used to calculate the transient temperature distribution. First, a full model containing all the blades was established. It was verified that there is no temperature difference among blades during and after grinding. However, the full model is very computational intensive in order to keep track the temperature distribution history of all the blades. A simplified model with one blade is used in this paper. Fig. 5 shows the model setup and the boundary conditions. There are 3 regions R1, R2, R3 during each workpiece revolution. Region R1 is the grinding region during which grinding heat flux calculated using Eq. (2) is applied at the top. Within Region R2, cooling is applied at portion of the top surface outside the grinding zone and the side surfaces. The bottom of the blade is set at a constant temperature of 20 because it is far from the top surface. There is no heating and only air cooling when the blade is in Region R3.
Fig. 2. Thermal model of interrupted grinding.
Fig. 5. Thermal model.
For calculating the heat flux at the grinding zone with Eq. (2), the grinding power per unit width P0 is calculated using the following grinding power model [16]: P
Fig. 3. Heating and cooling during interrupted grinding.
Secondly, the cooling can occur at both the top and the side surfaces of the blade as illustrated in Fig. 2. Cooling starts before the blade enters the grinding zone and it can also continue for a short time after it exists from the grinding zone. The region of cooling as illustrated in Fig. 2 depends on the cooling condition and the nozzle setup condition [14,15]. The cooling variation within each workpiece revolution is also illustrated in Fig. 3. Finally, the workpiece geometry is another contributor to the transient behaviour. For continuous cylindrical grinding, the heat into the workpiece can conduct into the workpiece in all directions as illustrated in Fig. 4b. For interrupted grinding, however, the workpiece is not available for heat conduction during both entry and exit as shown in Fig. 4a and c. This entry and exit situation occupies most, if
0
¼ uch ðavw Þ þ mpa Aðade Þ
0:5
vs þ F 0 pl vs
ð3Þ
where pa is the average contact pressure at the wheel-workpiece contact, which is proportional to the curvature difference as discussed in Ref. [16]. The model coefficients for the nickel alloy IN100 were obtained as: specific chip formation energy uch = 17.6 J/ mm3, coefficient of friction m = 0.27, plowing force per unit width Fpl = 0.42 N/mm, wheel wear flat area A = 0.01, and the constant for contact pressure p0 = 3.02 106 MPa mm [16]. The energy partition to the workpiece can vary with grinding conditions. In this paper, e = 25% is used for grinding Ni alloy with plated CBN wheels [17]. 3. Results and discussions In this section, model results for grinding a part resembling a rotor with a number of blades are presented to discuss the influence of grinding process parameters on the temperature rises. The blade is made of a nickel super alloy (IN100) with the following properties: thermal conductivity k = 11.4 W/(m K), specific heat cp = 435 J/(kg K), density r = 8000 kg/m3, and yield strength s s = 1100 MPa. Wheel diameter ds = 200 mm, diameter at the blade tip dw=500 mm, wheel speed vs = 60 m/s will be used for the examples below unless they are specified.
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3.1. An example An example is shown in Fig. 6 for grinding a blade tip under the following grinding condition: blade tip diameter dw = 500 mm, tip width t = 3 mm, work speed vw = 0.2 m/s, wheel diameter ds = 200 mm, wheel speed vs = 60 m/s, and depth of cut a = 0.05 mm. The convective heat transfer coefficient is set to 0 (dry grinding). The maximum temperature rises for the first 5 revolutions and the 1st revolution are shown in Fig. 6a and b. The temperature rises sharply when the blade starts entering the grinding zone. It reaches a “quasi–steady” value of 620 when the wheel is grinding the middle portion of the blade during the 1st workpiece revolution. This is comparable to the value calculated with Eq. (1) which is 624 . The temperature rises above this value when the wheel starts exiting from the workpiece. The maximum temperature reaches 646 . Because of no cooling to cool down the workpiece bulk, the maximum temperature keeps going up and reaches 760 at the end of the 5th revolution. Fig. 6c shows a contour of the temperature distribution of the blade tip to a depth of 0.6 mm near the end of the 1st revolution (Time = 0.028 s). It can be seen that the heat only reaches a shallow depth into the blade due to the low thermal conductivity.
Fig. 7. Influence of works peed on maximum temperature (computed).
3.3. Influence of cooling Fig. 8 shows the influence of cooling on maximum temperature rises. The figure shows the maximum temperature for the 1st and the 5th workpiece revolution under the same grinding condition as in Fig. 6. Three convective cooling coefficients (h = 1000, 4000, and 8000 W/(m2 K)) were applied on the top surface outside the grinding zone and the side surfaces when the blade is within Region R2 (Figs. 2 and 5). Result for the dry grinding case (h = 0) is also included for comparison. First, the cooling suppresses the additional temperature rise during the exit. At h = 8000 W/(m2 K), there is no additional temperature rise at the exit. Secondly, cooling reduces the bulk temperature of the part. The part has lower temperature when it comes into the grinding zone for the next revolution. With h = 8000 W/(m2 K), the maximum surface temperature is only 10 when it comes into grinding for the 5th revolution. It is 68 if h = 1000 W/(m2 K), and 115 if no cooling (Fig. 6). Fig. 8c plots the maximum temperature versus the blade length (depth) near the end of the 5th revolution. Nozzle setup is important to cooling on the side surfaces especially during exit.
Fig. 6. An example of temperature variation (computed). Fig. 8. Influence of cooling on maximum temperature (computed).
3.2. Influence of work speed and depth of cut 3.4. Influence of wheel diameter Under the same specific removal rate, the work speed and depth of cut can have different influence on the temperature rise. Fig. 7 shows the maximum temperature versus time for the 1st workpiece revolution under 3 work speeds and depths of cut while keeping a constant specific removal rate q0 = avw = 0.1 mm3/ (mm s). The maximum temperature reaches 688 C for work speed vw = 0.1 m/s, it drops to 645 C at vw = 0.2 m/s, and further down to 631 C at vw = 0.3 m/s. The temperature reduction is not linear with the increase of work speed. Optimization can be done to obtain the optimum work speed for a given grinding situation.
Grinding wheel diameter has influence on the wheel-workpiece contact length lc, the grinding power, and the heat flux at the grinding zone. Larger wheel diameter leads to longer wheelworkpiece contact and longer duration of grinding. It increases the grinding power (Eq. (3)) but reduces the heat flux. An example of the wheel diameter influence on maximum temperature is shown in Fig. 9. The maximum temperature is plotted for 3 wheel diameters. Other grinding conditions are the same as example in Fig. 6. Larger grinding wheel reduces the temperature. It should be
Please cite this article in press as: Guo C, Chen Y. Thermal modeling and optimization of interrupted grinding. CIRP Annals Manufacturing Technology (2018), https://doi.org/10.1016/j.cirp.2018.04.083
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C. Guo, Y. Chen / CIRP Annals - Manufacturing Technology xxx (2018) xxx–xxx
less thermally conductive materials such as nickel alloys. The high thermal concentration near the surface is one of the reasons why it is difficult to manage the thermal problem for grinding nickel alloys. 4. Conclusions
Fig. 9. Influence of wheel diameter on maximum temperature (computed).
noted that larger wheel makes it more challenging to apply coolant to the grinding zone which can be more important for some grinding situation. 3.5. Influence of workpiece thermal property Thermal property can have significant influence on grinding temperature. An example is shown in Fig. 10 to compare two materials. Thermal conductivity k = 11.4 W/(m K) represents nickel alloys and k = 60.5 W/(m K) represents carbon steels. In this example, the same grinding power calculated with Eq. (3) and the same energy partition of 25% are used even though the power will can be much lower for grinding carbon steels as compared to grinding nickel alloys [18]. It can be seen that the maximum temperature rise is much slower for workpiece with higher thermal conductivity. With the higher thermal conductivity case (k = 60.5 W/(m K)), the temperature has not reached a quasi–steady state for the tip width of t = 3 mm before the workpiece exiting from the grinding zone. The additional temperature rises are also higher for the highly thermal conductive materials. Thermal conductivity has a big influence on the depth of thermal penetration into the workpiece as shown in Fig. 10b. Higher thermal conductivity leads to deeper thermal penetration while heat is concentrated near the surface layer for
Fig. 10. Influence of thermal property on maximum workpiece temperature (computed).
A transient thermal model is developed for interrupted grinding. The model accounts for the 3 factors that distinguish interrupted grinding from continuous OD plunge grinding: the variable heat flux, the variable cooling, and the reduced thermal capacity of the workpiece during entry and exit. The model results show the following main findings: 1. Interrupt grinding leads to higher temperature than continuous OD plunge grinding under the same grinding condition. Temperature rises higher during exit. 2. Higher work speeds lead to less difference in temperatures between continuous plunge OD grinding and interrupted grinding. 3. Cooling from the side surfaces becomes critical to suppress temperature for interrupted grinding especially for slow work speed. Cooling is very important to keep lower temperature by cooling the bulk. 4. Higher workpiece thermal conductivity and lower work speeds lead to higher additional temperature rises for interrupted grinding during exit. The quasi–steady state temperature model of Eq. (1) should not be used under this condition.
References [1] Shaw MC (1990) A Simplified Approach to Workpiece Temperature in Fine Grinding. Annals of the CIRP 39(1):345–349. [2] Rowe WB, Black SCE, Mills B, Qi HS, Morgan MN (2005) Experimental Investigation of Heat Transfer in Grinding. Annals of the CIRP 44(1):329–332. [3] Guo C, Malkin S (1994) Analytical and Experimental Investigation of Burn-out in Creep-feed Grinding. Annals of the CIRP 43(1):283–286. [4] Malkin S, Guo C (2007) Thermal Analysis of Grinding. Annals of the CIRP 56 (2):760–782. [5] Jin T, Stephenson DJ (2008) A Study of the Convection Heat Transfer Coefficients of Grinding Fluids. Annals of the CIRP 57(1):367–370. [6] Jin T, Stephenson DJ, Xie GZ, Sheng XM (2011) Investigation on Cooling Efficiency of Grinding Fluids in Deep Grinding. Annals of the CIRP 60 (1):343–346. [7] Zheng HW, Gao H (1994) A General Thermal Model for Grinding with Slotted or Segmented Wheel. Annals of the CIRP 43(1):287–290. [8] Rowe WB, Pettit JA, Boyle A, Moruzzi JL (1988) Avoidance of Thermal Damage in Grinding and Prediction of the Damage Threshold. Annals of the CIRP 37 (1):327–330. [9] Oliveira JF, Silva EJ, Coelho RT, Brozek L, Bottene LC, Marcos GP (2015) Dry Grinding Process with Workpiece Precooling. Annals of the CIRP 64(1):329– 332. [10] Xiao G, Malkin S (1996) On-line Optimization for Internal Plunge Grinding. Annals of the CIRP 45(1):287–290. [11] Krajnik P, Drazumeric R, Badger J, Hashimoto F (2014) Cycle Optimization in Cam-lobe Grinding for High Productivity. Annals of the CIRP 63(1):333. [12] Sridharan U, Bedekar V, Kolarits FM (2017) A Functional Approach to Integrating Grinding Temperature Modeling and Barkhausen Noise Analysis for Prediction of Surface Integrity in Bearing Steels. Annals of the CIRP 66(1):333–336. [13] Krajnik P, Drazumeric R, Badger J (2013) Optimization of Peripheral Non-round Cylindrical Grinding via an Adaptable Constant-temperature Process. Annals of the CIRP 62(1):347–350. [14] Guo C, Malkin S (1992) Analysis of Fluid Flow in Grinding. ASME Journal of Engineering for Industry 114:427–434. [15] Engineer F, Guo C, Malkin S (1992) Experimental Investigation of Fluid Flow in Grinding. ASME Journal of Engineering for Industry 114:61–66. [16] Guo C, Shi Z, Attia H, McIntosh D (2007) Power and Wheel Wear for Grinding Nickel Alloy with Plated CBN Wheels. Annals of the CIRP 56(1):343–346. [17] Kohli S, Guo C, Malkin S (1993) Energy Partition to the Workpiece for Grinding with Aluminium Oxide and CBN Abrasive Wheels. ASME Journal of Engineering for Industry 117:160–168. [18] Shi Z (2004) Grinding with Electroplated Cubic Boron Nitride (CBN) Wheels. Ph.D. Thesis, University of Massachusetts, Amherst.
Please cite this article in press as: Guo C, Chen Y. Thermal modeling and optimization of interrupted grinding. CIRP Annals Manufacturing Technology (2018), https://doi.org/10.1016/j.cirp.2018.04.083