Influence of resistant forces on the positioning precision of kinematic feed chains used on CNC machine tools

FUNARU Marian1, a, STAN Gheorghe1,b 1 “Vasile Alecsandri” University of Bacau, Department of Industrial Engineering, Calea Marasesti

Street, No. 157, 600115 Bacau, Romania amarian_funaru@yahoo.com, bghstan@ub.ro

Keywords: kinematic feed chain, resistance forces, dead zone, backlash, positioning precision

Abstract. Many researches from the international literature and also those of the specialised companies from the machine tools domain, have focused in the past years on increasing the positioning precision and implicitly, the manufacturing precision of the numerically controlled machine tools. The results of these efforts have led to the elimination or compensation of different factors which affect the positioning precision of the kinematic feed chains. Nevertheless, the effects of some factors still find themselves in the positioning error of the kinematic feed chains, an important component of this error being represented by the cutting and friction force induced error (resistant errors). This paper presents a new method of experimental analysis for establishing the influence of resistant forces on the positioning precision of the kinematic feed axis. Due to the fact that measuring the positioning precision during the cutting process is difficult to achieve, the experiments were carried out using a simulated force. In order to simulate an axial force, a hydraulic system was adopted, composed of a hydraulic cylinder, a distributor valve and a check valve.

Introduction

Recent researches from the international literature and specialised companies from the machine tools domain have concentrated on increasing the manufacturing precision of the numerically controlled machine tools, which cannot be achieved without increased the positioning precision of the kinematic feed chains which represent a very important part of the machine tools structure [1].

The results of these efforts have led to the elimination or compensation of different factors which affect the positioning precision of the kinematic feed chains. Nevertheless, the effects of some factors still find themselves in the positioning error of the kinematic feed chains, an important component of this error being represented by the cutting and friction force induced error (resistant errors) [2].

Increasing the positioning precision with regard to the errors induced by the resistant forces is mainly based on using two methods: eliminating/minimising the error or compensating it [3]. The first method represents a structural approach and regards the error minimisation from the machine tool design stage and the second method uses the software compensation of these errors as they appear [4].

This paper presents a new method of experimental analysis for establishing the influence of resistant forces on the positioning precision of the kinematic feed axis. Experiments were carried out on a kinematic feed chain, which uses a ballscrew-nut mechanism as the motion transmission system.

Due to the fact that measuring the positioning precision during the cutting process is difficult to achieve, the cutting force components values being difficult to measure as well, the experiments were carried out using a simulated force, which was achieved by means of a hydraulic circuit, formed mainly from a hydraulic cylinder, a distributor valve and a check valve. Measurements of

the values of the resistant force were achieved using a force transducer, as a part of the experimental setup.

Experimental design and setup

Experimental researches have been conducted on a test stand, having the structure presented in figure 1. The kinematic feed chain is mainly composed of the electromechanical actuator 1, having the rod 5 fixed against the moving element 8. The table has the dimensions of 250x400mm and the axial guiding is achieved using two linear rolling cylindrical guiderails 4, with the dimensions of Ø20x1000mm, provided with several supporting elements 3, with the purpose of assuring a high stiffness of the table-guideway assembly.

The structure of the electromechanical actuator is mainly composed of a precision ballscrew (precision class 7, in conformity with ISO 3408), having the diameter of 20mm and a 5mm pitch. The ballscrew is supported by two sets of angular contact ball bearings on the motor side. Using this type of bearing allows the development of high axial forces, reaching a maximum of 9300N, in both moving ways and also leads to obtaining a minimum backlash when reversing the moving direction. On the side opposite to the motor, the ballscrew is supported by a polymer sliding bearing, which has the advantages of a high service life and a vibration free functioning.

Fig.1. General view of the experimental test stand

The ballscrew mechanism is actuated by an AC servomotor, having a rated torque of 1.4Nm and

which is electrically controlled by a servodrive. The servomotor and the ballscrew are coupled directly using an elastic coupling.

Fig. 2. Hydraulic system adopted for simulating the resistant force

Given the difficulties of measuring the position of the moving table during the manufacturing process and also of placing the elements of the measuring system on the table, the experiments were carried out using a simulated force. In order to achieve this simulated force, a hydraulic system was adopted, being presented in figure 2, mainly composed of the hydraulic cylinder 3, the distributor valve 4 and the check valve 5. By pushing the cylinder rod 1, the pressure inside the circuit will grow, until the check valve opens, the value of the pressure being controlled. The presence of the distributor valve enables the restarting of the cycle. The force transducer incorporated in the experimental setup and the interface of the electromechanical actuator allow real-time readings of the resistant force values.

Description of the experimental method

Several international standards are used for determining the positioning precision of the numerically controlled axes from CNC machine tools, from which the most commonly used in the present time are VDI/DGQ 3441 and ISO 230:2. These standards establish the methodology regarding the testing, testing conditions and evaluation procedure for processing the measuring results. Testing procedure is based on repeated measurements of the effective position of the tested feed axis, discreted in several points (target positions), placed at equal distances along the table stroke.

For measuring the positioning precision of the researched feed axis, a calibrated measuring system consisting of a Renishaw ML 10 laser interferometer was used, having the measuring accuracy of 0.1 µm. The evaluation of the positioning precision of the moving table, in conformity with VDI/DGQ 3441, is done through the following main parameters: positioning inaccuracy P, mean repeatability Ps and mean reversal error U. It is necessary for the precision parameters to be determined using statistical methods, because of the large number of measuring points and measuring runs which are done for each point. This is required in order to evaluate the evolution of the position deviations with high accuracy [5].

Experimental results and discussion

Experimental data was aquired in order to determine the positioning precision of the moving table, for two directions of the resistant force in relation to the ballscrew position: centered and asymmetric. The method of placing the rod of the hydraulic cylinder on the moving table in both cases, is graphically represented in figure 3. In order to determine the positioning precision in the case of the asymmetrical resistant force, the cylinder rod was placed at a distance l=100mm in relation to the ballscrew symmetry axis. The static parameters of the positioning precision were measured and calculated for several values of the resistant force: 530, 1239 and 1547N for the centered resistant force and 579, 755 and 1284N for the asymmetrical resistant force.

Fig. 3. Emplacement of the resistant force on the moving table in relation to the ballscrew symmetry axis

Working parameters for the experiments which were carried out using a centered resistant force

are given in table 1, for a feed rate of 6m/min and in table 2 are presented the parameters of the

kinematic feed chain used for the experimental test carried out using an asymmetrical resistant force. From the obtained experimental data, several positioning precision diagrams were drawn, being given in figure 4 for the centered resistant force. Due to the fact that the curves of the other diagrams for the asymmetrical resistant force present the same trend, they were not included in the paper.

Table 1. Kinematic feed chain parameters used for different values of the centered resistant force

Setul nr.

Mm [Nm]

Fa [N]

I [A]

a [mm/s2

]

V [m/min]

P [µm]

sP [µm]

U [µm]

1 0.462 530 0.364 100 6 19.499 3.671 4.704 2 1.080 1239 0.842 100 6 24.018 4.822 5.640 3 1.348 1547 1.052 100 6 25.709 4.415 6.332

Table 2. Kinematic feed chain parameters used for different values of the asymmetric resistant force

Setul nr.

Mm [Nm]

Fa [N]

I [A]

a [mm/s2

]

V [m/min]

P [µm]

sP [µm]

U [µm]

1 0.504 579 0.393 100 6 26.417 2.819 7.132 2 0.658 755 0.513 100 6 26.628 2.652 8.584 3 1.119 1284 0.873 100 6 27.295 2.545 10.164

a.

b.

c.

Fig. 4. Positioning precision diagrams, for the centered resistant force: a. Fr=530N, b. Fr=1239N, c. Fr=1544N

Conclusions

Analysis of the obtained experimental data and diagrams shows that the size of the resistant force placed on the center of the moving table has a relatively small influence on the static parameters of the positioning precision, a higher impact being found in the value of the positioning inaccuracy, which ranges between 19 and 25µm. The mean repeatability value maintains quasi-constant, at about 4µm and the mean reversal error varies very little, from 5 to 7µm.

When placing the resistant force asymmetrically on the moving table, although the values of the resistant force are very close to the ones used in the case of the centered force, the values of the positioning precision parameters are slightly modified, particularily in the case of the reversal error, its value ranging from 7 to 10µm, for a resistant force of 579 and 1284N, respectively. This is due to the fact that the moving table rotates when the direction of the resistant force is assymetrical in relation to the ballscrew symmetry axis. The small rotation values are translated into a deadzone, which has a direct impact on the positioning precision, especially when using the indirect position measuring system.

From the obtained results, an experimental database is formed, which is useful for the designers and builders of CNC machine tools when establishing the maximum values of the axial force available at the moving table. Also, the experimental results represent a guide for selecting the type of guideways which are to be used and the rolling element type, in order to obtain a high ridigity of the moving table-guideway assembly.

References

[1] M.S. Hong, H. Su, Comment and strategy of motion accuracy diagnosis of CNC machine tool, J. Mech. Eng. 38 (2002), 91-94. [2] H. Wu, G. Turyagyenda, J.G. Yang, Modeling and real-time compensation of cutting force-induced errors on NC turning center, Key Engineering Materials 315-316 (2006), 274-278. [3] R. Ramesh, M.A. Mannan, A.N. Poo: Error compensation in machine tools - a review Part I: geometric, cutting-force induced and fixture-dependent errors, International Journal of Machine Tools and Manufacture 40 (2000), 1235–1256. [4] M. Samir, O. Tunde, A review of machine tool accuracy enhancement through error compensation in serial and parallel kinematic machines, International Journal of Precision Technology, vol. 3-4 (2010), 251–286. [5] VDI/DGQ 3441, Statistical Testing of the Operational and Positional Accuracy of Machine Tools. Basis.