Matthew Chung Phys 420 Term Project: Van De Graaff Generator

Note on formatting of equations: I experienced some issues with uploading equations to this web page, so I have had to use bolded text to represent vector quantities and I have underlined symbols that represent unit vectors ( a unit vector is a vector with a length of 1 and is generally used to indicate the direction of a physical quantity).

 

PDF version: You can find a pdf version of this web page here if you have trouble seeing the images on the web page.

 

Background: Electrostatics

When two charged particles meet each other, they exert forces on one another due to something called an electric field. All charged objects produce electric fields, which are alterations in the space around them that cause other charged particles to experience forces. The strength of the electric field produced by a charged object is proportional to the object’s charge and inversely proportional to the square of the distance from the object to the measurement. More specifically, the electric field strength exerted by a charged object on a point in space is given by:

 

E = (kq/r²)r

 

·      r is the distance from the object to the point

·      q is the charge of the object

·      k is Coulomb’s constant, given by: k = 8.99 x 10⁹ Nm²/C²

 

The force exerted by a charged object A on a second charged object B is given by:

 

F_e = QE = (kqQ/r²)r

 

·      r, q and k are defined as above

·      Q is the charge on object B.

 

F_e and E  are both vector quantities. The electric force is a central force, so F_e and E point along the direction of r. In other words, F_e and E point radially outwards or inwards. The direction of the electric field strength at a point is the direction a positive test charge would move if placed at that point.

 

Van De Graaff generators are machines that us built up charges to ionize air. A Van De Graaff generator is topped with a metal sphere that stores electric charge. Eventually, enough charge builds up on the sphere that the force it exerts pulls electrons off of air molecules. This is called ionization because it leaves charged ions behind. The charges in the generator are attracted to these ions and will leave the sphere and move towards the ionized air due to this attractive force. This process is called discharging and creates the sparks characteristic of a Van De Graaff generator.

 

Background: Van De Graaff Generators

The triboelectric effect is the process through which two electrically neutral materials become charged when brought in contact with each other and then separated. The triboelectric series is a list of materials ordered by their ability to acquire a negative or positive charge through triboelectrification. This is a list that has been created through empirical measurements of materials, and the properties that determine a material’s place on this list are not yet well understood. The triboelectric effect is the theoretical basis for the Van De Graaff generator.

 

Figure 1: The triboelectric series orders materials by their ability to acquire negative or positive charge through triboelectrification

 

A Van De Graaff generator has a supporting column made of an insulating material that supports two rollers, one near the base of the column and one at the top of the column inside a metal sphere. There is a rubber belt that is wrapped around both rollers. The bottom roller is attached to a motor that rotates it, which in turn rotates the belt and the top roller. The rollers are made of materials on opposite ends of the triboelectric series, and there is a belt that wraps around both rollers. The belt must be made of a material whose position on the triboelectric series is between the positions of the materials of the two rollers so that it can transfer one charge to the bottom roller and then transfer the opposite charge to the top roller. The contact between the bottom roller and the belt transfers a negative charge to the bottom roller and a positive charge to the surface of the belt, and the contact between the top roller and the belt transfers a positive charge to the top roller and neutralizes the surface of the belt.

 

Another key component of a Van De Graaff generator is that it has metal brushes near the two rollers. The brush at the bottom of the generator is placed so that the points of the bristles are nearly touching the belt by the roller. The negative charge on the roller ionizes the air between the roller and the brush, and the delocalized electrons are repelled from the belt. They then flow through the bristles on the brush to the wire grounding the brush and through the wire to ground. This flow of electrons to ground is maintained by the electrostatic repulsion between electrons. The bottom brush on a Van De Graaff generator acts as an electron sink via the flow of electrons through the bottom brush to ground. When the belt passes over the top roller, there is a second metal brush that acts as a source of electrons to neutralize the charge on the belt by the same process that gives it a positive charge when it passes over the bottom roller. However, the top brush is not grounded but rather is connected to a metal sphere at the top of the supporting column, which is the final component of a Van De Graaff generator.

 

The purpose of the metal sphere is to store the charge that builds up on the top roller. The top brush acts as an electron source by pulling electrons from the metal sphere it is connected to. This causes a buildup of positive charge on the metal sphere, and since electrical charges will disperse themselves evenly across as large a surface area as possible, they will disperse themselves across the surface of the metal sphere. The metal sphere has a much larger area than the top roller, so the sphere allows much more charge to build up. The maximum charge that can be stored by a Van De Graaff generator is determined by the area of the sphere because there is a maximum charge density that can build up on the surface of the sphere before it begins discharging to the surrounding air.

 

While this is not necessary for proper function, a Van De Graaff generator should have a grounding rod for safety purposes. This is usually a smaller metal sphere connected to ground via a wire. The purpose of the grounding rod is to give you a safe way to discharge the generator at any time so that you don’t run the risk of shocking anyone by accident.

 

Figure 2: Labelled diagram of a Van De Graaff Generator

 

Background: Formation of Lightning

Cumulonimbus clouds contain pieces of soft hail called graupel as well as small ice crystals. When pieces of graupel collide with ice crystals, electrons are transferred to the graupel to give the graupel a negative charge and the ice crystals a positive charge. Since the ice crystals in a cloud are much lighter than the graupel, they rise to the upper regions of the cloud in updrafts, whereas the graupel collects in the lower regions. Over time, this process of charge transfer in individual collisions followed by the separation of ice crystals from graupel creates large areas of net positive charge in the upper regions of a cloud and net negative charge in the lower regions (while the entire cloud remains overall electrically neutral).

 

Figure 3: Charged regions in a cloud that form due to separation of ice crystals and graupel

Lightning strikes can occur within a cloud (intra-cloud lightning), between two clouds (inter-cloud lightning), from a cloud to the surrounding air (cloud-to-air lightning), and between a cloud and the ground (cloud-to-ground lightning). I will focus on the latter. A cloud-to-ground lightning strike occurs when the charge in the upper or lower region of a cloud builds up enough that it discharges through the air to the ground. Discharge happens when the air around the charged region of a cloud is ionized due to the strength of the electric field created by the charged region, and the delocalized electrons in the air flow towards or away from the charged region (towards it if it is a positively charged region and away from it if it is a negatively charged region). The cloud then begins to discharge into the oppositely charged region of air that is formed by the ionization.

Figure 4: Diagram illustrating intra-cloud, inter-cloud and cloud-to-ground lightning

If there is enough built up charge, the process of ionizing air and discharging into the region of ionized air continues until the region of discharge is close enough to the ground to connect to air that is discharging upwards from the ground due to the charged region of the ground induced by the discharge from the cloud. Since the lower region of a cloud is closer to the ground, cloud-to-ground lightning strikes generally involve negative charges discharging to the ground, but the opposite is also possible. It is also possible for a lightning strike to be initiated by the ground, but this is much less common. Lightning strikes initiated from the ground occur when there is an elevated peak such as a mountain or a skyscraper where charge can build up due to electrical attraction to a charged region in a cloud.

 

 

Project Construction

I used these instructions that I found online as a basis for creating my Van De Graaff generator. I used CAD software to design each piece of the generator, then I built the generator in the UBC Engineering Physics lab. The process went fairly smoothly, but the two areas where I ran into trouble were creating the metal brushes and designing rollers that would prevent the belt from sliding off of them. I have listed the materials and main components of my generator below, and I have included brief explanations of how I overcame these two issues.

 

Materials list:

·      Two stainless steel bowls (I used bowls with a 9-inch diameter)

·      Two 12-inch lengths of copper wire

·      Aluminum tape

·      One 24’’ length of PVC pipe with a 3’’ inside diameter

·      One toilet flange with inside diameter slightly larger than 3’’

·      One 2’’ length of 1.5’’ diameter aluminum rod

·      One 2’’ length of 1.5’’ diameter teflon rod

·      One 3.5’’ length of 0.8cm diameter aluminum rod

·      One 4.5’’ length of 0.8cm diameter aluminum rod

·      Four ball bearings with 0.8cm inside diameter, along with 3D-printed holders to set them in place in holes in the PVC pipe

·      One 42’’ nylon strip (maximum 1.5’’ width)

·      Six 3/4’’ screws

·      Sixteen 1’’ screws

·      Twenty washers

·      Four set screws

·      Six 2’’ x 2’’ squares of aluminum mesh

·      Silicone sealant caulk

·      One 12’’ x 12’’ sheet of plexiglass with a minimum thickness of 6mm

·      Motor to drive the bottom roller of the Van De Graaff generator, along with 3D-printed mount to secure it in place on the wooden board

·      One pliable strip of metal to hold the motor in place in the 3D-printed mount

·      One 12’’ x 18’’ wooden board

 

The main components of my Van De Graaff generator include:

1.    A wooden base that holds the motor and the supporting column. The base of the generator is a 12’’ x 18’’ wooden plank.

2.    A motor that connects to the bottom roller. The motor connects to the generator via a metal rod on the motor. The rollers in my generator both have aluminum rods through the centre, and the aluminum rod in the bottom roller is long enough that it sticks out of the supporting column. The bottom roller in the generator is placed at a height such that the aluminum rod is lined up with the metal rod on the motor. The two rods are connected by a ring that has two set screws to hold it in place on both rods.

3.    Two rollers and a belt connecting the rollers. The bottom roller is made of Teflon and the top roller is made of aluminum with an acetate sheet wrapped around it. The rollers each have a diameter of 1.5’’ and a length of 2’’. The belt is made of nylon. I initially planned to use a rubber belt, but it would slide off the rollers every time I turned the motor on. My initial solution to this problem was to attach disks to each end of the two rollers. The disks had a slightly larger diameter than the two rollers, but the rubber was flexible enough that it could still climb over the disks and slip off of the rollers. I then switched out the rubber belt for a nylon belt, which was too stiff to climb over the barrier created by the disks. The next problem that arose was that nylon is not between Teflon and aluminum on the triboelectric scale, but I fixed this by wrapping a sheet of acetate around the aluminum roller.

4.    Two metal brushes made from aluminum mesh. One brush was attached to the wooden base directly below the bottom roller and grounded through the motor. The second brush was set inside the spherical dome just above the top roller and connected to the spherical dome with a copper wire. This brush acted as an electron source by pulling electrons from the spherical dome, which ultimately results in the buildup of positive charge in the dome.

5.    A supporting column made from PVC pipe. The supporting column has a height of 24” and an inside diameter of 3”. I secured the bottom of the supporting column in a toilet flange nailed to the wooden base. The two rollers had aluminum rods through their centres that sat in holes I drilled through the supporting column. There were ball bearings set in the holes and held in place by 3D printed mounts, and the aluminum rods were threaded through the call bearings. This design served the purpose of holding the rollers in place while still allowing them to spin.

6.    A spherical dome made of two stainless steel bowls. The rims were removed from the bowls and I taped the two bowls together using aluminum tape to create a conductive sphere.

 

When creating my Van De Graaff generator, I used the instructions linked above as a starting point for my design process (you can also find the instructions here). I have listed the specific steps in my design an construction process below.

 

Van De Graaff generator design and construction process:

1.     I began by using CAD software to model each component of the Van De Graaff generator that I would be building. I have included some images of my CAD designs below, and the document with my designs can be found at the following link: https://cad.onshape.com/documents/24306f85d5a24158871f766d/w/7423e2f5b562451b4e1a6f43/e/2bf60bb26d6a275e36ccce4c?renderMode=0&uiState=662f02afe729d32a701d21a8

Figure 5: CAD model of rollers for Van De Graaff generator, including axle and ball bearings.

Figure 6: Drawing of Support Column Based on Digital Model

Figure 7: CAD model of motor and base of Van De Graaff Generator, as well as the initial design for

connecting the motor to the axle of the bottom roller.

2.     Once I had created digital models of each component of the Van De Graaff generator, I began building individual components. I started with the metal sphere for the top of the generator. I used two stainless steel bowls to create the sphere, and the UBC machine shop was able to cut the rims off the bowls so that the bowls would create a spherical shape when put together. The machine shop also cut a hole in the bottom of one of the bowls so it would fit on top of the PVC pipe I used as the supporting column. Once the machine shop had cut the rims off the bowls, I taped them together using aluminum tape to create a conducting sphere.

Figure 8: Stainless steel bowl with a circle cut out of the bottom so it could

be fitted on a supporting column (a section of 3'' diameter PVC pipe).

Figure 9: Two stainless steel bowls taped together to create a metal sphere.

In this photo, the bowls were taped with electrical tape, but this was later

replaced with aluminum tape to create a conducting sphere.

3.    I cut a 24’’ length of PVC pipe (3’’ diameter) to use as the supporting column. I later used a hole saw to drill holes into the pipe for the rollers, but there were several steps that came before that.

4.     The UBC machine shop cut a 2’’ length of aluminum rod and a 2’’ length of Teflon rod for my rollers. I used rods with a 1.5’’ diameter. The rollers both had holes drilled through the centre axis to fit an aluminum rod as an axle. The aluminum rods were slightly longer than 3’’ in length so that they could be fed through the holes in the PVC pipe and could be used to hold the rollers at the correct height inside the supporting column. The aluminum rods were secured in place in the rollers with set screws.

Figure 10: Roller with axle. This image shows the bottom roller. The axle is longer on

one end so that it will stick out of the PVC pipe and can be connected to a motor that

drives the rollers.

5.     I used a laser cutter to cut out four plexiglass discs. I used silicone sealant caulk to glue the discs onto the ends of the rollers, as shown in the figure below. The purpose of the discs was to prevent the belt from sliding off the rollers.

Figure 11: Rollers with plexiglass discs.

6.    I initially planned to use a flexible silicon loop for the belt, so I looped it around the two rollers and held the rollers far enough apart to create a moderate amount of tension in the silicon. I measured the distance between the axles of the two rollers when I had the desired amount of tension in the silicon and marked two points on the PVC pipe that were separated vertically by this distance.

7.     I found two ball bearings to place on either end of the axles for each roller. I then designed and 3D-printed holders for each ball bearing, which are shown below. The holders were designed to sit on the outside of the PVC pipe. Each holder had a circular indent that the ball bearing could fit into. Once I had printed the holders, I used a hole saw to cut holes into the PVC pipe at the positions I marked in step 6. I ensured that the holes for the top roller were aligned vertically with the holes for the bottom roller. I cut two holes for each roller on opposite sides of the PVC pipe so the axles could line up with the centres of both holes.

Figure 12: 3D-printed holders for ball bearings.

8.     I cut a vertical strip from the holes for the bottom rollers to the bottom of the PVC pipe. This enabled me to hold the PVC pipe upside down and lower the bottom roller into it until the axle was aligned with the bottom holes.

Figure 13: Vertical strip cut into PVC pipe to allow placement of bottom roller and axle.

9.     I inserted the rollers and the silicon belt into the PVC pipe, then placed the holders outside the PVC pipe such that the ends of the axles of the rollers sit in the centres of the ball bearings so the rollers are secured in place but can still rotate. I had drilled holes in the top and bottom of each roller and I used these to screw the holders onto the PVC pipe.

Figure 14: Ball bearing holder screwed to the PVC pipe.

10. I secured the bottom of the PVC pipe in a toilet flange screwed to a wooden board that I used as the base for the Van De Graaff generator.

11. When I created the axles for the rollers, I set the axle for the bottom roller to be longer than the axle for the top roller so that it stuck out of one of the ball bearings. I measured the height of the axle and the height of the axle on the motor I used to rotate the bottom roller. I then 3D-printed a mount for the motor that would set the motor’s axle in line with the axle of the bottom roller.

12. I positioned the mount for the motor so that the motor’s axle would line up with the axle from the bottom roller, then I screwed each corner of the mount to the wooden board. I placed the motor in the mount and used a pliable strip of metal to hold the motor in place. I did this by screwing each end of the metal strip to the wooden board. I used a hollow piece of aluminum and two set screws to secure the motor’s axle to the axle of the bottom roller.

13.  I used the laser cutter to cut out a plexiglass disc with a slit through the centre for a piece of aluminum mesh. I temporarily removed the bottom roller from the toilet flange and screwed the disc into the wooden board so it would align with the bottom of the PVC pipe. I placed a piece of aluminum mesh in the slit in the plexiglass disc. The mesh was not thick enough to be secured in place, so I added two more layer of mesh. At this point there were enough layers to keep the mesh secured in place in the slit in the plexiglass. The pieces of aluminum mesh were large enough to almost touch the belt when the PVC pipe was placed back into the toilet flange. The mesh served as a metal brush that acted as an electron sink for the bottom roller.

Figure 15: Plexiglass disc screwed to wooden board inside toilet flange.

The aluminum mesh was later placed in the slit in the disc so that it stuck

 out enough to almost touch the bottom roller.

           

           

Figure 16: Once the aluminum mesh was inserted, it was also connected to the
motor with a wire. This grounded the mesh so it could effectively act as an
electron sink.

 

14. I removed the tape from the metal sphere so that it would separate into two halves. I 3D-printed a strip of Plexiglass with a length equal to the diameter of the metal sphere. The plexiglass had a slit cut into its centre for a second piece of aluminum mesh. I secured three pieces of aluminum mesh in the slit, then placed the plexiglass strip into the top half of the metal sphere and glued the ends to the inside of the sphere using silicone sealant caulk. The aluminum mesh was long enough to almost touch the belt over the top roller when the metal sphere was reassembled and placed on top of the PVC pipe. The mesh served as a metal brush that acted as an electron source for the bottom roller.

15.  I soldered a piece of copper wire to the aluminum mesh and the metal sphere. This connected the mesh to the sphere so it could pull electrons from the sphere to act as an electron source for the top roller. This is the mechanism that allows charge to build up on the metal sphere on top of a Van De Graaff generator. I then re-taped the two halves of the metal sphere together.

Figure 17: Metal sphere with aluminum mesh inside it to act as a

metal brush near the top roller of the Van De Graaff generator.

 

            See image here

 

16. I placed the sphere on top of the PVC pipe, and the Van De Graaff generator was ready for testing!

17.  I tested the generator, but it was not yet functional because the silicon belt kept sliding off the rollers. The discs on the ends of the rollers did not prevent the sliding because the silicon was flexible enough to move over them. To combat this, I replaced the silicon belt with an inflexible nylon belt. The nylon was unable to slide off the rollers, but it was not in between aluminum and Teflon on the triboelectric scale (a Van De Graaff generator only works if the material of the belt is between the materials of the two rollers on the triboelectric scale), so the generators was still not functional. I fixed this by wrapping a sheet of acetate around the aluminum roller. Nylon is between Teflon and acetate on the triboelectric scale, so when I tested the generator again, it was functional.

Figure 18: The silicon belt around the rollers was replaced with a nylon belt.

 

           

Figure 19: Roller inside the supporting column of the Van De Graaff

generator (PVC pipe). This is an image of the bottom roller.

Short video of Van De Graaff Generator: https://drive.google.com/file/d/1AGNCOFj34HnFKJAAh6MKrWnjStOdMb5C/view?usp=sharing

Demonstration Slides: https://drive.google.com/file/d/130gdxb3FtN04XcLqSsPA1zNWGCJNfVln/view?usp=drive_link

Demonstration Worksheet:

https://docs.google.com/document/d/1-gXKHaQuw7Z_rKdWA1AvNMWdR7VzG3Eo7VnbF8ldbaE/edit?usp=drive_link