1、1 A Generalized Approach for the Acceleration and Deceleration of CNC Machine Tools Jae Wook Jeon Department of Control and Instrumentation Engineering Sungkyunkwan University 300 Chunchun-Dong,Jangan-Gu,Suwon City,Korea Abstract Many techniques for the acceleration and deceleration of CNC machine t
2、ools have been proposed in order to make CNC machine tools perform given machining tasks efficiently. Since they should be calculated in a limited time, most of them are not computationally intensive. However, these previous techniques cannot generate velocity profiles having some kinds of accelerat
3、ion and deceleration characteristics though they can generate velocity profiles having various acceleration and deceleration characteristics. This paper proposes a generalized approach for generating velocity profiles which cannot be generated by previous techniques as well as velocity profiles gene
4、rated by them. According to the desired characteristics of acceleration and deceleration, each set of coefficients is calculated and is stored. Given a moving distance, an acceleration interval, and a deceleration interval for CNC machine tools, a velocity profile having the desired characteristics
5、of acceleration and deceleration can be efficiently generated by using these coefficients. It will be shown how to generate typical velocity profiles by the proposed technique. I. INTRODUCTION The demand for better accuracy in the manufacturing of complicated parts and the desire to increase product
6、ivity have developed CNC systems so that CNC machine tools move more accurately and more quickly. Since the combined characteristics of the control and the machine tool determine the final accuracy and productivity of the CNC system, there are many factors to consider for improving these quantities.
7、 One of the important factors is efficiently generating velocity profiles which have the desired acceleration and deceleration characteristics which in turn are determined according to given machining tasks. Many researchers have proposed techniques for generating velocity profiles of CNC 2 machine
8、tools. One of them is generating velocity profiles by the selection of polynomial functions 1. This technique can generate so many kinds of velocity profiles and furthermore can make the characteristics of deceleration be independent from that of acceleration. The major problem of this technique is
9、computational load to increase almost exponentially with the order of polynomial in the acceleration or that in the deceleration. Due to time constraints, it is very difficult to apply these techniques to controlling CNC systems. Other previous techniques for generating velocity profiles is based on
10、 a digital convolution 2-6. These techniques are much more efficient than the techniques selecting polynomial functions and are easily implemented by a hardware. But, in velocity profiles generated by these techniques, the acceleration interval is always same as the deceleration interval and the cha
11、racteristics of deceleration are dependent on that of the acceleration. Thus, some velocity profiles cannot be generated by these techniques. In this paper, a generalized approach for the acceleration and deceleration of CNC machine tools is proposed. The proposed technique is as simple and efficien
12、t as the techniques based on a digital convolution and can generate velocity profiles which have more various characteristics of acceleration and deceleration than the techniques based on a digital convolution can. That is, the proposed technique can generate velocity profiles of which the decelerat
13、ion characteristics are independent from the acceleration characteristics. First, some coefficients are calculated and are stored according to the acceleration characteristic, the deceleration characteristic, and the acceleration interval, and the deceleration interval. Then given a desired moving d
14、istance, a velocity profile which has the desired characteristics is generated by calculating the position increment during each sampling time. The position increment during each sampling is calculated by multiplying the stored coefficients with the product of one sampling time and the velocity afte
15、r acceleration. In section II, existing techniques for generating velocity profiles of CNC machine tools will be explained. In section III, it will be explained how to generate a desired velocity profile by the proposed technique. The proposed technique and other existing techniques will be compared
16、. In section IV, it will be shown that the proposed technique can generate some useful velocity profiles for CNC machine tools. II. PREVIOUS TECHNIQUES 3 For the illustration of the previous techniques, let us consider one single-axis control system of which the maximum velocity, the maximum acceler
17、ation, and the sampling time are V max， Amax ， and Ts respectively. If this system moves the given distance S at the maximum velocity V max, then the movement time T1 in the rectangular velocity profile will be T1 = S / V max = p Ts, (1) Selecting an integer n which is the smallest integer among int
18、egers which are equal to or greater than p, the resulting rectangular velocity profile is constructed as in Fig. 1. The velocity and position equations for this profile are The position increment during each sampling time is 0 0 0( ) ( ) ( ( 1 ) ) / , 1 ( 4 )s s sP k T P k T P k T S n k n where 0()s
19、P kT and 0( 1) )sP k T are the position commands at the k th and the ( 1)k th sampling times respectively. That is, the position increment during every sampling time is the same. However, since no physical system can achieve the above rectangular velocity profile due to impulse acceleration, the acc
20、eleration interval to increase velocity from the rest to a specified value and the deceleration interval to decrease velocity from the specified value to the rest are needed. II-A. Selection of Polynomial Functions Given an acceleration interval Ts = naTs, a deceleration interval Td= ndTs where na=
21、nd, and a distance S, a trapezoidal velocity profile which has the linear acceleration and deceleration characteristics can be constructed as in Fig.2. If this profile has the constant velocity interval, then n=S/(VmaxTs) is larger than na . The velocity and position equations for this profile are And 1 ()asaasss s as a a sSttTn T TSV t T t n TnTS t n Sn T t n T Tn T T n n T (5) 00( ) / ( ) 0 , ( 2 )( ) / ( ) 0 , ( 3 )ssV t S n T t n TP t S n T t n T
