In a previous post we discussed timing belt factors to consider when designing a linear drive. Within those considerations is repeatability - a topic so important it warrants a dedicated post.
The in-depth information and calculations below are summarized in this video with Machine Design called How to "Help Customers Achieve the Best Possible Result with Timing Belts."
A frequent question posed to our applications department concerns the expected repeatability of a timing belt drive. Common examples concerning repeatability include positioning a linear drive carriage at a station for loading, accuracy of work performed on a product indexed by a profile belt, or rotary positioning of a turn table. In the following article we will present our approach to estimating total drive repeatability and steps to make improvements.
The first step is to identify the typical error components based on the drive type.
Linear components listed above plus driven pulley backlash
The three Linear components listed above plus…
A practical approach to summing the errors is to take a statistical estimate made by taking the square root of the sum of the individual errors identified above. Errors may be neglected if they are small relative to other error components.
B = pulley backlash
E = Elongation under load (static friction, dynamic, applied forces)
L = Length tolerance consistency
N = additional errors for special cases such as profile belt indexing
Example Case Study: A customer contacted our Applications Engineering department for an estimate of achievable repeatability for a new design. The drive layout was a two-pulley linear drive which is typical for 90% of linear drives. A 25mm wide AT10 belt was previously correctly sized for the application loading. The application involved moving a 900lb heat sealing head which needed to pick up a group of 16 parts and heat seal them while moving them to a drop point 3 meters away. The carriage was supported by typical 0.05 friction coefficient linear rails. The customer was concerned with accuracy at the pickup and drop off locations.
Backlash = 0.4mm for AT10 pitch (See table below)
Static Elongation = 408kg(9.8)(0.05µ) = 200N. According to the chart in the appendix a 25mm wide AT10 will have an elongation of 1.13mm at 200N.
Length Tolerance Consistency = 3m travel (0.1mm/m consistency) = 0.3mm
The major sources of error will be readily apparent in the equation above. Address the major sources of error for best overall improvement in system repeatability. Note that pretension elongation and length tolerance are not typically included in the sources of error because they can be accommodated for with a setup procedure. Install, pretension and break in the system for a few hours followed by setting any station locations to the product locations on the belt. A belt change or change in pretension will require repeating these steps.
Improvements can be made, and the impact is readily visible in the components of the equation. In the example above we can improve the elongation error with a stiffer 25 AT10 MOV belt and eliminate the backlash by using a zero-backlash pulley for a 40% error reduction without major design modifications. Additional improvements are possible with design modifications such as a wider belt or possibly a layout change to reduce belt length. A wide variety of linear drive products are available to you in order to find the combination of improvements that will work best for your application.
We trust this method will aid you in optimizing your next high precision timing belt drive. You can contact our applications engineering department to assist in reviewing your design and helping you meet your goals. If you have specifications available and would like to calculate your linear drive, please fill out the linear drive calculation form.
Elongated Graph - derived from 4mm per meter elongation at max allowable tensile force (See B212 Catalog Spec Charts)