Topology Optimization of Sprocket and 3D Printing

Abstract

A chain drive is designed as a final reduction for an FSAE (Formula Student) Vehicle along with topology optimised geometry. Different geometrical shapes were iterated using the results from the topology optimisation and the design was finalised based on the magnitude of max stress concentration. The topology optimization was done under several constraints.

Introduction

I. INTRODUCTION

Formula Student cars are independently designed and built by team members and enter FSAE competitions funded by universities or automotive companies under rules promulgated by the Society of Automotive Engineering (SAE). Designers must consider structural design rationality, design cost, performance, fuel efficiency, driving stability and durability, and the overall design requirements are high. As one of the key parts of power transmission, the main reducer has been introduced in many publications over the years. 

Chain-Sprocket is one of the most crucial elements of the drivetrain system. With its wide range of applications right from basic final reduction of two wheelers to precise timing chain of internal combustion engines. It offers up to 98% efficiency and being a positive drive, it has the ability to transmit power without any slip or lag. 

As there is higher torque transmission and torsional load, the geometry that is fully filled leads to more weight of the overall sheet. Weight reduction is extremely important especially in any motorsport, as it directly affects the responsiveness to acceleration performance of a vehicle due to increased inertia of the vehicle. Also, the sprocket is a rotating component of the power transmission system, and the rotational moment of inertia of all rotating components directly affects the efficiency of power transmission and power loss. So, it's important to optimise all the rotating components for a lesser moment of inertia, and all other components for lesser weight. The geometry obtained through topology optimization is extremely complex with irregular shape and size `and not feasible to manufacture as it is. However, with appropriate shape and size optimization, the sprocket can be 3D printed easily.   3D printing is arguably only 30 years old, but it is already having a tremendous impact on a wide range of industries, from medical devices to consumer goods and pretty much everything in between1. A key driver of growth has been the ability to prototype components quickly and at very low cost. However, as 3D printing technology matures, industry players are experimenting with printing components for production and long-term use, rather than just using prototypes.

II. LITERATURE REVIEW

1. Yixuan Zhang-Topology Optimization of a Chain Drive’s Sprocket of Aprilia RS 125 Sport Bike- International Journal of Frontiers in Sociology
2. Parag Nikam1, Rahul Tanpure2- Design Optimization Of Chain Sprocket Using Finite Element Analysis- Int. Journal of Engineering Research and Application.
3. Vishnuvel., Kajendran., Akil Saran- Design and Optimisation of Chain Sprocket of a Formula Student Car- International Journal of Engineering Science and Computing

III. METHODOLOGY/EXPERIMENTAL

A. Design Methodology

The chain drive is designed considering the torque on the driven sprocket. A chain of minimum pitch available for a rated load required. The design needs to be safe enough to resist the torsional loads acting on the sprocket.

Input Data:

Max Motor torque: 150Nm

Reduction ratio required: 5.5

Teeth Ratio Selected: 72/13

The reduction ratio required is estimated from maximum tractive torque the tires can sustain and the max motor torque. The maximum torque capacity of both the tyres before slipping was estimated at 825Nm, hence the ratio reduction ratio of 5.5 was estimated. However, this doesn’t mean this ratio will lead to fastest lap for all events (i.e., autocross, skidpad, acceleration etc)

The final reduction will be practically tested after lap time simulations. And the final reduction which leads to fastest lap time for all events is not necessarily the steepest one (i.e., the one which utilises full tyre capacity). The max forces acting on the teeth and chain will be for greater speed reduction hence; maximum possible reduction was considered for chain selection and overall design.

Chain Selection: The tension in chain is roughly estimated using the reduction ratio required and assumed size of the sprocket. From this, the maximum tensile load acting on the chain is calculated to be 6kN. Based on this, the chain is selected. The chain is also subjected to continues dynamic and varying loads with shock loading. Hence, considering a factor of safety of 3, a chain of 18.6kN breaking load is selected.

Chain Specifications:

• ROLON Chain Number: R1278T
• Pitch: 12.7
• Inner Width: 7.9
• Roller diameter: 8.51
• Ultimate Tensile Strength/ Breaking Load: 18.6kN

B. Static Analysis

In reality, the force acting on each tooth is different; it progressively goes on reducing for each consecutive teeth from the first engaged tooth. This force on each tooth is calculated considering the centre-to-centre distance and size of both sprockets.

The forces are calculated as shown below:

V. LIMITATIONS

The only limitation and requirement t for a topology optimized part is that the boundary conditions should be accurate. That means failure to calculate accurate boundary conditions will lead to failure of part. The major limitation is that the topology optimized part may not sustain loads in different directions apart from what it’s designed for. So unexpected impact loading from other directions or different loading condition may lead to failure of the topology optimized part.

VI. FUTURE SCOPE

The sprocket can be further optimized by varying the chain pitch. The mounting position and the PCD of the bolts can be varied and iterated for further optimization.

Conclusion

1) The weight of the sprocket after topology optimization has reduced by 45.2%. 2) The moment of inertia about the axis of sprocket has reduced by 47% after topology optimization. 3) The weight after Shape and Size Optimization has increased by 80%. 4) The overall weight reduction is 1.713 kg. 5) The reduced weight and moment of inertia leads to increased responsive performance and efficiency of the vehicle.

References

[1] Yixuan Zhang, “Topology Optimization of a Chain Drive’s Sprocket of Aprilia RS 125 Sport Bike”, International Journal of Frontiers in Sociology, Vol. 2, no 9, pp. 35-47 [2] Parag Nikam and Rahul Tanpure, “Design Optimization of Chain Sprocket Using Finite Element Analysis”, Int. Journal of Engineering Research and Application, Vol. 6, no 9, pp. 66-69 [3] Vishnuvel, Kajendran and Akil Saran, “Design and Optimisation of Chain Sprocket of a Formula Student Car”, International Journal of Engineering Science and Computing Vol. 10, no 6, [4] V.B. Bhandari, Design of Machine Elements, ? 2nd ed., McGraw Hill Education (India) Private Limited, B-4, Sector-63, Dist. Gautam Budh Nagar, Noida – 201 301 [5] Richard G. Budynas, J. Keith Nisbett - Shigley’s Mechanical Engineering Design, 10th ed., McGraw Hill Education (India) Private Limited, B-4, Sector-63, Dist. Gautam Budh Nagar, Noida – 201 301

Copyright

Copyright © 2023 Krishna Amonkar, Shreyan Mathapati, Mihir Mandhare, Aditya Mistry, Yash Mohalkar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.