Effects of Tooth Indexing Errors on Load Distribution and Tooth Load Sharing of Splines Under Combined Loading Conditions

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
J. Hong ◽  
D. Talbot ◽  
A. Kahraman
Keyword(s):  
Load Distribution ◽  
Probability Distributions ◽  
Random Sequence ◽  
Load Sharing ◽  
Spur Gear ◽  
Combined Loading ◽  
Distribution Model ◽  
Loading Conditions ◽  
Manufacturing Tolerance ◽  
Single Tooth

In this paper, influences of tooth indexing errors on load distribution and tooth load sharing of spline joints are investigated by modifying an existing semi-analytical load distribution model for side-fit involute splines. Two commonly observed loading conditions, namely (i) combined torsion and radial loads representative of a spline joint of a spur gear with shaft and (ii) combined torsion, radial loads, and tilting moment representative of a spline joint of a helical gear with shaft are considered in this study. Numerical results of an example spline having (i) no tooth indexing error, (ii) a single tooth with indexing error, and (iii) a random sequence of tooth indexing errors under these two loading conditions are presented to demonstrate the effects of tooth indexing errors. In addition, a practical study of the robustness to manufacturing tolerances is also presented where probability distributions of load sharing factor of the critical tooth of an example spline designed to certain manufacturing tolerance classes are obtained with a large number of randomly generated indexing error sequences.

A generalized semi-analytical load distribution model for clearance-fit, major-fit, minor-fit, and mismatched splines

2015 ◽  
Vol 230 (7-8) ◽  
pp. 1126-1138 ◽  
Author(s):  
J Hong ◽  
D Talbot ◽  
A Kahraman
Keyword(s):  
Load Distribution ◽  
Load Sharing ◽  
Helical Gear ◽  
Distribution Model ◽  
Radial Clearance ◽  
Loading Conditions ◽  
Involute Spline

A generalized semi-analytical load distribution model for all common types of involute spline joints is proposed. It is formulated to model clearance-fit (side-fit) involute splines with contacts happening only at the drive flanks of the spline teeth, major or minor-diameter fit splines where additional contact occurs along the top land and the root land of the external spline teeth, respectively, as well as mismatched splines where an intentional lead mismatch is introduced to initiate contact along both drive and back (coast) flanks. Using this model, load distribution and tooth-to-tooth load sharing of example major and minor diameter-fit spline joints under typical multi-directional spur and helical gear loading conditions are characterized and compared to those of the corresponding side-fit spline joint. Further, self-centralizing performance of major and minor-fit splines versus side-fit splines is quantified including its sensitivity to the radial clearance magnitude. Finally, load distribution of an example side-fit spline having various intentional mismatch magnitudes at different torque level is investigated to show that a given mismatch value is optimal at a certain design torque.

scholarly journals An Improved Algorithm for Calculating Friction Force and Torque in Involute Helical Gears

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Lin Han ◽  
Wentie Niu ◽  
Dawei Zhang ◽  
Fujun Wang
Keyword(s):  
Friction Coefficient ◽  
Friction Force ◽  
Load Distribution ◽  
Distribution Model ◽  
Contact Lines ◽  
Helical Gears ◽  
Constant Friction ◽  
Single Tooth ◽  
The Difference ◽  
Typical Design

Time varying frictional force and torque are one of the main exciting sources of vibration in helical gears. This paper presents an approach to determine the friction force and torque in involute helical gears considering nonuniform load distribution along contact lines. An analytical load distribution model is employed and extended to obtain the load per unit of length along contact lines. Friction force and torque models under nonuniform assumption are derived. Comparisons of the determined friction force and torque with the results from uniform assumption are made. In addition, the differences between constant friction coefficient and varying coefficient are revealed. Moreover, two typical design cases of helical gears are studied. Results show that the fluctuations of friction force and torque under uniform assumption are more significant than those under nonuniform assumption in sample I for a single tooth, but less significant for the sum of those of the three teeth, while in sample II, the fluctuations under uniform assumption are less significant than those under nonuniform assumption. The friction coefficient induced difference is negligible compared with the difference induced by load distribution assumptions.

Effect of Drive Side Contact Ratio on Direct Design Asymmetric High Contact Ratio Spur Gear Based on Load Sharing

2014 ◽  
Vol 592-594 ◽  
pp. 2292-2296 ◽  
Author(s):  
P. Marimuthu ◽  
G. Muthuveerappan
Keyword(s):  
Parametric Design ◽  
Load Sharing ◽  
Spur Gear ◽  
Spur Gears ◽  
Bending Stress ◽  
Contact Ratio ◽  
Normal Contact ◽  
Critical Loading ◽  
Direct Design ◽  
Single Tooth

The aim of this paper is to determine the effect on direct design asymmetric high contact ratio spur gear based on tooth load sharing. A unique Ansys parametric design language code is developed for this study. The load sharing based bending and contact stresses are determined for different drive side contact ratios. In addition to that the location of critical loading point is determined. Because the critical loading point for high contact ratio spur gear not lies on fixed point like normal contact ratio spur gears namely highest point of single tooth contact. In conclusion an increase in drive side contact ratio leads to increase in the load sharing based bending stress and decrease in the contact stress at the critical loading point.

Experimental and Theoretical Investigation of Quasi-Static System Level Behavior of Planetary Gear Sets

2021 ◽  
Vol 143 (10) ◽  
Author(s):  
Lokaditya Ryali ◽  
Abhishek Verma ◽  
Isaac Hong ◽  
David Talbot ◽  
Farong Zhu
Keyword(s):  
Load Distribution ◽  
Planetary Gear ◽  
Load Sharing ◽  
Operating Conditions ◽  
Experimental Methodology ◽  
System Level ◽  
Distribution Model ◽  
Design Parameters ◽  
Static System ◽  
Planetary Gear Sets

Abstract This study presents a unique experimental methodology that synchronously measures various quasi-static responses of a simple four-planet planetary gear set, namely, planet load sharing, overall transmission error (OTE), and floating sun gear orbits. Strain gauges mounted directly on the planet pins were used to monitor the load shared among the planets, which is a crucial design criterion for durability and performance. High-precision optical encoders were used to measure the OTE of the gear set to explore its diagnostic value in identifying system errors. Radial motions of the floating sun gear, which are critical to the self-centering and load sharing behavior of the gear set, were monitored using magnetic proximity probes. The influence of various design parameters and operating conditions such as planet mesh phasing, carrier pin position errors, gear tooth modifications, and input torque on the system’s response will be investigated by performing an extensive set of experiments in a repeatable and accurate manner. Finally, these experimental results will be recreated theoretically using the static planetary load distribution model of Hu et al. (2018, “A Load Distribution Model for Planetary Gear Sets,” ASME J. Mech. Des., 140(5), p. 53302) to not only validate the model but also comprehend the measured behavior.

Design of Pipeline Composite Repairs: From Lab Scale Tests to FEA and Full Scale Testing

2014 ◽  
Author(s):  
Remy Her ◽  
Jacques Renard ◽  
Vincent Gaffard ◽  
Yves Favry ◽  
Paul Wiet
Keyword(s):  
Finite Element ◽  
Full Scale ◽  
Combined Loading ◽  
Material Strength ◽  
Repair System ◽  
Loading Conditions ◽  
Original Design ◽  
Composite Repair ◽  
Repair Systems ◽  
Composite Properties

Composite repair systems are used for many years to restore locally the pipe strength where it has been affected by damage such as wall thickness reduction due to corrosion, dent, lamination or cracks. Composite repair systems are commonly qualified, designed and installed according to ASME PCC2 code or ISO 24817 standard requirements. In both of these codes, the Maximum Allowable Working Pressure (MAWP) of the damaged section must be determined to design the composite repair. To do so, codes such as ASME B31G for example for corrosion, are used. The composite repair systems is designed to “bridge the gap” between the MAWP of the damaged pipe and the original design pressure. The main weakness of available approaches is their applicability to combined loading conditions and various types of defects. The objective of this work is to set-up a “universal” methodology to design the composite repair by finite element calculations with directly taking into consideration the loading conditions and the influence of the defect on pipe strength (whatever its geometry and type). First a program of mechanical tests is defined to allow determining all the composite properties necessary to run the finite elements calculations. It consists in compression and tensile tests in various directions to account for the composite anisotropy and of Arcan tests to determine steel to composite interface behaviors in tension and shear. In parallel, a full scale burst test is performed on a repaired pipe section where a local wall thinning is previously machined. For this test, the composite repair was designed according to ISO 24817. Then, a finite element model integrating damaged pipe and composite repair system is built. It allowed simulating the test, comparing the results with experiments and validating damage models implemented to capture the various possible types of failures. In addition, sensitivity analysis considering composite properties variations evidenced by experiments are run. The composite behavior considered in this study is not time dependent. No degradation of the composite material strength due to ageing is taking into account. The roadmap for the next steps of this work is to clearly identify the ageing mechanisms, to perform tests in relevant conditions and to introduce ageing effects in the design process (and in particular in the composite constitutive laws).

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