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湖南科技大學(xué)本科生畢業(yè)設(shè)計（論文）
摘 要
激光切割的適用對象主要是難切割材料，如高強度、高韌性材料以及精密細(xì)小和形狀復(fù)雜的零件，因而數(shù)控激光切割在我國制造業(yè)中正發(fā)揮出巨大的優(yōu)性。
本文設(shè)計了一臺單片機控制的數(shù)控激光切割機床，主要完成了：機床整體結(jié)構(gòu)設(shè)計，Z軸、XY軸的結(jié)構(gòu)設(shè)計計算、滾珠絲杠、直線滾動導(dǎo)軌的選擇及其強度分析；以步進電機為進給驅(qū)動的驅(qū)動系統(tǒng)及其傳動機構(gòu)的分析設(shè)計計算。
關(guān)鍵詞：CNC；激光切割機床；結(jié)構(gòu)；設(shè)計
ABSTRACT
Laser cutting machine tool was usually used for the hard-cutting material, such as high-strength material, high precision ductile materials, and smart and complicated components. So, CNC laser cutting has been playing an important role in China's manufacturing industry.
This paper describes the design of a SCM-controlled CNC laser cutting machine tools. More attention was paid on the overall machine design, Z axis, XY axis in the design, ball-screw and the choice of linear motion guide and intensity analysis; the drive system into which stepper motor was put and the analysis of the drive system design.
KeyWords：CNC；laser cutting machine tools；architectured；esign
目 錄
第1章 緒論………………………………………………………………………1
1.1 課題背景…………………………………………………………………1
1.2 本課題主要研究內(nèi)容……………………………………………………1
1.3 國內(nèi)外研究現(xiàn)狀…………………………………………………………2
第2章 總體方案的擬定………………………………………………………3
2.1設(shè)計任務(wù)……………………………………………………………………3
2.2總體方案的選擇和擬定……………………………………………………3
第3章 激光切割系統(tǒng)的設(shè)計………………………………………………5
3.1 激光器……………………………………………………………………5
3.1.1激光器的組成………………………………………………………5
3.1.2激光切的分類………………………………………………………5
3.2 激光切割設(shè)備……………………………………………………………6
3.2.1激光切割設(shè)備的組成………………………………………………6
3.2.2激光切割用的激光器……………………………………………8
3.2.3激光切割用割炬…………………………………………………9
3.3激光切割頭設(shè)計…………………………………………………………10
第4章 傳動系統(tǒng)設(shè)計………………………………………………………12
4.1 XY工作臺設(shè)計…………………………………………………………12
4.1.1主要設(shè)計參數(shù)及依據(jù)…………………………………………12
4.1.2XY進給系統(tǒng)手里分析……………………………………………12
4.1.3初步確定工作臺尺寸及估算質(zhì)量………………………………12
4.2 Z軸隨動系統(tǒng)設(shè)計………………………………………………………13
4.3 滾珠絲趕副設(shè)計計算………………………………………………… 14
4.3.1滾珠絲桿的特點…………………………………………………14
4.3.2主要參數(shù)…………………………………………………………14
4.3.3導(dǎo)程計算…………………………………………………………15
4.3.4確定當(dāng)量轉(zhuǎn)速與當(dāng)量載荷………………………………………16
4.3.5初選滾珠絲桿副…………………………………………………17
4.3.6確定允許的最小螺紋底徑………………………………………17
4.3.7確定滾珠絲桿副的規(guī)格代號……………………………………18
4.3.8確定絲桿副的預(yù)緊力…………………………………………18
4.3.9行程補償值與拉伸力…………………………………………18
4.3.10確定滾珠絲桿副支承用的軸承代號，規(guī)格…………………19
4.3.11滾珠絲桿副工作圖設(shè)計………………………………………20
4.3.12傳動系統(tǒng)剛度…………………………………………………20
4.3.13剛度驗算和精度選擇…………………………………………21
4.3.14驗算臨界壓縮載荷……………………………………………22
4.3.15驗算臨界轉(zhuǎn)速……………………………………………………23
4.3.16效率驗算………………………………………………………23
第5章 導(dǎo)軌的選定…………………………………………………………25
5.1 主要要求及種類…………………………………………………………25
5.1.1對導(dǎo)軌的基本要求………………………………………………25
5.1.2導(dǎo)軌的技術(shù)要求…………………………………………………25
5.1.3分類及特點………………………………………………………25
5.2 導(dǎo)軌的選用………………………………………………………………26
第6章 步進電機及其傳動機構(gòu)的確定…………………………………28
6.1 步進電機的選用………………………………………………………28
6.1.1脈沖當(dāng)量和步距角………………………………………………28
6.1.2步進電機上起動力矩的近似計算………………………………28
6.1.3確定步進電機最高工作頻率……………………………………29
6.2 齒輪傳動機構(gòu)的確定…………………………………………………29
6.2.1傳動比的確定……………………………………………………29
6.2.2齒輪結(jié)構(gòu)主要參數(shù)的確定………………………………………30
6.3 步進電機慣性負(fù)載的計算……………………………………………30
第7章 傳動系統(tǒng)剛度分析…………………………………………………33
7.1 根據(jù)工作臺不出現(xiàn)爬行的條件來確定傳動系統(tǒng)剛度………………33
7.2 根據(jù)微量進給的靈敏度來確定傳動系統(tǒng)的剛度……………………33
第8章 消隙方法與預(yù)緊……………………………………………………35
8.1 消隙方法………………………………………………………………35
8.1.1偏心軸套調(diào)整法…………………………………………………35
8.1.2錐度齒輪調(diào)整法…………………………………………………35
8.1.3雙片齒輪錯齒調(diào)整法……………………………………………36
8.2 預(yù)緊……………………………………………………………………37
第9章 結(jié)論……………………………………………………………………38
參考文獻…………………………………………………………………………39
致謝…………………………………………………………………………………40
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VSS motion control for a laser-cutting machine
Abstract
An advanced position-tracking control algorithm has been developed and applied to a CNC motion controller in a laser-cutting machine. The drive trains of the laser-cutting machine are composed of belt-drives. The elastic servomechanism can be described by a two-mass system interconnected by a spring. Owing to the presence of elasticity, friction and disturbances, the closed-loop performance using a conventional control approach is limited. Therefore, the motion control algorithm is derived using the variable system structure control theory. It is shown that the proposed control e!ectively suppresses the mechanical vibrations and ensures compensation of the system uncertainties. Thus, accurate position tracking is guaranteed.
1. Introduction
For many industrial drives, the performance of motion control is of particular importance. Rapid dynamic behaviour and accurate position trajectory tracking are of the highest interest. Applications such as machine tools have to satisfy these high demands. Rapid movement with high accuracy at high speed is demanded for laser cutting machines too. This paper describes motion control algorithm for a low-cost laser-cutting machine that has been built on the base of a planar Cartesian table with two degrees-of-freedom (Fig. 1). The drive trains of the laser-cutting machine are composed of belt-drives with a timing belt. The use of timing belts in the drive system is attractive because of their high speed, high efficiency, long travel lengths and low-cost (Haus, 1996). On the other hand, they yield more uncertain dynamics and a higher transmission error ( Kagotani, Koyama & Ueda, 1993). Consequently, belt-drives suffer from lower repeatability and accuracy. Moreover, the belt-drive dynamics include more resonance frequencies, which are a destabilising factor in a feedback control (Moon, 1997). Therefore, a conventional control approach like PI, PD or PID control fails to achieve acceptable performance. Plant parameter variations, uncertain dynamics and load torque disturbances, as well as mechanical vibrations, are factors that have to be addressed to guarantee robust system stability and the high performance of the system. An advanced robust motion control scheme is introduced in this paper, which deals with the issues related to motion control of the drives with timing belts. The control scheme is developed on the basis of the motion control algorithm introduced by Jezernik, Curk and Harnik (1994). It possesses robust properties against the disturbances that are associated with a nominal plant model, as it has been developed with the use of the variable structure system (VSS) theory (Utkin, 1992). The crucial part of the control scheme is the asymptotic disturbance estimator. However, as shown in this paper, it fails to stabilise resonant belt dynamics, since it was developed for a rigid robot mechanism. Therefore, this paper introduces an improved motion control scheme, which suppresses the vibrations that would arise due to the non-rigid, elastic drive. Consequently, a rapid response with low position tracking error is guaranteed.
The paper is set out as follows. The laser-cutting machine is presented and the control plant model of the machine drives is developed in Section 2. In Section 3, the VSS control regarding the elastic servomechanism is discussed and the derivation of the motion control scheme is described. Section 4 presents the experimental results and a follow-up discussion. The paper is summarized and concluded in Section 5.
2. The control plant
2.1. The machine description
The laser-cutting machine consists of the XY horizontal table and a laser system (Fig. 1). The fundamental components of the laser system are:
● the power supply unit, which is placed off the table and thus is not considered in the motion control design;
● the laser-beam source, which generates the laser beam (the laser-generator);
●the laser-head, which directs the laser beam onto the desired position in the cutting plane.
The table has to move and position the laser head in a horizontal plane. This is achieved by the means of a drive system with two independent motion axes. They provide movement along the Cartesians' XY axes of 2 and 1m, respectively. The X-drive provides the motion of the laser-head in X-direction. The drive and the laser-head as well as the laser-generator are placed on the bridge to ensure a high-quality optical path for the laser-beam. The movement of the bridge along the Y-axis is provided by the Y-drive. The laser-head represents the X-drive load, while the Y-drive is loaded by the bridge, which carries the complete X-drive system, the laser-head, and the laser-generator. The loads slide over the frictionless slide surface.
The positioning system consists of the motion controller, the amplifiers, the DC-motors and the drive trains. The X-drive train is composed of a gearbox and a belt-drive (Fig. 2). The gearbox reduces the motor speed, while the belt-drive converts rotary motion into linear motion. The belt-drive consists of a timing belt and of two pulleys: a driving pulley and a driven pulley that stretch the belt. The Y-drive train is more complex. The heavy bridge is driven by two parallel belt-drives; each bridge-side is connected to one of the belt-drives. The driving pulleys of the belt-drives are linked to the driving axis, which is driven via the additional belt-drive and the gearbox is used to reduce the speed of the motor.
2.2. Assumptions
The machine drives represent a complex non-linear distributed parameter system. The high-order system possesses several resonant frequencies that can be observed by the drives' step response (see Section 4). From a control design perspective, difficulties arise from mechanical vibrations that are met in the desired control bandwidth (~10 Hz). On the other hand, the design objective is to have a high-performance control system while simultaneously reducing the complexity of the controller. Therefore, a simple mathematical model would only consider the first-order resonance and neglect high-order dynamics. In other words, the design model of the control plant will closely match the frequency response of the real system up to the first resonance. Next, the controller should be adequately designed to cope with the higher-order resonance in such a way that the resonance peaks drop significantly to maintain the system stability. Thus, according to the signal analysis and the drives' features, the following assumptions could be made:
●the DC-servos operating in the current control mode ensure a high-dynamic torque response on the motor axis with a negligible time constant;
●the small backlash in the gearboxes and the backlash of the belt-drives due to the applied pre-tension of the timing belts is negligible;
●a rigid link between a motor shaft and a driving pulley of the belt-drive could be adopted;
●the inertia of the belt-drives' driven pulleys is negligible in comparison to other components of the drive system.
Using the assumptions above, dynamic modeling could be reduced to a two-mass model of the belt-drives that only includes the first resonance. In the control design, the uncertain positioning of the load due to the low repeatability and accuracy of the belt-drive has to be considered as well.
Note, that no attention is paid to the coupled dynamics of the Y-drive due to the parallel driving, thus, the double belt-drive is considered as an equivalent single belt-drive.
3. The motion control algorithm
The erroneous control model with structured and unstructured uncertainties demands a robust control law. VSS control ensures robust stability for the systems with a non-accurate model, namely, it has been proven in the VSS theory that the closed-loop behavior is determined by selection of a sliding manifold. The goal of the VSS control design is to find a control input so that the motion of the system states is restricted to the sliding manifold. If the system states are restricted to the sliding manifold then the sliding mode occurs. The conventional approach utilises discontinuous switching control to guarantee a sliding motion in the sliding mode. The sliding motion is governed by the reduced order system, which is not affected by system uncertainties. Consequently, the sliding motion is insensitive to disturbance and parameter variations (Utkin, 1992).
The essential part of VSS control is its discontinuous control action. In the control of electrical motor drives power switching is normal. In this case, the conventional continuous-time/discontinuous VSS control approach can be successfully applied. However, in many control applications the discontinuous VSS control fails, and chattering arises (S[abanovicH, Jezernik, & Wada, 1996; Young, Utkin & OG zguK ner, 1999). Chattering is an undesirable phenomenon in the control of mechanical systems, since the demanded performance cannot be achieved, or even worse―mechanical parts of the servo system can be destroyed. The main causes of the chattering are neglected high-order control plant dynamics, actuator dynamics, sensor noise, and computer controlled discrete-time implementation in sampled-data systems. Since the main purpose of VSS control is to reject disturbances and to desensitise the system against unknown parametric perturbations, the need to evoke discontinuous feedback control vanishes if the disturbance is sufficiently compensated for, e.g. by the use of a disturbance estimator (Jezernik et al., 1994; Kawamura, Itoh & Sakamoto, 1994). Jezernik has developed a control algorithm for a rigid robot mechanism by combining conventional VSS theory and the disturbance estimation approach. However, the rigid body assumption, which neglects the presence of distributed or concentrated elasticity, can make that control input frequencies of the switcher excite neglected resonant modes. Furthermore, in discrete-time systems discontinuous control fails to ensure the sliding mode and has to be replaced by continuous control (Young et al., 1999). Avoiding discontinuous-feedback control issues associated with unmodelled dynamics and related chattering are no longer critical. Chattering becomes a non-issue.
In plants where control actuators have limited bandwidth there are two possibilities: actuator bandwidth is outside the required closed-loop bandwidth, or, the desired closed-loop bandwidth is beyond the actuator bandwidth. In the fist case, the actuator dynamics are to be considered as the non-modelled dynamics. Consequently, the sliding mode using discontinuous VSS control cannot occur, because the control plant input is continuous. Therefore, the disturbance estimation approach is preferred rather than VSS disturbance rejection. In the second case, the actuator dynamics are to be lumped together with the plant. The matching conditions (Draz\enovicH, 1969) for disturbance rejection and insensitivity to parameter variations in the sliding mode are violated. This results from having dominant dynamics inserted between the physical input to the plant and the controller output. When unmatched disturbances exist the VSS control cannot guarantee the invariant sliding motion. This restriction may be relaxed by introducing a high-order sliding mode control in which the sliding manifold is chosen so that the associated transfer function has a relative degree larger than one (Fridman
& Levant, 1996). Such a control scheme has been used in a number of recently developed VSS control designs, e.g. in Bartolini, Ferrara and Usai (1998). In the latter, the second-order sliding mode control is invoked to create a dynamical controller that eliminates the chattering problem by passing discontinuous control action onto a derivative of the control input.
The system to be controlled is given by Eqs. (1) ―(5) and the system output is the load position. The control objective is the position trajectory tracking. The control algorithm that is proposed in this paper has been developed following the idea of the VSS motion control presented by Jezernik. Since the elastic belt-drive behaves as a low bandwidth actuator, the conventional VSS control algorithm failed to achieve the prescribed control objective. Thus, the robust position trajectory tracking control algorithm presented in the paper has been derived using second-order sliding mode control. In order to eliminate the chattering problem and preserve robustness, the control algorithm uses the continuous control law. Following the VSS disturbance estimation approach, it will be shown that the disturbance estimation feature of the proposed motion control algorithm is similar to the control approach of Jezernik (Jezernik et al., 1994). Additionally, the proposed control algorithm considers the actuator dynamics in order to reshape the poorly damped actuator bandwidth. Consequently, the proposed motion controller consists of a robust position-tracking controller in the outer loop and a vibration controller in the inner loop .