Linear Motion Drivers
Threaded Rods
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| 1/4 inch threaded rod with nut |
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| Close up of 1/4 inch threaded rod |
If you are aiming for precision or desire to cut harder materials like aluminium and possibly steel, you do not want to cheap out on the lead screws and go with threaded rods. The main reason is the tolerances for the thread and nut pitch is low. This will cause an axis to move at uneven speeds, due to friction between the threads, which will have a negative affect the finish (smoothness) of the surface. Also the motors will, in general, need to apply more torque since large amounts of friction will be created by the mismatch in thread pitch. If the motor drivers do not have a current protection circuit, you could very well blow your motors if the friction between threads is greater than the peak torque generated by your motor.
Backlash is one other issue that arises with mismatched pitches. Backlash occurs when the pitch of the screw is larger than the pitch of the nut (when it is reversed, the nut will be unable to move along the screw). However, in a threaded rod, the pitch is not consistent across the entire rod so the amount of backlash will change from position to position which makes it impossible for any CNC controller on the market to compensate. It would be near impossible to program your own controller since you would need to know the backlash at every point along the screw. Backlash will cause the dimensions of the part being made to be thrown off. Granted, if you don't care too much about accuracy, then this is of little concern. The gap between the two threads and the nut thread can also cause chatter in the machine because the nut threads are free to bounce from one screw thread to the other without resistance. While the spindle is spinning, it could cause the nut to oscillate back and forth within the gap between the screw threads and cause this phenomenon known as chatter.
If threaded rods are still the preference, we advise that you test a nut with a rod before you purchase them to see that the movement is fairly smooth. To connect the rod with your motor shaft, you can use shaft couplers off ebay or attempt to make your own by buying a longer nut and making set a pair of set screw holes on each end. If the motor shaft does not fit in the other end of the nut, simply drill half way into the hole using a drill bit the size of the motor shaft. This home made shaft coupler is cheaper than buying a shaft coupler off ebay most likely.
Here is a CNC machine that was made with threaded rods.
Summary
pros:
- cheap!!!
cons:
- largest amount of backlash out of all the lead screws I will mention
- rotation of nut along thread is rough and uneven due to a lack of precision
- low manufacturing tolerances
Timing Belts
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| Timing belt with pulley |
Timing belts are suitable for machines that require quick and smooth movements and cut softer materials like wood. However, there can be backlash issues as well since a belt, made of rubber, is able to stretch to some degree. Generally a fresh belt will hold its length fairly well; after all, they are made for automobiles and other machinery. Tensioning the belts appropriately can be difficult in order to squeeze as much precision out of the belt without having it stretch too much or be too tight to so that the torque required to turn one of the pulleys is too much for the motor. Belts will need to be replaced overtime, more so than screws, and the harder they are run, the faster they will wear out and stretch. In conclusion, I would recommend belts if you are making a smaller machine with the intention to cut wood and other softer materials.
Summary
pros:
- relatively inexpensive
- able to drive an axis at higher speeds
cons:
- belts will stretch over time
- difficult to tension properly
- backlash issues increase as load on the router increases due to stretching
- belts wear and tear faster than screws
Acme Threaded Rods
Acme threaded rods are an excellent choice for those who want precision but are still constrained by a budget. These types of rods use a trapezoidal shape for the threads which allow transmission of higher torque loads and greater precision in comparison to the options mentioned above. These components are often used in lathes because they have a self locking property.
The threads, being trapezoidal, have a large amount of contact surface area, which is prone to high friction under certain forces. When the nut, threaded onto the screw, has minimal load (i.e. just itself), the force of friction is minimal. The small force of friction only occurs because the nut is moving axially. In order for the nut to move, the threads of the rod must push against the threads of the nut creating friction. Therefore, we can conclude that axial force give acme threaded rods their self locking property.
However, not all threads have a self locking property. The main factors that contribute to the self locking property are the materials of the thread on both rod and nut, and the angle of each thread, which is associated with pitch. The reason material and angle are the main factors is due to the friction equation:
A rough diagram below was drawn for a bit of a visual. In each sub-diagram, the rod is on the left hand side while the nut is on the right. The threads are assumed to be right handed. When a force is applied on the nut in the y direction, it is transferred to the rod's threads and broken up into two components, Fthread and Fnormal. In order to accurately discuss the directions of the force, you will have to imagine the force vectors in 3D as we describe them.
First of all, with a right handed thread, the nut will spin the direction noted by the rotation arrow in order to move in the positive y direction. The interlocking threads prevent the nut from just sliding along the thread and as a result, the force is split up at the contacting threads. Fthread is the component of Force that is parallel to the thread's surface and in these pictures, the z component of the Fthread vector is pointing into the screen. Fthread encourages the thread of the nut to slide along the thread of the rod, therefore causing a rotation and positive y displacement. Fnormal is the force that is perpendicular to the thread's surface and has a z component that is sticking out of the screen. The Fnormal force causes friction which acts in the opposite direction of Fthread, therefore opposing thread sliding. It is to be noted that the force of friction can never cause the thread to slide in the opposite direction of Fthread.
We hope that you understand the forces and will compare the two scenarios. It can be seen in the diagram below that a constant force and decreasing pitch (and thread angle) will cause Fthread to increase and Fnormal to increase. In laymen terms, the force that causes rotation decreases AND the force of friction increases.
Now looking at these fundamentals at a point on the thread, we can say that at a 45 degree thread angle and a coefficient of friction of 1, the Fthread force and Fnormal force balance and therefore no motion will occur. However, most amce threaded rods will have a thread angle considerably smaller than 45 degrees so that the threads aren't spread out as much and giving more rigidity to the system.
Another way to picture this is think of a really long swirly slide that represents the threaded rod and a long spring shaped object resting on the slide like the threads of a nut does with the rod. When the spiral shaped object sits on the slide, the force of gravity will act on it. The angle of the slide (or steepness) and the materials of the slide and object.
The backlash on acme threaded rods is minimal in comparison to the options mentioned above and is further reduce by making this custom nut since it was moulded to thread of the rod. There is still space between the nut's thread and rod's thread which will create some backlash; if there wasn't any space, the nut would not be able to move along the thread. A caution should be mentioned that as the nut is pushed along the screw more and more under a load, the nut could wear and backlash will increase. We have not looked too much into ways to further minimize backlash but we suspect it would involve two separate nuts that are locked in rotation with a heavy spring in between.
One more thing to note about acme threaded rods is that they can have multiple starts (see the wikipedia page under the subheading "Lead, pitch, and start"). The number of starts refers to the number of different threads that spiral along the rod. In the picture below, it shows a threaded rod with 5 starts. As the number of starts increases, with pitch and thread width remaining constant, the lead increases (the space between a single thread's threads) since with extra threads, each thread is forced to be stretched out axially. The advantage of multiple starts is to increase speed but at the same time, precision is sacrificed. Speed can be increased because each thread alone is spaced out more which causes the nut to move further in one rotation. Multiple number of starts helps to stabilize the nut as it moves along the screw. Also note that as the number of starts increase, so does the cost.
There was a post on CNCzone about cheap acme threaded rods from an online store by the name of Enco. We have personally not tested them but it is worth taking a look at if you would like
Summary
pros:
- very robust
- minimal backlash
cons:
- most expensive (in general)
- lots of friction
One last note, and it should be common sense, is that for CNC machines, lubrication becomes crucial, especially for single start rods, so that your motors will be able to drive the screw. If you have unlimited torque in your motor, then you can ignore this note :)
Ball Screws
Ball screws improve upon the basic concept behind threaded rods. Instead of direct bearing between the screw and nut surfaces, ball screws contain ball bearings which fit in between the two surfaces. This makes the transfer of motion far more efficient (aka less friction), since there is now rolling friction as oppose to two surfaces sliding across one another (which is easier: rolling a cart or sliding a box across a floor?). This is significant when you consider that acme threaded rods are generally about 30% efficient, while ball screws can be up to 95% efficient.
With less friction in between the nut and the screw, the ball screw, in contrast with the acme threaded rod, requires more force to stop the nut and any attached load when they are in motion since the system has less friction. As a result, the motor size will increase if the desired maximum speed increases. Also, if a ball screw is used in a vertical application, you MUST keep in mind that once power is removed from the motor, a load on a vertical ball screw assembly (like gravity acting on a spindle) will cause the ball nut to spiral down. This is considered back drive. One way to avoid this is to increase the threads per inch on your ball screw (maybe 10 tpi) or add in a locking mechanism for when you shut the machine off (this is your safest bet).
The main drawback of ball screws is their price. However, the added quality could be worth the investment depending on the application. Since the nut and screw aren't grinding against each other, the life span of ball screws is usually longer and therefore they require less replacement.
Summary
pros:
- very good precision (very little backlash)
- longer life time
- minimal friction
cons:
- cost
- require more braking force due to less friction
- require a locking system in vertical applications
- require a lubricant
Summary
pros:
- relatively inexpensive
- able to drive an axis at higher speeds
cons:
- belts will stretch over time
- difficult to tension properly
- backlash issues increase as load on the router increases due to stretching
- belts wear and tear faster than screws
Acme Threaded Rods
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| Acme Threaded Rod |
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| Acme Threaded Rod Nut |
Acme threaded rods are an excellent choice for those who want precision but are still constrained by a budget. These types of rods use a trapezoidal shape for the threads which allow transmission of higher torque loads and greater precision in comparison to the options mentioned above. These components are often used in lathes because they have a self locking property.
The threads, being trapezoidal, have a large amount of contact surface area, which is prone to high friction under certain forces. When the nut, threaded onto the screw, has minimal load (i.e. just itself), the force of friction is minimal. The small force of friction only occurs because the nut is moving axially. In order for the nut to move, the threads of the rod must push against the threads of the nut creating friction. Therefore, we can conclude that axial force give acme threaded rods their self locking property.
However, not all threads have a self locking property. The main factors that contribute to the self locking property are the materials of the thread on both rod and nut, and the angle of each thread, which is associated with pitch. The reason material and angle are the main factors is due to the friction equation:
Friction Force = (Coefficient of Friction) * (Normal Force).
The material(s) of the threads will influence the coefficient of friction, which is determined through lookup tables (these tables will show pairs of materials and their respective coefficients, static and kinetic), while the angle of the thread will affect how much of an axial force gets translated into a normal force.A rough diagram below was drawn for a bit of a visual. In each sub-diagram, the rod is on the left hand side while the nut is on the right. The threads are assumed to be right handed. When a force is applied on the nut in the y direction, it is transferred to the rod's threads and broken up into two components, Fthread and Fnormal. In order to accurately discuss the directions of the force, you will have to imagine the force vectors in 3D as we describe them.
First of all, with a right handed thread, the nut will spin the direction noted by the rotation arrow in order to move in the positive y direction. The interlocking threads prevent the nut from just sliding along the thread and as a result, the force is split up at the contacting threads. Fthread is the component of Force that is parallel to the thread's surface and in these pictures, the z component of the Fthread vector is pointing into the screen. Fthread encourages the thread of the nut to slide along the thread of the rod, therefore causing a rotation and positive y displacement. Fnormal is the force that is perpendicular to the thread's surface and has a z component that is sticking out of the screen. The Fnormal force causes friction which acts in the opposite direction of Fthread, therefore opposing thread sliding. It is to be noted that the force of friction can never cause the thread to slide in the opposite direction of Fthread.
We hope that you understand the forces and will compare the two scenarios. It can be seen in the diagram below that a constant force and decreasing pitch (and thread angle) will cause Fthread to increase and Fnormal to increase. In laymen terms, the force that causes rotation decreases AND the force of friction increases.
Now looking at these fundamentals at a point on the thread, we can say that at a 45 degree thread angle and a coefficient of friction of 1, the Fthread force and Fnormal force balance and therefore no motion will occur. However, most amce threaded rods will have a thread angle considerably smaller than 45 degrees so that the threads aren't spread out as much and giving more rigidity to the system.
Generally, acme threaded rods use some sort of plastic-like nut. One of the most common materials is delrin and can be purchased on ebay once again. Search "delrin rod" and you will find a variety of diameters and lengths. We took a look on ebay today (March 11/2014) and found a 40mm diameter X 4.25 inch length rod for $4.50 USD plus $10 shipping. We suggest you message the seller to see if you can get a discount if you buy more than one. Some sellers advertise free shipping if you order multiple products from them. Once you have your delrin, follow this link to find out how to make the nut. In case the thread goes missing, here is a summary of the instructions:
1. Make a hole through the centre of the rod with the diameter of your acme threaded rod minus the depth of one thread.
2. Cut the rod down the centre so that the hole is cut in half.
3. Prepare the lead acme threaded rod by polishing the surface and in between the threads. Wipe on a thin film of mineral oil.
4. Place the two halves of delrin around the acme threaded rod and square up the delrin so that when the delrin is heated, the two halves will join back together and create a cylinder.
5. Place the two halve delrin rods (which wrap around the acme threaded rod) in a vise with the gaps facing upwards and downwards. The vise will push the two halves of delrin to deform around the nut and eventually meet up and melt together.
6. Take a heat gut and aim at a part of the acme threaded rod that is not covered by the nut. Do not aim it at the delrin itself because it could cause the surface that is exposed to heat to melt at a higher rate. Allow the heat to travel through the acme threaded rod and melt the delrin from the inside so that it is moulded to fit in between the threads. Slowly tighten the vise in order to encourage the two halves to come together and eventually melt together. This process is said to take 10-15 minutes.
7. Chuck the nut in a lathe (put the nut in the part that grips a round object) and use a hand vise to grip. Turn the screw with the hand vise and do this slowly since there will be a lot of heat generated from the friction between the nut and screw. Use some oil as a lubricate.
The backlash on acme threaded rods is minimal in comparison to the options mentioned above and is further reduce by making this custom nut since it was moulded to thread of the rod. There is still space between the nut's thread and rod's thread which will create some backlash; if there wasn't any space, the nut would not be able to move along the thread. A caution should be mentioned that as the nut is pushed along the screw more and more under a load, the nut could wear and backlash will increase. We have not looked too much into ways to further minimize backlash but we suspect it would involve two separate nuts that are locked in rotation with a heavy spring in between.
One more thing to note about acme threaded rods is that they can have multiple starts (see the wikipedia page under the subheading "Lead, pitch, and start"). The number of starts refers to the number of different threads that spiral along the rod. In the picture below, it shows a threaded rod with 5 starts. As the number of starts increases, with pitch and thread width remaining constant, the lead increases (the space between a single thread's threads) since with extra threads, each thread is forced to be stretched out axially. The advantage of multiple starts is to increase speed but at the same time, precision is sacrificed. Speed can be increased because each thread alone is spaced out more which causes the nut to move further in one rotation. Multiple number of starts helps to stabilize the nut as it moves along the screw. Also note that as the number of starts increase, so does the cost.
There was a post on CNCzone about cheap acme threaded rods from an online store by the name of Enco. We have personally not tested them but it is worth taking a look at if you would like
Summary
pros:
- very robust
- minimal backlash
cons:
- most expensive (in general)
- lots of friction
One last note, and it should be common sense, is that for CNC machines, lubrication becomes crucial, especially for single start rods, so that your motors will be able to drive the screw. If you have unlimited torque in your motor, then you can ignore this note :)
Ball Screws
Ball screws improve upon the basic concept behind threaded rods. Instead of direct bearing between the screw and nut surfaces, ball screws contain ball bearings which fit in between the two surfaces. This makes the transfer of motion far more efficient (aka less friction), since there is now rolling friction as oppose to two surfaces sliding across one another (which is easier: rolling a cart or sliding a box across a floor?). This is significant when you consider that acme threaded rods are generally about 30% efficient, while ball screws can be up to 95% efficient.
With less friction in between the nut and the screw, the ball screw, in contrast with the acme threaded rod, requires more force to stop the nut and any attached load when they are in motion since the system has less friction. As a result, the motor size will increase if the desired maximum speed increases. Also, if a ball screw is used in a vertical application, you MUST keep in mind that once power is removed from the motor, a load on a vertical ball screw assembly (like gravity acting on a spindle) will cause the ball nut to spiral down. This is considered back drive. One way to avoid this is to increase the threads per inch on your ball screw (maybe 10 tpi) or add in a locking mechanism for when you shut the machine off (this is your safest bet).
The main drawback of ball screws is their price. However, the added quality could be worth the investment depending on the application. Since the nut and screw aren't grinding against each other, the life span of ball screws is usually longer and therefore they require less replacement.
Summary
pros:
- very good precision (very little backlash)
- longer life time
- minimal friction
cons:
- cost
- require more braking force due to less friction
- require a locking system in vertical applications
- require a lubricant
CONCLUSION
The recommendations we have for each linear motion driver will be listed below:
Threaded rod: Only use if you are on a budget!!!!!
Timing Belt and Pulley: Use if you are intending to limit the machine to wood.
Acme Threaded Rod: Can be used for any machine. Select higher grades if you want to cut harder materials with higher precision. Be prepared to use bigger motors in order to overcome the friction forces
Ball Screws: Preferable if budget is not an issue. Ball screws will give you the most efficiency (reduce the energy spent to move the CNC machine around).
These are general remarks on each type of linear motion driver. Another large factor that will come into play is the type of material each one is made of and how much force the component can withstand.
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