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高速凸轮机构动力学试验平台研制【3D-PROE】【16张CAD图纸和说明书】

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高速凸轮机构动力学试验平台研制【3D-PROE】【16张CAD图纸和说明书】.zip

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关键词：: 高速凸轮机构动力学试验平台研制 3d-proe 16张 cad 图纸说明书

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摘要

凸轮从动件系统在各个领域如纺织机械、包装机与食品机械、自动化工业、印刷行业、内燃机、农业机具都广泛被应用。在一般情况下它被认为是刚性系统。但随着机械效率的提高，凸轮转速随之上升，因而产生了较大的弹性变形。从动件运动规律大大偏离了理论值。因此对凸轮从动件系统先进行测试是很重要的。

本文通过对高速凸轮的理论分析，针对几种影响高速凸轮运动规律的因素。

研制特定的的试验平台，实验中可采用三种不同规律的凸轮，采用不同刚度的摆杆，使用不同的压紧弹簧，并在不同转速下进行实验。在试验台一定位置安装相应的传感器，测试出在不同条件下他们的真实运动规律，从而了解各种影响因素对它们的影响。由于没有进行实验，本文对高速凸轮系统进行了一定的动力学建模分析。

关键词：高速凸轮；传感器；试验台；动力学建模

Abstract

Cam follower system in various fields such as textile machinery, packaging machine and food machinery, automation industry, printing industry, internal combustion engines, agricultural machinery are widely applied. Under normal circumstances it is considered to be a rigid system. But with the mechanical efficiency, the cam speed rise, thus creating a greater elastic deformation. Follower motion rule greatly deviated from the theoretical value. Therefore tested against the cam follower system is very important.

In this paper, the theoretical analysis of the high-speed cam, high-speed cam motion law for several impact factors.

Developed a lot of the test platform, three different laws of the cam can be used in the experiment, different rigidity of the swing lever, the type of use to compress the springs, and experiments at different speeds. Install the appropriate sensors, a certain position in the test rig to test out their true law of motion under different conditions, to understand the impact of various factors affecting them. In the absence of experimental, high-speed cam system dynamics modeling.

Key words: high-speed cam；sensing element；test bench；dynamic modeling

摘要

Abstract

第1章绪论 1

1.1选题的背景与意义 1

1.2 国内外研究现状和发展趋势 2

1.2.1 国内对这方面的研究 2

1.2.3 国外对这方面的研究 3

1.3 课题研究主要内容 4

第2章高速凸轮的理论基础 5

2.1 凸轮-从动件系统动态运动分析 5

2.2 影响凸轮系统运动的因素 6

2.3 高速凸轮的判断 7

第3章高速凸轮试验台设计 9

3.1 试验台的参数 9

3.2 试验台的简介 11

3.3 电机的选择.......................................................................................................................12

3.4 带的选择...........................................................................................................................13

3.4.1 已知参数 13

3.4.2 设计计算 13

3.4.3 5M同步带的几何尺寸已知参数 14

3.4.4 5M同步带轮的几何尺寸 14

3.5 轴的结构与校核 15

3.6 凸轮的设计.......................................................................................................................16

3.6.1 偏心轮的设计 16

3.6.2 等加速等减速规律凸轮 17

3.6.3 正弦加速度规律凸轮 19

3.7 摆杆的设计.......................................................................................................................20

3.8 三维模型的建立...............................................................................................................21

第4章传感器的选型 22

4.1 传感器的选用原理 22

4.2 旋转编码器的选用 23

4.2.1 编码器的简介 23

4.2.2 编码器的分类 24

4.2.3 编码器的型号 24

4.3 加速度传感器的选用 26

4.3.1 压电式传感器 27

4.3.2 加速度传感器的型号 27

4.4 位移传感器的选用 28

4.5 应变片的选用 29

4.5.1 应变片原理 29

4.5.2 应变片的型号 29

4.5.3 应变片的测量 30

第5章试验台的动力学建模分析 32

5.1 构件的动力学模型 32

5.1.1 滚子摆杆的动力学建模 32

5.1.2 推杆的动力学建模 32

5.2 试验台动力学模型建立 33

第6章总结 35

参考文献 36

致谢 37

第1章绪论

1.1 选题的背景与意义

凸轮运动机构是一种非常典型的机构,它可以将回转轴的转动运动输出为所需要的特定运动形式。因为它能以简单紧凑的结构，却能实现任意复杂的预期运动。而且具有良好的精度和运动刚性,长期都被广泛的应用于各种机械当中。还因为凸轮机构相对于其他运动机构(比如连杆)相比，具有比较高可靠性、寿命长、容易于设计和能精确的预测所产生的运动等优点,尤其是在要求机构产生给定的运动规律、速度规律和加速度规律时,这个优点更加明显和突出[1]。

因为以上优点,所以在纺织机械、农业机具、自动机床、矿山机械、自动化专用机床、包装机与食品机械、数控机床、印刷工业、内燃机、建筑机械等等机械产品中,凸轮都被广泛的应用。

而在其应用中,凸轮机构转动速度随着机械工业的不断发展,和对机械系统技术要求的不断提高,而表现出越来越高的趋势,从而导致系统当中运动构件的惯性力也大幅增大,构件的弹性形变也随之而变大。尤其是当机构转速到达在共振频率附近时,那么凸轮机构输出端的运动规律将可能远远偏离预期的设计。

针对高速凸轮系统在工程应用中出现的实际问题,大家正在从各种不同的角度去研究。不过因为对工程问题实验研究的消耗较高,花费时间也多,从而导致通过实验去研究相关问题的案例相对较少。本文望能通过理论上对高速凸轮试验台研究,在相关方面做出一点点有益的工作。

1.2. 国内外研究现状和发展趋势

1.2.1国内对这方面的研究

现在国内对高速凸轮研究有以下几个方向:

1.首先在弹性理论学基础上,建立高速凸轮机构的动力学模型及得到其运动微分方程,然后把高速凸轮机构动力学模型的运动方程式进行分析,之后得到了凸轮机构输出端的动态响应,就可以找到确定的凸轮机构输出端运动规律。还可以在建立一个能准确描述凸轮动力特性的数学模型的基础上,通过仿真分析,得到高速凸轮机构在不同的轮廓或结构参数下的动力学特性的曲线。

2.还有从凸轮的廓线设计出发,提出在高速条件下适合采用的推杆运动规律,并且要结合现代加工的技术,设计制造出一系列新型凸轮机构,来满足高速工况。这方面的研究方向主要体现为:运动分析和静力分析、考虑几何尺寸、润滑、误差影响、考虑动力学、弹性变形等。

3.当然由于数值计算方法的发展，再加上计算机技术、各种机械软件的普遍应用,使人们逐渐摆脱了繁重的重复的计算工作,而且可以在计算机的帮助下实现凸轮研究可视化。像凸轮机构CAD/CAM的设计、凸轮机构优化设计、UG环境下的基于虚拟样机技术条件下的凸轮动力学仿真分析的研究和数字化凸轮设计及其实现等。这一系列研究都是国内的热门。

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内容简介：: Pergamon Mech. Mach. Theory Vol. 31, No. 4, pp. 397-412, 1996 Copyright 1996 Elsevier Science Ltd 0094-114X(95)00087-9 Printed in Great Britain. All fights reserved 0094-114X/96 $15.00 + 0.00 AN EXPERIMENTAL STUDY OF THE EFFECTS OF CAM SPEEDS ON CAM-FOLLOWER SYSTEMS H. S. YAN and M. C. TSAI Department of Mechanical Engineering, National Cheng Kung University, Tainan 70101, Taiwan, Republic of China M. H. HSU Department of Mechanical Engineering, Kung Shah Institute of Technology and Commerce, Yungkang, Tainan 71016, Taiwan, Republic of China (Received 9 September 1994; received for publication 26 October 1995) Altraet-Traditionally, in a cam-follower system, the cam is often operated at a constant speed and the motion characteristics of the follower are determined once the cam displacement curve is designed. From the kinematic point of view, the approach by varying cam input driving speed is an alternative way for improving the follower motion characteristics. Here we show how to find a polynomial speed trajectory for reducing the peak values of the motion characteristics. Furthermore, constraints and systematic design procedures for generating an appropriate trajectory of the cam angular velocities are developed. Design examples are given to illustrate the procedure for getting an appropriate speed trajectory as variable speed cam-follower systems. Furthermore, an experimental setup with a servo controller is developed to study the feasibility of this approach. Experimental data show that the results are very close to those of theory. NOMENCLATURE a-acceleration of the follower A, At-normalized acceleration of the follower c, d, e, n, Ta, Tb, x, y-constant parameters h-maximum displacement of the follower j-jerk of the follower J, Jc-normalized jerk of the follower s-displacement of the follower S-normalized displacement of the follower t-time for the cam to rotate through angle 0 T, Tp, Tpj, Tpv-normalized time v-velocity of the follower V, Vc-normalized velocity of the follower t-cam angle rotation for total rise h tim, t2, f13, t4 -cam rotation angle ?-normalized cam angle of rotation O-cam angle of rotation -time of cam rotation for total rise h T, %, %, r4-time of cam rotation ca-cam angluar velocity COave-average cam angular velocity of a complete cycle tOsm , cos2, co, co4-average cam angular velocity in a follower motion period oh-the 1st derivative of co 6b-the 2nd derivative of to t-normalized cam angular velocity tF-the 1st derivative of f the 2nd derivative of f INTRODUCTION In a cam-follower system, the load produced by inertia forces is prone to deflection and creates vibrations; and the load introduced by jerks may cause vibrations as well, These will affect the operating life of the cam. Therefore, the design of motion curves to minimize dynamic loading is of importance for high speed cam mechanisms. It is well known that the velocity and acceleration curves are required to be continuous and to have smaller peak values. In addition, the jerk curve should be finite. 397 398 H.S. Yan et al. A cam is often assumed to be operated at a constant speed in designing a cam-follower system. However, the motion characteristics of the follower are changed as the cam speed varies, Traditionally, to achieve the desired motion is an application of synthesis for obtaining new displacement curves which have better dynamic characteristics. In this paper, we propose an alternative method by varying the cam speeds. The concept of using variable speeds in a cam-follower system design was seldom studied in the literature. Rothbart 1 designed a variable speed cam mechanism in which the input to the cam is the output of a Withworth quick-return mechanism. Tesar and Matthew 2 derived the motion equations of the follower by considering the case of variable speed cams. The criteria for selecting proper angular velocities which will eliminate the discontinuity in motion characteristics of the follower are investigated by Yan et al. 3. From the kinematic point of view, the objective of this work is to find cam speed trajectory for reducing the peak values of the follower-output motion. Furthermore, constraints and system design procedures for generating a proper trajectory of the cam angular velocities are deve!oped. Design examples are given to illustrate the procedure for getting a proper angular speed for a given follower system. An experimental cam-follower system is set up in which a servo motor is controlled to generate the desired speed trajectory for performance evaluations. MOTION EQUATIONS For a cam-follower system, the follower displacement, s(t), is a function of cam rotation angle O(t). Mathematically, it can be expressed as: s(t) =f(O(t) (1) where O(t) is the cam rotation angle at time t. The follower velocity, v(t), of the follower is then given by: v(t) = f(O)o(t) (2) where f(O)=df(O)/dO, and co(t)=dO(t)/dt is the cam angular velocity. Furthermore, the corresponding follower acceleration, a(t), and jerk, j(t), are: a(t) = f(O)co2(t) + f(O)dg(t) (3) j(t) = f(O)co3(t) + 3f(O)co(t)cb(t) + f (O)6J(t) (4) where f(O) = df2(O)/dO 2, f(O) = df3(O)/dO 3, (t) = dco(t)/dt, and c3(t) = dcoZ(t)/dt 2. Equations (1)-(4) present the relationship between cam input angular velocity co(t) and follower-output motions s(t), v(t), a(t), and j(t). Obviously if co(t) is a constant, they can be greatly simplified. Let h be the total displacement of the follower as the cam rotates an angle in time period 3. Furthermore, denote T = t/r, = 0/8, and S -s/h. Now we have T0, 1, Vt 0, r, 0, 1, V00,/ and Se0, 1, Vs0, h. Then, equations (1)-(4) can be rewritten in terms of their normalized forms as follows: s(t) S(T)=g(),)= h (5) V(T) = g(y )t2 (T) (6) A (T) = g(y)fl2(T) -I- g(y)il(T) (7) J(T) = g (y) 3(T) + 3g (7)t2(T)tI(T) + g(y)(T) (8) where t2(T) = dy (T)/d T is the normalized cam angular velocity and V(T), A (T), and J(T) are the normalized velocity, acceleration, and jerk of the follower, respectively. The relationship between equations (1) to (8) can be found as: s = hs (9) h v =- v (10) T Effects of cam speeds on cam-follower systems 399 h a =A (ll) _hj j - . (12) When the cam operates at a constant speed, i.e. f(T)= 1, the normalized velocity, Vc(T), acceleration, At(T), and jerk, J(T), of the follower can be expressed as: V(T) = g(7) (13) Ac(T) = g(7) (14) J(T) = g() (15) where 7(T) = T. CRITERIA FOR DESIGN (T) For a given cam-follower system, the peak values of the normalized velocity, acceleration, and jerk resulting from a constant driving speed may possibly be reduced if we properly control its input speed trajectory f(T). For example, to reduce the peak values of normalized velocity, f(T) can be chosen so that I V(Tpv)l 0, i.e. the direction of cam speed is not changed. As a result, design criteria for selecting fZ(T) to reduce the peak values of follower-outputs are: (a) (I) for the case of reducing the peak value of the normalized velocity: -l 0. Let equations (5)-(8) represent the normalized motion characteristics of the follower in the rising period. Then, the motion characteristics in the falling period are: S(T) = 1 - g() (22) V(T) = -g(,)fZ(T) (23) A (T) = - g(?)fZ2(T) - g()(T) (24) J(T) = -g(,)n3(T) - 3g(r)n(T)t(T) - g(r)t)(T). (25) It is easy to find that the absolute values of the normalized velocity, acceleration, and jerk in the falling period are equal to those in the rising period, respectively. Hence, we have the following fact: If the same displacement curve is used in the rising and falling periods of a follower, the functions of fl(T) in these two periods are identical. ANGULAR VELOCITY f(T) Consider a cam-follower system which has a cam providing a cycloidal motion curve where cam-input fZ(t) is a polynomial. In the rising (or falling) period and applying criteria (a) and (g) to reduce the peak values of motion curves, we choose the following polynomial fZ(T), Fig. 1: . .t_ _.3 . d t i t i T 0 T a T b 1 Fig. 1. Polynomial angular velocity in rising or falling period. Effects of cam speeds on cam-follower systems (W) 0 0.5 Fig. 2. Polynomial angular velocity in dwell period. 401 ffr) sfr) VO3 Aft) J(T) 1.15 1.101-.,. 051 ,.001 . 2 (27) x = y = 0, 2, 4 . (28) Parameters x and y are determined based on the type of cam displacement curves and the design criteria (e). Furthermore, parameter e subject to design criteria (f) is given by: 30 e = (Ta- Tb) 5 (29) Apparently, we can properly select d, Ta, and Tb tO obtain the lowest peak values of motion characteristic under the polynomial f(T) of Fig. 1. Since the cycloidal motion curve is of symmetry, we let Tb = 1 - T for simplicity and symmetry. In addition, when the follower is in the dwell period, from design criteria (c) and (g) and equations (26)-(29), we obtain f(T), Fig. 2, as follows: fl(T) = 2n(2T 3 - 3T 2) + 1 + n. (30) Under design criterion (d) and equation (30), we have: y(T) - n(T 4 - 2T 3) + (1 + n)T (31) and from design criteria (c) and (g), we imply: (T) = 12n(T 2- T) (32) 8 C0sl .0 ave . . I I t Time (t) 0 1 1+t2 1+2+3 1+2+3+g4 Fig. 4. Angular velocity of a variable-sled cam-follower system. Effects of cam speeds on cam-follower systems 403 g 110 105 100 95 90 85 I I I I 0 O. 12 0.24 0.36 0.48 0.6 Time(s) D .,) 35 30 25 20 15 10 5 0 -5 J I I 0.12 0.24 I 0.36 I 0.48 0.6 Time(s) 300 - 200 100 ,.-, 0 . -100 o -200 -300 I I I 0.12 0.24 0.36 0.48 0.6 Time(s) .- 5,000 2,500 0 O -2,500 -5,000 U . / / r t / 0.(5 011 0.15 012 0.25 Time (sec)- offHne theory - on_line theory -. measure (a) Response of motor speed Fig. lOa-Caption on p. 409 408 H.S. Yan et al. to drive the cam-follower system. The achievement of this angular velocity by the motor can be accomplished most easily by employing a velocity control system 4. An IBM-PC AT plug-in evaluation board, TMS320C30 system board 5, 6, is used in the real-time experiment setup. The hardware configuration of the experimental system is depicted in Fig. 9. In addition to digital communications through the AT-bus, the input/output analog signals are accessed through on-board A/D converters (ADC) and D/A converters (DAC). These input and output channels are for the feedback signals to the DSP and for the control signals to the controlled plant respectively. In the real-time control, the sampling rate 60 #sec is adopted in our experiments so that controller design can be done from the continuous-time. The controlled 30 25 20 8 t 0.05 0.1 0.15 0.2 0.25 Time (scc) - theory - measure (b) Response of follower displacement Fig. lOb.-Caption on p. 409 600 400 200 -200 -4O0 -6000 012 0.1 0.15 Time (scc) - theory - measure (c) Response of follower velocity Fig. lOc.-Caption on p. 409 0. Effects of cam speeds on cam-follower systems 409 output responses are measured through an on-board ADC and DAC, and stored on the on-board memories. The speed of driving motor is picked up from the driver of the motor, i.e. the voltage signal of built in tachometer, and fed to a PC486 personal computer. The acceleration and displacement signals of the follower can be measured by using the accelerometer (PCB, 353A34), linear encoder (HEIDENHAIN, LS404) as shown in Fig. 8. The signal from the accelerometer is conditioned by ( o -0.5 -1 -1.5 xl04 2 1.5 1 0.5 , , * 1 l k , : , :, , 20 0.05 011 0.15 012 0.25 Time (see) - theory - measure (d) Response of follower acceleration Fig. 10d. i v d xl06 1.5 11.5 41.5 -1 :vii ,J 150 0J)5 I t ,li I, Ii o11 0.15 0.2 Time (see) - theory - measure (e) Response of follower jerk Fig. 10e. ., 0.5 Fig. 10. Experimental results of a cycloidal cam-follower system (n = 0, d = 0.1, and to, e = 200 rpm). 410 H.S. Yan et al. a power unit (PCB, mode 480E09 ICP). Using least square fit method 7, we can obtain the velocity of follower from the displacement signal, and the jerk from the acceleration signal. The measured data are then passed back to the PC host for performance evaluation. Both of the theoretical and experimental results of n = 0, d = 0.1 at the average cam speed of 200 and 150 rpm are presented in Figs 10 and 11, respectively. Although the fluctuation of the driving speed occurs, Figs 10 and 11 demonstrate good agreement between the theoretical and experimental results of each cycle. The experimental results show the proposed approach is feasible. 170 160 2 150 8 140 130 120 ,V,:J,;,., ,., , ! . it d db . ! , ?, / -. , /. 4 ,I , , ,/ / , / h / , , i , i 1 110 0.05 011 0.15 0.2 0.25 013 0.35 Time (see) - off_line theory - online theory -. measure (a) Response of motor speed Fig. lla.-Caption on p. 412. ,j v 30 25 20 15 10 01 0.1)5 i 0.1 0.15 0,2 0.25 0.3 0,35 Time (see) - theory - masure (b) Response of follower displacement Fig. lib.-Caption on p. 412. Effects of cam speeds on cam-follower systems 411 40( 30( 200 100 0 -I00 -200 -300 -4OO -5000 o.b5 011 0.15 012 0. Time (sec)- theory - measure (c) Response of follower velocity Fig. 11c.-Caption on p. 412. k/ 013 0.5 xlO 1.5 G ( B e .=o ,o 0.5 0 -0.5 -1 -1.5 0 , , ; 0.)5 011 0.15 012 0.25 013 0.15 Time (sec)- theory - measure (d) Response of follower acceleration Fig. 1 ld.-Caption on p. 412. 412 H.S. Yan et al. xl06 1 fl v 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -10 jV iii I, !i o. 5 o11 o.15 012 0. 013 0.35 Time (sec)- theory - measure (e) Response of follower jerk Fig. lie. Fig. I1. Experimental results of a cycloidal cam-follower system (n = 0, d = 0.1, and toav e = 150 rpm). CONCLUSION In this work, from the kinematic point of view and based on the controlling of the cam input driving speed, we have presented an alternative method to improve the motion characteristics of cam-follower systems. Cons

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