J. Cent. South Univ. (2018) 25: 1799-1812

DOI: https://doi.org/10.1007/s11771-018-3870-0

Structure design and characteristics analysis of a cylindrical giant magnetostrictive actuator for ball screw preload

JU Xiao-jun(鞠晓君), LIN Ming-xing(林明星), FAN Wen-tao(范文涛),BU Qing-qiang(卜庆强), WU Xiao-jian(吴筱坚)

Key Laboratory of High-efficiency and Clean Mechanical Manufacture of Ministry of Education, School of Mechanical Engineering, Shandong University, Jinan 250061, China

Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Abstract: In order to achieve automatic adjustment of the double-nut ball screw preload, a magnetostrictive ball screw preload system is proposed. A new cylindrical giant magnetostrictive actuator (CGMA), which is the core component of the preload system, is developed using giant magnetostrictive material (GMM) with a hole. The pretightening force of the CGMA is determined by testing. And the magnetic circuit analysis method is introduced to calculate magnetic field intensity of the actuator with a ball screw shaft. To suppress the thermal effects on the magnetostrictive outputs, an oil cooling method which can directly cool the heat source is adopted. A CGMA test platform is established and the static and dynamic output characteristics are respectively studied. The experimental results indicate that the CGMA has good linearity and no double-frequency effect under the bias magnetic field and the output accuracy of the CGMA is significantly improved with cooling measures. Although the output decreased with screw shaft through the actuator, the performance of CGMA meets the design requirements for ball screw preload with output displacement more than 26 μm and force up to 6200 N. The development of a CGMA will provide a new approach for automatic adjustment of double-nut ball screw preload.

Key words: ball screw preload; cylindrical giant magnetostrictive actuator (CGMA); structure design; output characteristics

Cite this article as: JU Xiao-jun, LIN Ming-xing, FAN Wen-tao, BU Qing-qiang, WU Xiao-jian. Structure design and characteristics analysis of a cylindrical giant magnetostrictive actuator for ball screw preload [J]. Journal of Central South University, 2018, 25(7): 1799-1812. DOI: https://doi.org/10.1007/s11771-018-3870-0.

1 Introduction

Ball screws are widely used in the drive system of computer numerical control (CNC) machine and machining center with features of low friction, high stiffness and high transmission accuracy [1, 2]. The preload force can affect the stiffness of ball screw [3–5], eliminate the axial clearance caused by manufacturing and fabrication error, and reduce the friction torque of ball screw pair, so it is critically important to the dynamic performance and service life of the ball screw pair [6, 7]. Typically, the preload force is preset by the manufacturer before coming into service, and it is not adjustable while running. But the fatigue wear will cause the preload change after long time operation, so that the transmission accuracy is reduced. And it is quite difficult and time- consuming to adjust the preload force because the system has to be dismantled by manual work. In order to reduce the cost and improve the transmission accuracy, it is necessary to design a novel automatically adjusting preload force system.Giant magnetostrictive material (GMM) is a unique smart material which can generate giant magnetostrictive deformation. Efficient actuators based on GMM are widely used in ultra-precision positioning, ultra-precision machining, intelligent structure, active vibration control etc. for its simple structure, large driving force, high magneto- mechanical coupling and high displacement resolution [8–11]. OHMATA et al [12] proposed a three-link arm type vibration control device which can generate controllable friction force and friction torque with giant magnetostrictive actuator (GMA). RAKHOVSKY et al [13] designed a precise positioning GMA which has 10 nm step distance and 10000 N output force. MOON et al [14] developed a linear GMA with 27 μm output displacement and 4000 N output force. And the GMA was introduced into asymmetric pinhole machining and it provided a new method for precision machining of high-load oval pinhole [15]. LIN et al [16, 17] developed a hinge-levers device with GMA to automatically adjust the preload force, but the structure is complex so the fabrication and control is more difficult, in addition, the elastic deformation will reduce the output force of GMA.

Worldwide research on GMA is quite mature, but most actuators take the GMM rod as a core. So far few literatures focusing on the structure analysis, output characteristics and applications of the cylindrical giant magnetostrictive actuator (CGMA) have been found. In this paper, a novel CGMA is proposed to develop a double-nut ball screw preload system, and the static and dynamic characteristics of output displacement and force are tested on platform established with self-developed CGMA. Development and research of the novel actuator will provide theoretical foundation and technology support for the design of high- performance ball screw drive system.

2 Principle of magnetostrictive preload system

2.1 Structure of preload system

The overall structural drawing of magnetostrictive preload system is shown in Figure 1. The double-nut ball screw is equipped with a CGMA, therefore, the preload is controlled by output force of the CGMA. On the basis of spacer preload principle, initial preload force is determined according to the maximum axial load. Automatic adjustment is done by changing the current of a drive coil which drives the CGMA to produce different preload force in order to reduce the axial clearance or friction torque caused by fatigue wear or varying axial load. Meanwhile, the preload can be monitored in real time through the sensor. As a result, a close-loop system is formed and the double-nut ball screw can be in an optimal preload state by controlling the current. Construction of the magnetostrictive preload system is significantly simplified using CGMA instead of hinge-levers in literature [17]. And the sensor is employed to ensure the fast response of CGMA. Therefore, the preload system has the advantages of simple structure and being easy to realize automatic adjustment of preload force, which make the ball screw feature higher transmission precision.

Figure 1 Schematic diagram of magnetostrictive preload system (1–Nut A; 2–CGMA; 3–Nut B; 4–Screw)

2.2 Working characteristics of cylindrical giant magnetostrictive material

Cylindrical giant magnetostrictive material (CGMM), which can be used as a magneto- electro-elastic coupling media, is the critical component of CGMA. As shown in Eq. (1), the coupling relationship of the main characteristics can be expressed as the piezoelectric equations [18], where ε and B respectively represent magnetostrictive strain and magnetic flux density; σ and H represent stress and magnetic field intensity in the longitude direction; d₃₃, S^H and μ^σ are respectively piezomagnetic coefficient, elastic compliance coefficient and permeability; α is the thermal expansion coefficient; △T is the average temperature change. It can be seen from Eq. (1) that the size, initial prestress and internal magnetic field intensity of the CGMM determine magnetostrictive strain, and further determine the output displacement and force. Obviously, the magnetic field intensity, temperature and mechanical stress are the main factors which affect the output characteristics of CGMA.

                    (1)

3 Structure analysis and design of CGMA

3.1 Structure design and working principle of CGMA

In this work, a novel giant magnetostrictive actuator for ball screw preload is developed using the CGMM. The magnetostrictive deformation caused by external magnetic field is transferred to nut to realize automatic preload. Structure of the CGMA is shown in Figure 2. To make the screw shaft pass through, the CGMA is designed to be hollow. With changing the current of the drive coil, the internal magnetic field of CGMA changes, so that the axial length of the CGMM differs and the conversion of electromagnetic energy to mechanical energy is achieved. The bias magnetic field avoiding double-frequency effect is generated by permanent magnets at both ends. An adjustable prestress can be obtained from disc spring and pretightening nut. In order to keep the temperature constant, an oil cooling system is introduced into the CGMA.

Figure 2 Structure diagram of CGMA:

3.2 Analysis of prestress

For the design of the CGMA, the giant magnetostrictive material TbDyFe produced by ETREMA Products, Inc. is used as a core. Based on the physical properties provided by the manufacturer, the compressive strength is about 700 MPa, while the tensile strength is 28 MPa. It is noticeable that the TbDyFe has low tensile strength and high brittleness. Consequently, the CGMM is easy to break under the external magnetic field without prestress. Also prestress can make the internal domain array in a direction perpendicular to the axial line without external magnetic field. And large axial magnetostrictive deformation appears due to domain deflection under the action of driving magnetic field. In addition, the appropriate prestress can improve the magneto- mechanical coupling coefficient [19].

According to empirical value, the output force density of GMM, f, is around 1700 N/cm², and one third of the maximum axial load is generally chosen as the ball screw preload force. If select the double- nut ball screw of 2504 version as preload object, the output force of CGMA should reach 6000 N, which is to satisfy Eq. (2).

            (2)

where S is the cross-sectional area of cylindrical GMM; d_e and d_i are respectively the outer diameter and inner diameter.

Based on above analysis, the parameters of CGMM are chosen as d_e=40 mm and d_i=30 mm. The output force calculated from Eq.(2) is 9340 N, which is greater than 6000 N. And thus it meets the ball screw preload requirement. Refer to the accuracy grade of 2504 ball screw, the output displacement should be greater than 20 μm. Considering the elastic deformation of the shaft, the length of CGMM is set to 50 mm.

In practical application, most giant magnetostrictive materials need a prestress from several to dozens MPa. However, different materials have different optimal prestress. In this research, the optimal prestress of used material is less than 10 MPa, and therefore the pretightening force produced by the disk spring is at least 5495 N in accordance with the size of CGMM. So as to install the disc spring, its inner diameter should be greater than the outer diameter of the CGMM 40 mm. And parameters of the disk spring are as shown in Table 1. Under the assumption of TIMASHENKO, the relationship between the force and deformation of the single plate spring is demonstrated as in Eq. (3) [20].

             (3)

where T is a correction coefficient corresponding to the ratio D/d; x is the axial deformation of disc spring under the action of force.

Table 1 Parameters of disc spring

Different axial deformation of the spring is acquired by rotating the pretightening nut of CGMA, and the corresponding force exerted to the CGMM is derived from Eq. (3). To determine the optimal pretightening force, the characteristic curves, showing displacement versus applied current at various force, are measured without bias magnetic field. The current range is from 0 to 6 A and the forces are respectively 2100, 2700, 3400, 3900 and 4400 N in the test. As illustrated in Figure 3, the output characteristics do not change monotonically with the increasing pretightening force, but achieve the best under a certain value. In the five sets of test data, when the disc spring force is 2700 N, the output displacement reaches the maximum value of 51 μm, and notably the curve owns the maximum variation with the same current range. Consequently, the pritightening force 2700 N corresponding to the prestress 4.91 MPa is preferred.

Figure 3 Current–displacement curves under different pretightening forces

3.3 Analysis of bias magnetic field and magnetic circuit structure

The GMM has elongation both in forward and reverse magnetic field, so that the output displacement and force of CGMA has double-frequency effect under the action of AC excitation as shown in Figure 4 [21]. The bias magnetic field can be applied in advance to make the CGMM stay in a suitable initial magnetic field to avoid double-frequency effect, and also surmount the non sensitive area of the dynamic response. As a result, linearity of the output characteristic is improved, and thus it is easy to realize the accurate control of CGMA.

Figure 4 Double-frequency effect:

Generally, the bias magnetic field can be provided by the permanent magnet (NdFeB alloy) or DC coil. The CGMA structure with bias magnetic field generated from DC coil is simple, and it is flexible to adjust the magnetic field. However, the large volume and temperature rise caused by electromagnetic coil are major drawbacks which make against the magnetostrictive preload. In this paper, permanent magnet bias method is employed to reduce the coil volume and less heat release. As analyzed in Refs. [22, 23], the bias magnetic field can be applied to the CGMA in two ways as shown in Figure 5. The permanent magnet is placed in outer circumference of the CGMA in Figure 5(a), the design requires its internal diameter to be around 150 mm, and large size permanent magnet has superior magnetic force leading to difficulties in machining and installation. On the contrary, the diameter 40 mm, which is far less than 150 mm, is proper with permanent magnet at both ends of the CGMM in Figure 5(b). Accordingly, the bias mode with permanent magnet at both ends is employed and the NdFeB alloy is chosen as permanent magnetic material.

In the magnetostrictive preload system, the screw shaft needs to pass through the CGMA. In view of the fact that most screw materials features with magnetoconductivity, the internal magnetic circuit and equivalent magnetic circuit model of the CGMA are shown in Figure 6. Based on the magnetic circuit Kirchhoff’s law, the Eq. (4) is established without considering magnetic leakage in air.

                           (4)

whereis the total magnetic flux which is equal to the fluxgetting through the yoke,is the branch flux getting through screw shaft and internal air andis another branch flux getting through the CGMM and permanent magnet. Once all branches are determined, Ohm law of magnetic circuit and loop analysis method can be applied, resulting in the following equations:

                    (5)

                      (6)

where R_g, R_pm and R_y are respectively the reluctance of CGMM, permanent magnet and yoke; R_a is the reluctance of air gap inside the CGMA and R_s is the reluctance of screw shaft. And the magnetomotive force produced by the drive coil plus one produced by the permanent magnet equals the total magnetomotive force F_M, the relationship can be expressed as

                       (7)

where k_c is a leakage compensation factor of drive coil, N is the coil turns, I is the current value, l_pm is the length of permanent magnet and H_pm is the magnetic field intensity per unit length. From Eq. (4) to Eq. (7), the explicit expressions of magnetic flux andare deduced as

                 (8)

Figure 5 Permanent magnet bias mode:

Figure 6 Magnetic circuit of cylindrical GMA:

                 (9)

               (10)

According to Eq. (8), the increase of the total magnetic flux can be achieved by reducing the reluctance of each component under a certain magnetomotive force. In order to improve the conversion efficiency from magnetic energy to mechanical energy, the magnetomotive force of CGMM should be increased, i.e., increase the magnetic flux in the case of a certain size. The reluctance of each section can be obtained from the definition as described in Eq. (11).

                   (11)

where μ₀ denotes permeability of vacuum; A_a denotes equivalent cross-sectional area of air gap; l_y, μ_y and A_y denote equivalent length, relative permeability and equivalent cross-sectional area of yoke respectively; l_g, l_a and l_s denote the effective length of CGMM, air gap and screw shaft, respectively; μ_pm, μ_g and μ_s are respectively the relative permeability of permanent magnet, CGMM and screw shaft; r_e and r_i are outer radius and inner radius of CGMM, and r_s is radius of screw shaft.

As shown in Eq. (12), the magnetic fluxis obtained by substituting Eq. (11) into Eq. (10). Fixing magnetomotive force (i.e., coil turns and parameters of permanent magnet) and size of components, some qualitative conclusion could be summarized from Eq. (12): to begin with, a higher relative permeability of yoke will increase the magnetic flux getting through the CGMM; moreover, the flux value is influenced by the thickness of the air gap, which is between two adjacent yokes, yoke and permanent magnet, permanent magnet and CGMM, the thinner the air gap is, the larger the magnetic flux is; then a lower relative permeability of screw shaft will increase the reluctance R_s, resulting in the smaller denominator in Eq. (12), and therefore the flux will become larger. Obviously, selecting high permeability materials as magnetic yoke, reducing contact gap and increasing the ratio of yoke permeability to screw permeability is an effective approach to improve the efficiency of energy conversion.

In addition, the eveness of magnetic field is also an important factor affecting output characteristics of the material. If the CGMM is segmented and applied with bias magnetic field, the eveness would be increased. But segmented materials will introduce series errors, so as to ensure machining accuracy and mechanical property, the CGMM keeps whole in the design. Furthermore, permanent magnet with large size and magnetic yoke with high permeability are selected to improve intensity and performance of bias magnetic field.

       (12)

3.4 Analysis of thermal effect and temperature control structure

It can be seen from Eq. (1) that the magnetostrictive process is a complex process of multi-field coupling and the temperature is a major factor affecting the output characteristics of CGMA. The changing current is employed for ball-screw preload, so the temperature rise is mainly caused by the heat generated from the drive coil. The three thermal effects on the actuator are as follows [24, 25]: Firstly, the thermal deformation of the CGMM is introduced by the temperature rise, and it can be calculated from Eq. (13), in which △y is the thermal deformation, α is the thermal expansion coefficient of the CGMM, r_i and r_o represent the inner and the outer diameter, T₁ and T₂ represent the temperatures before and after thermal deformation respectively. Secondly, the changing temperature affects the giant magnetostrictive coefficient, and the temperature range corresponding to the maximum saturation magnetostriction coefficient differs according to the material ratio. In addition, the temperature rise causes the thermal deformation of the other parts of the CGMA, such as the base, the output shaft, etc.

                 (13)

Refer to the data from manufacturer, the thermal expansion coefficient is 12×10^{–6 °C–1}, and the maximum saturation magnetostriction coefficient appears between 40 °C and 50 °C. For a CGMM with a length of 50 mm, the thermal deformation is up to 6 μm when the temperature changes 10 °C. Thus to suppress the thermal deformation error and improve the output accuracy, the oil cooling method is adopted according to the operating characteristics of the CGMA. A new temperature control structure is designed as shown in Figure 7. The drive coil, coil skeleton and cylindrical yoke forms a cooling cavity, in which the cooling oil circulates continuously so as to carry out the heat generated by the drive coil. For easy installation, cooling oil inlet and outlet are designed on the same side, however, such structure can cause the cooling oil fail to circulate. To prevent cooling oil coming out directly from inlet to the outlet without circulating, a rubber tube is connected with the oil inlet to the bottom of the cooling cavity, which can ensure the circulation of the cooling oil. This cooling method has the following advantages: 1) No additional structure is developed, so the CGMA structure is simple and compact. 2) The heating source is immersed directly in the cooling oil so that the cooling efficiency is high. 3) The good insulation of the cooling oil keeps the actuator away from the danger of short circuit and being rusted. By adjusting the temperature and velocity of the cooling oil, the actuator can work in the range of 40 °C–50 °C, and in the thermal equilibrium state, the thermal deformation is small and the output characteristics are stable, which meets the requirement of preload adjustment of the ball screw.

Figure 7 Schematic diagram of temperature control structure (1–Drive coil; 2–Rubber tube; 3–Oil inlet; 4–Oil outlet; 5–Cooling cavity)

Based on the above analysis, the main parameters of CGMA designed in this work are as listed in Table 2.

Table 2 Parameters of CGMA

4 Experiment and result analysis

In order to study the output characteristics of the CGMA, a test platform with and without ball screw was established, as shown in Figure 8. The hardware used in the test included CGMA, oscilloscope, digital controlled current source, laser displacement sensor, data acquisition module, and ball screw. The bipolar programmable power supply was used as digital controlled current source to provide current for actuator with the maximum output current ±10 A and voltage ±30 V. The power control and data acquisition interface was implemented by using C++ programming. And the output displacement and force were measured by the laser displacement sensor and strain force sensor. The data acquisition USB-4711A-AE with 16 channels, 12 bits resolution and 150×10³ sample/s sampling rates was adopted as data conversion module. The analog oscilloscope was used to trace and display during data acquisition.

4.1 Static characteristics of CGMA

Loaded the CGMA with 2700 N pretightening force, measured the output displacements under 0– 5 A input current with step 0.1 A, the results with and without bias magnetic field are shown in Figure 9. It is noticeable that the output displacement without bias magnetic field is larger, but the curve slope changed a lot, linearity of the whole curve is also poor besides the relatively better input range 2.1–5.0 A. The output displacements with bias magnetic field decrease obviously under the same current, but the linearity is improved, especially in range 0.3–3.0 A. The results show that the two have similar linearity range length. And the bias magnetic field in the ball screw preload system can increase the output linearity of CGMA in order that help the automatic control system.

Figure 8 Experimental test system:

Figure 9 Effect of bias magnetic field on static displacement

The test of magnetostrictive displacement in the natural cooling and the oil cooling state was carried out to verify the cooling effect. When the driving current changes in the three ranges of 0–3 A, 0–4 A and 0–5 A, the measured results are shown in Figure 10. It is clear that the three output characteristic curves are not consistent in the process of current increase and the hysteresis errors are different and large when the current returns to the zero point as shown in Figure 10(a), all of which indicate that the magnetostrictive and hysteresis characteristics of the CGMA are unstable without cooling measures. However, when the oil cooling is employed, the output characteristic curves of magnetostrictive displacement are in good agreement and the errors are close and small at the zero point of return as shown in Figure 10(b). Compared Figure 10(a) with Figure 10(b), it can be found the output displacement with oil cooling is obviously smaller than that with natural cooling under the action of the same current. The experimental results show that oil cooling method can effectively reduce the thermal deformation and improve the output accuracy of the CGMA.

Figure 10 Thermal effects on static magnetostrictive displacement:

In the repeatability experimental test, the bias magnetic field of CGMA was applied in advance by permanent magnet and the pretightening force was maintained at 2700 N. Under the same conditions, the output displacements of CGMA were repeatedly measured, and the results are shown in Figure 11. According to the results, the maximum displacement of the biased CGMA may reach to 28 μm, which meets the design requirements of the preload system. However, the output has obvious nonlinear hysteretic characteristics as shown in Figure 11(a). Apparently most of the later measured values are larger than the previous measured ones. Such a difference is mainly caused by inherent hysteresis of the CGMM. In the current range of 0–1 A, the relative error is large since the accuracy of the sensor and the measurement error have significant influence on output displacement under a small current. As illustrated in Figure 11(b), the repeatability error of CGMA is less than 1.3 μm,and the result indicates that the CGMA has good repeatability for preload adjustment.

Figure 11 Hysteresis and repeatability of displacement curve:

As analyzed in Section 3.3, the ball screw changes magnetic circuit and reduces the magnetic field intensity of the CGMA. In order to study the influence of the ball screw, a screw shaft (material is bearing steel) with diameter 25 mm was put through the CGMA, and the output displacements between 0 and 5 A input current were measured.Figure 12 shows the measured results with and without the screw shaft in the case of the same other operation conditions. It is noted that hysteresis and linearity of the CGMA with a screw shaft is not influenced clearly and the maximum output displacement can reach to 26 μm which still meets the demands. But the output displacements of the CGMA with screw shaft passing through are smaller than ones of the hollow CGMA as illustrated in Figure 12(b). The conclusion, drawn from the experimental test, agrees with the analysis result which is discussed in Section 3.3.

The magnetostrictive preload system with assembled ball screw and CGMA is shown in Figure 8(b). Initial preload force of the ball screw was set to 1600 N and the scanning current varies from 0 A to 10 A with step 0.5 A. Then the experimental test of output force was carried out, the results are shown in Table 3, and the corresponding static output force curve is shown in Figure 13.

Figure 12 Effect of ball screw on static displacement:

Table 3 Relation of current and output force

Figure 13 Output characteristics of static force

According to above results, the static preload force of CGMA also has hysteresis nonlinearity and the maximum output force is up to 8200 N. When the drive current is 6 A, the output force is more than 6000 N, which is one third of the maximum axial load of 2504 ball screw. Such results mean that the design achieves the expected requirements for ball screw preload. In addition, Figure 13 shows the linearity and stability of the output force is good between 2 A and 5 A input current, so the interval can be chosen as the best operating range for preload adjustment. Comparing the force and displacement curve, the linear range is found to be different, that is mainly because the ball screw preload force changes the pretightening force of the CGMA.

The PZT and electromagnet actuators are also used for the timely adjustment of the preload force. The maximum preload force produced by the PZT actuator is about 90 kg when the input voltage is 1000 V, and that of electromagnet actuator is 153.7 N when the graduation is 9.1 [26, 27]. The comparison between the CGMA, PZT and electromagnet is shown in Table 4. Compared with PZT and electromagnet actuator, the CGMA is a novel actuator for ball screw preload, its preload force is up to 8200 N, which is 9 times that of PZT and 50 times that of electromagnet.

Table 4 Maximum preload force of several actuators

It can be seen from the above analysis, if the CGMA is applied for double nut ball-screw preload, the preload force can be timely adjusted and also the value and variation range can be significantly increased. The development of the CGMA provides a new method for heavy-load and high-precision double-nut ball screw preload.

4.2 Dynamic characteristics of CGMA

In order to study the dynamic characteristics of the CGMA, the validity of bias magnetic field and the influence of ball screw on the dynamic performance, a fixed frequency sinusoidal AC signal was input to the coil under different case. The preload force adjusting speed is rather low in practical application, so low frequency tests were mainly carried out.

Figures 14 and 15 respectively show influence of bias magnetic field on the dynamic output displacement and force. The amplitude and frequency of input sinusoidal current were 2 A,10 Hz in Figure 14 and 3 A, 10 Hz in Figure 15. Horizontal axis in the figures represents time and vertical axis is voltage proportional to output displacement and force. The frequency of output is doubled without bias magnetic field, which indicates double-frequency effect is eliminated by bias magnet field. Compared with force, the output displacement is reverse-phased due to different sensor principle, but the waveform will display the same trend after reversed. The positive and negative half-wave is asymmetry in Figures 14(b) and 15(b). This phenomenon is primarily because the bias magnetic field point is close to the turning point due to large curve slope change of CGMM as shown in Figure 10. And peak value of half wave as well as peak to peak value of whole wave is close by comparing unbiased CGMA and biased CGMA, the reason of which is also the location of bias magnetic field point.

Figure 14 Effect of bias magnetic field on dynamic displacement:

Figure 16 shows the dynamic output displacements of CGMA with and without ball screw shaft. Two sinusoidal input signals had the same frequency 10 Hz, but the amplitude was different with 2 A and 3 A. Figure 16(b) indicates that the positive and negative half-wave is more symmetrical with screw shaft than that without it. This is because the ball screw shaft changes the bias magnetic field, which makes the bias point far from the turning point and drives the output characteristic of CGMM into a linear area. The peak value of AC output waveform with screw shaft under the 3 A input is close to that without screw shaft under the 2 A input. The result further confirms the statement that screw shaft reduces the magnetic field intensity in the CGMA as analyzed in Section 3.3.

Figure 15 Effect of bias magnetic field on dynamic force:

Figure 16 Effect of ball screw on dynamic displacement:

Compared to waves of output displacement and force, it is found that the output signal distortion begins to appear after 4 A with increasing the amplitude of input current to 1, 2, 3, 4, 5 and 6 A. When the input current comes up to 6 A, a distinct notch appears at the peak of the wave, as demonstrated in Figure 17. Actually such a signal distortion is mainly caused by an inadequate bias magnetic field. At initial state, the CGMA has elongated under bias magnetic field, then the increasing reverse magnet field caused by negative current reduces the bias magnetic field, and the elongation is reduced accordingly. When the coupling magnetic field is zero, the CGMA has no elongation. With the increasing of the reverse magnetic field, the CGMA elongates again. Then the elongation caused by the reverse magnetic field reaches its maximum at the peak of negative current, which is the bottom of the output distortion notch as shown in Figure 17(a). With reducing the reverse magnetic field, the coupling magnetic field increases, which will again generate positive elongation of the CGMA.

Figure 17 Effect of amplitude on dynamic characteristics:

5 Conclusions

1) Based on the principle of ball screw preload, the feasibility of developing the CGMA as the force output device for ball screw preload is demonstrated. Compared with traditional method, the method using the CGMA to realize ball screw preload is of large force, easily assembled, adjustable, and easy to achieve timely automatic control.

2) A novel cylindrical giant magnetostrictive actuator is developed using giant magnetostrictive material with a hole. The influence of the disc spring prestress on the output characteristics is analyzed, and the pretightening force is determined with 2700 N by testing. The bias magnetic field method in CGMA is discussed, and the magnetic flux in the CGMM is calculated on the basis of magnetic circuit analysis. The result shows that parameters of yoke and screw shaft are the main factors which influence the magnetic field intensity in the CGMM. The higher the screw permeability is, the smaller the magnetic field intensity is, and the yoke permeability is on the contrary. The thermal effects on output characteristics are discussed, and a new oil cooling method is proposed.

3) A test platform is established and the dynamic and static characteristics of CGMA are measured. The experimental results show that the double-frequency effect is eliminated and the output linearity is improved under the action of the bias magnetic field, and the output accuracy of the magnetostrictive displacement is effectively improved by using an oil cooling method. The ball screw passing through the CGMA changes the output characteristics, but the influence is inconspicuous. The output displacement of the CGMA with ball screw is more than 26 μm and the output force up to 6200 N, which means the design meets that the preload demands.

Design and research of the novel CGMA develops a new approach for the automatic adjustment of the ball screw preload force, which is significantly meaningful for the improving of ball screw rigidity and transmission accuracy. It will surely promote the development of high precision machine tools and intelligent machining centers. In order to accelerate the practical application of the magnetostrictive preload system, our upcoming research will focus on the eveness of bias magnetic field distribution in CGMA, the automatic control of output preload force and the performance of preloaded ball screw with CGMA.

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(Edited by HE Yun-bin)

中文导读

滚珠丝杠预紧用环状磁致伸缩致动器的设计与特性研究

摘要：为实现双螺母滚珠丝杠副预紧力的自动调整，提出一种磁致伸缩滚珠丝杠副预紧系统。以中空的超磁致伸缩材料（GMM）为核心，完成了新型环状超磁致伸缩致动器（CGMA）的结构设计；通过测试数据确定了CGMA的预压力；利用磁路分析法对穿入丝杠后致动器内部磁场进行了分析计算；为抑制发热对磁致伸缩输出的影响，提出了直接冷却发热源的油冷散热方法。对自行研制的预紧用致动器输出的位移和力进行了实验研究，结果表明，偏置磁场可以消除CGMA的倍频效应，改善线性度；油冷散热可有效减小热变形影响，使CGMA磁致伸缩输出特性稳定；穿入滚珠丝杠后致动器的输出减小，但在工作区间内输出位移可达26 μm、输出力超过6200 N，满足所选滚珠丝杠副预紧系统设计要求。新型CGMA的研制为双螺母滚珠丝杠副预紧力的自动调整提供一种新的方法。

关键词：滚珠丝杠副预紧；环状超磁致伸缩致动器（CGMA）；结构设计；输出特性

Foundation item: Project(51475267) supported by the National Natural Science Foundation of China

Received date: 2017-04-26; Accepted date: 2017-12-24

Corresponding author: LIN Ming-xing, PhD, Professor; Tel: +86–531–88392700; E-mail: mxlin@sdu.edu.cn; ORCID: 0000-0003- 0291-0158