Backlash is the slop in any toothed (gears) or threaded (screws) drive system. Here’s info on what it is, how it is measured, and what the designer of such systems can do to reduce it. This article is not aimed at the engineer but rather at the woodworker or other user of shop-built machines, some of which may use screws for linear positioning. The impetus for writing this came from questions posed about the decision to use relatively costly precision lead screws and anti-backlash nuts in the shop-built CNC machine described on this site.
Last updated: Tuesday, May 08, 2012
Take a large machine screw and thread a nut onto it. Now hold the head of the screw between the fingers of one hand and hold the nut between the finger of the other. If you push and pull on it as if you are trying to push the nut onto the bolt and then pull it off you’ll be able to feel a small amount of movement between the screw and the nut. This movement is the result of the fact that the threads of the nut do not fit snugly around the threads of the screw – there is some space in there. Figure 1 shows a hunk of threaded rod and a cutaway of a nut around it. You can see the space between the threads of rod and the threads of the nut. This space is called backlash.
Backlash is a measurable quantity. The simplest way to measure it in a screw and nut is to push the nut as far as it will go in one direction and then to measure how far it can move in the other direction. Figure 2 shows the same cutaway diagram of the screw and nut with the nut pushed all the way to the left and the backlash distance shown.
The problem with backlash is that it can impose positioning error in a positioning system. For example, if the screw in figure 2 has five teeth per inch (5 TPI) and you turn the screw five times so that the nut moves to the right, the nut will move exactly one inch to the right. But starting from the position of the nut in figure 2, if you turn the screw five times so that the nut moves to the left, the nut will move one inch minus the amount of backlash. This is because the initial turning of the screw takes up the backlash but does not move the nut. The nut only moves after the screw has turned enough so its threads are bearing on the right side surfaces of the nut threads. This can be a problem in positioning systems that depend on a given number of rotations of the screw resulting in a given positioning of the nut. In cases where the amount of backlash is known and it is always known which side of the screw thread is contacting the nut thread, it is possible to simply subtract out the backlash where appropriate. But as a practical matter such cases are rare.
There are a number of ways of dealing with backlash in a linear positioning system. Which method is appropriate depends on the requirements of the positioning system. Some possibilities are discussed below.
If the positioning accuracy requirement of the system you are designing is less than that of the backlash in the linear drive components you intend to use then the backlash can simply be ignored. For example a shop-built woodworking machine intended to do very rough hogging out of waste wood might not need positional accuracy of any more than 0.1”. I know someone that built a machine to cut lengths of tubing, and that machine only had to be accurate to within an inch. So sometimes the application calls for less accuracy than there is backlash in the linear positioning system, and in those cases the backlash can be ignored. Now I know this rankles the aesthetic sensibilities of some, but it should be noted in such cases that it is aesthetics we are talking about and not sound engineering practice. Engineering is designing to specifications, and if the positioning tolerances (and of course other tolerances as well) can be met by a system with a lot of backlash in it then the engineering is sound. Outside the context of requirement specifications, tighter tolerances are not better tolerances.
This is a good place to discuss the backlash specifications of various screws that could be used as linear positioning devices in shop-built machines. Probably the cheapest screw that can be used for positioning drives is standard hardware store threaded rod. This material is beloved by hobbyists and tinkerers since it is inexpensive and readily available. It wasn’t designed for motion applications and it wears very quickly, but it can still be used to good effect in machines which will only see light and intermittent duty. Its tolerances are not that hot either, but in an application where backlash would not be an issue this wouldn’t matter much. Typical backlash in threaded rod and machine nuts varies with rod diameter and thread pitch, and of course with wear.
Applications which need linear positioning in machines that will see heavy and continuous duty will generally make use of Acme threaded rod and Acme nuts. The threads of Acme rod provide more contact area on the side walls of the threads and so do not wear as quickly as plain threaded rod. Tolerance specs are better and initial backlash specs are better too. There are two Acme thread standards. General purpose (G) Acme thread is available in three classes 2G, 3G, and 4G. The 2G class is the most common and the least expensive. The higher classes offer reduced backlash. The other Acme thread standard is called Centralizing (C) Acme thread, and is often referred to as precision Acme thread. It too is available in three classes – 2C, 3C, and 4C. See Machinery’s Handbook or other references for more on Acme thread specifications. But the point here is that it is possible to buy Acme threaded rod and nuts that offer very good backlash specifications, and that these specifications may be good enough so that backlash can simply be ignored.
In the introductory paragraphs it was mentioned that there are cases where the amount of backlash is known and it is always known which side of the screw thread is contacting the nut thread, and in these cases it is possible to simply subtract out the backlash where appropriate. This is the essence of software backlash compensation, which is offered by some of the computer software available to drive Computer Numerical Control (CNC) machines. If the machine you are designing is not a CNC machine than this would not be an option of course.
The software works like this. When it is configured you specify the backlash of each of the linear positioning devices of your machine. The software knows which side of the nut thread that the screw thread is in contact with at all times. It “knows” this because it knows which way it turned the screw last. If it turns the screw in the same direction as it was last turned it knows there will be no backlash and so does no compensation. Whenever it turns the screw in the opposite way from the way it was last turned it knows it has to add enough turn of the screw to take up the backlash before it will actually start moving the nut and the carriage to which it is attached.
Although such a scheme works fine in theory, movement of the carriage and nut that is not done explicitly by the positioning software can render this unworkable in actual practice. The conditions under which software backlash compensation will work are enumerated below. Note that all conditions must be met for it to work.
Most backlash reduction schemes involve mechanical pre-loading of the nut for movement in both directions. In the examples above when the screw was actually driving the nut and carriage, the screw was driving the load of the carriage assembly. If it starts turning the other way it is unloaded until the backlash is taken up, at which point it begins driving the load of the carriage assembly the other way. Preloading, that is, imposing a load on both sides of the screw thread simultaneously even while it is not moving means there is never backlash that needs to be taken up.
The generalized way to preload is to make sure the nut is in contact with both sides of the screw threads at all times. One of the most common ways to do this is to use two nuts, each in contact with one of the surfaces of the screw thread, as in figure 3. One way to do this is to secure both nuts to the carriage in some way that allows both adjustment of their positions along the thread and some way to secure them once properly positioned. In practice such an arrangement has some problems when metal nuts are used with metal screw, as tolerances of the screw and nuts, small positioning irregularities and expansion and contraction of the metal components with changes in temperature tend to make things bind up. But this can work surprisingly well when plastic nuts are used on a metal screw. Another common way to preload the screw is to mount only one of the nuts to the carriage and have the other secured to the mounted nut by some linear slide mechanism that keeps it from spinning on the screw. The two nuts are then pushed apart (or pulled together) by a spring. The problem with this approach is that the spring force must exceed that presented by the load of the carriage assembly and this can cause considerable friction and wear of the screw and/or nut. Again, this is less of an issue with some plastic nuts. The advantage of this arrangement is that the assembly is self adjusting for wear.
The other common mechanism for preloading is to use a split nut. A kerf is sawed into the nut so that it crosses the threaded surface but does not cut the nut in half. Adjusting screws are placed which can be used to squeeze together (or push apart) the nut over the split. As this part of the thread is bent, it can make contact with the screw thread, thus preloading the nut. Self-adjusting versions of this approach are also used. These usually have the split on the end of the nut and the outside of the nut widens out over the split. A metal collar around the nut, forced out by a spring squeezes the split together and makes the threads contact those of the screw. This is the approach used in most commercially available self adjusting anti backlash nuts.