Effects of process parameters on cutting temperature in dry machining of ball screw

Journal Pre-proof Effects of process parameters on cutting temperature in dry machining of ball screw Chao Liu, Yan He, Yulin Wang, Yufeng Li, Shilong Wang, Lexiang Wang, Yan Wang

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S0019-0578(20)30042-2 https://doi.org/10.1016/j.isatra.2020.01.031 ISATRA 3472

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ISA Transactions

Received date : 20 September 2019 Revised date : 9 January 2020 Accepted date : 22 January 2020 Please cite this article as: C. Liu, Y. He, Y. Wang et al., Effects of process parameters on cutting temperature in dry machining of ball screw. ISA Transactions (2020), doi: https://doi.org/10.1016/j.isatra.2020.01.031. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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*Title page showing Author Details

Effects of process parameters on cutting temperature in dry machining of ball screw

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Chao Liu a, Yan He a,*, Yulin Wang b,*, Yufeng Li a, Shilong Wang a, Lexiang Wang a, Yan Wang c State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400030, China b School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China c Department of Computing, Mathematics and Engineering, University of Brighton, Brighton, BN2 4GJ, United Kingdom *Corresponding author.

Acknowledgements

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E-mail address: [email protected] (Chao Liu) [email protected] (Yan He) [email protected] (Yulin Wang) [email protected] (Yufeng Li) [email protected] (Shilong Wang) [email protected] (Lexiang Wang) [email protected] (Yan Wang)

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This work was supported by the National Key R&D Program of China (Grant No. 2018YFB2002201), the National Natural Science Foundation of China (Grant No. 51575072), and the Fundamental Research Funds for the Central Universities, China

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(Grant No. 2018CDQYJX033).

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*Highlights (for review)

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Highlights

Experimental study of cutting temperature in dry machining of ball screw is described.

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Process parameters on the maximum and average temperatures are analyzed in details.

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Influencing degree of parameters on cutting temperature is affected by the value

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ranges.

Predictive models have been developed to estimate maximum and average

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temperatures.

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*Blinded Manuscript - without Author Details Click here to view linked References

Effects of process parameters on cutting temperature in dry machining of ball screw

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Abstract

Temperature in the cutting zone during dry machining has a significant effect on the tool life and surface integrity of the workpiece. This paper describes a comprehensive research on the cutting temperature in dry machining of ball screw under whirling milling by using infrared imaging. The effects of tool parameter and geometric parameter of workpiece together with the cutting parameters on the maximum and average temperatures in the cutting zone were analyzed in full detail. The influencing degree of these parameters on the maximum and average temperatures was affected

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by the value ranges of the parameters. In addition, the regression model and back propagation (BP) neural network model were proposed for predicting the maximum and average temperatures in the cutting zone. The verification of the predictive models showed that compared to the regression model, BP neural network model could predict the cutting temperature with high precision. The R 2 of BP neural

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network model for predicting the maximum and average cutting temperatures in the cutting zone was higher than 99.8%, and the mean relative error and root mean square error were less than 4% and 19%, respectively.

Key words: Cutting temperature; Predictive models; Dry machining; Process

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parameters 1. Introduction

Developing effective manufacturing technology to turn the raw materials into finished products with the lowest energy consumption and environmental pollution has become the focus of the manufacturing research community [1]. Dry machining technology achieves sustainable machining without emission and pollution, and then eliminate hazardous effects on the environment and reduce the economic burden of manufacturing enterprises [2]. Dry machining, processing the hardened workpiece

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with the hardness values of 45-70 HRC [3], is widely used for producing the mechanical transmission components such as bearings and screw [4]. With the development of the cutting tool material such as cubic boron nitride (CBN), dry machining has found increasing interest as the finish machining process [5]. The 1

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traditional machining processing methods of ball screw need turning/milling and grinding procedures which are complicated and have low productivity [6]. In addition, cutting fluids used in the traditional machining of ball screw have led to a large

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number of ecological problems, such as waste disposal, the release of harmful substances into the environment and hazardous working conditions for the operators [7]. Furthermore, the cost of cutting fluids and their management system can go up to 17% of the total cost of the machined part [8]. The dry machining method with the advantages of environmentally friendly and efficient [9] has been regarded as an attractive alternative to the wet cutting method [10]. Unfortunately, dry machining has not yet widely accepted by the industry due to the mass generation of heat in the cutting area which is the inherent problem in dry machining. It is stated that most of the power (90-95%) generated in the machining operation is converted to heat [11].

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The aggregation of the cutting heat is dissipated by the tool, workpiece and chip. Soler et al. [12] found that the increase of the tool temperature would reduce the tool life. The reduction of tool life will increase the update times of the tool, and eventually increase the economic cost. More importantly, the cutting temperature will also affect the surface integrity of the workpiece in dry machining [13-14]. The burn

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of the workpiece and stress concentration will reduce the service time of the workpiece, and thus increase the maintenance/ replacement cost and reduce the machining efficiency. This problem is more serious in the service of ball screw which is always in contact with the ball and in constant motion. Therefore, heat generation is considered to play a vital role in machining process because of its interactions with

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the performance of the cutting tool and workpiece, thus it is necessary to investigate the machining-induced temperature in the cutting process. The cutting temperatures of the cutting zone have been explored by many researchers under the different cutting parameters in dry machining process by the theoretical method. The theoretical method which defined as a white-box method could reveal the variation of the temperature from the theoretical perspective. Ning and Liang [15] presented an analytical model for predicting the cutting temperatures in the primary shear zone and tool-chip interface based on the relationship between

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force and temperature. The temperature can be calculated with high accuracy and efficiency by inputting the cutting condition parameters (including cutting velocity and depth of cut), machining forces and constitutive model constants. To solve the problem of the temperature increase and decrease phase, an analytical model-based 2

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method was established for estimating the tool temperature in end milling by Wu et al. [16]. The influences of the cutting conditions of cutting speed, feed per tooth and depth of cut on the tool temperature were investigated by their study, and they found

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that the tool temperature increased with feed per tooth and decreased with the cutting speed. In addition, Mirkoohi et al. [17] developed a physics-based analytical model to determine the machining temperature. The goal of their model was to design the cutting speed and depth of cut for the desired temperature based on the iterative gradient search method. Furthermore, Richardson et al. [18] proposed a theoretical model for evaluating the effects of cutting parameters on the workpiece temperature in dry milling. The research found that workpiece temperature declined dramatically with the increased of the cutting speed and federate. To analysis the cutting parameters on tool temperature, Karaguzel et al. [11, 19] presented a fully analytical

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temperature model to study the milling parameters on cutting tool temperature during dry milling. The study has shown that the cutting tool temperature raised with the increasing of the cutting speed and depth of cut. Based on the heat transfer theory and constitutive equation of workpiece material, Li et al. [20] proposed a thermal model for forecasting the temperature distributions in the cutting zone during the dry cutting

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process. The theoretical and experiment results indicated that the tool temperature decreased with the cutting speed at the low level of cutting speed and increased again at the relatively higher range of cutting speed, while the temperature in the flank face decreased with the increasing of the cutting speed. In addition, semi analytical model which defined as a grey-box method has been proved efficient to the theoretical

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method [21]. In order to simplify the temperature model, Sutter and Ranc [22] proposed a combination of experimental and analytical methods to predict the temperature field in the chip. In their combined method, the input parameters of the analytical model such as the chip contact length and frictional coefficient were obtained based on the experimental method. On the basis of the analytical method, Kryzhanivskyy et al. [23] developed an inverse model to computed the heat fluxes and heat transfer coefficients based on the experimental data for estimating the cutting tool temperature in drying machining. By considering the effect of heating time on the

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workpiece, Huang and Yang [24] presented an improved temperature model to analysis the temperature distribution of the workpiece in the cutting process. In their temperature model, the effect of heating time on the thermal conductivity has been formulated by polynomial fitting method based on the experimental data. The effects 3

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of cutting parameters on the cutting temperature obtained by the grey-box method are consistent with that of the white-box method. The cutting speed, feed rate and depth of cut are selected as the main parameters when studying the influences of process

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parameters on cutting temperature by the white-box and grey-box methods in dry machining. However, the effects of tool and workpiece parameters on the cutting temperature can not be reflected in the theoretical and semi analytical methods.

Comparing with the theoretical and semi analytical methods, the experimental method can also study the influences of tool and workpiece parameters except for the cutting parameters on the temperature during dry machining. In addition, as Lazoglu and Altintas [25] raised an issue that most published articles or researches rely on the experimental data which demonstrates that there has a strong demand in the scientific community for experimental method of the cutting temperature. Thus, the

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experimental method has gained more attention from scholars in recent years during dry machining. Soler et al. [26] developed a new measurement method without calibrating the emissivity of the infrared thermography to study the effects of cutting speed and feed rate on temperature distribution of rake face in dry cutting. The study showed tool temperature raised together with the cutting speed and feed rate, and this

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phenomenon has been verified by Artozoul et al. [27]. Furtherly, the combined impacts of tool condition and cutting parameters on chip temperature in dry cutting have been estimated by Toh [28]. The tool geometry is also the main factor affecting the cutting temperature in dry machining [29]. Saglam et al. [30] considered that the positive rake angle can effectively decrease cutting temperature, in addition, the tool

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temperature increased with cutting speed and lowered with entering angle in dry cutting condition. The workpiece parameter is another factor should be considered in the investigation of the cutting temperature. By employing three experimental methods, Aspinwall et al. [31] investigated the temperature of workpieces with two different alloy materials under dry milling. The results showed that high positive rake angle of the tool could reduce the workpiece temperature for ductile workpiece materials; while the variation of the tool geometry/coating had little effect on workpiece temperature for brittle workpiece materials. This is mainly because large

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deformation of ductile workpiece and associated higher strain have contributed to the high temperature [32]. It can be found that the experimental method can effectively investigate the influences of tool and workpiece parameters on the cutting temperature, but can not predict the variation of the cutting temperature. 4

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Based on the experimental data, black-box method was developed by many researchers to predict the cutting temperature. As a kind of black-box method, regression analysis can effectively solve the linear and nonlinear problems [33].

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Sreejith et al. [34] developed a multiple regression model to investigate the effect of machining conditions on the cutting temperature. In their regression model, the cutting speed and depth of cut were taken as the input parameters. In addition, another kind of efficient tool to deal with nonlinear systems is the neural networks nowadays [35]. By considering the effect of coated tool on temperature, Kara et al. [36] proposed a method of predicting the cutting temperature based on the artificial neural network in turning of AISI 316L stainless steel. In their neural network, the input layer includes the cutting speed, feed rate and cutting force. Besides the cutting speed and feed rate, the material hardness of the workpiece was employed to predict the

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cutting temperature by Mia and Dhar [37] based on the neural network in the dry turning process. They found that the material hardness played an important influence on cutting temperature, and exerted a contribution of 67% on the cutting temperature in dry cutting. These researches are of great significance to the temperature analysis of dry machining. However, the cutting temperature origins from the number of tools

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and geometric parameter of workpiece have not been conducted in dry machining. The number of tools in the interrupted cutting process can control the heat dissipation and conduction, thereby regulate the cutting temperature. In addition, the geometric parameter of workpiece has an effect on the area of heat dissipation. Therefore, the influences of the number of tools and geometric parameter of workpiece on the

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cutting temperature are yet to be revealed in dry machining. The contribution of this paper is to determine the real effect of cutting parameters, tool parameter and workpiece parameter on the cutting temperature, which can not be fully illuminated by the white-box and grey-box methods. Based on the experimental values, two predictive models which consider the tool parameter and geometric parameter of workpiece besides the cutting parameters are developed to calculate the cutting temperature. In addition, the accuracy of the regression model and BP neural network model is compared and analyzed.

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The remainder of this paper is structured as follows: In Section 2, a detailed

experimental method is proposed to obtain the accurate temperature variations. Section 3 describes the temperature variations in the complete cutting cycle, and then the effects of process parameters on the cutting temperature are analyzed. In Section 4, 5

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two predictive models are proposed for estimating the maximum and average temperatures in the cutting zone. Finally, some conclusions are provided in Section 5.

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2. Experimental procedures 2.1. Experimental condition

The cutting temperature tests in the dry machining of ball screw were conducted in a CNC whirling milling machining center (model “HJ092X80”, Hanjiang Machine Tool Co., Ltd.), shown in Fig. 1. The maximum rotation speeds of the tool ring spindle and workpiece spindle are 640 r/min and 25r/min, respectively. The maximum number of threads that can be machined in whirling milling is 99. The experimental

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conditions used in the experiment are listed in Table 1 for analyzing the temperature distribution and constructing the predictive models. The dry cutting condition has been adopted during cutting temperature tests.

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Workpiece spindle

Thermal imaging

Workpiece

Tool ring

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Rotary head spindle

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Fig. 1. Experimental set-up.

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Table 1 Number of threads, S 3 3 3 2 3 2 3 2 2 2 2 2 3 3 2

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Maximum depth of cut, Dc (mm) 0.06 0.06 0.04 0.01 0.06 0.008 0.06 0.06 0.01 0.008 0.006 0.006 0.006 0.08 0.006

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Experimental conditions. Number of Cutting speed , No. tools, N Vt (m/min) 1 4 160 2 4 180 3 4 180 4 4 180 5 4 200 6 4 200 7 4 220 8 4 220 9 6 200 10 6 200 11 4 220 12 4 260 13 4 260 14 4 180 15 6 200

The diameter of the workpiece (cylinder) was 78.5 mm. The workpiece material was AISI 52100, and the hardness of the workpiece was 63HRC. The root diameter of

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the ball screw was 73.9 mm with the axial pitch of 10mm. The material of the forming tool was polycrystalline cubic boron nitride (PCBN), and the radius of the semicircle arc of the tool was 4.86 mm with the chamfer of 0.15mm×20°. In each set of the cutting conditions, sharp tools were employed to remove the influence of the abrasion on cutting temperature. The relative motion of the workpiece and tool during whirling

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milling are illustrated in Fig. 2. In whirling milling, the tool ring inserted with the cutting tools rotates with high speed, and the workpiece rotates with low speed. Both

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Ø 78.5 mm

of the tool ring and the workpiece have been in a rotating state.

Tool ring

Workpiece

nw

Cutting direction

nt Workpiece

Cutting tool

Cutting tool

Fig. 2. Relative motion of the workpiece and cutting tool. 7

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2.2. Temperature measuring apparatus

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The methods for measuring the cutting temperature mainly include the contact method by various types of thermocouples [38] and non-contact method by infrared imaging [39]. The thermocouples are widely used in the machining process to capture the temperature distribution but the limited transient response [26] and difficult to obtain the accurate temperature gradients [40] are the disadvantages of the wired or wireless thermocouples. In addition, the tool and workpiece are always in a state of rotation as shown in Fig. 2. Consequently, the contact measurement method can not accurately measure cutting temperature in whirling milling due to the installation and sampling frequency problems. Compared to the thermocouples, infrared imaging can

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be used as a fast and accurate temperature measurement method [41]. Therefore, the infrared imaging used in this work can be more suitable for measuring cutting temperature during whirling milling.

The temperature of cutting area (including workpiece, tool and chip) during the whirling milling process was measured by infrared imaging provided by FLIR

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systems company. The temperature measuring method is illustrated in Fig. 1. The software BM_IR was adopted to analysis the pictures information captured by the infrared imaging. The response time of the infrared imaging was 2 ms at the spectrum ranges from 2.5 to 5 mm. The measured window gave a field of view of 640 × 512 pixels to obtain a higher image resolution. In order to capture the accurate temperature

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variations in the complete cutting cycle during whirling milling, the sampling frequency of the infrared imaging was set to 200 pictures per second. Before the temperature measurement in the whirling milling, the infrared imaging was calibrated by painting method. The calibration steps are as follows: i) spray the black paint (acrylic resin with the emissivity of 0.97) evenly on the workpiece surface; ii) adjust the emissivity of thermal imaging until the temperature value of the workpiece surface is same or close to that of the surface sprayed with the black paint. Through multiple calibration experiments, the emissivity of the thermal imaging was defined as 0.85 at

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30 °C. From Fig. 1, the main temperature area of the cutting area does not appear near the workpiece surface. In the metal cutting process, most of the heat in the cutting zone is transferred to the chip [42]. Therefore, the heat absorbed by the chip in the cutting zone is relatively high, and the heat is finally reflected by the high temperature. 8

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There has a time delay between the heat transfer and release of the chip. Within this time delay, the chip is brought out of the workpiece surface by the tool ring with high imaging is not near the workpiece surface. 3. Experimental results and discussions 3.1. Experimental results of the temperature

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speed rotation. Eventually, the main temperature area captured by the infrared

The instantaneous variation of the cutting temperature during the three complete cutting cycles are shown in Fig. 3. Two sets of experimental conditions (No.14 and No.15) with different values of the number of tools, cutting speed, maximum depth of

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cut and number of threads are employed to exhibit the variation of cutting temperature. A complete cutting cycle consisting of the cutting stage and noncutting stage is shown in Fig. 3. The time consumption was discrepancy at the different cutting conditions to accomplish a complete cutting cycle. The variation of cutting temperature during cutting stage was as follows: increased rapidly at the beginning and then had some

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fluctuations and subsequently decreased rapidly. In the noncutting stage, the cutting temperature in the cutting zone remained essentially unchanged. During the cutting stage, the temperature variation is divided into three stages: stage one (S-I), the cutting temperature increased rapidly until it reached the maximum peak; stage two (S-II), the cutting temperature had some fluctuations but with relatively stable; stage

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three (S-III), the cutting temperature decreased rapidly until the cutting stage was completed. In stage one, the variation of the uncut chip thickness from zero to maximum led the heat sources area in the primary and second deformation zone to increase rapidly [43]. This was the main reason for the rapid increased of the cutting temperature in stage one. In stage two, the uncut chip thickness had a slight variation and accordingly the cutting temperature did not have much change. In stage three, the values of the uncut chip thickness and width became to zero, and thus the cutting

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temperature decreased rapidly.

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S-I S-II S-III

One cutting cycle

750

600 400

200 0

600

450 300

Cutting stage

Noncutting stage

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Temperature (℃ )

Temperature (℃ )

800

150

0 0.03 0.05 0.08 0.1 0.13 0.15 0.18 0.2 0.23 0.25

0 0.02 0.05 0.07 0.1 0.12 0.15 0.17 0.2 0.22 0.25 0.27

0

Time (s)

Time (s)

(a) (b) Fig. 3. Variation of cutting temperature at experiment tests of (a) No. 14 and (b) No. 15.

The instantaneous cutting temperature of cutting area has a great variation during one cutting cycle. It is inconvenient to analysis the influences of process parameters

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on temperature with the instantaneous value. The maximum and average temperatures have been considered in this work to realize the temperature affection analysis. The maximum and average cutting temperatures of the different cutting conditions (a total of 15 sets of cutting experiments) were gained by averaging the peak and all values in

Table 2

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the measured values under the stable cutting, shown in Table 2.

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Maximum and average cutting temperatures of the different cutting conditions. Maximum Average No. temperature (℃) temperature (℃) 1 348 275 2 595 416 3 364 247 4 603 325 5 711 427 6 849 429 7 721 431 8 801 452 9 766 432 10 703 400 11 838 447 12 810 453 13 726 376 14 729 430 15 653 390

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3.2. Temperature analysis The tool parameter, geometric parameter of workpiece and cutting parameters

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have been employed to analyze the cutting temperature in whirling milling. The relationship between these parameters and cutting temperature can be revealed by the analysis of the experimental values of maximum and average cutting temperatures. 3.2.1. Number of tools

The process of whirling milling is characterized by intermittent cutting realized by multiple tools which are inserted into the tool ring, shown in Fig. 2. During dry machining process, tool ring drives the tools to accomplish the high speed cutting in the case of low speed rotation of the workpiece.

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In this study, four and six tools were adopted to investigate the impact of number of tools on temperature variation at the cutting condition of Vt=200 m/min, Dc=0.008 mm, S=2. From Fig. 4, the maximum and average temperatures declined with the increased of number of tools and decreased by 17.1% and 11.4%, respectively. The heat produced in cutting area was identical at the same cutting conditions. Therefore,

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the more of the number of tools, the more heat they took away and dissipated. Accordingly, the temperature of cutting area decreased with the increased of number

Maximum temperature Average temperature

900

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Temperature (℃ )

of tools.

600 300 0

4

N

6

Fig. 4. Temperature variation at different number of tools.

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3.2.2. Number of threads

The number of threads is the important geometric parameter of the ball screw. It

can control the transmission torque and movement between the ball screw and balls. The lead of multiple threads is large than that of the single thread which can decrease 11

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the capability of self-locking to improve the transmission performance. In addition, the multiple threads can reduce the axial force on the ball screw, thereby reducing the friction between the ball screw and balls. Therefore, as an important feature of the

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geometric parameter of workpiece, the number of threads has been chosen to study its effect on cutting temperature in whirling milling.

The temperature variation at the different number of threads is exhibited in Fig. 5. Fig. 5 (a) and (b) show the maximum and average temperatures in whirling milling with respect to N=4, Vt=260 m/min, Dc=0.006 mm and N=4, Vt=220 m/min, Dc=0.06 mm, respectively. From Fig. 5 (a), the maximum temperature and average temperature at S=3 have decreased by 10.5% and 17.2%, respectively, compared with S=2. From Fig. 5 (b), the maximum temperature and average temperature at S=3 have decreased by 10.1% and 4.4%, respectively, compared with S=2. It is mainly because that the

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more of the number of threads the larger area of heat dissipation. At the same cutting conditions, the decline of the maximum and average temperatures is obvious with the increase of number of threads. It indicates that the increase of the number of threads can effectively reduce the temperature in the cutting area under whirling milling, and simultaneously can improve the transmission performance and reduce the contact

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900 600

Temperature (℃ )

Maximum temperature Average temperature

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Temperature (℃ )

friction.

300 0

2

S

3

Maximum temperature Average temperature 900 600 300 0 2

S

3

(a) (b) Fig. 5. Influence of number of threads on temperatures at cutting conditions of (a) N=4, Vt=260 m/min, Dc=0.006 mm and (b) N=4, Vt=220 m/min, Dc=0.06 mm.

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3.2.3. Cutting parameters

In whirling milling, the rotation speed of workpiece is controlled by tool ring

rotation speed (reflected by the cutting speed) and maximum depth of cut. Therefore, the cutting speed and maximum depth of cut have been chosen as the independent parameters to research the influences of parameters on cutting temperature in whirling 12

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milling. The effect of cutting speed on the maximum and average temperatures is shown in Fig. 6 at the cutting condition of N=4, Dc=0.06 mm, S=3. The maximum and average

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temperatures showed a trend of growth as the increased of cutting speed. The increased of cutting temperature in the low-speed region was larger than that in the high-speed region. The material removal volume in unit time increases with the cutting speed which induces the increasing of heat generation. Therefore, the cutting temperature of cutting area will increase accordingly. At high cutting speed, the tool ring with high speed rotation interacts with air to form a stronger convective system which can take a part of the heat into the air. The greater the cutting speed, the more heat produced and more heat transferred to the air, therefore, the increasing of the

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cutting temperature is not significant at high speed region.

Fig. 6. Variation of cutting temperatures at different cutting speed.

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During whirling milling, transient variation is a characteristic of the depth of cut. This change will lead to the variation of the heat source in shear zone and frictional zone. Variation of the heat source induces an instantaneous variation of the cutting temperature in the cutting zone. This indicates that the depth of cut has a great impact on cutting temperature. Fig. 7 (a) and (b) show the maximum and average temperatures in whirling milling with respect to the maximum depth of cut at the cutting conditions of N=4, Vt=180 m/min, S=3 and N=6, Vt=200 m/min, S=2, respectively. The cutting temperature has raised as the increasing of the maximum

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depth of cut. The values of the maximum and average temperatures were significantly raised as the maximum depth of cut at the high depth of cut region. When the depth of cut is low, the increased of cutting temperature was not very great. In metal cutting, the depth of cut equates to the uncut chip thickness which directly determines the size 13

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of the heat source at the same machining condition. The greater the maximum depth of cut, the more heat generated in the heat source region. Therefore, the temperature

800 600

400 200 0

0.04

0.06

0.08

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Maximum temperature Average temperature

Temperature (℃ )

Temperature (℃ )

of cutting area will increase along with the rise of the maximum cutting depth.

Maximum temperature Average temperature

800 600 400

200 0

0.006

Dc (mm)

0.008

0.01

Dc (mm)

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(a) (b) Fig. 7. Variation of temperatures at different maximum depth of cut at cutting conditions of (a) N=4, Vt=180 m/min, S=3 and (b) N=6, Vt=200 m/min, S=2.

3.3. Parameters influence analysis

It is observed that these parameters have different effects on the cutting

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temperature in the process of whirling milling. The parameter influence analysis for the maximum and average temperatures by main effect plots is shown in Fig. 8. It can be seen that the degrees of the influences of the number of tools, cutting speed, maximum depth of cut and number of threads on the cutting temperature are different.

700

600

500 400

300

4

6

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N

160 180 200 220 260 0.006 0.008 0.010 0.040 0.060 0.080

Means for maximum temperature (

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800

Vt (m/min)

(a)

14

Dc (mm)

2

3 S

450 400

300 250 4

6

pro of

350

160 180 200 220 260 0.006 0.008 0.010 0.040 0.060 0.080

Means for average temperature (

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N

Vt (m/min)

(b)

Dc (mm)

2

3

S

Fig. 8. Main effect plots for (a) maximum temperature and (b) average temperature.

From Fig. 8 (a) and (b), cutting speed was the sensitive parameter affecting the maximum and average temperatures in whirling milling when cutting speed is low.

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The maximum depth of cut was the significant parameter when the depth of cut was large. However, at high level of cutting speed and low level of maximum depth of cut, the number of tools and number of threads became the significant parameters affecting the cutting temperature. It can be concluded that the degree of the influences

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of parameters on the maximum and average temperatures will be affected by the value ranges of the parameters.

4. Cutting temperature predictive models

Based on the above experimental results, two predictive models are proposed for

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estimating the cutting temperature during ball screw whirling milling. The predictive models take the tool parameter, geometric parameter of workpiece and cutting parameters as the input variables. The proposed predictive models include the regression model and BP neural network model. As black box method, the regression model and BP neural network model can effectively deal with the nonlinear problems such as the cutting temperature. In this section, the two predictive models are analyzed to compare their accuracy of the prediction of the cutting temperature.

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Finally, a suitable model for predicting the cutting temperature in dry machining of ball screw under whirling milling can be found. The first thirteen sets of experimental results were used to construct the proposed predictive models, and the latter two sets of experiments results were used to verify the validity of the models. 15

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4.1. Regression model The regression method adopted in this paper includes two steps regression

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processes. The first step regression model is based on the empirical model with ten sets of processing parameters. Then the second step linear regression analysis is carried out with thirteen sets of cutting parameters based on the first step regression model.

The empirical model with exponential function is often used in the prediction of cutting temperature under the determined tool geometry parameters and workpiece materials. The use of exponential function in the analysis of linear regression can realize the data preprocessing. A new empirical model considering the process parameters of ball screw whirling milling is proposed, as shown in Eq. (1).

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Ti  CTiVt m1i Dc m2 i N m3i S m4 i

(1)

where i is the type of cutting temperature in the cutting cycle ( i  1 represents the maximum temperature and i  2 represents the average temperature), Ti is the first step regressive cutting temperature in the cutting cycle, CTi is the temperature

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coefficient, Vt is the cutting speed, Dc is the maximum depth of cut, N is the number of tools, S is the number of threads and m1i to m4i are the corresponding indices.

The Eq. (1) is a non-linear function which can be transformed into the linear function by taking logarithms in the following.

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ln Ti  ln CTi  m1i ln Vt  m2i ln Dc  m3i ln N  m4i ln S

(2)

The logarithmic function can be replaced as follows.

Yi  ln Ti , m0i  ln CTi , X1  ln Vt , X 2  ln Dc , X 3  ln N , X 4  ln S

(3)

Then the Eq. (2) can be converted into the multiple linear regression equation to calculate the temperature coefficients, shown in the following.

Yi  m0i  m1i X1  m2i X 2  m3i X 3  m4i X 4

(4)

The coefficients of the Eq. (4) can be obtained with the numerical computation

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software MATLAB R2016a, and the corresponding coefficients in Eq. (1) can be acquired by transformation, shown in Table 3. The experimental values of cutting condition 1 to 10 in Table1 were adopted for the first step regression analysis. 16

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Table 3 The coefficients in the first step regression model. CT 1

m11

m21

m31

m41

Values

0.0023

2.4128

-0.0772

-0.171

-0.2634

Coefficients of T2

CT 2

m12

m22

m32

m42

Values

0.1191

1.5364

0.0254

0.1347

-0.1514

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Coefficients of T1

After the first step linear regression, the basic cutting temperature model can be developed. Then the second step linear regression is analyzed to modify the basic cutting temperature model.

(5)

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TPi  ai  bT i i

where TPi is the prediction value of the cutting temperature in the cutting cycle, ai and bi are the correction coefficients in the second step linear regression. The experimental values of cutting condition 1 to 13 in Table 1 were employed to modify the temperature coefficients in the second step linear regression. Finally, the

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correction coefficients ai and bi in the cutting cycle can be obtained, shown in Table 4. The regression model for predicting the cutting temperature can be established with the coefficients obtained by the two steps regression analysis.

Table 4

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The coefficients in the second step regression model. Coefficients of T1

a1

b1

Values

431.2375

0.3167

Coefficients of T2

a2

b2

Values

191.1175

0.4871

4.2. BP neural network model

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BP neural network can approach arbitrary non-linear continuous function with the

appropriate weights and structure. The back-propagation algorithm is adopted in BP neural network for adjusting and training the weights and deviations of networks to make the output vector close to the expected vector. The topological construction of 17

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BP neural network model mainly includes the layer of input, hidden and output, and the structure of BP model in this paper is exhibited in Fig. 9. The input layer has four neurons which correspond to the process parameters: cutting speed, maximum depth

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of cut, number of tools and number of threads. The output layer has one neuron which corresponds to the cutting temperature. The back propagation will be happening to influence the values of weight ( wij and w jk ) if there has a certain error between the actual and the expected values.

wij Rotation speed

w jk

Maximum depth of cut

Cutting temperature

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Number of tools Number of leads

Input layer

Hidden layer

Output layer

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Fig. 9. The structure of BP neural network [44].

In this study, the input vector has four elements (cutting speed, maximum depth of cut, number of tools and number of threads) with three different physical meanings. Therefore, to eliminate the dimension effect between the indexes, the process of normalization should be conducted before the prediction of BP neural network. The

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normalization will accelerate the solving process and improve the prediction precision of the network. The normalization process is shown in Eq. (6). y

x  xmin ( ymax  ymin )  ymin ( xmax  xmin ) xmax  xmin

(6)

where y is the normalized data, ymax =1 and ymin  1 ; x is the pretreatment data,

xmax and xmin are the maximum and minimum values of the pretreatment data. If xmax  xmin , the data remains unchanged. In BP neural network, the sigmoid function is generally selected as the activation

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function which is shown in Eq. (7) [45]. f ( z) 

1 1  e z

(7)

where z is the weighted sum of the inputs and the function f ( z ) is used for 18

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changing the value of weight. The connection weight of BP neural network can be formulated as follows [46] : L

wij  wijn 1  wijn   X i f ( z j )  k w jk

(8)

pro of

k 1

wjk  wnjk1  wnjk   EkYj f ( zk )

(9)

where w corresponds to the increment of the connection weight; w is the connection weight;  is the learning rate of the network;  k is the partial derivative of error function to neurons in the input layer; L is the number of neurons in the output layer; Ek is the difference value of the output node; Y j is the actual output vector; X i is the actual input vector; f ( z ) is the derivative of the transfer function. The algorithm of BP neural network was conducted in MATLAB R2016a. The

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operation parameters of the BP neural network were given as follows: target error of the network was set to 1×10-3; the maximum training step was set to 2×105; the learning speed was set to 5×10-2; the display period of the results was set to 50. The BP neural network was trained based on the above settings.

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4.3. Verification of the predictive models

The last two sets of experiments (No. 14 and 15) in Table 1 were adopted to verify the predictive models. The comparisons between experimental and prediction values of maximum and average cutting temperatures calculated by the predictive models are

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exhibited in Fig. 10. The calculated cutting temperatures by proposed predictive models agree well with the measured cutting temperatures for the cases No. 14 and

Prediction value Maximum value

667

800

653

575

600

391 430

400

353 390

200

0

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Temperature(℃ )

800

Prediction value Maximum value

Measured value Average value

729

Temperature(℃ )

15.

No.14

No.14

No.15

741 729

600

661 653 454 430

381 390

400 200 0 No.14

No.15

Measured value Average value

No.14

No.15

No.15

Cutting conditions

Cutting conditions

(a) (b) Fig. 10. Verification of the predictive models: (a) regression model and (b) BP neural network model. 19

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Relative error ( RE ) based on the prediction values and measured values can be formulated by the following equation.

Tm  Tp

pro of

RE 

(10)

Tm

where Tm is the measured value and T p is the prediction value of the cutting temperature. The comparison of the prediction values and measured values are exhibited in Fig. 11 with the relative errors. Also, the relative errors of cutting temperature values estimated by the theoretical model (proposed by our previous work [43]) are exhibited in Fig. 11. The maximum and average temperatures calculated by the theoretical model are 884℃and 426℃ at the condition of No. 14, and the maximum and average temperatures are 725℃and 230℃ at the condition of No. 15.

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From Fig. 11, the prediction accuracy of the proposed models is relatively high. The maximum relative errors of the regression model for the prediction of the maximum and average temperatures are 11.94% and 9.49%, respectively. For the BP neural network model, the maximum relative errors of the maximum and average

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temperatures are 1.65% and 5.58%, respectively. Compared with the theoretical model, the relative errors of the regression and BP neural network models are relatively low. One reason is that the theoretical model has not considered the influence of the geometric parameter of the workpiece on the cutting temperature. It indicates that the BP neural network model can be used as effective method in comparison with the regression model to predict the cutting temperature in whirling

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Measured value Measured value

800

RE=8.50

Prediction value Prediction value RE=11.94

600

600

400 200

800

400

RE=9.07

RE=9.49

0

200 0

NO.14

NO.15

Cutting conditions

(a)

20

Average temperature (℃)

Maximum temperature (℃)

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milling.

800

RE=1.65

Prediction value Prediction value RE=1.23

600

600

400

200

800

400 RE=5.58

RE=2.31

0

200 0

NO.14

Average temperature (℃)

Measured value Measured value

pro of

Maximum temperature (℃)

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NO.15

Cutting conditions

1000 800 600 400 200 0

Measured value Measured value

Prediction value Prediction value

800

RE=21.26

RE=11.03

600 400

RE=0.93

RE=41.03

200 0

NO.14

NO.15

Average temperature (℃)

Maximum temperature (℃ )

(b)

Cutting conditions

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(c) Fig. 11. Comparison of the prediction values and measured values for (a) regression model, (b) BP neural network model and (c) theoretical model.

To evaluate the proposed models more deeply, the statistical methods of R 2

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(absolute fraction of variance), MRE (mean relative error) and RMS (root mean square error) have been used for the comparison. As an evaluation index, the range of

R 2 is [0, 1], and the value closer 1 the higher accuracy of the prediction. The proposed regression model and BP neural network model can be evaluated by these error analyses. These errors can be calculated in the following:

R 2  1   M 1

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N

MRE 

RMS 

(Tm, M  Tp , M )2 Tm2,M

1 N Tm, M  Tp , M  N M 1 Tm, M



N

M 1

(Tm , M  Tp , M ) 2 N

(11)

(12)

(13)

where Tm , M is the measured value, T p , M is the prediction value and N is the

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number of samples. These errors of the regression model, BP neural network model and theoretical model are shown in Table 5.

Table 5

21

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Comparison between the models. Predictive models

BP neural network

MRE

Theoretical model

R2

MRE

RMS

R2

Maximum

97.85

10.22

70.46

99.96

1.44

10.20

94.26

16.14

120.85

Average

98.28

9.28

38.01

99.64

3.95

18.12

83.16

20.98

113.17

RMS

R2

MRE

RMS

pro of

Errors (%) Temperature type

Regression model

It can be seen from Table 5, the black-box method has excellent performance compared with the theoretical model. The R 2 of the BP neural network model was higher than regression model for predicting the maximum and average cutting temperatures. It indicated that the fitting degree of the BP neural network model was better than that of the regression model. In addition, the values of MRE and RMS

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of the BP neural network model for maximum and average cutting temperatures were lower than that of the regression model. The R 2 of BP model for predicting the maximum and average cutting temperatures was higher than 99.8%, and the MRE and RMS were less than 4% and 19%, respectively. The contrast validation of the predictive models showed that the BP neural network model could predict the cutting

5. Conclusion

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temperature with high precision.

An experimental method has been described to measure the cutting temperature

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under different number of tools, number of threads, cutting speed and maximum depth of cut in dry machining of ball screw under whirling milling. The influences of these parameters on the cutting temperature have been investigated, and the predictive models have been developed based on the experimental values for predicting the maximum and average temperatures in the cutting zone. The main conclusions were obtained in the following:

1) A complete cutting cycle in dry machining of ball screw under whirling milling has consisted of the cutting stage and noncutting stage. In the cutting stage, the

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variation of the temperature in the cutting zone can be divided into three stages: increased rapidly at the beginning and then had some fluctuations and subsequently decreased rapidly. In the noncutting stage, the value of the temperature in the cutting zone was almost constant. 22

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2) The maximum and average temperatures in the cutting zone decreased by 17.1% and 11.4% as the number of tools changed from 2 to 3 at the cutting condition of Vt=200 m/min, Dc=0.008 mm, S=2. Both the maximum and average temperatures

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at S=3 have decreased by an average of 10% compared with S=2. In addition, the temperature of cutting area increased as cutting speed, and the increasing rate of cutting temperature in the low-speed region was larger than that in the high-speed region. Different from the influence of cutting speed on cutting temperature, maximum and average temperatures were significantly raised as the increasing of maximum depth of cut in the high level of depth of cut.

3) The analysis of the maximum and average temperatures revealed that the cutting speed was the significant parameter affecting the cutting temperature at low level of cutting speed, and the maximum depth of cut was the significant parameter

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when the depth of cut is large. However, the number of tools and number of threads were the significant parameters affecting the cutting temperature at high level of cutting speed and low level of maximum depth of cut. 4) The proposed predictive models can be used for predicting the maximum and average temperatures of cutting area. The contrast validation of predictive models

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showed that the BP neural network model could predict the cutting temperature with high precision. In this study, the goodness of fit of BP neural network for the prediction of maximum and average cutting temperatures was higher than 99.8%, and the MRE and RMS were less than 4% and 19% respectively. For the time being the predictive models were just developed from the

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experimental data and were realized with the data fitting technology. In this investigation, the process parameters covered the different number of tools, number of threads, cutting speed and maximum depth of cut. A more complete research and model covering the effects of more tool parameters and material parameters on the cutting temperature will be the direction of the future research to realize real-time monitoring of temperature in the cutting area.

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*Conflict of Interest

Conflict of interest

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We would like to submit the enclosed manuscript entitled “Effects of process parameters on cutting temperature in dry machining of ball screw”, which we wish to be considered for publication in “ISA Transactions”. No conflict of interest exits in the submission of this manuscript, and the manuscript is approved by all authors for publication. I would like to declare on behalf of my co-authors that the work described was original research that has not been published previously, and not under consideration for publication elsewhere, in whole or in part. All the authors listed have approved the manuscript that is enclosed.