Nominal Stiffness of GT-2 Rubber-Fiberglass Timing Belts for Dynamic System Modeling and Design

• Main Authors: Bozun Wang, Yefei Si, Charul Chadha, James T. Allison, Albert E. Patterson
• Format: Article
• Language: English
• Published: MDPI AG 2018-11-01
• Series: Robotics
• Subjects: timing belt; belt stiffness; dynamic system modeling; mechatronic systems; 3D printers; robotics
• Online Access: https://www.mdpi.com/2218-6581/7/4/75

GT-style rubber-fiberglass (RF) timing belts are designed to effectively transfer rotational motion from pulleys to linear motion in robots, small machines, and other important mechatronic systems. One of the characteristics of belts under this type of loading condition is that the length between load and pulleys changes during operation, thereby changing their effective stiffness. It has been shown that the effective stiffness of such a belt is a function of a &#8220;nominal stiffness&#8222; and the real-time belt section lengths. However, this nominal stiffness is not necessarily constant; it is common to assume linear proportional stiffness, but this often results in system modeling error. This technical note describes a brief study where the nominal stiffness of two lengths (<inline-formula> <math display="inline"> <semantics> <mrow> <mn>400</mn> <mspace width="3.33333pt"></mspace> <mi>m</mi> <mi>m</mi> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mn>760</mn> <mspace width="3.33333pt"></mspace> <mi>m</mi> <mi>m</mi> </mrow> </semantics> </math> </inline-formula>) of GT-2 RF timing belt was tested up to breaking point; regression analysis was performed on the results to best model the observed stiffness. The experiments were performed three times, providing a total of six stiffness curves. It was found that cubic regression mod els (<inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>R</mi> <mn>2</mn> </msup> <mo>&gt;</mo> <mn>0.999</mn> </mrow> </semantics> </math> </inline-formula>) were the best fit, but that quadratic and linear models still provided acceptable representations of the whole dataset with <inline-formula> <math display="inline"> <semantics> <msup> <mi>R</mi> <mn>2</mn> </msup> </semantics> </math> </inline-formula> values above <inline-formula> <math display="inline"> <semantics> <mrow> <mn>0.940</mn> </mrow> </semantics> </math> </inline-formula>.