|
<< Click to Display Table of Contents >> Navigation: MotionDesigner Reference & User Interface > Motion Design Considerations > Motion: Dynamic Considerations |
We can use vibration terminology to describe the dynamic response of a mechanical system to a motion command.
Nominal Motion: The motion command you want a mechanical part to follow. This is your motion-design from MotionDesigner.
Transient Motion: The dynamic response of the mechanical system within the period of the motion command.
Residual Vibration: The dynamic response of the mechanical system after the motion-command. This term usually applies to the dwell period after an indexing motion period.
When we look at the Dynamic-Performance, it is easier to discuss the acceleration of the motion-command and the motion-response.
All mechanical systems have a degree of elasticity, mass, and mass moment of inertia. The means that the acceleration response of the system is greater than that of the acceleration command. This is a reality of all mechanical systems.
The Dynamic Performance is a function of many factors, that include:
•the speed of the drive shaft (cycle speed),
•the natural frequency of the mechanical system (derived from its stiffness and mass, or its rigidity and mass moment of inertia).
•the segment period (time) in the motion-command
•the continuity of the motion-law
•the magnitude of the movement (lift) = the LEAST significant.
The maximum allowable operating speed is also influenced by the manufacturing accuracy of a cam-profile. The adverse effect of profile inaccuracies is aggravated as the machine-speed increases. Very stiff mechanisms (to give a high natural frequency) are to be preferred in all cases, provided the cam-profile is smooth.
Vibrations do not stop when the motion segment is finished! Residual vibration levels should be considered. If high vibration levels are experienced by the system in a dwell immediately after a segment, then frequently the machine tooling may be out of position while another mechanism attempts to interact with it. Some designers then redesign the motion with an even longer dwell (= shorter motion segment) to give a longer time for the vibrations to cease. However, this is not usually good solution to the problem as accelerations increase, and the Period-Ratio decreases.
In order to provide an accurate definition of the dynamic-performance of a mechanism, we use a non-dimensional parameter called Period-Ratio.
The Period-Ratio is the:
The Period (time duration) of the motion segment divided by the Period (time duration) of the fundamental vibration of the following system.
A high Period-Ratio is always better than a low one.
Period-Ratio > 10 : indicates a combination of a stiff, low mass system, operating at a medium or low cam-shaft speed.
5 < Period-Ratio 5 < 10 : a combination less stiffness, greater driven mass/inertia, and greater cam-shaft speed.
Period Ratio < 5 : a combination of low stiffness, high mass/inertia, and/or high speed cam-shaft
When the motion-law of the motion command is continuous in position, velocity, and acceleration, and if the Period-Ratio is more than 20, the acceleration of the mechanical system approaches the acceleration as predicted by the Motion-Law. The dynamic response of the follower system may be neglected when determining actual accelerations.
However, in the case of the Simple-Harmonic-Motion and the Constant-Acceleration motion-laws, which are not continuous in acceleration, the acceleration of the dynamic-response is always significantly more than the acceleration of the motion-command, even if the Period-Ratio is greater than 20.
Motion-Laws that are discontinuous in acceleration (infinite jerk), at any point in their cam profile, produce vibrations of the mechanical-system. The actual acceleration/deceleration of the driven system is up to 2 times the nominal acceleration when driven by a cam motion with infinite jerk.
The pressure angle and the way in which it varies throughout a motion depends upon the basic dimension of the cam, the type of the follower (roller, or flat faced) and, to a lesser extent on the particular motion-law.
The operating torques for a cam system depends on the Motion-Law.
In general, you want the cam-shaft to rotate as near as possible to constant-velocity. You should design the input drive system to reduce the effect of the varying Drive Torque on the speed of the cam-shaft.
Typically, the drive shaft should be short, and have a large a diameter as possible. Add a flywheel to the input near to the Cam.
Maximize the rotating speed of the drive motor with a gear-box. The armature of the motor acts as a flywheel. The Load Torque (and its variation), referred to the motor are minimized.
There are three Torque factors to consider:
This is the component of torque required to overcome the constant component of the external load on the Follower. The constant load is usually due to the weight of the following system (or the referred weight), the load at the start of the motion due to any spring constraint, and also friction. This is usually the least significant of the three, for a 'normal' cam driven system - but it depends on the other two!
This is the component of torque required to accelerate the mass of the follower assembly. It is usually the most significant in normal systems - but that depends on the others!
This component is due to the linear change of spring constraint with the follower movement. This factor is based on the minimum spring force required at the point of maximum deceleration to maintain contact between the follower and the cam. The spring, might be an 'air-cylinder' which might be either a 'constant force' or as a 'fixed air mass'.
The magnitude of the total drive torque gives some indication of the amount of torsional deflection in the drive shaft and therefore the amount of segment motion distortion that may occur. The distortion tends to attenuate (reduce) the accelerations and amplify (increase) the decelerations of the follower. An abrupt reversal of torque (e.g. due to backlash in the drive train) results in torsional vibration in the driving shaft which is transmitted through the cam to the driven system. Such distortions can be reduced by increasing the torsional stiffness of the shaft and by increasing the mass moment of inertia, especially near the cam.
Motion distortion can result from shaft bending/flexing ( due to cam contact forces)The shaft size and the position of its support bearings should be chosen to minimize any distortion of the cam-shaft.
Motion distortion can also result from the deflection of the Follower support shaft due to the pressure angle and cam contact-force.
The rate-of-change of the strain-energy is related to the maximum value of jerk in the motion.
Jerk should be considered in addition to the system's rigidity/stiffness, and its operating speed.
Jerk values can be compared for different motions. Such as the:
•Start and End Jerk: At the start and end of a motion or segment
•Maximum Jerk: Motions with zero jerk at the start, may have a large maximum acceleration. The mechanical system strains more when the acceleration is increased.
•Crossover Jerk: The value of jerk as the acceleration changes sign from positive to negative, or vice versa. Low values of crossover jerk are beneficial for systems with backlash. Backlash typically traverses as and after the velocity reaches its maximum and begins to reduce. Motion-Laws with low crossover jerk values usually also have lower maximum velocity values. A low peak velocity means a reduced impact as the backlash completes its traverses.
•Steps in Jerk: For many of the Traditional Motion-Laws, jerk changes instantaneously from zero to some finite value immediately after the motion segment starts. Steps in jerk induce vibrations in the mechanical system being driven. Other motions start and end with infinite jerk, which is an even worse.
•Infinite Jerk: Motion-Laws that have a step in acceleration also have infinite jerk-values at the acceleration step. We have already stated that acceleration continuity is important.