About RRG CamMotion

Using RRG CamMotion

Step 1. Specifying motion program parameters

Step 2. Interacting with the motion program

Step 3. Dynamics

Step 4. Results

Motion Curve Criteria - Explanation

Dynamic Criteria - Explanation

Guidelines for Motion Programming and System Design

About RRG CamMotion: RRG CamMotion is an interactive trapezoidal motion specification program for one degree of freedom systems. It provides the user with the ability to visualize the effects of variation of trapezium breakpoints in the overall motion program and the various design criteria. This software also provides a dynamic analysis of the 1 Dof system.

Using RRG CamMotion: This software is used in three steps. First, the user specifies the various parameters for motion the motion program. The software then performs the necessary calculations and integrations and plots the motion program. Secondly, the user can alter the motion program by clicking and dragging on the trapezium vertices in the plot. While this is done the program automatically recalculates the motion program and the criteria values and displays it, thereby enabling the user to visualize the effects of the change. Third, the user can go the dynamics section, where it calculates the dynamic criteria values based on the system parameters specified by the user.

The following parameters are to be specified:

1. Motion Type: This is a radio button where the user has to indicate whether the motion program is to be trapezoidal or detached trapezoidal. In trapezoidal specification, the last vertex of one trapezium will be the beginning vertex of next and so that vertex need not be specified. The following picture explains the difference.



 

2. Specified Derivative: This is the derivative at which the trapezoidal motion specification is made. For example, if the user wants the acceleration profile to be trapezoidal, then enter 2 in this column. The shock number ‘p’ is this number plus one. So if the trapezoidal spec is made for acceleration, then this is shock level 3 curve (p=3).
3. BreakPoints: Breakpoints are the theta values (or x values in the plot) corresponding to the trapezium vertices. The number of breakpoints required to be specified depends on the Specified Derivative and Motion Type. The number of breakpoints entered and the total number of them required will be displayed by the information box below. The white edit box is where the breakpoints are to be entered. They are to be entered in the increasing order from theta0 to thetaN. After entering each value, press the button. This button acts as an enter key and registers the value into the program. To view or edit previously entered values, use the button. After the value has been edited, remember to press the button. Otherwise the change will not be registered. The breakpoint entry area looks like this: . As the breakpoints are entered, the information regarding the number of points and the actual breakpoints will be displayed in the information boxes below the buttons. The breakpoints will also be displayed on the plot simultaneously.
4. Initial Conditions: Here the initial conditions for the different derivatives are to be specified. These are the values of y, y’, y’’ …. when theta takes the initial value. The number of derivatives for which the initial conditions have to be entered depends on the Specified Derivative. So if Specified Derivative is 3, the 4 values need to be entered in the Initial Conditions box – corresponding to y(0), y’(0), y’’(0), y’’’(0). The way to enter these values are similar to how the breakpoints were entered – using the and buttons and the conditions should be entered in the increasing order, ie, y(0) first, y’(0) second, and so on. For simplicity, we use zero initial conditions for normal applications. So all the values are specified as zero. However, the software is general and will work even if non-zero initial conditions are specified.
5. Final Conditions: Here the final conditions for the different derivatives are to be specified. These are the values of y, y’, y’’ …. when theta takes the final value. In the normalized case, theta varies from 0 to 1 and so the values to be entered in this box are those of y(1), y’(1), y’’(1) and so on, in that order. Again, for simplicity, we generally specify y(1) = 1 and all other values to be zero. The user is not restricted to this choice though.

Once all the motion parameters are entered, click the "DrawGraph" button. The program will then do the calculations and plot the profile in all derivatives lower to the specified one. For example, if the trapezoidal specification was made for the acceleration profile, the program will plot acceleration, velocity and position curves. Simultaneously, the values of different design criteria are calculated and displayed along with the optimums, in the information boxes below the plot. The plot and the information boxes looks like the following:

There is also a legend window that shows which plot is what. This window can be displayed by clicking on the "Legend" button. The window looks like this:

Now, the user can interactively modify the trapezium breakpoints and see the effects of the change on the shape of the curves and the criteria values. The user’s aim in doing this exercise is to design a geometric profile, which matches some desired performance, in terms of the geometric criteria listed. The only parameter that can be changed is the trapezium breakpoints. For this, click on the plot at or near the breaks. The following message box appears:

Click OK and drag the breakpoint. When the cursor is released, the following message box appears:

Click OK and then if needed, the user can click on other breakpoints and continue varying the profile until the geometric performance is satisfactory.

This section deals with the dynamics part of motion programming. Here the user specifies the model parameters of the one degree of freedom system (a cam in this software), and the program calculates the various dynamics parameters like cyclic and transient distortion. It also plots the transient and cyclic distortion curves showing the difference between tuned and untuned system and the performance gain achieved by tuning the system. The following parameters have to be entered in the respective boxes: Mass of Cam in pounds (lb), Design Speed of Cam in rpm and Stiffness (Spring Constant) of the system in lb/inch. After entering these values, click on either "Cyclic Distorion" or "Transient Distortion" button to perform the calculations and plot the graphs. The results and comments box will give the comments on the dynamic analysis. The Dynamics window looks somewhat as follows:

The x-axis for these plots is the ratio w/wd, where w is the operating speed of the system and wd is the design speed. The red and blue plots are those for untuned and tuned systems. The horizontal green line shows the accuracy level at which the performance increase in speed is calculated. The vertical drops of the green line shows the w/wd ratio corresponding to the intersection of the tuned and untuned plots to the accuracy level. Clicking on the "Done" button will dismiss the Dynamics window and will save the necessary information to the program database.

There is a "Results" button in the main window. When this button is clicked, it will generate a text file summarizing the geometric and dynamic analysis. This text file can be viewed using any standard editor like NotePad and can be printed out for further use. After generating the text file, the user is given the option of generating a data file that contains the plot data. This data file would be handy if the user wants to export the plot information on to another program like for example, a synthesis program. The plots are listed in the order – theta(th), y(th), y’(th), y’’(th), etc upto the specified derivative.

There are five motion curve criteria that is used in this system. These represent a basic set of parameters that prove to be invaluable in the study of motion programs. The following is a brief description of their nature and the effect that they have on the output motion of a machine.

• Y' max: This is the maximum value of the pressure angle and is proportional to the pressure angle. An increase in the value of y'_max results in the increase of the horizontal component of the contact force, which increases the lateral deformation of the follower. This results in a higher distortion of the output. A higher value of y'_max also indicates an increase in the inertial energy of the system which then makes it difficult to control. Thus a higher value of y'_max is an indicator of reduced control of the system, higher wear and reduces precision due to force magnification within the structure.
• Y'' rms: The root mean square acceleration is a rough indicator of overall cam acceleration. The force on the follower system is given by My'' w_d^2 . A higher output force would result in more distortion. Thus, a reduced value of y'' rms would indicates a higher level of precision and a reduction on internal forces, resulting in reduced distortion.
• delta y'' : The peak-to-peak value of the acceleration curve is an indicator of the range of distortion as well as the magnitude of internal forces. Hence D y'' should be kept to a minimum.
• delta t : This is the peak-to-peak value of the driving torque curve. The torque at the prime mover is proportional to the input force and Fi/Fo = dy/dx . The output force F_out is equal to My''w_d^2 , and this implies that M w_d^2 y''y' = Ct (where C is the proportionality constant). The shape of y''y' gives an idea of the input torque characteristics. Thus delta t is an indication of the dynamic wind-up in the machine at the input shaft. It would be necessary to minimize the value of delta t during the design process.
• t' max : This is an indicator of the maximum rate of change in the driving torque and hence the sensitivity to cross-over shock of the driving force. It is a high priority to keep the value of this term low during motion programming as it would result in a less noisy device which is not very sensitive to wear.

Shock Level: Shock level is the term used to indicate at which derivative of the motion program, does a shock (or an impulse as you might say) occur. For example, if you have a trapezoidal profile in velocity, the acceleration will have a shock and so shock level is 2.

The dynamic response of a system essentially deals with the distortion introduced by a motion program. This occurs due to the following reasons:

1. An operating speed w distinct from the design speed w _d.
2. An actual mass m and spring constant k, giving a natural frequency w _n' , distinct from the modeled natural frequency wn for the one degree of freedom system.

Distortions are induced by shocks and shocks are implicit in systems where there is a change in system parameters such as the change in the position of the mass. The dynamic criteria used in this software are mainly two - cyclic distortion and transient distortion. The ratio of design speed to natural speed is also an important criterion that gives a good idea about the nature of the system.

• Cyclic Distortion: This is the distortion caused by the inertial forces in the system. This is given by the ratio of input force to the stiff ness of the system. Thus the distortion is given by d_u = Fi/K = (M/K) wd^2 y''. This gives the cyclic distortion in the untuned case. For a tuned system this becomes, d_t = [ (w/wn') ^2 - (wd/wn)^2 ] * y''. Thus, if the modeling is accurate, (ie, wn' = wn ), then the distortion would vanish to zero when the operating speed equals the design speed.
• Transient Distortion: Distortion occurs as a transient response of the system to a shock. The total transient distortion (A) is the summation of all such responses in all modes. Thus the final output motion is the summed up result of transient distortion, cyclic distortion and the input motion. The following equations give the value of transient distortion.

Tuned: A_T = Cpp! [(wnw/wn'w_d)^2 - 1 ][(wnw/wn 'w_d)^p-2][(w_d/wn)]^p

Untuned: A_U = Cpp![w/wn]^p

Tuning: Tuning essentially means, generating an input motion curve based on the full synthesis equations. For an untuned system, we assume that the input motion to be supplied to the system (for example, a cam profile), is exactly the same as the output. This simplifies the system considerably, but the assumption is true only in the case when operating speed is zero. Since the system contains mass and a finite stiffness, distortions are bound to occur. Tuning is the process of generating the input curve in such a way that at design speed these distortions can be tuned out. In this case the input curve is generated using the full synthesis equation given by s = (1/K) [ Mw_d^2 y'' + Cw_dy' + (K +Kr)y ].

Here are certain guidelines that could be useful for the motion programming and system design of one degree of freedom precision machines.

• The ratio of design speed to natural speed (w _d/w _n) gives an idea of how much care should be given towards system design motion programming and manufacturing of the system. A large value of this ratio, like 0.01 would demand extreme care in design, while a small value of the ratio, like 0.001 would give more flexibility in design, programming and manufacturing.
• The ratio R of cyclic to transient distortion should have a value greater than 10. The greater this value is, the better the performance is. Both cyclic distortion and transient distortion should be as low as possible by themselves, but transient distortion is more undesirable than cyclic distortion and hence the ratio should be high.
• Motion Curve Criteria: The five motion curve criteria, namely, y’_max, y’’_rms, delta_y’’, delta_tau, and tau’_max, should all be minimized for normalized curves. These have optimum values corresponding to a normalized system for each shock level. The values of the current motion curve should be as close to the optimum values as possible.
• Shock Level P: Higher P values require much greater care in manufacturing. This increased manufacturing costs is only warranted if wd/wn > 0.01
• Synthesis: Synthesize the motion program (y, y’, y’’, y’’’ -> s ) with full synthesis and tuning equations. The benefits are 4 to 5 times less distortion at 10% overspeed or an expected 40% increase in speed of operation for the same level of distortion.