## 1 Introduction  
Aluminum alloys have been widely used in applications where materials with high strength-to-weight ratio are required, especially in the rapidly growing automobile and aerospace industries. Although these kinds of materials have good machinability in other cutting operations, they are also considered the most critical materials for drilling [1; 2]. Drilling is a preferable machining process, as it takes about one-third of all manufacturing operations [3]. On the one side, dry drilling as well as other dry cutting operations are preferable as environmentally friendly machining techniques. On the other side, it creates greater challenges in the deep drilling of aluminum alloys [4]. During the dry drilling of brittle materials, including aluminum alloys, long and ductile chips tend to bend and coil and thus cause packing of the drill flutes, which interferes with chip ejection [5]. At the deeperdrilled depth, the increased amount of chips fill up the flutes, leading to chip-clogging, which causes the total torque to increase exponentially [6; 7; 8; 9; 10; 11]. The addition of such a chip evacuation torque results in excessive torsional stress, leading to a common failure of the tools known as drill breakage [8; 11; 12]. Whenever the drill broke inside the drilled hole, it was difficult to take out the broken part of the tool from the workpiece, causing catastrophic damage to the parts as well as considerable economic lost [13]. Consequently, chip evacuation has become the main constrain of deep drilling [14]. Specialized drilling tools and techniques have been developed for deep hole drilling, such as the single-lip gun drill, double-tube and single tube drill, boring and trepanning association [15], groove-type chip breaker [16], and peck drilling [12]. Nevertheless, twist drills are still used as a dominant tool, as much as 75% of the drilling operations in the deep hole drilling industry because of their low cost, versatility, and flexibility [17]. Numerous previous drilling torque models, which are commonly shown in many engineering books, are independent of drilling depth and thus cannot be applied in the practical drilling of deep holes. Therefore, modeling the total torque in deep hole drilling, including the chip evacuation torque, in order to predict the critical drilling depth where the total torque exceeds the allowance torque, becomes a more essential demand for automation and smart machining. Several attempts to model the chip evacuation torque for deep drilling using twist drill bits have been made in recent studies. The very early exponential model was first developed by [PERSON] et al. [8] for the drilling of aluminum 356-T6. [PERSON] et al. [16] evaluated several improvements of chip evacuation criteria in terms of critical depth, chip segmentation, thrust force and torque reduction of groove-type chip breakers on a twist drill. Another model similar to the [PERSON] et al. attempt was applied in the drilling of bone for orthopedic surgery [18]. Recently, a practical chip evacuation force model for the deep hole drilling of Al-6061 with three chip evacuation force coefficients was recently developed by [PERSON] et al. [14] to avoid difficulties in measuring and experimental calibrations of several parameters in the model proposed by [PERSON] et al. Nevertheless, the three coefficient model developed by [PERSON] et al. still has difficulties in comparing different drilling processes. To address this issue, a more practical chip evacuation torque model for deep hole drilling with only one chip evacuation force coefficient is proposed and validated in this study. The new model provides an ability to highlight the effectiveness of a modern technique, which is well known as ultrasonic assisted drilling (UAD). Compared to conventional drilling (CD), UAD has been proved to provide a significant reduction of thrust force [19; 20; 21; 22; 23], improvements in built-up edge [19; 24], burr size [19; 25], tool life, and hole oversize ([PERSON] et al., 2013).