Study of Effect of Friction on the Pin of Pantograph Mechanism

Copyright © 2019 by author(s) and International Journal of Trend in Scientific Research and Development Journal. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0) (http://creativecommons.org/licenses/ by/4.0) ABSTRACT The research paper study the equivalent stress and shear stress generated on the pin due to friction between pin and links of a pantograph mechanism. The pin is subjected to biaxial loading of varying magnitude. The analysis comprises CAD model and simulated using a FEM solver. Materials of pin and links are selected considering real life applications and their coefficient of friction values are referred from variety of sources. Both static and dynamic coefficient of friction values are taken into consideration for analysis. Results thus obtained are tabulated and graphically demonstrated for better understanding of the outcomes.


INTRODUCTION
Pantograph is a four bar mechanical linkage used to trace a motion and can scale it up or down. Widely used in railways and milling machines, this mechanism has a simple but very effective design. Problem generally faced in applying this mechanism into practical application includes reduced accuracy in tracing the figures. Reason for this is the enlarged values of stresses due to friction, inertia and gravity effects for bigger mechanism. Here, we have analyzed the effect of friction in terms of equivalent stress and shear stress.

II.
Literature Review S. K. Saha, Rajendra Prasad and Ananta K. Mandal [1] have built a compact, lightweight, easily operated, economic carpet cleaning machine utilizing a pantograph mechanism made to work along with Hoe ken's mechanism. The machine is expected to ease the work of the carpet manufacturing labour and reduce the labour and production cost.
Coyote Steel and Co. [2] handbook on steel sizes and weights provide a large tabulation of data for various steel bars of different cross sections and lengths. The geometrical ratios are very helpful in determining the size of the links of pantograph mechanism in CAD modeling. Engineers Handbook [3] is a website that provides value of coefficient of friction for different materials like aluminum, steel, copper, etc. This data is used throughout the simulation of the pin and links.

III.
Design of mechanism For the better understanding of the working of pantograph mechanism, a wooden model was constructed. A CAD modeled using SOLIDWORKS 2019 is generated. The dimensions of the links are given in Table. 1   The thickness of the links is taken as 9.525mm (3/8 in) [2] for the width of 50.8mm (2 in) shown in Fig.2 and Fig.3.The width of the link is taken after referring the handbook data [2]. To ease the simulation, only two links are made in SOLIDWORKS. These links are GD and DT named link A and link B respectively.  Table.2 The links are made rigid to allow the entire load to transfer to the pin whereas pin is kept flexible to study the effects of friction on it. The loading conditions are biaxial. A tangential load and a radial load with respect to the pin is applied on links A and B as shown in Fig.6. Links are simulated in four conditions with different load magnitude given in Table.3.  The shank of the pin is held fixed to mimic the fixed point of rotation of links.

V. Simulation and results
For solving the problem, ANSYS 19.2 is used. The assembly used is shown in Fig.7 is solved in Explicit Dynamics analysis system

VI. Observations
From the obtained data, we can see that for combination 1, the values of equivalent stress and maximum shear stress at 50N tangential load, 5N radial load is minimum, and highest value of minimum shear stress is obtained here.
For combination 2, at 75N tangential load and 7.5N radial load, only minimum equivalent stress shows a deviation from general trend of increment.

VII.
Conclusion From obtained data we can tell that under same loading conditions, Steel 4340 shows less equivalent stress and shear stress at pin hence much better for construction Equivalent stress and maximum shear stress curves for Aluminum-Aluminum combination has an inverted bell shape and upright bell shape for minimum shear stress Steel 4340-Steel 4340 shows continuously increasing trend in maximum equivalent stress and maximum shear stress. The value of minimum equivalent stress for Steel 4340-Steel 4340 experiences a reduction