Transmission Error Due to Resonance in Synchronous Belt Drive With Eccentric Pulley

2017 ◽  
Vol 139 (12) ◽  
Author(s):  
Masanori Kagotani ◽  
Hiroyuki Ueda
Keyword(s):  
Transverse Vibration ◽  
Rotation Frequency ◽  
Transmission Error ◽  
The Other ◽  
Belt Drive ◽  
Integer Multiple ◽  
Belt Drives ◽  
Eccentric Shaft ◽  
Synchronous Belt Drive ◽  
Frequency Variations

In synchronous belt drives, it is generally difficult to eliminate pulley eccentricity, because the pulley teeth and shaft hole are produced separately and the pulley is installed on an eccentric shaft. This eccentricity affects the accuracy of rotation transmission, so that the belt tension changes during a single rotation of the pulley. This in turn affects the occurrence of resonance in the spans. In the present study, the transmission error in a synchronous belt drive with an eccentric pulley in the absence of a transmitted load was experimentally investigated for the case in which the spans undergo first-mode transverse vibration due to resonance. The transmission error was found to have a component with a period equal to the span displacement, in addition to a component with a period of half the span displacement. During a single rotation of the pulley, the magnitude of the transmission error increased, and its frequency decreased, with decreasing belt tension. The transmission error exhibited the large value when two frequency conditions were satisfied: one was that the meshing frequency was within the range of span frequency variations due to the eccentricity, and the other was that the minimum span frequency was close to an integer multiple of the pulley rotation frequency. Even if both of these conditions occurred, if the range of span frequency variations due to the eccentricity was larger than 13 Hz, the transmission error could be eliminated by adjusting the belt tension, so that the average span frequency corresponded to the meshing frequency.

Transmission Error due to Resonance in Synchronous Belt Drive With Eccentric Pulley

2016 ◽  
Author(s):  
Masanori Kagotani ◽  
Hiroyuki Ueda
Keyword(s):  
Rotation Frequency ◽  
Transmission Error ◽  
Average Frequency ◽  
The Other ◽  
Belt Drive ◽  
Minimum Frequency ◽  
Integer Multiple ◽  
Belt Drives ◽  
Synchronous Belt Drive ◽  
Frequency Variations

In synchronous belt drives, it is generally difficult to eliminate pulley eccentricity, because the pulley teeth and shaft hole are produced separately. This eccentricity affects the accuracy of rotation transmission, so that the belt tension changes during a single rotation of the pulley. This in turn affects the occurrence of resonance in the spans. In the present study, the transmission error in a synchronous belt drive with an eccentric pulley in the absence of a transmitted load was experimentally investigated for the case in which the spans undergo first-mode transverse vibration due to resonance. The transmission error was found to have a component with a period equal to the displacement of the span, in addition to a component with a period of half the displacement of the span. During a single rotation of the pulley, the magnitude of the transmission error increased, and its frequency decreased, with decreasing belt tension. The transmission error exhibited the large value when two frequency conditions were satisfied: one was that the meshing frequency was within the range of span frequency variations due to the eccentricity, and the other was that the minimum frequency of the span was close to an integer multiple of the rotation frequency of the pulley. Even if both of these conditions occurred, if the range of span frequency variations due to the eccentricity was larger than 13 Hz, the transmission error could be eliminated by adjusting the belt tension so that the average frequency of the span corresponded to the meshing frequency.

Influence of Installation Tension on Transmission Error Due to Resonance in a Synchronous Belt

2015 ◽  
Vol 137 (8) ◽  
Author(s):  
Masanori Kagotani ◽  
Hiroyuki Ueda
Keyword(s):  
Natural Frequency ◽  
Transmission Error ◽  
Experimental Results ◽  
The Other ◽  
Belt Drive ◽  
Analysis Method ◽  
Belt Drives ◽  
Mode Vibration ◽  
Synchronous Belt Drive ◽  
Good Agreement

In synchronous belt drives, a transmission error is generated due to resonance of the belt spanning the driving and driven pulleys when the transverse natural frequency of the belt approaches the meshing frequency of the belt and the pulley teeth. The behavior of this transmission error has been assumed to be dependent on the installation tension. In the present study, the influence of the installation tension on the transmission error in a synchronous belt drive under no transmitted load was experimentally investigated for the case in which first mode vibration due to resonance was induced in both the upper and lower spans. In addition, an analysis of the transmission error based on the experimental results was carried out. A method for reducing the error was also investigated. The transmission error contains two components: one with a period equal to the pitch of the pulley, and the other with a period of half the pulley pitch. Good agreement was found between the calculation and experimental results, thus confirming the validity of the analysis method. For a fixed pulley speed, the transmission error was largest when the installation tension was applied at a position where the displacement of the upper span was equal to that of the lower span. It was found that the transmission error could be reduced by pushing an idler lightly against the center of the span of the belt that was undergoing the largest displacement.

Influence of Installation Tension on Transmission Error due to Resonance in a Synchronous Belt

2014 ◽  
Author(s):  
Masanori Kagotani ◽  
Hiroyuki Ueda
Keyword(s):  
Natural Frequency ◽  
Transmission Error ◽  
Experimental Results ◽  
The Other ◽  
Belt Drive ◽  
Analysis Method ◽  
Belt Drives ◽  
Mode Vibration ◽  
Synchronous Belt Drive ◽  
Good Agreement

In synchronous belt drives, transmission error is generated due to resonance of the belt spanning the driving and driven pulleys when the transverse natural frequency of the belt approaches the meshing frequency of the belt and the pulley teeth. The behavior of the transmission error caused by resonance has been assumed to be dependent on the installation tension. In the present study, the influence of installation tension on the transmission error in a synchronous belt drive was experimentally investigated for a case in which first mode vibration due to resonance was induced in both the upper and lower spans. In addition, an analysis of the transmission error based on the experimental results was carried out. A transmission error contains two components: one with a period equal to the pitch of the pulley, and the other with a period of half the pulley pitch. Good agreement was found between the calculation and experimental results, thus confirming the validity of the analysis method. For a fixed pulley speed, the transmission error was largest when the installation tension was applied at a position where the displacement of the upper span was equal to that of the lower span. When the installation tension was varied and the pulley speed was adjusted so that the belt experienced resonance, the transmission error decreased with an increase in installation tension.

Transmission Error in Helical Synchronous Belt Drives in Bidirectional Operation: Influence of Pulley Flange Under No Load

2003 ◽  
Author(s):  
Masanori Kagotani ◽  
Kenichi Makita ◽  
Hiroyuki Ueda ◽  
Tomio Koyama
Keyword(s):  
Theoretical Analysis ◽  
Helix Angle ◽  
Transmission Error ◽  
Belt Drive ◽  
Alignment Error ◽  
Belt Drives ◽  
The Difference ◽  
Case Transmission ◽  
Synchronous Belt Drive ◽  
Outside Diameter

Helical synchronous belt drives are more effective than conventional synchronous belt drives with respect to reducing noise and transmission error per single pitch of the pulley. However, the helix angle of the tooth trace causes axial belt movement. Therefore, a flanged pulley is used in a helical synchronous belt drive. In the present study, the transmission error in a helical synchronous belt drive using a flanged pulley under installation tension was investigated both theoretically and experimentally for the case where the pulley was rotated in bidirectional operation. The computed transmission error agrees well with the experimental results, thereby confirming the applicability of the proposed theoretical analysis for transmission error. In this case, transmission error is found to be generated by the difference in axial belt movement between the driving and driven sides, and by a change in the state of contact between the belt and pulley teeth flanks. The transmission error is reduced when the installation tension is set higher than the tension that causes a change in contact direction between the tooth flanks. In addition, transmission error does not occur when the driving and driven pulleys are of equal outside diameter and have no pulley alignment error.

Transmission Error in Synchronous Belt Drives With Idler (Influence of Thickness Error of Belt Back Face Under No Load Conditions)

2004 ◽  
Vol 126 (1) ◽  
pp. 148-155 ◽  
Author(s):  
Kenichi Makita ◽  
Masanori Kagotani ◽  
Hiroyuki Ueda ◽  
Tomio Koyama
Keyword(s):  
Experimental Data ◽  
Transmission Error ◽  
Belt Drive ◽  
Analysis Method ◽  
Belt Drives ◽  
Back Face ◽  
Thickness Error ◽  
Synchronous Belt Drive ◽  
Load Conditions

Synchronous belt drives are commonly used in conjunction with an idler on the back face of the belt. However, thickness errors between the belt pitch line and back face of the belt, if present, will result in a change in belt tension on the span, and are considered to affect transmission error. In the present study, the transmission error in a synchronous belt drive with an idler under no load was investigated both theoretically and experimentally using a belt of known thickness error. The computed transmission error agrees well with the experimental data thereby verifying the applicability of the analysis method. In addition, a transmission error was mainly generated by the change in length of the belt pitch line due to the thickness error of the belt. It is shown that the transmission error due to the belt thickness error can be removed by using an automatic tensioner.

Transmission Error in Helical Synchronous Belt Drives in Bidirectional Operation Under No Transmitted Load (Influence of Pulley Flanges)

2004 ◽  
Vol 126 (5) ◽  
pp. 881-888 ◽  
Author(s):  
Masanori Kagotani ◽  
Kenichi Makita ◽  
Hiroyuki Ueda ◽  
Tomio Koyama
Keyword(s):  
Axial Direction ◽  
Helix Angle ◽  
Transmission Error ◽  
Belt Drive ◽  
Alignment Error ◽  
Belt Drives ◽  
The Difference ◽  
Case Transmission ◽  
Synchronous Belt Drive ◽  
Outside Diameter

Helical synchronous belt drives are more effective than conventional synchronous belt drives with respect to reducing noise and transmission error per single pitch of the pulley. However, the helix angle of the tooth trace causes axial belt movement. Therefore, flanged pulleys are used in a helical synchronous belt drive, in order to prevent the belt from running off the pulley. In the present study, the transmission error in a helical synchronous belt drive using flanged pulleys under no transmitted load was investigated both theoretically and experimentally for the case where the pulley was rotated in bidirectional operation. The computed transmission error agrees well with the experimental results, thereby confirming the applicability of the proposed theoretical analysis for transmission error. In this case, transmission error is found to be generated by the difference in axial belt movement between the driving and driven sides, and by a change in the state of contact between the belt and pulley teeth flanks. The transmission error is reduced when the installation tension is set higher than the tension that causes a change in contact direction between the tooth flanks. In addition, transmission error does not occur when the driving and driven pulleys are of equal outside diameter and have no alignment error between the driving and driven pulleys in the axial direction.

Influence of Idler on Transmission Error in Synchronous Belt Drives (Under Transmission Force)

2003 ◽  
Vol 125 (2) ◽  
pp. 404-410 ◽  
Author(s):  
Kenichi Makita ◽  
Masanori Kagotani ◽  
Hiroyuki Ueda ◽  
Tomio Koyama
Keyword(s):  
Helix Angle ◽  
Transmission Error ◽  
Experimental Results ◽  
Belt Drive ◽  
Belt Drives ◽  
Synchronous Belt Drive

Synchronous belt drives are widely used in various machines in order to transmit rotation accurately and synchronously. In these machines, idlers are commonly used to increase the angle of contact on the pulley and to avoid obstacles. However, the generating source of the transmission error under a transmission force with an idler remains unclear. In the present study, transmission error over a period of one pitch of the pulley was investigated both theoretically and experimentally for a synchronous belt drive attached an idler when a transmission force acted on the belt span. The experimental results agree closely with the computed results. The transmission error is greatly affected by change in the meshing state in the incomplete meshing sections. The idler position at which the transmission error is reduced exists even if the transmission torque increases. In addition, transmission error is reduced when the helix angle is increased.

Theoretical Analysis of Transmission Error in Helical Synchronous Belt With Error on Belt Side Face Under Bidirectional Operation

2009 ◽  
Vol 131 (8) ◽  
Author(s):  
Masanori Kagotani ◽  
Hiroyuki Ueda
Keyword(s):  
Theoretical Analysis ◽  
Helix Angle ◽  
Transmission Error ◽  
Belt Drive ◽  
Belt Drives ◽  
Axial Movement ◽  
Side Face ◽  
The Difference ◽  
Synchronous Belt Drive

Synchronous belt drives are occasionally required to transmit rotation accurately and are often employed in bidirectional operation. For transmission error per single pitch of the pulley, a helical synchronous belt with a helix angle of the tooth trace is effective. However, this belt causes axial movement because of the axial belt tooth load. When the belt comes into contact with the pulley flange or the belt moves away from the pulley flange due to bidirectional operation, the accuracy of finishing on the belt side face affects the transmission error. In the present study, the transmission error considering the error on the belt side face in a helical synchronous belt drive that uses flanged pulleys under the quasistatic condition and transmitted torque was investigated theoretically and experimentally for the case in which the pulley was rotated in bidirectional operation. The calculated transmission error coincided well with the experimentally obtained transmission error. Under forward rotation, the transmission error having a period of one rotation of the belt is caused by the error on the belt side face when the belt comes into contact with the pulley flange. Under reverse rotation, the transmission error is generated by a change in the belt tension due to the application of a transmitted torque and by the difference in axial belt movements between the driving and driven sides when the belt moves away from the pulley flange.

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