Abstract: This paper analyzes and studies the speed control of machine tool spindle positioning using frequency conversion drive, and proposes a new positioning speed control method combining delayed deceleration and minimum deceleration time. An example is used for analysis and calculation. The results show that this method can effectively improve the stability and accuracy of positioning and reduce auxiliary time in practical use.
Keywords: spindle positioning; speed control; frequency conversion speed regulation; combination machine tool
Chinese Library Classification Number: TG65; TP276
Document Identification Code: A
Study on Bearing Positioning Speed Control Technology of Machine Tool Du jun, Wu xiao, Qiang yujian (School of Electric Engineering, Nantong University, Nantong 226019, Jiangsu, China)
Abstract : The paper studies the bearing positioning speed control technology of machine tool adopting the variable-frequency drive, sets up a new method of positioning speed control, namely combining slowing speed by using of delay time with shortest slowing speed time. Finally an example is analyzed and computed, the result proves the method can improve positioning steadiness and veracity effectively and decrease man-time.
Keywords: Bearing Positioning, Speed Control, Variable-Frequency Adjustable-Speed, Combined Machine Tool
0 Introduction
When the workpiece or tool and fixture are in the specified position after each machining operation, a spindle positioning mechanism is required. Traditional automatic spindle positioning mechanisms often use an electric reduction mechanical positioning method, that is, the spindle is braked and stopped after machining, and then the spindle is slowly rotated to a mechanical device (such as a positioning hook mechanism) for accurate positioning. The speed of the spindle braking process is usually out of control and may cause a large current surge. Its slow rotation is generally in a "semi-braking" state (usually AC and DC power are applied at the same time) or a positioning motor is added. Although spindle positioning can be achieved in this way, it puts the motor in a worse condition or adds auxiliary equipment [1].
With the widespread application of frequency conversion speed regulation technology in machining equipment, in the case where frequency conversion speed regulation is used to achieve stepless speed change of the spindle, if the spindle has positioning requirements, the advantages of frequency conversion speed regulation can be fully utilized to conveniently realize spindle positioning [2]. Reference [3] gives a fast braking positioning method for the speed of the drive motor by delaying the braking parameter and then braking to decelerate during linear motion positioning. Spindle positioning is a rotational motion, and the deceleration process may involve multiple rotations. This paper takes the control of the spindle motor speed in the electromechanical positioning method as the research object and proposes a new positioning speed control method that combines segmented delay deceleration based on the number of rotations with the shortest deceleration time. This method can effectively improve the stability and accuracy of positioning and reduce auxiliary time.
1. The concept of spindle positioning speed control
The spindle speed control curve based on the traditional positioning method can be represented by Figure 1. After the workpiece is finished machining, it enters the spindle positioning stage. The spindle decelerates and rotates slowly after reaching a certain crawling speed. The positioning hook actuates, and its end slides on the circumferential surface of the positioning plate until it falls into the positioning groove, at which point the spindle stops rotating. During this process, the deceleration start point is the machining end point, and the deceleration time is arbitrarily set, resulting in an arbitrary end point. This leads to arbitrary waiting times for the positioning hook to fall into the positioning groove, sometimes reaching up to one full slow rotation. Furthermore, the sliding of the hook end on the circumference of the positioning plate increases friction, preventing the crawling speed from being too low, and increasing auxiliary machining time and mechanical impact during positioning.
Figure 1 Spindle speed based on traditional positioning method
The improvement to the spindle speed control curve is shown in Figure 2. Figure 2(a) adds a position monitoring point called the deceleration delay start calculation point to the positioning plate. The deceleration delay time t <sub>js0</sub> is pre-calculated based on the current spindle operating speed. After the workpiece is finished, the spindle does not immediately begin deceleration. Instead, this point is detected and a delay of t<sub>js0 </sub> is applied. The spindle then decelerates at the shortest possible time t<sub> d </sub>, ensuring that the positioning plate decelerates to the crawling speed when the positioning groove aligns with the positioning hook. The positioning hook then actuates and falls precisely into the positioning groove. In this way, although the worst-case deceleration delay time may be as long as one full rotation of the spindle, this is a full rotation at a high operating speed, which shortens the auxiliary time compared to a slow crawling rotation. Furthermore, the positioning hook engages the positioning groove immediately upon actuation, reducing friction caused by sliding on the circumference of the positioning plate. This allows for a lower crawling speed setting, reducing mechanical impact during positioning.
Further improvements to the spindle speed control curve consider that spindle positioning is a rotary positioning. If the time for one revolution at a speed of nr is tnr , and the calculated tjs0 exceeds tnr , meaning the spindle will needlessly rotate one more revolution during the delay, then the time of that extra revolution can be deducted, and only the remaining time tjs can be delayed (Figure 2(b)). If the deceleration time tdmax at the highest operating speed causes the spindle to rotate multiple revolutions, then the calculated tjs0 may exceed k times tnr , meaning the spindle will needlessly rotate k more revolutions during the delay, then the time of those k revolutions can be deducted. Thus, the deceleration delay time tjs can be calculated in segments based on the number of revolutions k, which greatly reduces auxiliary time. This is precisely where rotary positioning differs from linear positioning. In Figure 2, for the convenience of later research, the machining end point is deliberately misaligned, and the deceleration delay calculation start point is aligned and used as the coordinate origin.
2. Design calculation of spindle positioning speed curve
Referring to Figure 2, the spindle speed control curve is designed. In actual work, the parameters that need to be calculated and determined are: deceleration delay time t<sub> js </sub>, time required for one revolution at the current working speed n<sub>r</sub> t<sub> nr</sub> , minimum deceleration time t <sub>d</sub> , crawling speed n <sub>min </sub>, etc. Among them, t<sub> d</sub> and n<sub> min</sub> can be determined offline, while t <sub>js</sub> and t<sub> nr</sub> need to be calculated in real time during spindle positioning.
2.1 Calculation of deceleration delay time tjs
2.1.1 Calculation of basic deceleration delay time tjs0
First, the deceleration delay time t <sub>js0</sub> , which is not considered in segments based on the number of rotations, is calculated and is called the basic deceleration delay time. To calculate t <sub>js0 </sub>, the relationship between t <sub>js0 </sub> and the current operating speed n<sub> r </sub> of the spindle must be determined: t <sub>js0</sub> = f(n<sub>r</sub>). Clearly, to shorten the deceleration time, the spindle should decelerate at the fastest speed under all conditions; therefore, the deceleration rate a should be the same, which is reflected in Figure 2(a) as the same slope of the speed decrease curves in both cases. Furthermore, at different operating speeds, the total number of rotations (angles) during deceleration is consistent from the starting point of the deceleration delay calculation, i.e., equal to the number of rotations at the highest operating speed. Using the basic formulas of kinematics:
2.1.2 Consider calculating the deceleration delay time t <sub>js</sub> in segments based on the number of rotations k. According to the previous discussion, when the calculated t <sub>js0</sub> exceeds k times t<sub> nr</sub> , this kt<sub> nr </sub> must be subtracted. Let n<sub> r </sub> (k=1, 2, ...) be the value when t <sub>js0 </sub> = kt<sub> nr </sub>.
Figure 3 shows the curves of the computational model.
(b) The computational model curve of t js
Figure 3 shows the calculation model curve of deceleration delay time tjs.
2.2 Calculation of the shortest deceleration time td
The starting point for calculating the acceleration and deceleration time of the motor is the equation of motion of the system. The key point of the calculation is to limit the acceleration current to within the allowable value of the inverter overcurrent during acceleration and to make the feedback braking voltage less than the pump-up voltage action value of the inverter during deceleration. For constant torque load, the formula for calculating the shortest deceleration time is as follows [4]:
It must be pointed out that the deceleration time calculated here refers to the time taken to decelerate from n'r to n'min , not the "deceleration time" parameter set in the frequency converter. Since the deceleration is the same, it is not necessary to calculate different td online for different operating speeds nr . Instead, it is only necessary to calculate the deceleration time when nr = nmax offline and convert it into the setting parameter in the frequency converter beforehand.
2.3 Determination of Crawling Speed
The crawling speed should be such that the motor can drive the spindle mechanism to crawl slowly, but as low as possible. The variable frequency speed regulation is affected by factors such as stator resistance voltage drop and heat generation, and the load-carrying capacity decreases at low speeds. Therefore, in actual work, the crawling speed can be determined by experimentation while ensuring rotation without impact [4]. Reducing the frictional resistance of the positioning hook on the circumference of the positioning plate during crawling is an effective measure to reduce the crawling speed.
3. Calculation of spindle positioning speed curve
The piston ring simultaneous inner and outer circle contour turning and milling combination machine tool is a combination machine tool used for the two processes of simultaneous turning and milling of the inner and outer circles in the machining of elliptical piston rings[5]. In the turning process, the spindle clamps and drives the piston ring to rotate. Since it is an elliptical contour, it is necessary to accurately position it after the contour turning is completed to ensure that the section that is milled off in the second process of milling the opening is always facing upward. Therefore, spindle positioning must be implemented. Taking the spindle positioning of this machine tool as an example, the positioning speed curve is calculated.
Given: the spindle motor has a power output of P <sub>N</sub> = 7.5kW, n<sub> N</sub> = 2945rpm, and a transmission reduction ratio of 1:20. According to the process requirements, the spindle speed n<sub> max </sub> = 120rpm = 2r/s, which means the maximum motor speed n' <sub>max</sub> = 2400rpm. The minimum operating speed of the spindle is nr<sub> min </sub> = 30rpm = 0.5r/s. After repeated experiments, the spindle crawling speed is determined to be n<sub> min</sub> = 3rpm = 0.05r/s, which means the minimum motor speed n'<sub> min </sub> = 60rpm. Additionally, GD<sub>2</sub> = 0.475kgm<sup> 2 </sup> and TL <sub>min</sub> = 0.496kgm.
Calculate the worst-case time taken for the spindle positioning process under both positioning methods, i.e.:
Method A: Traditional positioning method, where the positioning hook just passes the positioning groove at the end of machining. Therefore, the spindle will need to rotate one more revolution after slowing down to the crawling speed.
Method B: An improved positioning method is used, and the detection point at the end of machining exactly crosses the deceleration delay start calculation point. Therefore, the spindle will need to rotate one more revolution before timing begins.
Based on the aforementioned equations (1)-(4) and the basic kinematic formula n²min - n²r = 2ar, calculate the velocity and time of several points such as nr1 and nr2 . The time for main axis positioning under methods A and B is shown in Table 1 (Figure 3 is drawn according to the data in the table):
Table 1 Comparison of spindle positioning time under worst-case conditions for the two positioning methods.The remaining 1 - 0.1896 = 0.8104 revolutions, crawling slowly, takes 20 × 0.8104 = 16.207 seconds, for a total time of 0.69 + 16.207 = 16.897 seconds. Method B: The spindle takes 2 seconds to rotate one more revolution, with a 1.75-second delay and a 0.69-second deceleration, for a total time of 2 + 1.75 + 0.69 = 4.44 seconds. As can be seen from the above analysis, regardless of the situation, the improved positioning speed control method will significantly reduce auxiliary time. Its effect is considerable for machining processes that may involve frequent start-stop positioning.
4. Conclusion
Using the improved spindle positioning speed control method described above, calculations show that auxiliary time is significantly reduced and production efficiency is improved. Simultaneously, the sliding distance of the positioning hook on the positioning plate is greatly shortened, reducing friction and crawling speed, thereby reducing impact during positioning and improving positioning stability. Actual system usage and operation results demonstrate that this method not only meets production process requirements but also simplifies equipment structure and control procedures, making it convenient, practical, and reliable in operation.
References :
[1] Dalian Modular Machine Tool Research Institute (ed.). Modular Machine Tool Design (Volume 1: Mechanical Part) [Z]. Beijing: Machinery Industry Press, 1975.
[2] Qi Kun, Li Hong. Research status and development prospect of asynchronous motor positioning control technology [J]. Journal of Beijing Institute of Mechanical Industry, 2001, 16(3): 13-16
[3] Du Dong, Huang Shangxian. Application of PLC in Precision Positioning System [J]. Electrical Drive, 2000, (1): 47-49
[4] Xu Zhenmao, Zhao Yao, Wang Junyue. Variable Frequency Speed Controller User Manual [M]. Beijing: Ordnance Industry Press, 1992: 141-144
[5] Wu Xiao, Du Jun. Research on PLC control of piston ring copying turning and milling combination machine tool [J]. Journal of Nantong Institute of Technology, 1999, 15(4): 5-8
