# Temperature Fluctuation Attenuation of Circulating Cooling Water Using Dynamic Thermal Filtering
## 2 Principle  
The basic concept of the proposed DTFM is shown in Figure 1. The DTFM attenuator consists of a heat exchanger, two servo valves, two precision temperature sensors, and a control module. The control module is used to implement on/off control of the servo valves according to the feedback of the temperature sensors. The attenuator is cascaded together with a CCW machine and a thermal load to compose an enhanced CCW temperature control system.  
The high temperature stability of CCW is achieved by thermal filtering. As shown in Figure 1, some CCW is bypassed and blocked in one chamber of the heat exchanger, serving as thermal capacity medium. Temperature fluctuation of CCW, which flows through the other chamber of the heat exchanger, is attenuated by the heat exchanging with the medium. Therefore, the temperature stability of the CCW is significantly improved through thermal filtering effect.  
The quick response of CCW temperature control is achieved by making the temperature of thermal capacity medium dynamically follow the set value of CCW temperature through the real time updating of the medium. When the temperature set value of the CCW machine changes, temperature sensor A detects the change, then provides feedback signal to the control module. Then the control module switches on servo valve 1 and switched off servo valve 2 to make CCW flow into the thermal capacity medium chamber to update the medium. Meanwhile, the temperature of the outflow from the medium chamber is monitored by temperature sensor B. When the temperature at point B equals to the temperature at point A, which means that the water in the medium chamber is totally updated, the servo valve 1 is switched off and the servo valve 2 is switched on. In this way, the change of temperature set value of CCW is dynamically followed.  
The updating time of the thermal capacity medium \(T_{\text{med}}\) can be given by  
\[T_{\text{med}}=\frac{V_{\text{med}}}{F_{\text{med}}} \tag{1}\]  
where \(V_{\text{med}}\) is the volume of the thermal capacity medium chamber, and \(F_{\text{med}}\) is the volume flow rate of CCW.  
Before that the DTFM attenuator is introduced into the enhanced CCW system, the response time of CCW temperature control is determined by the dynamic performance of the temperature closed loop control of the CCW machine. In general, the response time of the temperature control of a CCW machine used in precision manufacturing ranges from tens of second to several minutes. After the DTFM attenuator is cascaded into the system, the response time of the temperature control of the system \(T_{\text{sys}}\) can be expressed as  
\[T_{\text{sys}}=\text{max}(T_{\text{mac}},T_{\text{med}}) \tag{2}\]  
Figure 1: Schematic diagram of the enhanced circulating cooling water (CCW) system with the dynamic thermal filtering method (DTFM) attenuator.  
where \(T_{\rm mac}\) is the response time of temperature control of the CCW machine, and \(T_{\rm med}\) is the updating time of thermal capacity medium. Therefore, a design criterion of DTFM attenuator can be expressed as follows:  
\[T_{\rm mac}\geq T_{\rm med} \tag{3}\]  
If the criterion is satisfied, the quick response of CCW temperature control is not degraded.