Abstract
The noncircular synchronous belt drive mechanism has demonstrated certain achievements and has been used in special fields. Research regarding noncircular synchronous belt drive mechanisms has focused on optimization design and kinematic analysis in China, whereas two pulley noncircular synchronous belt transmissions have been developed overseas. However, owing to the noncircular characteristics of the belt pulley, the real-time variation in the belt length slack during the transmission of the noncircular synchronous belt is significant, resulting in high probabilities of skipping and vibration. In this study, a noncircular tensioning pulley is added to create a stable three-pulley noncircular synchronous belt driving mechanism and a good synchronous belt tensioning, with no skipping; hence, the non-uniform output characteristic of the driven pulley is consistent with the theoretical value. In the circular noncircular noncircular three-pulley noncircular synchronous belt mechanism, the pitch curve of the driving synchronous belt pulley is circular, whereas those of the driven synchronous belt and tensioning pulleys are noncircular. To minimize the slack of the belt length of the synchronous belt and the constraint of the concavity and circumference of the tensioning pulley, an automatic optimization model of the tensioning pulley pitch curve is established. The motion simulation, analysis, and optimization code for a three-belt-pulley noncircular synchronous belt drive mechanism is written, and the variation in belt length slack under different speed ratios is analyzed based on several examples. The testbed for a circular–noncircular–noncircular three-pulley noncircular synchronous belt transmission mechanism is developed. The test shows that the three-pulley noncircular synchronous belt drives well. This study proposes an automatic optimization algorithm for the tensioning pulley pitch curve of a noncircular synchronous belt transmission mechanism; it yields a stable transmission of the noncircular synchronous belt transmission mechanism as well as non-uniform output characteristics.
Highlights
1 Introduction During one rotation period of a noncircular synchronous belt transmission mechanism, the required theoretical belt length changes in real time owing to the real-time changes of the noncircular synchronous belt pulley diameters in a transmission cycle
Satchel [1] and Wu et al [2, 3] presented models for calculating the noncircular belt pulley pitch curve required for the transmission ratio based on different methods, but no discussion regarding tensioning was provided
Cao et al [14] established a continuous mapping model of two-belt pulley transmissions, and the speed ratio function was calculated while considering the polygon effect, and the law of belt transmission was obtained. Whether it is a two-pulley noncircular synchronous belt drive without a tensioner or a threepulley noncircular synchronous belt drive with a noncircular tensioner, the slack of the belt length is large when a slight change occurs in the transmission ratio
Summary
During one rotation period of a noncircular synchronous belt transmission mechanism, the required theoretical belt length changes in real time owing to the real-time changes of the noncircular synchronous belt pulley diameters in a transmission cycle. Cao et al [14] established a continuous mapping model of two-belt (chain) pulley transmissions, and the speed ratio function was calculated while considering the polygon effect, and the law of belt (chain) transmission was obtained Whether it is a two-pulley noncircular synchronous belt drive without a tensioner or a threepulley noncircular synchronous belt drive with a noncircular tensioner, the slack of the belt length is large when a slight change occurs in the transmission ratio. The uneven variation in the belt length slack during a noncircular synchronous belt transmission renders it difficult to achieve accurate non-uniform speed transmission in engineering applications He [15] proposed a circular–eccentric circular–noncircular belt pulley drive mechanism, in which the noncircular belt pulley was the tensioning pulley and the belt length slack was the objective function. Following the results of He [15], the author studied the variation in slack in a three-pulley noncircular synchronous belt transmission with a noncircular tensioning pulley, analyzed the characteristics of the three-pulley noncircular synchronous belt transmission, and conducted experimental research
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