INTERNAL GENEVA MECHANISM

MODELLING AND SIMULATION OF INTERNAL GENEVA MECHANISM

CONTENTS:

1. AIM
2. INTRODUCTION
3. CREATING THE 3D CAD MODEL OF INTERNAL GENEVA MACHANISM
4. MOTION STUDY 1 [10RPM WITHOUT PRECISE CONTACT]
5. MOTION STUDY 2 [20RPM WITHOUT PRECISE CONTACT]
6. MOTION STUDY 3 [10RPM WITH PRECISE CONTACT & 60 FPS]
7. MOTION STUDY 4 [20RPM WITH PRECISE CONTACT & 120 FPS]
8. ERROR CORRECTION
9. CONCLUSIONS & FUTURE SCOPE

AIM:

1. To create a 3D CAD Model (parts & assembly) of the Internal Geneva Mechanism.
2. To perform Motion Analysis by rotating the driver wheel at a constant speed of 10rpm and 20rpm and thereby plotting the following results:
   1. Contact force (between driving and the driven wheel) as a function of time.
   2. Angular displacement of the driven wheel.
   3. Angular velocity of the driving wheel.
3. Comparing the contact forces with and without Precise Contact.

INTRODUCTION:

Mechanism is a combination of the number of rigid or restraining bodies assembled in such a way that a predictable or a constrained motion is obtained. Thus, the basic function of a mechanism is to transmit and modify a motion.

Geneva or sometimes known as Maltese Cross is one such mechanism which converts the continuous rotary motion into an intermittent rotary motion. There are majorly two important components which governs this transformation of motion known as the driving wheel and the driven wheel. These are basically the parts that we have modelled and assembled further in this project but first let’s take a look on how this mechanism actually works.

The torque is provided to the driving wheel by the means of motor attached to it. As the driving wheel rotates, the pin reaches into a slot of the driven wheel advancing it by one step. It could be more clearly understood by watching the following two types of the Geneva mechanism.

External Geneva Mechanism:	Internal Geneva Mechanism:

There are also various other forms of Geneva mechanisms, but it is sufficient for this context.

Geneva is sometimes also referred to as a timing device since its use in mechanical watches to limit the tension of the spring, such that it would operate only in the range where its elastic force is nearly linear. Indexing tables in assembly lines, tool changers for CNC machines, pen change mechanism in plotters, automated sampling devices, modern film projectors, etc. are some other major application of this mechanism.

What is the motion study?

Motion study is the graphical simulation of motion for assembly models. Here, by motion study we are generally referring to a motion analysing in the SOLIDWORKS. Motion analysis is used for accurately simulating and analyzing the effects of motion elements (including forces, springs, dampers, and friction) on an assembly. It uses computationally strong kinematic solvers, and accounts for material properties as well as mass and inertia in the computations. We will use motion analysis to plot simulation results for further analysis. So, let’s just start from the first step.

CREATING THE 3D CAD MODEL OF INTERNAL GENEVA MACHANISM:

The DESIGN Process

Step 1: Sketches for the driving wheel and the driven wheel

Note that I have created the driving wheel profile on the driven wheel profile so that I can obtain the proper distance from the centre axis of the driving wheel to the driven wheel. This was done so that the proper mating alignments can be given to the resulting assembly from these parts. To achieve this, the Measure tool from the Evaluate tab of the SOLIDWORKS is used. It gives us the following results:

The centre distance between the two wheel is 226.21mm and,
The perpendicular distance below and to the right of the centre of the driving wheel is 159.96mm.

Also, to make an important note, our unit system must be changed to MMGS since most of our dimensions will be given in millimetres.

Step 2: Using the Extruded Boss command to obtain the following parts:

1_Driving_Wheel.sldprt

2_Driven_Wheel.sldprt

The ASSEMBLY

Step 4: Creating an Assembly:

Final_Assembly.sldasm

The mates are as follows:

Coincident1:
Front plane of driving wheel is coincident with the front plane of the assembly.

Note that the first part inserted in the assembly is always fixed. Therefore, it should be made float for giving such mates or for the required motion of the fixed parts.

Coincident2, Coincident3:
Centre axis of driving wheel is coincident with top and the right plane of the assembly respectively.

Coincident4:
Front plane of the driven wheel is coincident with the front plane of the assembly.

Note that my sketched were extruded blind on the opposite sides of the front plane for the driver and the driving wheel thereby no need to give the distance mate here.

Distance1, Distance2:
Centre axis of the driven wheel is 159.96mm below the top plane and 159.96mm to the right of the right plane of the assembly respectively.

Note that these distances were obtained using the measure tool from the sketch as described previously.

MOTION STUDY 1

[10rpm, without precision contact]

Establishing the Study:

To establish a motion analysis in SOLIDWORKS, it is important to note that the SOLIDWORKS Motion, in the Add-Ins tab of the SOLIDWORKS is enabled. If the Add-Ins tab is not visible on the screen, It can be made visible by right-clicking any of the tabs. The same goes with hiding and making any of the other tabs visible as per the convenience.

Step 1: Setting up the Motor at a constant speed of 10rpm

Step 2: Setting up the Contacts: The selected faces are shown below and the material used for both the wheels is Steel (Dry).

Step 3: Adjusting the time for the motion analysis, Calculate and Run:

This adjustment to time is the one parameter which lets us decide how long the analysis is to be performed. This can be achieved by dragging the end key of the Final_Assembly to the desired time on the timeline. It can be done, redone as per the no. of rotations you want, or the no. of times the pin enters and exits the slot, or as per any other subjects. Once done, just hit the Calculate button and the Motion Analysis has successfully run.

Now we are ready to plot the results we want.

Note that the SOLIDWORKS Motion must remain enabled during this whole process.

Plot 1: Contact force between driving and the driven wheel:

Click on the 'Results and Plots' button. Here is where we can choose from the number of categories to plot out the results we want. This can be the contact forces as we are calculating so that we know the strength the material requires for the functionality. Also, the values from the results can be used to perform the structural analysis and more.

The results from this plot are as follows:

Here we can see, that the contact force arises as the pin enters the slot. Just at the entrance there is hinderance clearly visible from the contact forces around 7.2 seconds and 19.2 seconds. The contact force between the driving wheel and the driven wheel is maximum when the pin enters the slot for the fourth time i.e., around 19.20 seconds from when the analysis is run. Its magnitude is 836 N and so the driving wheel material and the pin material must bear this amount of force to successfully function.

Also see the force after 4.8 seconds in the plot, it clearly tells us that the force is higher wen the pin is at the verge of exit. Thus, without the hindrance at the entrance of the slot our graph must have been a series of symmetric parabolas as seen between 13 seconds to 17 seconds.

A few milliseconds after the start and between 4.8 to 7.2 seconds the portion shows us 0 reaction force. This tells us that the pin is not in contact with the slot.

Plot 2: Angular displacement of the driven wheel:

This is plotted against the time for which our analysis will be run. It shows when the driven wheel rotates and by how much angles. It also will tell us the time for which there is no angular displacement of the driven wheel i.e., it is stationary. The setup is as follows:

The results from this plot are as follows:

It can be seen that the driven wheel starts to rotate at 1 second after the analysis is run and continues to rotate till 4.8 seconds. here the angular displacement is 90 degrees in the clockwise direction. To specify that this rotation is measured in clockwise direction from the horizontal, SOLIDWORKS specifies the portion on the negative y-axis of the plot.

The driven wheel almost remains stationary from 4.8 to 7.2 seconds and then further starts to rotate after 7.2 seconds down till around 11 seconds. Here the angular displacement of the driven wheel is 180 degrees and this can be specified both as +180 and -180 as measuring the angle in both clockwise and anticlockwise direction will give us the same position of the driving wheel.

Thus, this continuous graph from 0 to -90 to -180 to -270 (i.e., +90) to -360 (i.e., +0) degrees continue to plot for the time the analysis is run.

Plot 3: Angular velocity of the driving wheel:

We have also created an extra plot which shows us the angular velocity of the driving wheel. Since in this case the driving wheel was given a constant speed of 10rpm, by calculations, the angular velocity will also remain constant with an about the value of 60 degrees/second. This calculation can be depicted as follows:

10rpm = 10 revolutions/minute
10 revolutions = 1 minute = 60 seconds
360 x 10 degrees = 60 seconds

Angular Velocity = degrees/seconds
Therefore,
Angular Velocity = (360x 10)/60 = 60 degrees/seconds.

All the three plots of Motion Study 1 together are as shown below:

Plot13: Angular velocity of driven wheel:

To have a clearer understanding of what angular velocity means, we have plotted the angular velocity of driving wheel on the angular velocity of driven wheel. This results in the following plot.

Here it can be clearly seen how the angular velocity of the driven wheel shown in blue traces its path while the angular velocity of the driving wheel remains constant at a value of 60 degrees/seconds.

The maximum angular velocity of the driven wheel is 25 degrees/second and the angular velocity remains almost 0 for when the pin is not in contact with the slot, thereby resulting in a stationary motion of the driven wheel. A smoothly run mechanism should have only the symmetric parabolas shown in the graphs, however the extra lines are the results of hinderances or rough entrance of the pin into the slots.

All the above three plots excluding the one in which I compared the angular velocities of the driving and the driven wheels have been exported in the Excel files. These are as shown below:

Note that these plots have already been explained above.

MOTION STUDY 2

[20rpm, without precision contact]

Establishing the Study:

To create a new Motion Study, right-click on the 'Motion Study 1' tab on the SOLIDWORKS and select 'Create New Motion Study'. This study can be established by following the same procedure as in Motion Study 1 except for giving the Motor a constant speed value of 20rpm.

Another simple method to establish this study can be selecting 'Copy Study' by right-clicking on the Motion Study 1 and then make the following changes:

1. Right-click on 'RotaryMotor2' in the Motion Study 2 and select 'Edit Feature'.
2. Change the constant speed value of the motor to 20rpm and save.

Note that it is important to re calculate the copied study so that the results get updated. This method is more efficient for simple changes in the studies which require to plot the same results.

So now let's directly have the view on the results and plots of Motion Study 2. These are as follows:

Plot 4: Contact force between driving and the driven wheel:

Note that this is named as Plot 4 and not as Plot 1 as the name Plot 1 has already been used in the Motion Study 1. We can also change the name of the plots as per our convenience but the important thing to note is that the names must not repeat itself. Although this is the first plot in this study, we'll leave it as Plot 4 and name the same in this report for the better understanding.

The results of this plot are as follows:

It can be seen that there is an increase in the reaction force as compared with the Plot 1. The maximum reaction force in this study results 3170 N. while that in Study 1 was 836 N. Thus, we can say that Increase in the velocity of the driving wheel leads to increase in the reaction forces. Thus, our mechanism must have an economical speed that serves us the purpose in the given time. Other conclusions are as same in the Study 1 except for the increased values of the reaction forces.

Plot 5: Angular displacement of the driven wheel:

Comparing with Study 1 it can be seen that the angular displacement is achieved faster and the driving wheel undergoes the rotation for two times whereas that in case of Study 1, the driving wheel completed only one rotation in 24 seconds.

Plot 6: Angular velocity of the driving wheel:

Here too we have plotted the results for angular velocity of the driving wheel. this calculation with minor changes as done previously can be shown as follows:

20rpm = 20 revolutions/minute
20 revolutions = 1 minute = 60 seconds
360 x 20 degrees = 60 seconds

Angular Velocity = degrees/seconds
Therefore,
Angular Velocity = (360x 20)/60 = 120 degrees/seconds.

This can be seen in the following image showing all the three plots of the Motion Study 2.

Similar to the Study 1 all the above plots of Study 2 have been exported in the Excel files. These are as shown below:

Note that these plots have been already explained above.

MOTION STUDY 3

[10rpm, with precision contact and 60fps]

Establishing the study:

Copy the Motion Study 1 and click on the 'Motion Study Properties' in this new study (i.e., the Motion Study 3).

Change the 'Frames per second' to 60 and tick mark the 'Use Precise Contact'. This can be seen in the following image.

Note that it is important to re-Calculate the Study after its creation so as the results get updated. Now we are ready to analyse our plots.

Plot 7: Contact force between driving and the driven wheel:

For the same analysis as in Study 1 it can be seen here that without changing the speed of the driving wheel, the results for the contact forces between the driving and the driver wheel is more. This is due to the fact that the Precise contacts have been enabled and which gives us the more accurate results than the one acieved without the precise contacts.

Thus, we can say that the maximum contact force between the driving wheel and the driven wheel is about 4000 N for the first 24 seconds of the rotation at 10rpm.

Plot 8: Angular displacement of the driven wheel:

The results in this plot are same as that in the Motion Study 1 and so we can see that even the plots are also almost same as shown below.

Plot 9: Angular velocity of the driving wheel:

Just like in the previous Motion Studies here too we obtain the angular velocity of the driving wheel. It can be seen that this result is same as that plotted in the Motion Study 1. All the plots of this study (Motion Study 3) are as shown below.

The spreadsheet files exported for this study are as follows:

Note that these plots have already been explained above.

MOTION STUDY 4

[20rpm, with precision contact and 120fps]

Establishing the study:

Copy the Motion Study 2 and click on the 'Motion Study Properties' in this new study (i.e., the Motion Study 4).

Change the 'Frames per second' to 120 and tick mark the 'Use Precise Contact'. This can be seen in the following image.

Note that it is important to re-Calculate the Study after its creation so as the results get updated. Now we are ready to analyse our plots.

Plot 10: Contact force between driving and the driven wheel:

We can see that the maximum contact force between the driving wheel and the driven wheel is about 6700 N for the first 24 seconds of the rotation at 20rpm.

Plot 11: Angular displacement of the driven wheel:

The results in this plot are same as that in the Motion Study 2 and so we can see that even the plots are also almost same as shown below.

Plot 12: Angular velocity of the driving wheel:

Just like in the previous Motion Studies here too we obtain the angular velocity of the driving wheel. It can be seen that this result is same as that plotted in the Motion Study 2. All the plots of this study (Motion Study 4) are as shown below.

The spreadsheet files exported for this study are as follows:

Note that these plots have already been explained above.

ERROR CORRECTION

Instead of plotting the Angular velocity of Driven Wheel, the Angular Velocity of Driving Wheel was plotted. So as to make the correction we add the following required plots here.

Plot 13: Angular velocity of Driven Wheel in Motion Study 1:

The maximum angular velocity of the driven wheel in Motion Study 1 is 25 degrees/second.

Plot 14: Angular velocity of Driven Wheel in Motion Study 2:

The maximum angular velocity of the driven wheel in Motion Study 2 is 50 degrees/second.

Plot 15: Angular velocity of Driven Wheel in Motion Study 3:

The maximum angular velocity of the driven wheel in Motion Study 3 is 25 degrees/second. But, the plot shows the result as 32 degrees/second due to the jerk the driven wheel experiences while the pin enters the slot.

Plot 16: Angular velocity of Driven Wheel in Motion Study 4:

The maximum angular velocity of the driven wheel in Motion Study 4 is 50 degrees/second. But, the plot shows the result as 57 degrees/second due to the jerk the driven wheel experiences while the pin enters the slot.

The spreadsheet files for these error corrected plots are as follows:

Note that the precise contact give us a more smoother curve in the plot as seen by comparing the results of plot 13 and 14 with plots 15 and 16.

CONCLUSIONS & FUTURE SCOPE

From the above Motion Analysis though we have explained each and every plot, we can give some generalised statements here.

1. Both the 'rection forces between the wheels' and the 'angular velocity of the driven wheel' increases as the speed of the driving wheel increases.
2. The angular velocity of driving wheel remains constant while that of driven wheel varies continuously.
3. The maximum angular velocity of the driven wheel is less than that of the driver wheel due to larger diameter of the driven wheel.
4. The driven wheel experience jerk when the pin first comes in contact with the slot.
5. The angular displacement of driven wheel can be an obvious plot to inspect the rotation and the time for which the driven wheel remains constant.
6. Precise contact gives analytically more correct results.

Apart from performing a basic motion analysis in SOLIDWORKS, this project also enabled us to learn these following skills:

1. Creating Sketches
2. Creating Basic 3D CAD Parts
3. Assembling the Parts
4. And finally, Performing the Motion Analysis on the Assemblies and plotting out important results.

The future scope for this project can be as follows:

1. Making necessary changes in the CAD models of the driving and the driven wheel so that there are no hinderances in the motion especially that jerk the pin experiences when it enters the various slots on the driven wheel.
2. Application of this simple mechanism to more complex and new systems such as film frames, auto-roll punching machines, conveyors using geneva mechanism, etc.

Cited under: MBD