Transmission Error in Synchronous Belt With Resonance Under Installation Tension

2011 ◽  
Author(s):  
Masanori Kagotani ◽  
Hiroyuki Ueda
Keyword(s):  
Transmission Error ◽  
Speed Ratio ◽  
Experimental Transmission ◽  
Transmission Errors ◽  
Belt Drives ◽  
String Vibration ◽  
Mode Vibration ◽  
The Difference ◽  
The Moment ◽  
Good Agreement

Synchronous belt drives are widely employed to transmit rotation accurately. The belt spans between the driving and driven pulleys generate resonance when the transverse natural frequency of the belt, as in string vibration, matches the meshing frequency of the belt tooth and the pulley tooth. The resonance of the belt spans affects the behavior of the transmission error. In the present study, the mechanisms generating the transmission error in synchronous belt drives under installation tension and a pulley speed ratio of 1:1 are investigated theoretically and experimentally for the case in which the belt spans generate first mode vibration due to resonance. The calculated and experimental transmission errors show good agreement, and so the validity of our analysis is confirmed. The transmission error has a period of 1/2 of one pitch of the pulley, and is generated by the difference in displacement between the upper and lower belt spans, the difference in the amount of belt climbing at the beginning and end of meshing, and the generation of torque due to the moment of inertia on the driven side.

Transmission Error in Synchronous Belt With Resonance Under Installation Tension

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Masanori Kagotani ◽  
Hiroyuki Ueda
Keyword(s):  
Transmission Error ◽  
Speed Ratio ◽  
Experimental Transmission ◽  
Transmission Errors ◽  
Belt Drives ◽  
Concave Shape ◽  
Mode Vibration ◽  
The Difference ◽  
The Moment ◽  
Good Agreement

Synchronous belt drives generate resonance on the belt spans between the driving and driven pulleys when the transverse natural frequency of the belt, matches the meshing frequency of the belt tooth and the pulley tooth. The resonance of the belt spans affects the accuracy of rotation transmission. In the present study, the mechanisms generating the transmission error in synchronous belt drives under installation tension and a pulley speed ratio of 1:1 are investigated theoretically and experimentally for the case in which the belt spans generate first mode vibration due to resonance. In addition, the change in the shaft load caused by resonance is examined. The calculated and experimental transmission errors show good agreement, and so the validity of our analysis is confirmed. Transmission error is generated by the difference in displacement between the upper and lower belt spans due to the convex or concave shape, the difference in the amount of belt climbing at the beginning and end of meshing, and the generation of torque due to the moment of inertia on the driven side. The transmission error has a period of 1/2 of one pitch of the pulley, and the generated change in the shaft load, which is the sum of the displacement due to the convex or concave shape of the upper and lower spans and the sum of the belt climbing at the beginning and end of meshing, has a period of one pitch of the pulley.

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.

Experimental/Numerical Analysis of the Timing Belt Drive Behavior of a V6 Engine

2003 ◽  
Author(s):  
Lionel Manin ◽  
Didier Remond ◽  
Jean-Philippe Gaborel
Keyword(s):  
Rotation Speed ◽  
Transmission Error ◽  
Strain Gauges ◽  
Belt Drive ◽  
Automotive Engine ◽  
Transmission Errors ◽  
Belt Drives ◽  
Harmonic Content ◽  
Timing Belt ◽  
The Time Domain

The timing belts used for automotive engine are asked to last more and more, and to be less noisy. In this way, it is necessary to simulate the behavior of the engine timing belt drives for optimization, but also to understand it from experimental analysis. The first objective of the work was to analyze experimentally the behavior of a V6 engine timing belt drive in terms of: pulley speeds, belt span tensions, transmission error. The second objective was to compare the measurements with simulations. The engine has four overhead camshafts and 4 valves per cylinder. The timing belt drive is composed of six pulleys, three idlers and an automatic tensioner. The crankshaft and the two first camshaft speeds are measured with optical encoders. Spans tensions are measured by means of strain gauges glued on the idler mounting axes. All the data are simultaneously recorded. Tests have been run from 800 rpm to 6000 rpm. Measured data are first analyzed in the time domain. Some phenomena like, nil span tensions, speeds acyclism and transmission error amplitude, are observed. Then, analyses of the harmonic content of the span tensions, pulley speeds and transmission errors between the crankshaft and the camshafts, are performed versus engine rotation speed. Finally, the tests have been simulated and comparisons are made between numerical and experimental results.

Design System for Composite Transmission Error Prediction for Automatic Transmissions

2004 ◽  
Author(s):  
Sameer Gudal ◽  
Yong Pan ◽  
Shuh-Yuan Liou ◽  
V. Sundararajan ◽  
Daniel Antonetti ◽  
...  
Keyword(s):  
Transmission Error ◽  
Transmission System ◽  
Design System ◽  
Speed Ratio ◽  
Single Pair ◽  
Contributing Factors ◽  
Transmission Errors ◽  
Automatic Transmissions ◽  
The Individual ◽  
The Relationship

Noise in vehicular automatic transmissions is a complex phenomenon involving several interacting factors. One of the contributing factors to noise for a single pair of meshing gears has been shown to be the transmission error. The transmission error (TE) is defined in terms of deviation of the speed ratio from the ideal speed ratio. It has since been hypothesized that the composite transmission error in a planetary system would be the key contributor to noise in automatic transmissions. This composite error would have to include the contributions from individual meshes and account for the configuration of the transmission system. This paper describes a design system that enables engineers to predict and study effects of parameter variation on the composite transmission error. The designer first specifies the configuration of the transmission using canonical graphs. The graph contains the elements such as gears, clutches and brakes of the transmission system as its nodes and the relationship among them for the edges. The design system uses the graph to solve for the speeds and torques. The transmission errors for the individual meshes are computed and then combined into the composite transmission error using a simple average.

Determining Side-by-Side Current Loads Using CFD and Model Tests

2016 ◽  
Author(s):  
Arjen Koop
Keyword(s):  
Reynolds Number ◽  
Model Test ◽  
Full Scale ◽  
Test Results ◽  
Model Scale ◽  
Moment Coefficient ◽  
The Difference ◽  
The Moment ◽  
Good Agreement ◽  
Shielding Effects

When two vessels are positioned close to each other in a current, significant shielding or interaction effects can be observed. In this paper the current loads are determined for a LNG carrier alone, a Shuttle tanker alone and both vessels in side-by-side configuration. The current loads are determined by means of tow tests in a water basin at scale 1:60 and by CFD calculations at model-scale and full-scale Reynolds number. The objective of the measurements was to obtain reference data including shielding effects. CFD calculations at model-scale Reynolds number are carried out and compared with the model test results to determine the capability of CFD to predict the side-by-side current load coefficients. Furthermore, CFD calculations at full-scale Reynolds number are performed to determine the scale effects on current loads. We estimate that the experimental uncertainty ranges between 3% and 5% for the force coefficients CY and CMZ and between 3% and 10% for CX. Based on a grid sensitivity study the numerical sensitivity is estimated to be below 5%. Considering the uncertainties mentioned above, we assume that a good agreement between experiments and CFD calculations is obtained when the difference is within 10%. The best agreement between the model test results and the CFD results for model-scale Reynolds number is obtained for the CY coefficient with differences around 5%. For the CX coefficient the difference can be larger as this coefficient is mainly dominated by the friction component. In the model tests this force is small and therefore difficult to measure. In the CFD calculations the turbulence model used may not be suitable to capture transition from laminar to turbulent flow. A good agreement (around 5% difference) is obtained for the moment coefficient for headings without shielding effects. With shielding effects larger differences can be obtained as for these headings a slight deviation in the wake behind the upstream vessel may result in a large difference for the moment coefficient. Comparing the CFD results at full-scale Reynolds number with the CFD results at model-scale Reynolds number significant differences are found for friction dominated forces. For the CX coefficient a reduction up to 50% can be observed at full-scale Reynolds number. The differences for pressure dominated forces are smaller. For the CY coefficient 5–10% lower values are obtained at full-scale Reynolds number. The moment coefficient CMZ is also dominated by the pressure force, but up to 30% lower values are found at full-scale Reynolds number. The shielding effects appear to be slightly smaller at full-scale Reynolds number as the wake from the upstream vessel is slightly smaller in size resulting in larger forces on the downstream vessel.

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.

Effect of Teeth Friction on Transmission Errors and Tooth Load of Spur Gears

2015 ◽  
Author(s):  
Chan Il Park
Keyword(s):  
Friction Force ◽  
Sliding Friction ◽  
Primary Source ◽  
Transmission Error ◽  
Spur Gears ◽  
Mesh Stiffness ◽  
Transmission Errors ◽  
Sliding Mechanism ◽  
The Moment ◽  
The Relationship

Transmission error is typically understood to act as the primary source of gearbox noise and vibration. This paper investigates the effect of sliding friction on the transmission error and tooth load of spur gears. To do so, the kinematic relation for the sliding mechanism of spur gears and mesh stiffness was calculated. The relationship between tooth load, tooth errors and mesh compliance as well as the moment balance equation in consideration of the teeth friction force are derived. Transmission error, tooth load, and the teeth friction force of gears with/without modification were investigated. As the results, friction caused an increase in tooth load and transmission error in gear approach and a decrease in tooth load and transmission error in gear recess.

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