MT Chap4 Force Analysis of Planar Mechanisms

2020-02-27 148浏览

  • 1.
  • 2.4.1 Introduction 1. Contents of Force Analysis 1) Knowing the external applied loads, calculate the constraint forces which occur in pairs. Constraint forces can be used to design kinematic pairs. 2) Knowing the resistance acting on driven link, calculate the forces acting on driving link, or knowing the driving force, calculate the resistance acting o n driven link. 3)The force analysis is the theoretical foundation to calculate the efficiency. 4) Make use of the force analysis, we can design some selflocking mech anism. 2. Methods of Force Analysis There are two general methods of performing a complete force analysis： Graphical force analysis & Analytical force analysis.
  • 3.4.2 Force Analysis Including Inertia Forces in Mechanisms 1. Inertia Forces Fig 4-1a shows a slider crank mechanism. Because of the constrained motion of the mechanism, accelerations, such as as2, α2 of the individual link 2 and aC3 of the slider 3, may be determined first, then the inertia forces Fi2 and torque Ms2 acting on the link 2 can be calculated respectively. Fig.4-1 Inertia force and inertia torque into resultant force(连杆的惯性力与惯性力矩的合成)
  • 4.2. Kineto static Analysis of Planar Mechanism (1) Kineto static analysis of planar mechanism by graphical method Example 4-1 Fig 4-2a shows a conventional shaper mechanism in which the angular velocity of the crank and all dimensions of links are known. Suppose the weight of the ram is G5, resistance acting on the ram is Fr, and inertia force acting on the ram is Fi5. The other weights and inertia forces need not to be considered. Determine the input torque Mb acting on the driving link and the constraint forces in pairs. Fig.4-2 Graphical force analysis of sharper(牛头刨床的动 态静力分析)
  • 5.(2) Kineto static analysis of planar mechanism by analytical method Example 4-2 Fig 4-3 shows a slider crank mechanism used in a lot of mac hines, such as internal combustion engine and reciprocating compressors. All the dimensions of links, angular position of the crank and angular velocit y of the crank are known. The kinematic analysis is first performed also. Fig.4-3 Analytical force analysis(动态静力分析的解析法)
  • 6.4.3 Force Analysis Including Friction in Mechanisms 1. Friction in Kinematic Pairs (1) Friction in sliding pairs The friction in sliding pairs can be divided into plan e surface friction and V surface friction. 1) Friction on plane surface. A slider 1 is rest on a smooth plane surface 2 which is horizontal. Suppose that the slider 1 is sliding relative to the surface 2 to the right at a constant velocity v 12 acted by a driving force F which is inclined at an angle α to the normal, as shown in Fig 4-4. Fig.4-4 Friction on the plane surface(平面中的摩擦)
  • 7.2) Friction on inclined plane surface. A block of weight G resting on a plane inclined at an angle α to the horizontal is acted on by a horizontal force Fd w hich tends to move the body up the plane with a uniform velocity v12. This is shown in Fig4-5a. Fig.4-5 Friction on the inclined plane surface(斜面摩擦)
  • 8.3) Friction on V plane surface. If the block shown in Fig 4-6a is changed into a V block with a included angle 2θ shown in Fig 46b, and its weight is G, there are two normal reaction forces N21, and from Fig4-6c, Fig.4-6 Friction on V-plane surface(槽面摩擦)
  • 9.(2) Friction in turning pairs The bearings are used extensively a s tuning pairs in machinery, and they can be divided into journal bearing and thrust bearing. 1) Friction in journal bearing. When a shaft rests in the bearing, the vertical load G acts through the axis of the shaft. The normal reactio n N21of the bearing acts in line with G in the vertically upward direc tion shown in Fig 4-7a. Fig.4-7 Friction in a journal bearing(径向轴承中的摩擦)
  • 10.2) Friction in thrust bearing . When a rotating shaft is subjected to an axial load, the thrust is taken by a collar bearing, or thrust bearing. Fig 4-8a shows a thrust bearing acted by an axial load G. Fig.4-8 Friction in a thrust bearing(推力轴承的摩擦)
  • 11.（3）Friction in helical pairs According to the tooth shape, the screw can be divided into square threads and V threads. A square thread screw is used to transmit power, and V threaded screw is used to fasten an element to another. Fig 4-9a shows a square threaded screw; it may be thought of simply as an inclined plane or wedge wrapped around a cylinder. Fig.4-9 Friction in square thread(矩形螺纹的摩擦)
  • 12.Fig 4-10a shows a V thread; its thread angle is 2β, and the angle between the V faces of the thread is 2θ. Fig 410b shows a triangle which is the development of a helix of diameter d and lead l. Fig.4-10 Friction in V-thread(三角形螺纹的摩擦)
  • 13.2. Force Analysis Including Friction Example 4-3 Fig 4-11 shows a slider crank mechanism in which resistant force Fr is applied to the piston 4. The crank 1 is rotating in the clockwise direction; t he dimensions of links and the frictional coefficient of pairs are known. Determi ne the constraint forces in pairs and the input torque. Fig.4-11 Force analysis considering the friction in a slider-crank linkage (考虑摩擦的曲柄滑块机构力分析)
  • 14.Example 4-4 Fig 4-12a shows a cam mechanism with an oscillating follower i n which resistant force Fr is applied to the follower at point F. The cam 1 is rot ating in the counterclockwise direction; the dimensions of the mechanism and the frictional coefficient of pairs are known. Determine the constraint forces in pairs and the input torque. Fig.4-12 Force analysis considering the friction in a cam mechanism (考虑摩擦的凸轮机构的力分析)
  • 15.4.4 Friction and Design of Self locking Mechanisms 1. Self locking in Kinematic Pairs There are two forces in a kinematic pair which is used to connect two links; the one is driving force and the other is friction force which resists the motion of the link. If the driving force acting in a pair is infinite, and the link is not movable, it is called as self locking of a pair. For a sliding pair, applied resultant force acts within the frictional angle of a body, the self locking will occur in the sliding pair. For a rotating pair, applied resultant force acts within the frictional circle of a body, the self locking will occur in the turning pair.
  • 16.2. Self locking Mechanisms (1) Travel of a mechanism 1) Positive travel of a mechanism. A driving force acts on the driver A shown in Fig4-13; the work is done by the resistant force acting on the driven link B. This travel is positive travel. 2) Negative travel of a mechanism. If take the resistant as a driving force and it acts on the link B, and the original driving link, such as A, becomes a driven link, this travel is negative travel. (2) Self locking mechanism If the negative travel of a mechanism is in self locking, it is called as self locking mechanism. Self locking mechanism can be used widely in mechanical engineering. Fig.4-13 Travel of mechanism (机构的行程)
  • 17.3. Design of Self-locking Mechanisms Example 4-5 Fig 4-14 shows a wedge expeller mechanism which is used to compress a body 4 with loaded Fr by applying a horizontal force F to the we dge 2. If the coefficient of friction of the contact surfaces are all the same an d known, analyze the condition of self locking of the wedges. Fig.4-14 Analysis of self-locking mechanism(自锁机构的分析)
  • 18.Example 4-6 Design an eccentric disc clamper shown in Fig 4-15, in which the link 1 is an eccentric disc, body 2 is a work piece which will be clamped. After t he work piece has been clamped, the force F acted on the handle must be remov ed. And then the work piece which has been clamped can not be loosed. Determ ine the position of the pivot of the eccentric disc. Fig.4-15 Design of self-locking mechanism(自锁机构的设计)