Masanori Kagotani

A Study on Timing Belt Noise (Theoretical Analysis for Forced Transverse Vibration of Timing Belt With Parametric Excitation)

A theoretical analysis is made for two kinds of noise reduction methods of timing belts. The methods are confirmed experimentally in a companion paper [1]. Modeling the traveling belt as a string with parametric excitation in tension and density, we obtain an approximate solution for the amplitude of the transverse vibration and carry out some numerical computations for the response of the belt. It is shown that the maximum amplitude of the transverse vibration at resonance is reduced by the two kinds of parametric excitation. The method of variable tension suppresses the maximum amplitude almost for all modes of vibration at resonance and that of the variable density is effective for higher modes except the first mode at resonance.

Noise and life of helical timing belt drives

A new helical timing belt has been developed to reduce noise. In the present study, three belts, each having a curvilinear tooth profile and helix angles of 3 deg, 5 deg and 10 deg, respectively, were designed. The noise and life of the helical timing belt under a constant transmission force are compared with those of a conventional timing belt, in which the helix angle is zero. The noise level of the new helical belts having helix angles of 5 deg or 10 deg was found to be around 5 dB(A) lower than the conventional belt. The belt life was found to be almost identical for each type when the installation tension was set while the slack side tension for the transmission force was lowest. The results of the present study showed that helical belts should be selected for applications in which noise is a crucial factor.

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

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

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.

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

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.

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

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.

Factors Affecting Transmission Error in Helical Synchronous Belt With Error on Belt Side Face Under Bidirectional Operation

Helical synchronous belt drives are effective for reducing the noise and transmission error per single pitch of a pulley, as compared with conventional synchronous belt drives. However, the helix angle of the tooth trace causes axial belt movement. When the belt comes into contact with the pulley flange or moves away from the pulley flange due to bidirectional operation, the accuracy of finishing on the belt side face affects the transmission error. In addition, various factors, such as the transmitted torque, installation tension, pitch difference between the belt and the pulley, and alignment error between the driving and driven pulleys in the axial direction, are considered to affect the behavior of the transmission error. In the present study, the influence of various factors on the transmission error in a helical synchronous belt with the error on the belt side face was investigated. Specifically, the case in which a flanged pulley is rotated in bidirectional operation under the quasi-static condition and transmitted torque was examined. The transmission error in bidirectional operation considering the error on the belt side face increased with an increase in the transmitted torque, but was reduced when the installation tension was set to be high and when the pitch difference on the driving side was smaller than that on the driven side. In addition, the accuracy of rotation transmission improved when the alignment between the pulleys in the axial direction was set so that the belt on the driving side came into contact-with the pulley flange earlier than the belt on the driven side.

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

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.

A Study on Jumping Characteristics in Synchronous Belt Drives: Experimental Results and FE Analysis at Driven Pulley Jumping

The jumping characteristics at the driven pulley of L type synchronous belt drives are experimentally and analytically discussed. The number of the driving and the driven pulley teeth is the same and the wrapping angle of the belt on both pulleys is π radian. In this paper, the meshing state of belts on both of the driving and driven pulleys just before jumping is analyzed using the Finite Element analysis. Standardized L type synchronous belts and pulleys are used for analysis and experiments of the meshing states between belt and pulley, load distribution stress analysis and jumping torque. A 337L075 trapezoidal tooth profile synchronous belt and a 36L075 synchronous pulley are used in the analysis and the experiments. The wrapping angle of belt on both the driving and the driven pulley is equal to π radian. “ABAQUS/Standard” is used for the simulation and analysis of the belt. The simulation of the FE analysis of the wrapping angle of the belt on the driven pulley is almost the same with the experimental result. FE analysis of the load distribution just before jumping on the driven pulley agrees well with the experimental results.Copyright

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

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.Copyright