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Analysis of Whitworth Quick Return Mechanism Using ANSYS

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Analysis of Whitworth Quick Return Mechanism Using ANSYS Research and Reviews: Journal of Mechanics and Machines Volume 3 Issue 1 Analysis of Whitworth Quick Return Mechanism using ANSYS Rupanshu Singh* 1Department of Mechanical Engineering, Delhi Technological University, Delhi, India *Corresponding Author E-Mail Id:[email protected] ABSTRACT Machines minimizes the effort and complete the work. They produce motion, by working on a specific mechanism. Machines in workshops like shaper machine works on the Whitworth quick return mechanism. It comprises the assemblage of cranks and sliders to convert rotatory motion into reciprocating motion. The aim of this report is to demonstrate the Whitworth mechanism by generating a virtual model and analyzing the motion of the setup. The velocity, acceleration, and force generated by the slider is determined and conclusion is provided for the application of mechanism for industrial purpose and providing a substitute for expensive automated machines used in packaging industries. Keywords:-Whitworth mechanism, quick return, ANSYS INTRODUCTION Mechanism is the assemblage of structures to perform a specific motion, and produce work. It includes a number of rods, chains and joints. This is basically, a combination of parts, such that movement one part results in the motion of another part. Whitworth Quick Return Mechanism: It is the arrangement of crank slider to convert the rotatory motion into reciprocating motion. It display a non-uniform stroking of crank, where the front stoke is slightly longer having a faster return. It transmits two strokes over one cycle of revolution. This mechanism is used in workshops, for material cutting purposes. Shaper is a machine tool that works on quick return mechanism, it provides linear strokes to remove the unwanted material. A constant feed is given to cutting tool to cover the whole surface, a fine surface is generated on completion of machining. The motor providing a rotatory motion is connected to the mechanism which generates the reciprocating motion. Fig.1:-Demonstration of Whitwroth Quick Return Mechanism HBRP Publication Page 1-8 2021. All Rights Reserved Page 1 Research and Reviews: Journal of Mechanics and Machines Volume 3 Issue 1 This mechanism is mostly used in shaping and slotting machines. In this mechanism, the link CD (link 2) forming the turning pair is fixed, as shown in Figure 1. The link 2 corresponds to a crank in a reciprocating steam engine. The driving crank CA (link 3) rotates at a uniform angular speed. Now when the driving crank moves from the position CA2 to CA1 (or the link DP from DP2 toDP1 ) through an angle β in the clockwise direction, the tool moves back from right hand end of its stroke to the left hand end. Since the crank link CA rotates at uniform angular velocity therefore time taken during the cutting stroke (or forward stroke) is more than the time taken during the return stroke. In other words, the mean speed of the ram during cutting stroke is less than the mean speed during the return stroke. The ratio between the time taken during the cutting and return strokes is given by 푇푖푚푒 표푓 푐푢푡푡푖푛푔 푠푡푟표푘푒 훼 훼 = = 푇푖푚푒 표푓 푟푒푡푢푟푛 푠푡푟표푘푒 훽 360 − 훼 An analysis on the mechanism is produced, to determine factors such as displacements, forces exerted, etc. Optimality of the mechanism’s working will be analyzed. The result will be considered for future application of the mechanism as shown in Figure 2. Fig.2:-Velocity in slider crank mechanism The angular velocity of the connecting rod AB (휔퐴퐵) may be determined as follows: 휔 푣 푎푏 퐴퐵= 퐵퐴= 퐴퐵 퐴퐵 The direction of vector ab (or ba) determines the sense of (휔퐴퐵) which shows that it is anticlockwise. Let the crank OB makes an angle θ with the inner dead centre (I.D.C) and rotates in a clockwise direction about the fixed point O with uniform angular velocity ωBO rad/s. We know that centripetal or radial acceleration of B with respect to O or acceleration of B(because O is a fixed point),(Figure 3). 푣 2 푎 = 휔2 푋퐵푂 = 퐵푂 퐵푂 푂퐵 HBRP Publication Page 1-8 2021. All Rights Reserved Page 2 Research and Reviews: Journal of Mechanics and Machines Volume 3 Issue 1 Fig.3:-Acceleration in slider crank mechanism Mathematical model of dynamic analysis of quick return mechanism is generated using D’Alembert principle [1]. LITERATURE REVIEW- Himanshu Chaudhary use maximum reclusive ness of a dynamic equation for the evaluation of bearing force, In this work author optimize vibration and improve the balancing of four bar mechanism.[2]; Selcuk Erkaya carried out dynamic analysis of slider crank mechanism with eccentric connector and planetary gears, in this study there are two type of slider-crank mechanism one is simple slider-crank and second one is modified slider-crank mechanism in modified has an additional extra link between connecting rod and crank pin as distinct from conventional mechanism, using dynamic analysis author conclude force output is grater in modified slider-crank mechanism [3]; Kevin Russell et. al. created method for designing slider crank mechanism to achieve multi-phase motion generation application typically accomplished by adjustable planer four bar motion generator.[4] Modelling A virtual CAD model was designed in Solidworks 2020 to analyze the motion generated by the Whitwroth Quick Return Mechanism as shown in Figure 4. Different parts were designed with accurate dimensions. Two cranks, two sliders, one slotted lever and one main stand were modelled and assembled in Solidworks 2020. The connections of joints and sliders were defined to obtain the motion of the mechanism[5]. The frame of the mechanism was made of 80/20 aluminum framing, connected with commercially available brackets. Fig.4:-Model setup of Whitworth quick return mechanism HBRP Publication Page 1-8 2021. All Rights Reserved Page 3 Research and Reviews: Journal of Mechanics and Machines Volume 3 Issue 1 Different parts generated were assembled together to analyze the motion of the mechanism as shown in Figure 5-7. Fig.5:-Main stand part generated and slotted sleeve and the crank and slider assembly Fig.6:-Crank connecting the slider and slotted lever Fig.7:-Full assembly of the crank slider mechanism HBRP Publication Page 1-8 2021. All Rights Reserved Page 4 Research and Reviews: Journal of Mechanics and Machines Volume 3 Issue 1 The model generated represents the quick return mechanism. The center crank is rotated about the x-axis and the relative motion of the slider (connected to the stand) is observed. The movement of the mechanism in a complete cycle of front and backward stroke is obtained. The motion of the model was analyzed on ANSYS software as shown in Figure 8. This analysis includes graphs that represent these values with relation to the angle of the crank. These functions were used to analyze the mechanism at the highest and lowest positions of the crank. Fig.8:-Working motion of quick return mechanism Fig.9:-Stress contours developed in the slotted lever RESULTS Using Mathematical model of kinematic analysis and ANSYS data is analyze for the variable length of each link, in that analysis velocity of slider (link-6) which is output of quick return mechanism is change with change of length of each link but total output ratio of velocity is remain constant, in that analysis only with change of height of slider (link-6) velocity ratio is change [6]. HBRP Publication Page 1-8 2021. All Rights Reserved Page 5 Research and Reviews: Journal of Mechanics and Machines Volume 3 Issue 1 The motion of the model represents the characteristics properties of the quick return mechanism. The stress contours developed in the slotted lever, throughout the cycle are shown in Figure 9. Position The position of crank (shown in the Figure modelling) is considered at 0 deg, then the position of the of the slider is shown in the graph below. The slider’s position analysis is done. The movement variation according to the angular position is obtained as shown in Figure 10. Fig.10:-Graph between displacement of slider and crank’s angular position Velocity- From the above graph, the velocity obtained is maximum at around 200 degrees from the starting position. A smooth curve is obtained for the relative velocity. Using the position analysis and the motor specifications, the velocity of the transmission pin between the slider link and the crank was determined. This was used to find the velocity of the slider link and slider block as shown in Figure 11. Fig.11:-Graph between velocity of slider relative to the stand and angular position Acceleration Using the velocity and position analyses, the linear and angular acceleration of the slider link was determined. Due to the nature of the mechanism, the graph of the acceleration of the slider link is the same shape as the graph of the acceleration of the slider block as shown in Figure 12. HBRP Publication Page 1-8 2021. All Rights Reserved Page 6 Research and Reviews: Journal of Mechanics and Machines Volume 3 Issue 1 Fig.12:-Acceleration of slider link Force The force exerted in the front and return stroke of the slider is analyzed. The graph in (Figure 13) shows that at the front stroke (around 150 degrees) force exerted is maximum, which comes to zero and beyond 200 degrees the force generated in the return stroke is depicted. Fig.13:-Graph between Force generated by the slider and angular position Now as per the design of quick return mechanism the relative velocity and output force is required to maximum, So from the dynamic analysis of quick return mechanism force output is analyzed for the future application of the mechanism.
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