Optimal Machine Tool Setting for Hypoid Gears Improving Load Distribution

2000 ◽  
Vol 123 (4) ◽  
pp. 577-582 ◽  
Author(s):  
Vilmos Simon
Keyword(s):  
Machine Tool ◽  
Load Distribution ◽  
Angular Position ◽  
Distribution Factor ◽  
Hypoid Gears ◽  
Gear Teeth ◽  
Transmission Errors ◽  
Tool Setting ◽  
Load Distribution Factor ◽  
Optimal Machine

A method for the determination of optimal machine tool setting for manufacturing modified (mismatched) hypoid gears based on improved load distribution and reduced transmission errors is presented. The applied load distribution calculation is based on the conditions that the total angular position errors of the gear teeth being instantaneously in contact under load must be the same, and along the contact line of every tooth pair instantaneously in contact, the composite displacements of tooth surface points—as the sums of tooth deformations, geometrical surface separations, gear body bending and torsion, deflections of the supporting shafts, misalignments, and composite tooth errors—should correspond to the angular position of the gear. The tooth deformations consists of the bending and shearing deflections of gear teeth and of the local contact deformations of the mating surfaces. The tooth deflections are calculated by the finite element method. As the equations governing the load sharing and load distribution are nonlinear, an approximate and iterative technique is used to solve this system of equations. The method is implemented by a computer program. Using the program that was developed the influence of machine tool setting parameters for pinion manufacture on maximum tooth contact pressure, load distribution factor, and transmission errors is investigated. By successively choosing the optimal value for every machine tool setting parameter, and by applying the optimal set of these parameters, the maximum tooth contact pressure is reduced by 5.8%, the load distribution factor by 5.9%, and the angular position error of the driven gear by 65.4%, in regard to the hypoid gear pair manufactured by the machine tool setting determined by the commonly used method.

Optimal Machine Tool Setting for Hypoid Gears Improving Load Distribution

2000 ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Machine Tool ◽  
Load Distribution ◽  
Angular Position ◽  
Distribution Factor ◽  
Hypoid Gears ◽  
Gear Teeth ◽  
Transmission Errors ◽  
Tool Setting ◽  
Load Distribution Factor ◽  
Optimal Machine

Abstract A method for the determination of optimal machine tool setting for manufacturing modified (mismatched) hypoid gears based on improved load distribution and reduced transmission errors is presented. The applied load distribution calculation is based on the conditions that the total angular position errors of the gear teeth being instantaneously in contact under load must be the same, and along the contact line of every tooth pair instantaneously in contact, the composite displacements of tooth surface points — as the sums of tooth deformations, geometrical surface separations, gear body bending and torsion, deflections of the supporting shafts, misalignments, and composite tooth errors — should correspond to the angular position of the gear. The tooth defonnations consists of the bending and shearing deflections of gear teeth and of the local contact deformations of the mating surfaces. The tooth deflections are calculated by the finite element method. As the equations governing the load sharing and load distribution are nonlinear, an approximate and iterative technique is used to solve this system of equations. The method is implemented by a computer program. Using the program that was developed the influence of machine tool setting parameters for pinion manufacture on maximum tooth contact pressure, load distribution factor, and transmission errors is investigated. By successively choosing the optimal value for every machine tool setting parameter, and by applying the optimal set of these parameters, the maximum tooth contact pressure is reduced by 5.8%, the load distribution factor by 5.9%, and the angular position error of the driven gear by 65.4%, in regard to the hypoid gear pair manufactured by the machine tool setting determined by the commonly used method.

Optimal Tooth Modifications in Hypoid Gears

2004 ◽  
Vol 127 (4) ◽  
pp. 646-655 ◽  
Author(s):  
Vilmos Simon
Keyword(s):  
Load Distribution ◽  
Angular Position ◽  
Point Contact ◽  
Tooth Surface ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Transmission Errors ◽  
Tool Profile

A method for the determination of optimal tooth modifications in hypoid gears based on improved load distribution and reduced transmission errors is presented. The modifications are introduced into the pinion tooth surface by using a cutter with bicircular profile and optimal diameter. In the optimization of tool parameters the influence of shaft misalignments of the mating members is included. As the result of these modifications a point contact of the meshed teeth surfaces appears instead of line contact; the hypoid gear pair becomes mismatched. By using the method presented in (Simon, V., 2000, “Load Distribution in Hypoid Gears,” ASME J. Mech. Des., 122, pp. 529–535) the influence of tooth modifications introduced on tooth contact and transmission errors is investigated. Based on the results that was obtained the radii and position of circular tool profile arcs and the diameter of the cutter for pinion teeth generation were optimized. By applying the optimal tool parameters, the maximum tooth contact pressure is reduced by 16.22% and the angular position error of the driven gear by 178.72%, in regard to the hypoid gear pair with a pinion manufactured by a cutter of straight-sided profile and of diameter determined by the commonly used methods.

Optimization of Machine Tool Settings on Hypoid Gear Dynamics

2019 ◽  
Author(s):  
Chia-Ching Lin ◽  
Yawen Wang ◽  
Teik C. Lim ◽  
Weiqing Zhang
Keyword(s):  
Dynamic Response ◽  
Machine Tool ◽  
Rotor System ◽  
Design Parameters ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Hypoid Gears ◽  
Tool Setting ◽  
Setting Parameters ◽  
Optimal Machine

Abstract Hypoid gears are widely used to transmit torque on cross axis shafts in a vehicle rear axle system. The dynamic responses of these hypoid geared rotor system have a significant effect on the performance of noise, vibration, and harshness (NVH) for the vehicle design. From past studies, the main source of excitation for this vibration energy comes from hypoid gear transmission error (TE). Thus, the design of hypoid gear pair with minimization of TE is one way to control the dynamic behavior of the vehicle axle system. In this paper, an approach to obtain minimum TE and improved dynamic response with optimal machine tool setting parameters for manufacturing hypoid gears is discussed. A neural network, named Feed-Forward Back Propagation (FFBP), with Particle Swarm Optimization (PSO) and Gradient Descent (GD) training algorithms are used to predict the TE. With the optimal machine tool setting parameters, a 14 degrees of freedom geared rotor system analysis is performed to verify the improvement on dynamic response aiming at minimizing the TE. A case study of a hypoid gear pair with specified design parameters and working condition is presented to validate the proposed method. The results conclude that minimization of TE, the main excitation of vehicle axle gear whine noise and vibration, with optimal machine tool setting parameters can improve the overall dynamic response. The proposed approach provides a better understanding of an optimal design hypoid gear set to minimize TE and effect on vehicle axle system dynamics.

Experimental evaluation of the lateral load distribution in the elastic-plastic phase of timber-steel hybrid structures with a novel light timber-steel diaphragm

2019 ◽  
Vol 22 (8) ◽  
pp. 1965-1976
Author(s):  
Zhong Ma ◽  
Minjuan He ◽  
Renle Ma ◽  
Zheng Li ◽  
Linlin Zhang
Keyword(s):  
Load Distribution ◽  
Failure Modes ◽  
Lateral Displacement ◽  
Lateral Load ◽  
Lateral Loads ◽  
Distribution Factor ◽  
Elastic Plastic ◽  
Plastic Phase ◽  
Lateral Load Distribution ◽  
Load Distribution Factor

A cyclic loading experiment involving a timber-steel hybrid structure consisting of a steel frame and a novel light timber-steel diaphragm is presented to quantify the flexibility of the diaphragm and its ability to distribute lateral loads in the elastic-plastic phase of the structure. A lateral load-distribution factor was proposed, and its relationship to the ratio of the stiffness of the diaphragm to that of the lateral load-resisting elements was investigated. The diaphragm was classified based on these variables. The results indicated that the failure modes of the structure were associated with the forms of damage experienced by the lateral load-resisting elements, whereas little damage was observed for the diaphragm. The diaphragm exhibited the ability to continuously adjust the distribution of lateral loads to each lateral load-resisting element; accordingly, each lateral load-resisting element had approximately the same shear force, the same lateral stiffness, and the same lateral displacement during the loading process. As the lateral displacement increased, the stiffness ratio and load-distribution factor both gradually increased, and the diaphragm correspondingly changed from semi-rigid to rigid. At times, as the lateral displacement increased, the diaphragm rapidly became rigid, and it was unnecessarily rigid during the initial loading phase when the in-plane stiffness reached a certain threshold.

Optimal Tooth Modifications in Hypoid Gears

2003 ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Angular Position ◽  
Point Contact ◽  
Tooth Surface ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Transmission Errors ◽  
Tool Profile

A method for the determination of optimal tooth modifications in hypoid gears based on improved load distribution and reduced transmission errors is presented. The modifications are introduced into the pinion tooth surface by using a cutter with bicircular profile and by changing the cutter diameter. In the optimization of tool parameters the influence of shaft misalignments of the mating members is included. As the result of these modifications a point contact of the meshed teeth surfaces appears instead of line contact; the hypoid gear pair becomes mismatched. By using the method presented in [1] the influence of tooth modifications introduced on tooth contact and transmission errors is investigated. Based on the results that was obtained the radii and position of circular tool profile arcs and the cutter diameter for pinion teeth generation were optimized. By applying the optimal tool parameters, the maximum tooth contact pressure is reduced by 16.22% and the angular position error of the driven gear by 178.72%, in regard to the hypoid gear pair with a pinion manufactured by a cutter of straight-sided profile and of diameter determined by the commonly used methods.

INFLUENCE OF SPAN LENGTH AND CROSSBEAM ON LOAD DISTRIBUTION FACTOR FOR GIRDER BRIDGES

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Hyo-Gyoung Kwak ◽  
Joungrae Kim
Keyword(s):  
Finite Element ◽  
Load Distribution ◽  
Span Length ◽  
Distribution Factor ◽  
Steel Girder ◽  
Girder Bridges ◽  
Load Distribution Factor ◽  
Exterior Girder ◽  
Grillage Method ◽  
Concrete Girder

Load distribution factor at concrete girder bridges and steel girder bridges are analyzed with finite element method to see effect of span length and cross beam to load distribution factor. Span lengths of analyzed bridge models are 30m, 40m, 50m and 60m. The number of intermediate cross beam is increased from one to until distance between cross beams becomes 5m. The finite element analysis results show that concrete girder and steel girder can use same load distribution factor and span length doesn’t affect to load distribution factor. Even though load distribution factor in interior girders is not influenced by cross beam, in exterior girders it is influenced by cross beam. Effect of cross beam in exterior girder is influenced by the number of lanes and distance from exterior girder to curb. Since design code introduces conservative load distribution factor, economically improved load distribution factor is proposed. The proposed load distribution factor includes cross beam effect with the number of lanes and distance from exterior girder to curb. The proposed equation is compared with AASHTO code and grillage method which is well-known method to calculate load distribution. The comparison results showed that the proposed equation is more efficient and useful than AASHTO and safer than the grillage method.

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