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An active coolant cooling system for applications in surface grinding
Applied Thermal Engineering 23 (2003) 523–537 www.elsevier.com/locate/apthermeng
An active coolant cooling system for applications in surface grinding Y. Gao *, S. Tse, H. Mak Department of Mechanical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong Received 14 August 2002; accepted 31 October 2002
Abstract In many precision machining processes such as surface grinding, coolant is typically used to provide functions such as lubrication and cooling. In order to reduce surface grinding temperatures effectively, an active coolant cooling system is proposed. The system is based on the use of forced convection of the heat generated during the machining process. The coolant cooling system utilizes a commonly used air conditioner for ease of use and to reduce costs. In the proposed design, the evaporator of the heat pump is connected to the coolant tank of a surface grinding machine to reduce grinding temperatures for improved stability of accuracy and surface quality. This can be done without compromising production efficiency. System structure is explained and a coolant temperature model presented. Experimental testing on a prototype active cooling system is presented. The coolant temperature can be reduced to approximately )2 °C under no load condition, and to approximately 3 °C under loaded condition. The time constants of the cooling system were estimated. The results of the experimental tests demonstrated the effectiveness of the proposed system for applications in surface grinding for active coolant cooling in comparison with passive cooling. Ó 2003 Elsevier Science Ltd. All rights reserved. Keywords: Active cooling; Grinding; Coolant; Forced convection; Time constant
1. Introduction During the process of material removal the heat will cause thermal deformation on the machine and the workpiece and as such the accuracy of the machining is limited. The thermal deformation
*
Corresponding author. Fax: +852-2358-1543. E-mail address: [email protected] (Y. Gao).
1359-4311/03/$ - see front matter Ó 2003 Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 4 3 1 1 ( 0 2 ) 0 0 2 1 4 - 4
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Nomenclature oq heat transferred over a small period of time ot m_ mass-flow rate c specific heat of the mass T ðtÞ coolant temperature under the active cooling U overall heat transfer coefficient A area for heat transfer temperature of the coolant at the equilibrium state T0 m coolant mass C constant time constant of the active cooling system Tn coefficient, kt ¼ eC kt Dt sampling interval N number of samples sampling period, tp ¼ ðN 1ÞDt tp Te ðtÞ coolant temperature obtained experimentally n sampling sequence number, n ¼ t=Dt þ 1, n ¼ 1; 2; . . . ; N t sampling time, t ¼ ðn 1ÞDt t1 , t2 , t3 time instances for the T0 estimation T1 , T2 , T3 coolant temperatures at the time instances t1 , t2 , and t3 , respectively i search sequence number for t1 , t1i ¼ ði 1ÞDt, i ¼ 1; 2; . . . ; N k k search sequence number for t2 , t2k ¼ t1 þ kDt, k ¼ 2; 4; . . . ; N 1 kt ðt1i ; t2k Þ variations of kt due to the changes of t1i and t2k Tn ðt1i ; t2k Þ variations of Tn due to the changes of t1i and t2k T0 ðt1i ; t2k Þ variations of T0 due to the changes of t1i and t2k e modeling error eðt1i ; t2k Þ modeling error due to the changes of t1i and t2k emin minimum value of the modeling error eðt1i ; t2k Þ eðt1i Þ modeling error due to the change of t1i but for a particular value of k eðt1i Þmin minimum value of eðt1i Þ related i value for eðt1i Þmin imin eðt2k Þ values of eðt1i Þmin due to the change of t2k eðt2k Þmin minimum value of eðt2k Þ, eðt2k Þmin ¼ emin kmin related k value for eðt2k Þmin kt ðt2k Þ variations of kt due to the change of t2k Tn ðt2k Þ variations of Tn due to the change of t2k T0 ðt2k Þ variations of T0 due to the change of t2k
during machining can be caused by various sources including the source from an uncontrolled environment, the friction that results from the interaction between the cutting tool and the
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workpiece, and the shear fracture that results from the formation of workpiece chips during machining. If the coolant is applied at the intersection of the cutting tool and the workpiece [1–6], the heat generation can be reduced by the lubrication function of the coolant and the effect of the heat that causes the thermal deformation is reduced or removed by the cooling function of the coolant. Therefore, the deformation is reduced and the machining accuracy is improved. As the heat is taken away from the intersection between the tool and the workpiece by the coolant, the temperature of the coolant will increase. The temperature rise will continue as the heat continuously being generated during the machining process until an equilibrium state is established. In this state, the heat generated will be equal to the amount of heat that goes to the surrounding environment of the machine system. However, it will take a long time for the coolant temperature to arrive at the equilibrium state. This will seriously affect the production efficiency. If the machining takes place without waiting before the equilibrium state, the deformation will be unstable and the accuracy of the machining will be seriously affected. Based on the background, if a cooling system is used to actively cool the cutting tool and the workpiece at the intersection [7–10], the effect of the heat generated will be reduced significantly and, in the mean time, the time to reach the equilibrium state can be significantly reduced. As such, the machining efficiency can be increased and the stability in accuracy improved. In addition, machining forces involved in the process are smaller and so as the residual stresses on the workpiece surface, due to reduced machining temperature [15]. An active coolant cooling system that can be used to implement active cooling through forced convection of heat transfer during the machining processes is developed. The system is of the liquid cooling type. Compared with the cryogenic active cooling [7–11], the proposed system can be easily and reliably applied to the surface grinding process that has a higher specific energy [11], while the advantages of the active cooling are possessed. The active cooling system is intended to utilize existing media such as the commonly used coolant for precision machining for improved ease of use and reduced costs, compared to other techniques such as using cooled air [12] and high-speed water jet [13,14]. The working principle and the structure of the system are presented. Experimental tests are carried out and the results presented to demonstrate the characteristics and the effectiveness of the developed prototype system for applications in surface grinding for active cooling.
2. Working principle The objective of the development is to provide a simple system structure to facilitate active cooling through forced convection of heat transfer in machining, in particular in grinding, so that the common residential or light commercial air conditioners can be easily adapted for such use to reduce costs. Therefore, the cooling system is of a vapor compression type, involving the evaporation and condensation of the refrigerant as illustrated in Fig. 1. The active cooling system for use in machining is shown in Fig. 2(a). The proposed active cooling involves two loops. One is the refrigeration cycle and the other is the coolant circulation. The coolant would pass through the evaporator or the heat exchanger and
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Fig. 1. Active cooling cycle.
Fig. 2. Active cooling for use in the surface grinding process: (a) active cooling of coolant, (b) layout of the surface grinding machine.
is cooled by the cooling action of the heat pump. The cooled coolant is then applied to the machining area through an applicator such as a nozzle through a hydraulic pump (Fig. 2). The machining area is the hot spot where the heat is generated (Fig. 2(b)).
3. System structure The system is built based on a residential type air conditioner that is commonly available and at low cost. The evaporator in the air conditioner unit can provide a large area for heat exchange (Fig. 3). The thin metal plate that is available provides good contacts with the coolant that can
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Fig. 3. Heat exchanger to implement the forced convection.
flow through the plates of the exchanger, thus permitting higher energy efficiency and a larger volume flow. The system consists of two tanks: one is to collect the used or warmed coolant through a filter from the grinding machine and the other one is to collect the cooled coolant after passing through the heat exchanger. A hydraulic switch is used to direct the flow of cooled coolant either to the grinding machine during the normal operation or directly to the warmed coolant collection tank without going through the grinding machine for testing. In this design, as the warmed coolant tank is located above the heat exchanger and the cooled coolant tank to utilize the gravity to transfer the coolant, the only one pump is required. The pump is to transfer the cooled coolant to the coolant applicator such as a nozzle on the grinding machine (Fig. 2) to the cutting area.
4. Temperature model A temperature model could be established to characterize the active coolant cooling system under the condition of no load. Due to the analogy of the structure of the proposed active cooling system (Fig. 4) to a cross flow heat exchanger [16], the heat transfer model could be utilized [16,17]. It shows that the heat transferred oq over a small period of time ot can be obtained as oq ¼ m_ cðoT ðtÞÞ
ð1Þ
where m_ represents the mass-flow rate, c is the specific heat of the mass, and oT ðtÞ represents the reduction of the coolant temperature. For the proposed cooling system, the two parameters m_ and c will remain constant under the normal operational conditions.
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Fig. 4. Developed prototype system for active cooling in grinding.
It is noted that a higher value in m_ , the mass-flow rate, and c, the specific heat of the mass, the coolant, if to be more specific, would represent a case, in which a larger amount of heat was brought to the cooler. In this case, it is expected to take a longer time to reduce the temperature T ðtÞ. In the meantime, the total heat transferred q is proportional to the overall heat transfer coefficient, the surface area for heat transfer, and the temperature difference [16], given as q ¼ UAðT ðtÞ T0 Þ
ð2Þ
where U is the overall heat transfer coefficient, A is the area for heat transfer, T0 is the temperature of the coolant at the equilibrium state. The two parameters U and A will depend on the specific structure design of the proposed heat exchanger or the active coolant cooling system (Figs. 2–4). Based on Eqs. (1) and (2), a differential equation can be obtained to characterize the coolant temperature changes as oT ðtÞ UA ¼ ðT ðtÞ T0 Þ ot mc The solution to the above differential equation can be obtained as T ðtÞ ¼ eC eðUA=mcÞt þ T0
ð3Þ
ð4Þ
where C is a constant due to the integration in Eq. (3). Eq. (4) is very close to the impulse response of a first-order dynamic system [18]. Therefore, the coefficients to the time t in the exponent part can be considered as the time constant Tn of the active cooling system. Based on the consideration, Eq. (4) can be simplified as T ðtÞ ¼ kt eðt=Tn Þ þ T0
ð5Þ C
where kt is a coefficient, kt ¼ e , and the time constant Tn is given as mc ð6Þ Tn ¼ UA From Eq. (6), it can be seen that a larger heat transfer coefficient U and a large surface area A should reduce the time constant Tn , which means the temperature reduction process will be faster.
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However, during a grinding process, heat will be generated. If the mass of the coolant or the flow rate of the coolant is large, the time constant Tn will be larger. In this case, the temperature reduction will be smaller or the process will take longer time.
5. Experimental testing and discussion The proposed active cooling system is designed to be compatible with the existing coolant circulation system of a surface grinding machine (Fig. 2(b)) for applications in surface grinding. For this purpose, the output pipe is connected to the coolant applicator on the grinding machine and the return pipe is connected to the coolant collection hose of the grinding machine. Based on the above design, a prototype active cooling system utilizing a domestic or light commercial type air conditioner is developed (Fig. 4) and is to be positioned next to a surface girding machine (Fig. 2(b)). The cooling capacity of the prototype system is 15000 Btu/h and the energy efficiency ratio for air cooling is 10.2 Btu/h W. The input voltage is 220 V and the current is 6.5 A. The maximum flow rate of the pump used in the active cooling system is 20 l/min. The heat exchanger was modified so that it can be connected to the warmed coolant tank. Polystyrene walls were attached to the heat exchanger (Fig. 3(b)) to provide improved insulation to prevent heat loss for higher energy efficiency. A waterproof function is provided to prevent leakage as the coolant flow through the exchanger. The capacity of the heat exchanger is 10 l. To validate the proposed design, experimental tests were carried out on an ESG-818ASD surface grinding machine (Fig. 2(b)). To measure the temperature of the coolant, a K-type thermostat is used to work with a data acquisition system. The thermostat is calibrated using a standard mercury thermometer. The data acquisition system consists of a 16-bit NI data acquisition card PCI-MIO-16XE-10 and a computer program NIDAQ that works with this card. A PC is used to facilitate the data collection and analysis. 5.1. No load condition Fig. 5 shows the temperature of the coolant under the no load condition, under which no material removal was involved in the grinding and the coolant was not heated. The coolant temperature was sampled every 5 s for a period of 470 s. Therefore, the sampling interval Dt ¼ 5 s, the number of samples N ¼ 95, and the sampling period tp ¼ 470 s. It can be seen that the temperature Te ðtÞ was reduced from the room temperature to slightly below 0 °C (Fig. 5), where Te ðtÞ represents the coolant temperature obtained in the experiment, and the time t ¼ ðn 1ÞDt, n ¼ 1; 2; . . . ; N . To establish the temperature model for the condition of no load, the three parameters, kt , Tn , and T0 , in Eq. (5) must be obtained. To simplify the mathematical treatment, Eq. (5) can be modified to the form as T ðtÞ T0 ¼ kt et=Tn . This will be convenient for further processing to use linear regression to obtain the three parameters kt , Tn , and T0 for the temperature model in Eq. (5). In the first step, the temperature at the equilibrium state T0 was estimated using three points on the temperature curve Te ððn 1ÞDtÞ, n ¼ 1; 2; . . . ; N, noted as (t1 ; T1 ), (t2 ; T2 ), and (t3 ; T3 ), respectively. The equation for the T0 estimation is given as
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Fig. 5. Coolant temperatures under the no load condition.
T0 ¼
T1 T2 T32 T1 þ T2 2T3
ð7Þ
The third point (t3 ; T3 ) was set between (t1 ; T1 ) and (t2 ; T2 ). The time t3 was set as t3 ¼ ðt1 þ t2 Þ=2. In addition, the time t2 , t2 ¼ t2k , was selected in relation to the time of the first point t1 as t2k ¼ t1 þ kDt
ð8Þ
where k was selected as an even integer, so that t3 can be conveniently determined, and k 2 ½2; N 1. Based on Eq. (7) and using a linear regression algorithm, a series of results for kt , Tn , and T0 (Eq. (5)) were obtained. To obtain the best estimation for kt , Tn , and T0 , the modeling errors between the experimental result Te ðtÞ (Fig. 5) and the theoretical result T ðtÞ (Eq. (5) and Fig. 5) were examined. It was noted that, for different first point t1 , where t1 ¼ t1i , the errors between the experimental results Te ððn 1ÞDtÞ and the theoretical results T ððn 1ÞDtÞ, n ¼ 1; 2; . . . ; N , varied (Fig. 6(a) and (b)). The time t1i could be selected as t1i ¼ ði 1ÞDt
ð9Þ
where i ¼ 1; 2; . . . ; N k. From Eqs. (7)–(9), it can be seen that T0 would depend on the choice of t1i and t2k . As such, T0 could be noted as T0 ðt1i ; t2k Þ. Due to kt and Tn being affected by T0 in the linear regression, kt and Tn could also be noted as kt ðt1i ; t2k Þ, and Tn ðt1i ; t2k Þ, respectively. Based on the above analysis, the average of absolute errors e, which should be noted as eðt1i ; t2k Þ, was utilized as an index to assess the modeling errors after the estimation. It could be expressed as
Y. Gao et al. / Applied Thermal Engineering 23 (2003) 523–537 e (t1i ) (ºC)
e (t 2 k ) (º C)
250
2.5
(a) 200
(b)
t1i =(i-1)∆t i=1,2,…,N-k imin=57 e (t1i )min =1.1117º C
t1i =(i-1)∆t i=1,2,…,N-k imin=57 2
150
k=24 t2k =t1i +k∆t (s) k=2,4,…,N-1
100
∆t=5 s N=95 t =470 s
50
1.5
i
0
531
t2k =t1i +k∆t (s) k=2,4,…,N-1 kmin=24 emin =1.1117ºC ∆t=5 s N=95 tp=470 s
1
k
Fig. 6. Modeling errors versus the time instances t1i and t2k used for T0 estimation under the no load condition.
eðt1i ; t2k Þ ¼
N 1 X jTe ððn 1ÞDtÞ T ððn 1ÞDt; t1i ; t2k Þj N n¼1
ð10Þ
where T ððn 1ÞDt, t1i ; t2k Þ means that the theoretical temperature is influenced by the estimation of kt , Tn , and T0 , which are affected by t1i and t2k . It can be seen that, in order to obtain the temperature model in Eq. (5), the searches for both k, k 2 ½2; N 1, and i, i 2 ½1; N k, would be needed, so that a minimum modeling error emin (Eq. (10)) could be achieved. Based on the above analysis and Eqs. (8) and (9), the search actually involved ðN 1Þ2 =4 times of parameter estimation for kt , Tn , and T0 , and error assessment for eðt1i Þ, for a particular value of k. Typical results of variations of the modeling errors eðt1i Þ due to the change of i or t1i are as shown in Fig. 6(a), for a particular value of k. The minimum value of eðt1i Þ is noted as eðt1i Þmin , and the related i value for t1i (Eq. (9)) is noted as imin . For the case in Fig. 6(a), eðt1i Þ reached minimum at imin ¼ 57, indicating that the first point t1i (Eqs. (7) and (9)) should be selected as t1 ¼ ð57 1Þ5 ¼ 280 s, for which n ¼ 57, indicating that Te ððn 1ÞDtÞjn¼57 should be utilized as T1 in Eq. (7). As k varied in the range of [2, N 1], different values of eðt1i Þmin , noted as eðt2k Þ, eðt2k Þ ¼ eðt1i Þmin , were obtained (Fig. 6(b)). Similarly, the minimum value of eðt2k Þ is noted as eðt2k Þmin , and the related k value for t2k (Eq. (8)) is noted as kmin . Since eðt2k Þ already includes the search for t1i , eðt2k Þmin should be the minimum of the 2-layer search including both t1i and t2k . In this case, eðt2k Þmin is also noted as emin , emin ¼ eðt2k Þmin , the minimum value of the modeling error eðt1i ; t2k Þ. Based on the results in Fig. 6(b), emin ¼ 1:1117 °C, for which imin ¼ 57 and kmin ¼ 24. The kmin result indicated that the second time instance t2k (Eq. (7) and (8)) should be selected as
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t2 ¼ t1 þ 24 5 ¼ 400 s, for which n ¼ 81, indicating that Te ððn 1ÞDtÞjn¼81 should be utilized as T2 in Eq. (7). Based on the above results for t1 and t2 (Eq. (7)), the three parameters in Eq. (5), kt , Tn , and T0 , were obtained as kt ¼ 22:5004 °C, Tn ¼ 142:8394 s, and T0 ¼ 2:3269 °C, respectively, for which a minimum value of modeling error was achieved (emin ¼ 1:1117 °C). The variations of kt , Tn , and T0 due to the change of k or t2k , noted as kt ðt2k Þ, Tn ðt2k Þ, and T0 ðt2k Þ, respectively, are shown in Fig. 7. It can be seen that kt varied near the value of 22.5004 °C (Fig. 7(a)), Tn varied near the value of 142.8394 s (Fig. 7(b)), T0 varied near the value of )2.3269 °C (Fig. 7(c)), except for the cases, in which k > 80 (Figs. 6 and 7), where the span between t1 and t2 was too large and the number of data points that could be used for comparison was quite small. The results of the estimation would give a temperature model as T ðtÞ ¼ 22:5004eðt=142:8394Þ 2:3269 ð°CÞ
ð11Þ
kt(t2k) (ºC )
Tn(t2k) (s)
36
(a) 34 32
200
(b)
t2k =t1i +k ∆t (s) k=2,4,…, N-1
180
t1i =(i-1)∆t i=1,2,…, N- k
160
k min=24
140
∆t=5 s N=95 tp=470 s
120
t2k =t1i +k t (s) k=2,4,…, N-1
24
100
t1i =(i-1)∆t
i=1,2,…, N -k
22
80
kmin=24 ∆t=5 s
N=95 tp=470 s
30 28 26
20 0
10
20
30
40
50
60
70
80
90
100
k
60 0
10
20
30
40
50
60
70
80
90
100
T0(t2k) (ºC) 0.5
(c) 0 -0.5
t2k =t1i +k∆t (s) k=2,4,…,N-1 t1i =(i-1)∆t i=1,2,…,N-k
-1
kmin=24 -1.5
∆t=5 s
N=95
tp=470 s
-2 -2.5 -3 -3.5
k
Fig. 7. Parameters estimation results versus the time instance t2k used for T0 under the no load condition.
k
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The above model is also illustrated in Fig. 5. It can be seen that the established model is quite suitable to fit the experimental data Te ðtÞ (Fig. 5). From Eq. (11), it can be seen that, under the no load condition, the coolant temperature would reach the equilibrium (T0 ¼ 2:3269 °C), after a sufficient time period. The result conformed to the experimental results in Fig. 5. 5.2. Loaded condition To examine the performance of the active cooling system, stable and sufficient heat should be induced to the coolant for the loaded condition, under which thermal energy was involved to increase the temperature due to the material removal in the surface grinding process. To do this, a hot wire heater was used to increase the temperature of the coolant. The heater was applied with a DC voltage of 15.2 V, and a current of 0.72 A, and would generate a temperature of 250 °C, if no coolant was used. If the hot wire was inserted into the coolant tank without circulation, the temperature near the heater was reduced to approximately 44 °C, after a sufficient period of time. The coolant system of the grinding machine was used to implement coolant circulation. The existing coolant system was a kind of passive cooling system. If the heater was subject to the circulation of the coolant, the temperature was reduced to approximately 19 °C (Fig. 8). Using the proposed active cooling system (Figs. 2–4), the coolant temperature Te ðtÞ near the heat source was measured (Fig. 8). In this case, the sampling interval Dt ¼ 5 s, the number of samples N ¼ 125, and the sampling period tp ¼ 620 s (Fig. 8).
T(t) (ºC) 25
Active cooling 20
T e(t) - Temperature obtained experimentally
15
Active cooling
10
5
0
∆t=5 s N=125 tp=620 s T(t) - Temperature obtained theoretically
-5
t (s) Fig. 8. Coolant temperatures under the loaded condition.
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It can be seen that the temperature Te ðtÞ was reduced from the room temperature to approximately 5 °C (Fig. 8), where t ¼ ðn 1ÞDt, n ¼ 1; 2; . . . ; N . To establish the temperature model for the loaded condition, the three parameters, kt , Tn , and T0 , in Eq. (5) must be obtained again. Using the same mathematical treatment as before for simplification in the linear regression, and using the three point method to estimate the temperature at the equilibrium T0 (Eqs. (7)–(9)), a series of results for kt , Tn , and T0 (Eq. (5)) were obtained from the linear regression. To obtain the best estimation for kt , Tn , and T0 , the modeling errors between the experimental result Te ðtÞ (Fig. 8) and the theoretical result T ðtÞ (Eq. (5) and Fig. 8) were examined. In order to obtain the temperature model in Eq. (5), extensive searches for both k, k 2 ½2; N 1, and i, i 2 ½1; N k, were carried out, so that a minimum modeling error emin (Eq. (10)) could be achieved. In the search process, the tasks of parameter estimation for kt , Tn , and T0 , and error assessment for eðt1i Þ, for a particular value of k, were repeatedly involved. Typical results of variations of the modeling errors eðt1i Þ due to the change of i or t1i (Eq. (9)) are as shown in Fig. 9(a), for a particular value of k. It is noted that in Fig. 9(a), the number of variations for t1i was small. This was due to a large k being used for the case shown in Fig. 9(a), and as such, the number of t1i variations, which should be equal to N k, was small. For the case in Fig. 9(a), eðt1i Þ reached minimum at imin ¼ 2, indicating that the first point t1i (Eqs. (7) and (9)) should be selected as t1 ¼ ð2 1Þ5 ¼ 5 s, for which n ¼ 2, indicating that Te ððn 1ÞDtÞjn¼2 should be utilized as T1 in Eq. (7). As k varied in the range of [2, N 1], different values of eðt1i Þmin , noted as eðt2k Þ, eðt2k Þ ¼ eðt1i Þmin , were obtained (Fig. 9(b)). Based on the results in Fig. 9(b), emin ¼ 1:1438 °C, for which imin ¼ 2 and kmin ¼ 112. The kmin result indicated that the second point t2k (Eqs. (7) and (8)) should be selected as t2 ¼ t1 þ 112 5 ¼ 565 s, for which n ¼ 114, indicating that Te ððn 1ÞDtÞjn¼114 should be utilized as T2 in Eq. (7).
e (t1i ) (ºC)
e (t 2 k ) (ºC)
1.9
1.9
(a) 1.8 1.7
k=112 t2k =t1i +k ∆t (s) k=2,4,… ,N-1
(b)
∆t=5 s N=125 tp=620 s
1.8 1.7
1.6
1.6
1.5
1.5 1.4
1.4 1.3 1.2 1.1
t1i =(i-1)∆t i=1,2,…,N-k imin=2 e (t1i ) min =1.1438ºC
1.3
t1i =(i-1)∆t i=1,2,…,N-k imin =2 t2k =t1i +k ∆t (s) k=2,4,…,N-1 k min=112 e min =1.1438ºC ∆t=5 s N=125 tp=620 s
1.2
i
1.1
k
Fig. 9. Modeling errors versus the time instances t1i and t2k used for the T0 estimation under the loaded condition.
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Based on the above results for t1 and t2 (Eq. (7)), the three parameters in Eq. (5), kt , Tn , and T0 , were obtained as kt ¼ 16:8835 °C, Tn ¼ 227:7105 s, and T0 ¼ 2:9801 °C, for which a minimum value of modeling error was achieved (emin ¼ 1:1438 °C). The variations of kt , Tn , and T0 due to the change of k or t2k , noted as kt ðt2k Þ, Tn ðt2k Þ, and T0 ðt2k Þ, respectively, are shown in Fig. 10. It can be seen that kt varied near the value of 16.8835 °C (Fig. 10(a)), Tn varied near the value of 227.7105 s (Fig. 10(b)), T0 varied near the value of 2.9801 °C (Fig. 10(c)), except the cases, in which k > 120 (Figs. 9 and 10), where the span between t1 and t2 was too large and the number of data points that could be used for comparison was quite small. The results of the estimation would give a temperature model as T ðtÞ ¼ 16:8835eðt=227:7105Þ 2:9801 °C
ð12Þ
The above model is also illustrated in Fig. 8. It can be seen that the established model is quite suitable to fit the experimental data Te ðtÞ (Fig. 8). kt(t2k) (ºC)
T n (t2k) (s)
28
250
26
t2k =t1i +k ∆t (s) k=2,4,…,N-1
24
t1i =(i-1)∆t i=1,2,…,N-k
(b)
(a)
200
t2k =t1i +k ∆t (s) k=2,4,…, N-1
k min=112 22
∆t=5 s N=125 tp=620 s
20
t1i =(i-1)∆ t i =1,2,…,N-k
150
k min=112 ∆t=5 s
18
16 0
20
40
60
80
100
120
140
k
N=125
tp=620 s
100 0
20
40
60
80
100
120
140
T0(t2k) (ºC) 5
(c)
t2k =t1i +k∆t (s) k=2,4,…, N-1 4.5
t1i =(i-1)∆t i=1,2,…, N-k 4
kmin=112 ∆ t =5 s
N=125
tp=620 s
3.5
3
2.5
k
Fig. 10. Parameters estimation results versus the time instance t2k used for T0 under the loaded condition.
k
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From Eq. (12), it can be seen that, under the loaded condition, the coolant temperature would reach the equilibrium (T0 ¼ 2:9801 °C), after a sufficient time period. As shown in Fig. 8, the final temperature was approximately 5 °C, higher than T0 . This indicates that the sampling process completed before the equilibrium temperature was reached (Fig. 8). It can be seen that a significant amount of temperature reduction was effectively achieved by the proposed active coolant cooling system under the loaded condition (Fig. 8). Eq. (12) shows that, under the loaded condition, the coolant temperature at the equilibrium state T0 was higher and the time constant Tn a bit larger, compared with the results under the no load condition (Eq. (11)). This is due to a larger amount of heat to be dealt with, using the same cooling system of limited capacity. It is noted that the data in Fig. 8 seemed to have two data points with excessive measurement errors, causing a slightly larger minimum error (emin ¼ 1:1438 °C) in the modeling.
6. Conclusions An active coolant cooling system utilizing a commonly used air conditioner is presented to reduce the machining temperatures in surface grinding through force convection for ease of use and for reduced costs. In the proposed system, the coolant tank is connected to the evaporator of the heat pump for heat exchange to remove the machining heat to reduce temperature in machining for improved accuracy and surface quality stability without compromising production efficiency. To improve the energy efficiency, thermal insulation was provided for the heat exchanger. For the proposed cooling system, a temperature model was established and a time constant model presented. The experimental tests using a prototype active cooling system show that the coolant temperature can be reduced to approximately )2 °C under no load condition, and to approximately 3 °C under loaded condition. The results demonstrate the effectiveness of the proposed system for applications in surface grinding for active coolant cooling, which is more advantageous in comparison with the passive coolant cooling.
References [1] P. Hryniewicz, A.Z. Szeri, S. Jahanmir, Coolant flow in surface grinding with non-porous wheels, International Journal of Mechanical Sciences 42 (12) (2000) 2347–2367. [2] E. Minke, Contribution to the role of coolants on grinding process and work results, SME Technical Paper (Series) MR, pp. 1–18. [3] C. Guo, S. Malkin, Energy partition and cooling during grinding, SME Technical Paper (Series) MR, pp. 1–10. [4] M. Emonds, Synthetic coolants improve the glass grinding process, Glass 76 (4) (1999) 2. [5] S.B. Wang, K.H. Fuh, Workpiece temperature, fluid cooling effectiveness and burning threshold of grinding energy in creep feed grinding, in: Proceedings of the Institution of Mechanical Engineers, Part B, Journal of Engineering Manufacture 212 (B5) (1998) 383–391. [6] S.-B. Wang, H.-S. Kou, Cooling effectiveness of cutting fluid in creep feed grinding, International Communications in Heat and Mass Transfer 24 (6) (1997) 771–783. [7] S. Paul, A.B. Chattopadhyay, Cryogenic cooling in grinding––a new concept, Revue M. Mecanique 42 (3) (1997) 131–135.
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[8] S. Paul, A.B. Chattopadhyay, Determination and control of grinding zone temperature under cryogenic cooling, International Journal of Machine Tools and Manufacture 36 (4) (1996) 491–501. [9] S. Paul, A.B. Chattopadhyay, Effect of cryogenic cooling on grinding forces, International Journal of Machine Tools and Manufacture 36 (1) (1996) 63–72. [10] S. Paul, A.B. Chattopadhyay, Study of effects of cryo-cooling in grinding, International Journal of Machine Tools and Manufacture 35 (1) (1995) 109–117. [11] S. Paul, A.B. Chattopadhyay, Effects of cryogenic cooling by liquid nitrogen jet on forces, temperature and surface residual stresses in grinding steels, Cryogenics 35 (8) (1995) 515–523. [12] H. Honma, K. Yokogawa, M. Yokogawa, Study of environment conscious CBN cooling air grinding technology, Journal of the Japan Society of Precision Engineering, Seimitsu Kogaku Kaishi 62 (11) (1996) 1638–1642. [13] R. Kovacevic, H.E. Beardsley, High-speed water jet as a coolant/lubricant in grinding, Abrasives, pp. 10–11, 18, 22, 27, 31, 34. [14] F. Klocke, A. Baus, T. Beck, Coolant induced forces in CBN high speed grinding with shoe nozzles, CIRP Annals 49 (1) (2000) 241–244. [15] X. Chen, W.B. Rowe, D.F. McCormack, Analysis of the transitional temperature for tensile residual stress in grinding, Journal of Materials Processing Technology 107 (2000) 216–221. [16] J.P. Holman, Heat Transfer, 8th edition, McGraw-Hill, New York, 1997. ISBN 0-07-844785-2. [17] G.A. Florides, S.A. Kalogirou, S.A. Tassou, L.C. Wrobel, Modeling, simulation and warming impact assessment of a domestic-size absorption solar cooling system, Applied Thermal Engineering 22 (2002) 1313–1325. [18] K. Ogata, Modern Control Engineering, Prentice-Hall, New Jersey, 1970. ISBN 0-13-590258-4.
An active coolant cooling system for applications in surface grinding Y. Gao *, S. Tse, H. Mak Department of Mechanical Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong Received 14 August 2002; accepted 31 October 2002
Abstract In many precision machining processes such as surface grinding, coolant is typically used to provide functions such as lubrication and cooling. In order to reduce surface grinding temperatures effectively, an active coolant cooling system is proposed. The system is based on the use of forced convection of the heat generated during the machining process. The coolant cooling system utilizes a commonly used air conditioner for ease of use and to reduce costs. In the proposed design, the evaporator of the heat pump is connected to the coolant tank of a surface grinding machine to reduce grinding temperatures for improved stability of accuracy and surface quality. This can be done without compromising production efficiency. System structure is explained and a coolant temperature model presented. Experimental testing on a prototype active cooling system is presented. The coolant temperature can be reduced to approximately )2 °C under no load condition, and to approximately 3 °C under loaded condition. The time constants of the cooling system were estimated. The results of the experimental tests demonstrated the effectiveness of the proposed system for applications in surface grinding for active coolant cooling in comparison with passive cooling. Ó 2003 Elsevier Science Ltd. All rights reserved. Keywords: Active cooling; Grinding; Coolant; Forced convection; Time constant
1. Introduction During the process of material removal the heat will cause thermal deformation on the machine and the workpiece and as such the accuracy of the machining is limited. The thermal deformation
*
Corresponding author. Fax: +852-2358-1543. E-mail address: [email protected] (Y. Gao).
1359-4311/03/$ - see front matter Ó 2003 Elsevier Science Ltd. All rights reserved. PII: S 1 3 5 9 - 4 3 1 1 ( 0 2 ) 0 0 2 1 4 - 4
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Nomenclature oq heat transferred over a small period of time ot m_ mass-flow rate c specific heat of the mass T ðtÞ coolant temperature under the active cooling U overall heat transfer coefficient A area for heat transfer temperature of the coolant at the equilibrium state T0 m coolant mass C constant time constant of the active cooling system Tn coefficient, kt ¼ eC kt Dt sampling interval N number of samples sampling period, tp ¼ ðN 1ÞDt tp Te ðtÞ coolant temperature obtained experimentally n sampling sequence number, n ¼ t=Dt þ 1, n ¼ 1; 2; . . . ; N t sampling time, t ¼ ðn 1ÞDt t1 , t2 , t3 time instances for the T0 estimation T1 , T2 , T3 coolant temperatures at the time instances t1 , t2 , and t3 , respectively i search sequence number for t1 , t1i ¼ ði 1ÞDt, i ¼ 1; 2; . . . ; N k k search sequence number for t2 , t2k ¼ t1 þ kDt, k ¼ 2; 4; . . . ; N 1 kt ðt1i ; t2k Þ variations of kt due to the changes of t1i and t2k Tn ðt1i ; t2k Þ variations of Tn due to the changes of t1i and t2k T0 ðt1i ; t2k Þ variations of T0 due to the changes of t1i and t2k e modeling error eðt1i ; t2k Þ modeling error due to the changes of t1i and t2k emin minimum value of the modeling error eðt1i ; t2k Þ eðt1i Þ modeling error due to the change of t1i but for a particular value of k eðt1i Þmin minimum value of eðt1i Þ related i value for eðt1i Þmin imin eðt2k Þ values of eðt1i Þmin due to the change of t2k eðt2k Þmin minimum value of eðt2k Þ, eðt2k Þmin ¼ emin kmin related k value for eðt2k Þmin kt ðt2k Þ variations of kt due to the change of t2k Tn ðt2k Þ variations of Tn due to the change of t2k T0 ðt2k Þ variations of T0 due to the change of t2k
during machining can be caused by various sources including the source from an uncontrolled environment, the friction that results from the interaction between the cutting tool and the
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workpiece, and the shear fracture that results from the formation of workpiece chips during machining. If the coolant is applied at the intersection of the cutting tool and the workpiece [1–6], the heat generation can be reduced by the lubrication function of the coolant and the effect of the heat that causes the thermal deformation is reduced or removed by the cooling function of the coolant. Therefore, the deformation is reduced and the machining accuracy is improved. As the heat is taken away from the intersection between the tool and the workpiece by the coolant, the temperature of the coolant will increase. The temperature rise will continue as the heat continuously being generated during the machining process until an equilibrium state is established. In this state, the heat generated will be equal to the amount of heat that goes to the surrounding environment of the machine system. However, it will take a long time for the coolant temperature to arrive at the equilibrium state. This will seriously affect the production efficiency. If the machining takes place without waiting before the equilibrium state, the deformation will be unstable and the accuracy of the machining will be seriously affected. Based on the background, if a cooling system is used to actively cool the cutting tool and the workpiece at the intersection [7–10], the effect of the heat generated will be reduced significantly and, in the mean time, the time to reach the equilibrium state can be significantly reduced. As such, the machining efficiency can be increased and the stability in accuracy improved. In addition, machining forces involved in the process are smaller and so as the residual stresses on the workpiece surface, due to reduced machining temperature [15]. An active coolant cooling system that can be used to implement active cooling through forced convection of heat transfer during the machining processes is developed. The system is of the liquid cooling type. Compared with the cryogenic active cooling [7–11], the proposed system can be easily and reliably applied to the surface grinding process that has a higher specific energy [11], while the advantages of the active cooling are possessed. The active cooling system is intended to utilize existing media such as the commonly used coolant for precision machining for improved ease of use and reduced costs, compared to other techniques such as using cooled air [12] and high-speed water jet [13,14]. The working principle and the structure of the system are presented. Experimental tests are carried out and the results presented to demonstrate the characteristics and the effectiveness of the developed prototype system for applications in surface grinding for active cooling.
2. Working principle The objective of the development is to provide a simple system structure to facilitate active cooling through forced convection of heat transfer in machining, in particular in grinding, so that the common residential or light commercial air conditioners can be easily adapted for such use to reduce costs. Therefore, the cooling system is of a vapor compression type, involving the evaporation and condensation of the refrigerant as illustrated in Fig. 1. The active cooling system for use in machining is shown in Fig. 2(a). The proposed active cooling involves two loops. One is the refrigeration cycle and the other is the coolant circulation. The coolant would pass through the evaporator or the heat exchanger and
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Fig. 1. Active cooling cycle.
Fig. 2. Active cooling for use in the surface grinding process: (a) active cooling of coolant, (b) layout of the surface grinding machine.
is cooled by the cooling action of the heat pump. The cooled coolant is then applied to the machining area through an applicator such as a nozzle through a hydraulic pump (Fig. 2). The machining area is the hot spot where the heat is generated (Fig. 2(b)).
3. System structure The system is built based on a residential type air conditioner that is commonly available and at low cost. The evaporator in the air conditioner unit can provide a large area for heat exchange (Fig. 3). The thin metal plate that is available provides good contacts with the coolant that can
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Fig. 3. Heat exchanger to implement the forced convection.
flow through the plates of the exchanger, thus permitting higher energy efficiency and a larger volume flow. The system consists of two tanks: one is to collect the used or warmed coolant through a filter from the grinding machine and the other one is to collect the cooled coolant after passing through the heat exchanger. A hydraulic switch is used to direct the flow of cooled coolant either to the grinding machine during the normal operation or directly to the warmed coolant collection tank without going through the grinding machine for testing. In this design, as the warmed coolant tank is located above the heat exchanger and the cooled coolant tank to utilize the gravity to transfer the coolant, the only one pump is required. The pump is to transfer the cooled coolant to the coolant applicator such as a nozzle on the grinding machine (Fig. 2) to the cutting area.
4. Temperature model A temperature model could be established to characterize the active coolant cooling system under the condition of no load. Due to the analogy of the structure of the proposed active cooling system (Fig. 4) to a cross flow heat exchanger [16], the heat transfer model could be utilized [16,17]. It shows that the heat transferred oq over a small period of time ot can be obtained as oq ¼ m_ cðoT ðtÞÞ
ð1Þ
where m_ represents the mass-flow rate, c is the specific heat of the mass, and oT ðtÞ represents the reduction of the coolant temperature. For the proposed cooling system, the two parameters m_ and c will remain constant under the normal operational conditions.
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Fig. 4. Developed prototype system for active cooling in grinding.
It is noted that a higher value in m_ , the mass-flow rate, and c, the specific heat of the mass, the coolant, if to be more specific, would represent a case, in which a larger amount of heat was brought to the cooler. In this case, it is expected to take a longer time to reduce the temperature T ðtÞ. In the meantime, the total heat transferred q is proportional to the overall heat transfer coefficient, the surface area for heat transfer, and the temperature difference [16], given as q ¼ UAðT ðtÞ T0 Þ
ð2Þ
where U is the overall heat transfer coefficient, A is the area for heat transfer, T0 is the temperature of the coolant at the equilibrium state. The two parameters U and A will depend on the specific structure design of the proposed heat exchanger or the active coolant cooling system (Figs. 2–4). Based on Eqs. (1) and (2), a differential equation can be obtained to characterize the coolant temperature changes as oT ðtÞ UA ¼ ðT ðtÞ T0 Þ ot mc The solution to the above differential equation can be obtained as T ðtÞ ¼ eC eðUA=mcÞt þ T0
ð3Þ
ð4Þ
where C is a constant due to the integration in Eq. (3). Eq. (4) is very close to the impulse response of a first-order dynamic system [18]. Therefore, the coefficients to the time t in the exponent part can be considered as the time constant Tn of the active cooling system. Based on the consideration, Eq. (4) can be simplified as T ðtÞ ¼ kt eðt=Tn Þ þ T0
ð5Þ C
where kt is a coefficient, kt ¼ e , and the time constant Tn is given as mc ð6Þ Tn ¼ UA From Eq. (6), it can be seen that a larger heat transfer coefficient U and a large surface area A should reduce the time constant Tn , which means the temperature reduction process will be faster.
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However, during a grinding process, heat will be generated. If the mass of the coolant or the flow rate of the coolant is large, the time constant Tn will be larger. In this case, the temperature reduction will be smaller or the process will take longer time.
5. Experimental testing and discussion The proposed active cooling system is designed to be compatible with the existing coolant circulation system of a surface grinding machine (Fig. 2(b)) for applications in surface grinding. For this purpose, the output pipe is connected to the coolant applicator on the grinding machine and the return pipe is connected to the coolant collection hose of the grinding machine. Based on the above design, a prototype active cooling system utilizing a domestic or light commercial type air conditioner is developed (Fig. 4) and is to be positioned next to a surface girding machine (Fig. 2(b)). The cooling capacity of the prototype system is 15000 Btu/h and the energy efficiency ratio for air cooling is 10.2 Btu/h W. The input voltage is 220 V and the current is 6.5 A. The maximum flow rate of the pump used in the active cooling system is 20 l/min. The heat exchanger was modified so that it can be connected to the warmed coolant tank. Polystyrene walls were attached to the heat exchanger (Fig. 3(b)) to provide improved insulation to prevent heat loss for higher energy efficiency. A waterproof function is provided to prevent leakage as the coolant flow through the exchanger. The capacity of the heat exchanger is 10 l. To validate the proposed design, experimental tests were carried out on an ESG-818ASD surface grinding machine (Fig. 2(b)). To measure the temperature of the coolant, a K-type thermostat is used to work with a data acquisition system. The thermostat is calibrated using a standard mercury thermometer. The data acquisition system consists of a 16-bit NI data acquisition card PCI-MIO-16XE-10 and a computer program NIDAQ that works with this card. A PC is used to facilitate the data collection and analysis. 5.1. No load condition Fig. 5 shows the temperature of the coolant under the no load condition, under which no material removal was involved in the grinding and the coolant was not heated. The coolant temperature was sampled every 5 s for a period of 470 s. Therefore, the sampling interval Dt ¼ 5 s, the number of samples N ¼ 95, and the sampling period tp ¼ 470 s. It can be seen that the temperature Te ðtÞ was reduced from the room temperature to slightly below 0 °C (Fig. 5), where Te ðtÞ represents the coolant temperature obtained in the experiment, and the time t ¼ ðn 1ÞDt, n ¼ 1; 2; . . . ; N . To establish the temperature model for the condition of no load, the three parameters, kt , Tn , and T0 , in Eq. (5) must be obtained. To simplify the mathematical treatment, Eq. (5) can be modified to the form as T ðtÞ T0 ¼ kt et=Tn . This will be convenient for further processing to use linear regression to obtain the three parameters kt , Tn , and T0 for the temperature model in Eq. (5). In the first step, the temperature at the equilibrium state T0 was estimated using three points on the temperature curve Te ððn 1ÞDtÞ, n ¼ 1; 2; . . . ; N, noted as (t1 ; T1 ), (t2 ; T2 ), and (t3 ; T3 ), respectively. The equation for the T0 estimation is given as
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Fig. 5. Coolant temperatures under the no load condition.
T0 ¼
T1 T2 T32 T1 þ T2 2T3
ð7Þ
The third point (t3 ; T3 ) was set between (t1 ; T1 ) and (t2 ; T2 ). The time t3 was set as t3 ¼ ðt1 þ t2 Þ=2. In addition, the time t2 , t2 ¼ t2k , was selected in relation to the time of the first point t1 as t2k ¼ t1 þ kDt
ð8Þ
where k was selected as an even integer, so that t3 can be conveniently determined, and k 2 ½2; N 1. Based on Eq. (7) and using a linear regression algorithm, a series of results for kt , Tn , and T0 (Eq. (5)) were obtained. To obtain the best estimation for kt , Tn , and T0 , the modeling errors between the experimental result Te ðtÞ (Fig. 5) and the theoretical result T ðtÞ (Eq. (5) and Fig. 5) were examined. It was noted that, for different first point t1 , where t1 ¼ t1i , the errors between the experimental results Te ððn 1ÞDtÞ and the theoretical results T ððn 1ÞDtÞ, n ¼ 1; 2; . . . ; N , varied (Fig. 6(a) and (b)). The time t1i could be selected as t1i ¼ ði 1ÞDt
ð9Þ
where i ¼ 1; 2; . . . ; N k. From Eqs. (7)–(9), it can be seen that T0 would depend on the choice of t1i and t2k . As such, T0 could be noted as T0 ðt1i ; t2k Þ. Due to kt and Tn being affected by T0 in the linear regression, kt and Tn could also be noted as kt ðt1i ; t2k Þ, and Tn ðt1i ; t2k Þ, respectively. Based on the above analysis, the average of absolute errors e, which should be noted as eðt1i ; t2k Þ, was utilized as an index to assess the modeling errors after the estimation. It could be expressed as
Y. Gao et al. / Applied Thermal Engineering 23 (2003) 523–537 e (t1i ) (ºC)
e (t 2 k ) (º C)
250
2.5
(a) 200
(b)
t1i =(i-1)∆t i=1,2,…,N-k imin=57 e (t1i )min =1.1117º C
t1i =(i-1)∆t i=1,2,…,N-k imin=57 2
150
k=24 t2k =t1i +k∆t (s) k=2,4,…,N-1
100
∆t=5 s N=95 t =470 s
50
1.5
i
0
531
t2k =t1i +k∆t (s) k=2,4,…,N-1 kmin=24 emin =1.1117ºC ∆t=5 s N=95 tp=470 s
1
k
Fig. 6. Modeling errors versus the time instances t1i and t2k used for T0 estimation under the no load condition.
eðt1i ; t2k Þ ¼
N 1 X jTe ððn 1ÞDtÞ T ððn 1ÞDt; t1i ; t2k Þj N n¼1
ð10Þ
where T ððn 1ÞDt, t1i ; t2k Þ means that the theoretical temperature is influenced by the estimation of kt , Tn , and T0 , which are affected by t1i and t2k . It can be seen that, in order to obtain the temperature model in Eq. (5), the searches for both k, k 2 ½2; N 1, and i, i 2 ½1; N k, would be needed, so that a minimum modeling error emin (Eq. (10)) could be achieved. Based on the above analysis and Eqs. (8) and (9), the search actually involved ðN 1Þ2 =4 times of parameter estimation for kt , Tn , and T0 , and error assessment for eðt1i Þ, for a particular value of k. Typical results of variations of the modeling errors eðt1i Þ due to the change of i or t1i are as shown in Fig. 6(a), for a particular value of k. The minimum value of eðt1i Þ is noted as eðt1i Þmin , and the related i value for t1i (Eq. (9)) is noted as imin . For the case in Fig. 6(a), eðt1i Þ reached minimum at imin ¼ 57, indicating that the first point t1i (Eqs. (7) and (9)) should be selected as t1 ¼ ð57 1Þ5 ¼ 280 s, for which n ¼ 57, indicating that Te ððn 1ÞDtÞjn¼57 should be utilized as T1 in Eq. (7). As k varied in the range of [2, N 1], different values of eðt1i Þmin , noted as eðt2k Þ, eðt2k Þ ¼ eðt1i Þmin , were obtained (Fig. 6(b)). Similarly, the minimum value of eðt2k Þ is noted as eðt2k Þmin , and the related k value for t2k (Eq. (8)) is noted as kmin . Since eðt2k Þ already includes the search for t1i , eðt2k Þmin should be the minimum of the 2-layer search including both t1i and t2k . In this case, eðt2k Þmin is also noted as emin , emin ¼ eðt2k Þmin , the minimum value of the modeling error eðt1i ; t2k Þ. Based on the results in Fig. 6(b), emin ¼ 1:1117 °C, for which imin ¼ 57 and kmin ¼ 24. The kmin result indicated that the second time instance t2k (Eq. (7) and (8)) should be selected as
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t2 ¼ t1 þ 24 5 ¼ 400 s, for which n ¼ 81, indicating that Te ððn 1ÞDtÞjn¼81 should be utilized as T2 in Eq. (7). Based on the above results for t1 and t2 (Eq. (7)), the three parameters in Eq. (5), kt , Tn , and T0 , were obtained as kt ¼ 22:5004 °C, Tn ¼ 142:8394 s, and T0 ¼ 2:3269 °C, respectively, for which a minimum value of modeling error was achieved (emin ¼ 1:1117 °C). The variations of kt , Tn , and T0 due to the change of k or t2k , noted as kt ðt2k Þ, Tn ðt2k Þ, and T0 ðt2k Þ, respectively, are shown in Fig. 7. It can be seen that kt varied near the value of 22.5004 °C (Fig. 7(a)), Tn varied near the value of 142.8394 s (Fig. 7(b)), T0 varied near the value of )2.3269 °C (Fig. 7(c)), except for the cases, in which k > 80 (Figs. 6 and 7), where the span between t1 and t2 was too large and the number of data points that could be used for comparison was quite small. The results of the estimation would give a temperature model as T ðtÞ ¼ 22:5004eðt=142:8394Þ 2:3269 ð°CÞ
ð11Þ
kt(t2k) (ºC )
Tn(t2k) (s)
36
(a) 34 32
200
(b)
t2k =t1i +k ∆t (s) k=2,4,…, N-1
180
t1i =(i-1)∆t i=1,2,…, N- k
160
k min=24
140
∆t=5 s N=95 tp=470 s
120
t2k =t1i +k t (s) k=2,4,…, N-1
24
100
t1i =(i-1)∆t
i=1,2,…, N -k
22
80
kmin=24 ∆t=5 s
N=95 tp=470 s
30 28 26
20 0
10
20
30
40
50
60
70
80
90
100
k
60 0
10
20
30
40
50
60
70
80
90
100
T0(t2k) (ºC) 0.5
(c) 0 -0.5
t2k =t1i +k∆t (s) k=2,4,…,N-1 t1i =(i-1)∆t i=1,2,…,N-k
-1
kmin=24 -1.5
∆t=5 s
N=95
tp=470 s
-2 -2.5 -3 -3.5
k
Fig. 7. Parameters estimation results versus the time instance t2k used for T0 under the no load condition.
k
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The above model is also illustrated in Fig. 5. It can be seen that the established model is quite suitable to fit the experimental data Te ðtÞ (Fig. 5). From Eq. (11), it can be seen that, under the no load condition, the coolant temperature would reach the equilibrium (T0 ¼ 2:3269 °C), after a sufficient time period. The result conformed to the experimental results in Fig. 5. 5.2. Loaded condition To examine the performance of the active cooling system, stable and sufficient heat should be induced to the coolant for the loaded condition, under which thermal energy was involved to increase the temperature due to the material removal in the surface grinding process. To do this, a hot wire heater was used to increase the temperature of the coolant. The heater was applied with a DC voltage of 15.2 V, and a current of 0.72 A, and would generate a temperature of 250 °C, if no coolant was used. If the hot wire was inserted into the coolant tank without circulation, the temperature near the heater was reduced to approximately 44 °C, after a sufficient period of time. The coolant system of the grinding machine was used to implement coolant circulation. The existing coolant system was a kind of passive cooling system. If the heater was subject to the circulation of the coolant, the temperature was reduced to approximately 19 °C (Fig. 8). Using the proposed active cooling system (Figs. 2–4), the coolant temperature Te ðtÞ near the heat source was measured (Fig. 8). In this case, the sampling interval Dt ¼ 5 s, the number of samples N ¼ 125, and the sampling period tp ¼ 620 s (Fig. 8).
T(t) (ºC) 25
Active cooling 20
T e(t) - Temperature obtained experimentally
15
Active cooling
10
5
0
∆t=5 s N=125 tp=620 s T(t) - Temperature obtained theoretically
-5
t (s) Fig. 8. Coolant temperatures under the loaded condition.
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It can be seen that the temperature Te ðtÞ was reduced from the room temperature to approximately 5 °C (Fig. 8), where t ¼ ðn 1ÞDt, n ¼ 1; 2; . . . ; N . To establish the temperature model for the loaded condition, the three parameters, kt , Tn , and T0 , in Eq. (5) must be obtained again. Using the same mathematical treatment as before for simplification in the linear regression, and using the three point method to estimate the temperature at the equilibrium T0 (Eqs. (7)–(9)), a series of results for kt , Tn , and T0 (Eq. (5)) were obtained from the linear regression. To obtain the best estimation for kt , Tn , and T0 , the modeling errors between the experimental result Te ðtÞ (Fig. 8) and the theoretical result T ðtÞ (Eq. (5) and Fig. 8) were examined. In order to obtain the temperature model in Eq. (5), extensive searches for both k, k 2 ½2; N 1, and i, i 2 ½1; N k, were carried out, so that a minimum modeling error emin (Eq. (10)) could be achieved. In the search process, the tasks of parameter estimation for kt , Tn , and T0 , and error assessment for eðt1i Þ, for a particular value of k, were repeatedly involved. Typical results of variations of the modeling errors eðt1i Þ due to the change of i or t1i (Eq. (9)) are as shown in Fig. 9(a), for a particular value of k. It is noted that in Fig. 9(a), the number of variations for t1i was small. This was due to a large k being used for the case shown in Fig. 9(a), and as such, the number of t1i variations, which should be equal to N k, was small. For the case in Fig. 9(a), eðt1i Þ reached minimum at imin ¼ 2, indicating that the first point t1i (Eqs. (7) and (9)) should be selected as t1 ¼ ð2 1Þ5 ¼ 5 s, for which n ¼ 2, indicating that Te ððn 1ÞDtÞjn¼2 should be utilized as T1 in Eq. (7). As k varied in the range of [2, N 1], different values of eðt1i Þmin , noted as eðt2k Þ, eðt2k Þ ¼ eðt1i Þmin , were obtained (Fig. 9(b)). Based on the results in Fig. 9(b), emin ¼ 1:1438 °C, for which imin ¼ 2 and kmin ¼ 112. The kmin result indicated that the second point t2k (Eqs. (7) and (8)) should be selected as t2 ¼ t1 þ 112 5 ¼ 565 s, for which n ¼ 114, indicating that Te ððn 1ÞDtÞjn¼114 should be utilized as T2 in Eq. (7).
e (t1i ) (ºC)
e (t 2 k ) (ºC)
1.9
1.9
(a) 1.8 1.7
k=112 t2k =t1i +k ∆t (s) k=2,4,… ,N-1
(b)
∆t=5 s N=125 tp=620 s
1.8 1.7
1.6
1.6
1.5
1.5 1.4
1.4 1.3 1.2 1.1
t1i =(i-1)∆t i=1,2,…,N-k imin=2 e (t1i ) min =1.1438ºC
1.3
t1i =(i-1)∆t i=1,2,…,N-k imin =2 t2k =t1i +k ∆t (s) k=2,4,…,N-1 k min=112 e min =1.1438ºC ∆t=5 s N=125 tp=620 s
1.2
i
1.1
k
Fig. 9. Modeling errors versus the time instances t1i and t2k used for the T0 estimation under the loaded condition.
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Based on the above results for t1 and t2 (Eq. (7)), the three parameters in Eq. (5), kt , Tn , and T0 , were obtained as kt ¼ 16:8835 °C, Tn ¼ 227:7105 s, and T0 ¼ 2:9801 °C, for which a minimum value of modeling error was achieved (emin ¼ 1:1438 °C). The variations of kt , Tn , and T0 due to the change of k or t2k , noted as kt ðt2k Þ, Tn ðt2k Þ, and T0 ðt2k Þ, respectively, are shown in Fig. 10. It can be seen that kt varied near the value of 16.8835 °C (Fig. 10(a)), Tn varied near the value of 227.7105 s (Fig. 10(b)), T0 varied near the value of 2.9801 °C (Fig. 10(c)), except the cases, in which k > 120 (Figs. 9 and 10), where the span between t1 and t2 was too large and the number of data points that could be used for comparison was quite small. The results of the estimation would give a temperature model as T ðtÞ ¼ 16:8835eðt=227:7105Þ 2:9801 °C
ð12Þ
The above model is also illustrated in Fig. 8. It can be seen that the established model is quite suitable to fit the experimental data Te ðtÞ (Fig. 8). kt(t2k) (ºC)
T n (t2k) (s)
28
250
26
t2k =t1i +k ∆t (s) k=2,4,…,N-1
24
t1i =(i-1)∆t i=1,2,…,N-k
(b)
(a)
200
t2k =t1i +k ∆t (s) k=2,4,…, N-1
k min=112 22
∆t=5 s N=125 tp=620 s
20
t1i =(i-1)∆ t i =1,2,…,N-k
150
k min=112 ∆t=5 s
18
16 0
20
40
60
80
100
120
140
k
N=125
tp=620 s
100 0
20
40
60
80
100
120
140
T0(t2k) (ºC) 5
(c)
t2k =t1i +k∆t (s) k=2,4,…, N-1 4.5
t1i =(i-1)∆t i=1,2,…, N-k 4
kmin=112 ∆ t =5 s
N=125
tp=620 s
3.5
3
2.5
k
Fig. 10. Parameters estimation results versus the time instance t2k used for T0 under the loaded condition.
k
536
Y. Gao et al. / Applied Thermal Engineering 23 (2003) 523–537
From Eq. (12), it can be seen that, under the loaded condition, the coolant temperature would reach the equilibrium (T0 ¼ 2:9801 °C), after a sufficient time period. As shown in Fig. 8, the final temperature was approximately 5 °C, higher than T0 . This indicates that the sampling process completed before the equilibrium temperature was reached (Fig. 8). It can be seen that a significant amount of temperature reduction was effectively achieved by the proposed active coolant cooling system under the loaded condition (Fig. 8). Eq. (12) shows that, under the loaded condition, the coolant temperature at the equilibrium state T0 was higher and the time constant Tn a bit larger, compared with the results under the no load condition (Eq. (11)). This is due to a larger amount of heat to be dealt with, using the same cooling system of limited capacity. It is noted that the data in Fig. 8 seemed to have two data points with excessive measurement errors, causing a slightly larger minimum error (emin ¼ 1:1438 °C) in the modeling.
6. Conclusions An active coolant cooling system utilizing a commonly used air conditioner is presented to reduce the machining temperatures in surface grinding through force convection for ease of use and for reduced costs. In the proposed system, the coolant tank is connected to the evaporator of the heat pump for heat exchange to remove the machining heat to reduce temperature in machining for improved accuracy and surface quality stability without compromising production efficiency. To improve the energy efficiency, thermal insulation was provided for the heat exchanger. For the proposed cooling system, a temperature model was established and a time constant model presented. The experimental tests using a prototype active cooling system show that the coolant temperature can be reduced to approximately )2 °C under no load condition, and to approximately 3 °C under loaded condition. The results demonstrate the effectiveness of the proposed system for applications in surface grinding for active coolant cooling, which is more advantageous in comparison with the passive coolant cooling.
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