A Method to Generate the Spiral Flutes of an Hourglass Worm Gear Hob

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Jie Yang ◽  
Haitao Li ◽  
Chengjie Rui ◽  
Wenjun Wei ◽  
Xuezhu Dong
Keyword(s):  
Mathematical Model ◽  
Manufacturing System ◽  
Worm Gear ◽  
Virtual Manufacturing ◽  
Cutting Performance ◽  
Curved Surface ◽  
Transmission Ratio ◽  
Multiple Threads ◽  
Different Shapes ◽  
The Absolute

All of the cutting edges on an hourglass worm gear hob have different shapes and spiral angles. If the spiral angles are small, straight flutes are typically adopted. However, for hobs with multiple threads, the absolute values of the negative rake angles on one side of the cutting teeth will greatly affect the cutting performance of the hob if straight flutes are still used. Therefore, spiral flutes are typically adopted to solve this problem. However, no method to determine the spiral flute of an hourglass worm gear hob has been proposed until now. Based on the curved surface generating theory and the hourglass worm forming principle, a method for generating the spiral flute of the planar double enveloping hourglass worm gear hob is proposed in this paper. A mathematical model was built to generate the spiral flute. The rake angles of all cutting teeth of the hob are calculated. The laws of the rake angles of the cutting teeth for four hobs with different threads from one to four threads were analyzed when straight flutes and spiral flutes are adopted. The laws between the value of the negative rake angles of the hob with four threads and the transmission ratio were studied. The most appropriate transmission ratio for generating the spiral flute was obtained. The machining of the spiral flutes was simulated using a virtual manufacturing system, and the results verify the correctness of the method.

Research on a Generating Method of Spiral Flutes of Hourglass Worm Gear Hob

2017 ◽  
Author(s):  
Yang Jie ◽  
Li Haitao ◽  
Rui Chengjie ◽  
Wei Wenjun ◽  
Dong Xuezhu
Keyword(s):  
Mathematical Model ◽  
Manufacturing System ◽  
Worm Gear ◽  
Virtual Manufacturing ◽  
Transmission Ratio ◽  
Method Of Determination ◽  
Generating Method ◽  
Multiple Threads ◽  
Different Shapes

All of the cutting edges on an hourglass worm gear hob have different shapes and spiral angles. If the spiral angles are small, straight flutes are usually adopted. But for the hob with multiple threads, the absolute values of the negative rake angles at one side of the cutting teeth will greatly affect the cutting performance of the hob if straight flutes are still used. Therefore, spiral flutes are usually adopted to solve the problem. However, no method of determination of the spiral flute of the hourglass worm gear hob has been put forward till now. Based on the curved surface generating theory and the hourglass worm forming principle, a generating method for the spiral flute of the planar double enveloping worm gear hob is put forward in this paper. A mathematical model is built to generate the spiral flute. The rake angles of all cutting teeth of the hob are calculated. The laws of the rake angles of the cutting teeth of four hobs with different threads from one to four threads are analyzed when straight flutes and spiral flutes are adopted respectively. The laws between the value of the negative rake angles of the hob with four threads and the milling transmission ratio are studied. The most appropriate milling transmission ratio for generating the spiral flute is obtained. The machining of the spiral flutes is simulated by a virtual manufacturing system and the results verify the correctness of the method.

Batch Splitting Activity in Scheduling of Virtual Cell with Capacity Constraints Based on Bi-Level Mathematical Model

2012 ◽  
Vol 263-266 ◽  
pp. 1257-1264 ◽  
Author(s):  
Wen Min Han ◽  
Juan Chen ◽  
Xiang Zun Bu
Keyword(s):  
Mathematical Model ◽  
Manufacturing System ◽  
Virtual Manufacturing ◽  
Virtual Cell ◽  
Virtual Cells ◽  
Lot Splitting ◽  
Hierarchical Decision ◽  
Decision Structure ◽  
Splitting Problem ◽  
Bottleneck Machine

Although there has been some researches about virtual cell manufacturing system, the existing literature lack of discussion about the scheduling model that considering with bottleneck machines in the virtual cells. In view of this deficiency and the new characteristics of the batch splitting problem, this paper considered the batch splitting (or lot splitting) problem in scheduling of virtual manufacturing cells with bottlenecks and multiple machine types, and each of which has several identical machines. In consideration of the hierarchical decision structure of the problem, we developed a bi-level multi-objective mathematical model. Scheduling results and batch splitting strategies of both bottleneck and non-bottleneck machines are given in separate decision levels and additional scheduling objectives are improved in the second model level, while maintaining the maximum use of the bottleneck machine ability. In order to demonstrate how this approach works, application example was shown in this paper.

Concurrent scheduling and layout of virtual manufacturing cells considering assembly aspects

2020 ◽  
pp. 095440542098068
Author(s):  
Kamran Forghani ◽  
S. M. T. Fatemi Ghomi ◽  
Reza Kia
Keyword(s):  
Mathematical Model ◽  
Simulated Annealing ◽  
Model Material ◽  
Virtual Manufacturing ◽  
Superior Performance ◽  
Shop Floor ◽  
Processing Route ◽  
Manufacturing Cells ◽  
Comparison Results ◽  
Virtual Manufacturing Cells

Cell formation, scheduling, and facility layout are three main decisions in designing manufacturing cells. In this paper, we address the integration of these decisions in virtual manufacturing cells considering assembly aspects and process routing. We develop a mathematical model to determine the machine cells, the layout of machines and workstations on the shop floor, the processing route of parts, and the production sequence of operations on the machines. In this mathematical model, material handling costs and cycle time are minimized. To the best of our knowledge, this is the first paper that concurrently addresses the scheduling and layout of virtual manufacturing cells with assembly aspects and so-called criteria. To effectively solve the problem, a Population-based Simulated Annealing (PSA) combined with linear programming is proposed. The practical usability of the developed model is demonstrated in a case study. Finally, instances from the literature are solved to evaluate the performance of the PSA. The comparison results showed the superior performance of the PSA in comparison with CPLEX solver and standard simulated annealing.

Evaluation of Overall Efficiency of Devices with Worm Gear

2015 ◽  
Vol 808 ◽  
pp. 9-14
Author(s):  
Alexandru Micaciu ◽  
Ioan Vuşcan ◽  
Nicolae Panc
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Model Validation ◽  
Manufacturing Technology ◽  
Qualitative Property ◽  
Worm Gear ◽  
Overall Efficiency

Overall efficiency represents an important qualitative property for devices used in manufacturing technology. This paper presents the mathematical modeling of calculating worm gear overall efficiency. The studied worm gear types goes into numerous manufacturing devices component. Mathematical model validation was experimentally performed on a tool sharpening device with a helicoidally profile. The analytical calculated results were closed to experimentally determined results, which partially validates the model proposed in the paper.

Compliant gripper design, prototyping, and modeling using screw theory formulation

2020 ◽  
pp. 027836492094781
Author(s):  
Irfan Hussain ◽  
Monica Malvezzi ◽  
Dongming Gan ◽  
Zubair Iqbal ◽  
Lakmal Seneviratne ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Screw Theory ◽  
Tracking System ◽  
Mathematical Formulation ◽  
Optical Tracking ◽  
Kinematic Structure ◽  
Optical Tracking System ◽  
Different Shapes ◽  
Manufacturing Parameters

This article investigates some aspects related to the design, modeling, prototyping, and testing of soft–rigid tendon-driven grippers. As a case study, we present the design and development of a two-finger soft gripper and exploit it as an example to demonstrate the application scenario of our mathematical model based on screw theory. A mathematical formulation based on screw theory is then presented to model gripper dynamics. The proposed formulation is the extension of a model previously introduced including the mechanical system dynamics. In this type of gripper, it is possible to achieve different behaviors, e.g., different fingertip trajectories, equivalent fingertip stiffness ellipsoids, etc., while keeping the same kinematic structure of the gripper and varying the properties of its passive deformable joints. These properties can be varied in the prototype by properly regulating some manufacturing parameters, such as percentage of printing infill density in a 3D printing process. We performed experiments with the prototype of the gripper and an optical tracking system to validate the proposed mathematical formulation, and to compare its results with other simplified formulations. We furthermore identified the main performance of the gripper in terms of payload and maximum horizontal resisted force, and verified the capabilities of the gripper to grasp objects with different shapes and weights.

Dynamical Analysis on Sugarcane Cutter Rigidity Enhancement

2011 ◽  
Vol 199-200 ◽  
pp. 1387-1390
Author(s):  
Xiao Lai ◽  
Shang Ping Li ◽  
Fang Lan Ma ◽  
Jing Hui Zhou ◽  
Zheng Zhong Zhang
Keyword(s):  
Mathematical Model ◽  
Simulation Analysis ◽  
Physical Experiment ◽  
Cutting Performance ◽  
Dynamical Analysis ◽  
Effect Factors ◽  
Dynamical Simulation ◽  
Actual Effect ◽  
Great Damage

Improving the cutting performance, especially the cutting quality of sugarcane harvesters is the most magnificent problem for popularizing the application of the havesters. Much research has been done on most effect factors but rare on the influence of rigidity enhancement of sugarcane cutter. Indeed, the rigidity of sugarcane cutter has notable influence on the quality of sugarcane cutting，as it effects its vibration and the vibration in turn brings great damage to the cutting quality. This paper analyzes how the rigidity of sugarcane cutter effects its working vibration by building up its mathematical model, then further investigates it by making a dynamical simulation analysis to compare two cutter structures with different rigidity based on ANSYS and ADAMS, and validate the actual effect of enhancing the cutter rigidity through a physical experiment. The result shows enhancing the rigidity of the cutter could lead to notable improvement of sugarcane cutting quality.

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