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1、5.2 Follower Motion Curves (从动件运动规律 ),Total follower travel, or the lift(行程), is denoted by h.,The cam angle for rise(推程角) is denoted by o.,Obviously, B0OB70, hOB7-OB0,The cam angle for outer dwell(远休止角) is denoted by S.,The cam angle for return (回程角) is denoted by o.,Obviously, B9OB140, hOB9-OB14,T
2、he cam angle for inner dwell(近休止角) is denoted by S.,The displacement curve of the cam mechanism.,the lift (行程)：h. the cam angle for rise (推程角): o. the cam angle for outer dwell (远休止角): S.the cam angle for return (回程角): o.the cam angle for inner dwell (近休止角): S.,Since is a constant, the curve has ash
3、ape similar to the Vt curve. So , denoted by S, is called the quasi-velocity(类速度).,Differentiating(微分) S with respect to time t will result in velocity V., or,Differentiating V with respect to t results in,Since is a constant, the curve has a shape similar to the at curve. So , denoted by S , is cal
4、led the quasi-acceleration (类加速度)., or,The dimensions(量纲) of both S and S are mm.,5.2.1 Constant Velocity Motion Curve,At the beginning of the rise, the velocity changes from zero to its maximum value in zero time. The differentiation of velocity (i.e. acceleration) at this point is therefore infini
5、te(无穷大).,Any real follower must have some mass, so at these two points, infinite acceleration will produce an infinite inertia(惯性) force. This will result in a very large amount of shock, which is called a rigid impulse(刚性冲击).,5.2.2 Constant Acceleration and Deceleration Motion Curve(等加速等减速运动规律),The
6、re are three abrupt(突然) changes in the acceleration of the follower, at the beginning of the rise, the midpoint and the end of the rise.,An abrupt change in the acceleration causes an abrupt change in the inertia force.,An abrupt change in the magnitude and/or direction of inertia force would initia
7、te(激发) undesired vibration(振动), which is called a soft impulse (柔性冲击).,5.2.3 Cosine Acceleration Motion Curve (or Simple Harmonic谐波 Motion Curve),The acceleration changes abruptly at the beginning and end points. That would produce soft impulses.,5.2.4 Sine Acceleration Motion Curve (or Cycloid(摆线)
8、Motion Curve),There is neither rigid impulse nor soft impulse. Therefore this motion curve gives a good dynamic characteristic and is especially recommended for high-speed cams,The equation of the quasi-acceleration in the rise will be:S =C1* sin( ) -(5-1),S =C1* sin( ) -(5-1) The equation of the qu
9、asi-velocity S can be created by the integration(积分) of the equation of S with respect to ,S =C2-C1* *cos( ) -(5-2),Integrating again with respect to results in the displacement equation,S =C3+C2*-C1* *sin( ) -(5-3),The constants C1, C2 and C3 can be found by applying the boundary(边界) conditions to
10、the equations.,S=0 when =0, S=0 when =o , S=h when =o.,Substituting(替代) the three boundary conditions into Eq.5-1 to Eq.5-3 yields three equations and solving the three equations simultaneously(同时地) results in C1= 2*h/(o)2, C2= h/o, and C3=0.,The constants C1, C2 and C3 can be found by applying the
11、boundary(边界) conditions to the equations.,S=0 when =0, S=0 when =o , S=h when =o.,Substituting these constants into Eqs(1-3) yields: S=h* - *sin( ) S= *1-cos( ) S= * sin( ) -(5-4),Note： All angles in all equations in this chapter should be expressed in radians(弧度), not in degrees.,Substituting these
12、 constants into Eqs(1-3) yields: S=h* - *sin( ) S= *1-cos( ) S= * sin( ) -(5-4),(S)MAX and (S)MAX , for the sine acceleration motion curve are 2*h/o and 2*h/(o)2, respectively.,The acceleration is negative during the first half of the return and positive during the second half of the return. The equ
13、ations for the return with a sine acceleration motion curve can be,derived in a similar way.,The equations for the return with a sine acceleration motion curve are: -(5-5),Note that the displacement S in the return is measured from the lowest position of the follower. Angles in all equations are mea
14、sured from the starting point of the rise.,5.2.5 3-4-5 Polynomial多项式 Motion Curve,The standard polynomial equation is S=C0+ C1*+ C2*2 + +Cn*nwhere the constants Ci depend on the boundary conditions.,The boundary conditions for the rise are: S=0, S=0 and S=0 when =0;S=h, S=0 and S=0 when =o.,Since there are six boundary conditions, a polynomial of six terms is required. Assume thatS=C0 +C1* +C2 *2 +C3 *3 +C4 *4 +C5 *5 -(5-6),
