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Only that part of the viscous damping force that is related to the change of velocity contributes to the reduction of vibration, and the relative change of velocity due to vibration, even in the in-motion period, is quite small. A constant friction is often present in the form of friction in bearings, slide-ways etc. This force, however, has no damping effect at all unless there is a change direction. That is, a reversal of the direction of motion. Such reversals do not take place until the vibration velocity exceeds the nominal follower velocity, that is during and just before the dwell period.

This form of damping is very effective in dissipating residual vibration, except in very high speed applications, but does not affect the majority of in-motion vibrations at all. If it is important in a particular application to eliminate vibration then the deliberate introduction of constant friction damping may be justified.

However, it has the drawback that the follower can come to rest slightly out of position in the dwell period, where it is being held by the friction force in a strained condition, either under-shooting or over-shooting its target. Using the equation of Torsion-Factor, with the associated table of parameters for each motion-law, we can plot:. We can use the plot to see which motion-laws is best based on Period-Ratio. The comparison is only valid where there is good input transmission and the peak load is mainly an inertia load.

In these circumstance it can be seen that the. However, Mod-Sine is by far the most useful of the three cam laws because, although it produces a slightly higher peak load than Mod-Trap , it is also very much more tolerant to an elastic input transmission [low Period Ratio].

The transmission systems of most industrial cams are such as to benefit from the use of the Mod-Sine cam law in preference to the Mod-Trap. Nevertheless, there is a positive advantage to use the Cycloidal for systems with a low Period-Ratio. It is recommended that Mod-Sine be the first choice for Period-Ratios above 6. The total backlash in a cam mechanism is the sum of all clearances, play or slack in the input and output transmissions adjusted, if necessary, by gearing ratios , and in the cam track and cam follower.

Typical examples are: slack chain drives, gear tooth clearances, oversize enclosed cam-tracks and worn follower roller bearings.

Mechanical Vibrations Research Papers -

There are many others. Any backlash, between the cam and follower or between any two force-transmitting components in the cam system gives rise to a shock load when there is a reversal of force or torque. Backlash can be often be eliminated by applying sufficient external force with a spring or the payload weight, or even a friction force, to ensure that there is not a force reversal at the operating speed. Spring loaded, open cam track cam systems are quite common, but to be fully effective in eliminating backlash the spring must be applied not just to the follower but at a point in the output transmission that closes ALL of the significant clearances.

This is illustrated in the image. When the direction of force reverses, typically at the cross-over in high inertia applications, there is a moment when the payload is in free-flight after losing contact with the 'positive force surface' and before making contact with the 'negative force surface'.

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The magnitude of the force in making contact - the impact force - is related to the impact velocity of the contact surfaces. This, in turn, is related to the values of cam acceleration and jerk at this point in the motion. The process can be seen in the simplified and exaggerated image. All of the cumulative backlash in system is represented by the separation of the two cam profiles and the payload is represented at a concentrated point running along the profiles.

The lower profile can only exert a positive contact force on the payload and the upper profile only a negative force. It is assumed for the purpose of this description that dynamic response vibration and any other detrimental effects are not significant compared with the impact force. The payload departs from the lower profile when its contact force becomes zero: this is when the inertia force due to the profile deceleration is about to exceed any other retarding force on the payload, such as friction, gravity.

From this point on, the payload takes a free-flight path with a natural deceleration which is determined by external forces - such as friction - until it makes contact with the upper profile. It strikes the profile with an impact velocity - which is the difference between the free-flight velocity and the profile velocity. The free-flight is now a little slower that at the point of departure due to its deceleration , and the profile velocity is even slower because the impact point is a little further along the profile past the point of maximum profile velocity.

It is obvious from the image that the cam follower separates and impacts in the deceleration phase of the motion and are separated by a time and distance very much dependent on the amount of backlash. How far into the declaration phase that these events occur is dependent on the magnitude of the external force in relation to the payload inertia force. In practice, the possible range of impact positions is fairly wide and occurs just after the nominal cross-over point of the motion.

To minimize the backlash impact force, it is necessary to have a motion-law with a low value of acceleration for a long period near the middle of the motion. In general, this condition is fulfilled by motions that have a low jerk at cross-over. The best 'low-impact' Traditional Motion-Law is Simple Harmonic , but special low impact motion-laws have been developed which improve on this.

Mechanical Design (Part 6: Cam Terminology)

It is difficult to quantify the impact effect of backlash in all circumstances, but an attempt is made here to indicate its importance in certain cases. To take account of various sizes, speeds and loads of all kinds of cam mechanisms it is convenient to normalize the variables on the same basis as:. The natural deceleration of the payload in free-flight can vary between zero at cross-over and the maximum deceleration of the motion-law: a higher deceleration would maintain contact with the positive force cam surface!

Mechanical Vibrations

The higher the natural deceleration, the lower the impact velocity. For any cam-law, a graph can be constructed to show how the normalized impact velocity varies with backlash and natural deceleration. All the motion-laws have similar impact velocities when the natural deceleration is zero and the backlash is large. The are considerable differences in impact velocities between motion-laws when the natural deceleration is medium to high.

The motion-laws with zero jerk at cross-over Simple-Harmonic and Mod-Sine are better than the others at low values of backlash - the sort of backlash values likely to occur in practice. For very high speed mechanisms, the value of the normalized natural deceleration must be low, because it is proportional to the square of the motion period, T. Also, the backlash is in practice kept to a minimum by precision manufacture.

A shock vibration is set up on impact, the amplitude of which depends on the impact velocity and the natural frequency of the system. We have already seen that natural frequency, f , can be calculated from the rigidity and stiffness of the system and the payload mass or inertia. The impact force or torque at the cam to follower contact point is given by :. In summary, the best way to minimize the detrimental effects of dynamic response is to :.

Mail This. The Spring expands until it matches its original length and the Payload's displacement is equal to the Cam-Follower displacement. As the spring continues to expand, the Payload's velocity decreases, relative to that of the Cam-Follower, until their velocities are the same. The widespread adoption of digital cameras to take the place of film cameras has also triggered a major turning point in the optical design of all-in-one zoom lenses.

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Consequences of their design

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There are two main types of chromatic aberration. We can also classify cams by the different types of motion events of the follower and by means of a great variety of the motion characteristics of the cam profile. Chen 82 Figure Classification of cam mechanisms 4.

Figure a,b,c,d,e Rotating follower Figure f : The follower arm swings or oscillates in a circular arc with respect to the follower pivot. Translating cam-translating follower Figure Stationary cam-rotating follower: The follower system revolves with respect to the center line of the vertical shaft. Figure Translating cam - translating follower 6. Offset follower: The center line of the follower does not pass through the center line of the cam shaft. The amount of offset is the distance between these two center lines. The offset causes a reduction of the side thrust present in the roller follower.

A translating or a swing arm follower must be constrained to maintain contact with the cam profile. Grooved cam or closed cam Figure : This is a plate cam with the follower riding in a groove in the face of the cam. Figure Grooved cam Cylindrical cam or barrel cam Figure a : The roller follower operates in a groove cut on the periphery of a cylinder. The follower may translate or oscillate.

If the cylindrical surface is replaced by a conical one, a conical cam results. End cam Figure b : This cam has a rotating portion of a cylinder. The follower translates or oscillates, whereas the cam usually rotates.

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The end cam is rarely used because of the cost and the difficulty in cutting its contour. Figure Cylindrical cam and end cam 6. Spring constraint: The spring must be properly designed to maintain contact. Positive mechanical constraint: A groove maintains positive action. Figure and Figure a For the cam in Figure , the follower has two rollers, separated by a fixed distance, which act as the constraint; the mating cam in such an arrangement is often called a constant-diameter cam.

Figure Constant diameter cam A mechanical constraint cam also be introduced by employing a dual or conjugate cam in arrangement similar to what shown in Figure Each cam has its own roller, but the rollers are mounted on the same reciprocating or oscillating follower. Figure Dual cam 6. If you turn the cam, the follower will move.

The weight of the follower keeps them in contact. This is called a gravity constraint cam. Notice that a roller is used at the end of the follower. In addition, a spring is used to maintain the contact of the cam and the roller. If you try to calculate the degrees of freedom DOF of the mechanism, you must imagine that the roller is welded onto the follower because turning the roller does not influence the motion of the follower.

It is used to generate the pitch curve. In the case of a roller follower , the trace point is at the center of the roller. Pitch curve : The path generated by the trace point at the follower is rotated about a stationary cam. Working curve : The working surface of a cam in contact with the follower.

Consequences of their design

For the knife-edge follower of the plate cam, the pitch curve and the working curves coincide. In a close or grooved cam there is an inner profile and an outer working curve. Pitch circle : A circle from the cam center through the pitch point. The pitch circle radius is used to calculate a cam of minimum size for a given pressure angle.

Prime circle reference circle : The smallest circle from the cam center through the pitch curve. Base circle : The smallest circle from the cam center through the cam profile curve. Stroke or throw :The greatest distance or angle through which the follower moves or rotates. Follower displacement : The position of the follower from a specific zero or rest position usually its the position when the f ollower contacts with the base circle of the cam in relation to time or the rotary angle of the cam.