Building A Bell-Crank Lever Component For Lifting

The Necessity of the Bell-Crank Lever

This project paper provides a detailed explanation on how to build a bell-crank lever component to facilitate the lifting process while ensuring that the weight of the component in the safe region is lowered with quite a significant percentage. The project besides giving a detailed explanation of the design, it goes ahead to explain how to select the materials necessary for manufacture, the process of manufacture, testing and analysis of the finished product

The project will entail designing of a Hand pallet through the utilization of the Bell-Crank lever mechanism for the base so that it can help in making work easier for whatever application it will be used for, either domestically, industrial use of commercially.

The project is designed to accomplish a specific set of purposes as stated below. Further use of special tools and software’s is utilized to ensure that the final product meets the objectives for which it is designed. This objectives are as listed below

• To utilize the principles of finite element method to design, build and analyze the bell crank lever mechanism.
• To determine and interpret the working stresses of a bell crank lever.
• To examine the upper limit or maximum failure in a bell crank lever.
• To utilize the photo elastic experiment to determine, draw and analyze the stress trends of the bell-crank.

The necessity of a bell-crank lever in the modern society cannot be under estimated. The lever has made the process of lifting weights both in domestic, industrial and commercial use easier. Heavier loads can be lifted with much less weight since the lever acts a force multiplier hence reducing the human effort.

The need for the bell-crank lever in the modern society can be visualized by looking at the scenario where weights are by a fork lift with and without the aid of the bell-crank lever. In the case where the crank lever is utilized to lift the weights, results show that much less force is applied at the input to lift a much greater force at the output. On the other hand, when the force is not applied, a lot of force; almost equivalent or greater than that at the output is used to lift a weight. This means that whenever the lever is utilized in lifting the weights, the weight is distributed in the lever mechanism, a process that ensures that only a small force is required in the input side to lift a bigger force in the output side hence reducing the human input force.

To make a reality the working of the bell-crank lever so that it can be used for different purposes, Engineers apply their intellectual and design skills to introduce the mechanism of the bell crank lever into mechanical devices such as Fork lifts, trolleys, hand pallets and other lifting devices.

The layout of a simple bell crank lever can be summarized by the figure below:

In the layout of the Bell-Crank lever shown above, the effort applied at point P is used to counter the weight of the load W. A represents the entry point of vertical end pin, while point B indicates the point of the pin that joins the lever extending up to the middle of the fulcrum. The fulcrum is the point denoted by F. To come up with the mathematical representation of the of the bell-crank lever, we let X be the distance separating the fulcrum and the point of the pin that joins the lever and Y be the length separating the fulcrum and the entry point of the vertical pin A. Furthermore the following constants are declared  is used to represent the most appropriate bending stress while the lever is in tension. Moreover,  is used to indicate the most appropriate stress while the lever is in shear and P the bearing pressure of the pin.

Layout of a Simple Bell Crank Lever

If the moments about the point F are to be considered, we come up with the following mathematical computation

Hence when we equate for P, we get the following expression

With the above two equations, the reaction on the fulcrum pin can be obtained with the below expression.

The next step in the design of the lever involves the design of the fulcrum point. The design of this point ensures proper functioning of the lever by ensuring that the weight from the input side is properly distributed to facilitate the heavier weight on the output side. In this design, we let L be the thickness of the fulcrum pin and d be its diameter.  If the fulcrum or the support is let to be in the bearing, then the following expression is drawn.

The above equation is factored to come up with the expression for the diameter of the fulcrum as below

Once the value of the diameter of the thickness of the fulcrum is determined, the permissible values for double shear stress that will be induced in the fulcrum pin is evaluated by the use of the following equation:

Once the fulcrum point is calculated and evaluated using the above set of equations, the points A and B are determined and evaluated a s well.

To determine this point, we first let the diameter of our pin A be d and L be the length of the length or the thickness of the pin. If know pin A is let to be in the bearing, then P can vbe determined using the following expression

Once the above equation is determined using the preset values the double shearing stress induced at this point is again determined using the expression similar to the one obtained in the case of the fulcrum design. If the determined and evaluated shear stress induced at this point is found to be within the permissible limits, then bending stress at this point is determined using the set of formula’s below:

The sectional modulus of this point is determined using the following equation:

Know, with the above two sets of equations the bending stress is determined as follows:

In the design process, the above value should always be let to be within the permissible limit to ensure safe, efficient and effect operation of the bell-crank lever.

The design of this point is much similar to the design of point A, the only difference occurs when we need to determine the bending stress induced at the point. Here, we apply the formula below:

All the other steps, resemble those of the design of point A. Again in the design of point B. It is of great importance to ensure that the values of stress determined lie within the required safe limits for sufficient operation.

In the design of the lever, we choose a section on the x-x plane and assume that it is the weak section at which there would occur a failure. The thickness and the width of the of the lever at the points x-x are assumed to be t and b. The maximum bending examined from the given section x-x is thereby given using the following equation:

Design of Fulcrum Point

The 40 is arrived at by assuming that the length of the given x-x examined form the middle point of the fulcrum lies between thirty and fifty millimeters.

Again in this case, the calculated values should be within the permissible safe limits for efficient operation and for ensuring the design objective is met perfectly.

In this case again, the thickness of the section x-x is assumed to be t while the thickness is assumed to be b. The maximum bending moment and the section modulus in determined using the criterion similar to the one above and values allowed to be with the permissible values.

The values of b and t and L for all the above designed components are determined from the expression in each section and making special assumptions that would ensure that the final product operates efficiently and effectively.

The bell crank lever is applied in a wide range of field, some of which require the lifting of very heavy materials. For this reason, the choice of the material to be used in its manufacture of great significance. Majorly, the materials that are used in the design of the bell-crank lever are usually metals. The metals selected should have a high value of stress and tension and shear. To ensure that the above conditions are met, the design phase usually comprises the use of very heavy load values to replicate practical loads. The commonly selected material for this purpose after design and testing and to ensure that the resultant bell-crank lever is of high quality and can perform well under any condition of load is usually any steel metal., the common one being the AISI 1045 Carbon steel (cold). The components in the steel used in the manufacture of the bell-crank lever and their composition are as shown in the table below:

Table 1:Composition of Materials in steel

The steel used despite having the above composition of materials, should have the following properties. Firstly, it should have an elongation of 12%, a Brinell hardness of 179, a shear strength of 77Kpsi and a tensile strength of 92psi.

The manufacture of the lever begins by making the die of the shape of the lever that was designed initially, after that, die casting is done to facilitate the process of bulk production. The dyeing process requires the use of sand casting which ensures the replica of the lever is created for die shape making. Once the above operation is complete, machining is done on the casting produced during the latter process of die casting. Surface finish with the aid of sand papers and grinders follows to finish the manufacturing process. During this manufacturing process, allowances are made to the calculated values so that the losses that occur as a result of shrinking, surface treatment and machining are catered for in advance.

In the above to figures, the first one represents the side view of the solid form of the designed bell-crank lever while the second represents the front view fo the designed bell crank lever.

Design of Point A and B

Once the bell-crank lever has been designed and manufactured, the tseting face follows. The testing of the lever requires the use of the Ansys software for analysis and the use of the FEM to develop mesh of specified node tetrahedral solid element. Weight of specified amount is used to determine if the design objectives are met. The figure below shows a sample image that is developed during the testing phase.

Results are repeated with different radii of the fillets to measure and examine the accuracy of the developed lever. The result for 5, 10 and 15mm radius fillet for a 100N force are as in the table below:

Table 2:Results Part 1

The second phase testing involves the use of volume of the bell-crank lever for the determination of the principal stress. If different shapes of different volumes were taken for testing the result would be a replica of the ones shown in the figure below:

Table 3:Result Part 2

This is a process that is used to verify whether the results obtained in the testing phase are a thing to go with. The process uses the principal of photo elasticity. In this process a model of the lever that is photo elastic together with circular discs are created with the aid of calibrated sheet of epoxy resin of specified thickness. The model created in this stage is examined using a polariscopic and special conditions of compressive force. The schematic of the process described can be represented by the figure below:

Once the setup is complete, results for various of fringe are taken and recorded. The sample results resemble the ones indicated in below.

Table 4:Result Part 3

Results, Discussion and Conclusion

From the result in the table 2 above, indicating the stress obtained for different values of stress, a plot to visualize the stress is drawn in excel and appears as below

From the above results, we can conclude that stress is inversely proportional to stress. That is to say, as the radius increases, the stress reduces. This is so because, it is expected as effort length increases, the stress and hence the force would reduce. It is therefore okay to use a higher radius to minimize stress concentration and to ensure that at greater amounts of loads, there is failure of crack formation.

From the result in the table three above, we can draw graph in excel and visualize our results as follows:

The above result indicates that as volume increases the stress also increases, this means that if we wanted a better performing bell-crank lever we had to reduce the volume. Reduction of this volume can be done by drilling of holes in the arm of the lever.

The results obtained above are much similar to the ones that are obtained using the process of photo elasticity with only a small error margin, this indicates that our design process was successful as the final product will have satisfied all the required conditions.

Bell crank lever plays a crucial role in minimizing the effort required by human to do work. It is for this reason that its design concept is of great importance to engineers. The design of the lever begins by determination of all the correct values for the design of the various elements of the bell crank.

Once this values have been determined and necessary calculations performed, manufacturing follows. During manufacturing allowances are made to cater for losses incurred. The next phase after manufacture is testing follows. Testing is done using special software such as ANSYS. This software analyses the stress using FEM or FEA. i.e. Finite element method of finite element analysis on various models of varying radius or optimized volume. The result obtained in the latter are compared to those of the photo elasticity method, and for successful proof of correct design, both the values should have a very low margin of error.

Conclusion

In the modern day society, majority of activities are quite bulky to be handled without any involvement of an external force to minimize the effort required. The bell-crank lever plays a crucial role in the purpose of reducing the effort needed in lifting this heavy weights. To ensure that the lever performs efficiently, manufacture of a quality lever is of supreme lever is great necessity, starting from the design stage, the manufacture up to the stage of analysis of the forces and the stresses. This can be made possible by ensuring that all the required values for manufacture to ensure sufficient operation are well catered for in the design stage.

Reference List

Brown, H.T. Mark’s Calculation of Machine Design. 2^nd ed. New York: McGraw-Hill.

Callister, W. D., and Rethwisch, D. G. 2014. Materials science and engineering: An introduction.

Kalpakjian, S., Schmid, S. R., and Sekar, K. S. 2016. Manufacturing engineering and technology.

Khurmi, R.S. and Gupta, J.K. 2005, Machine Design. 1^ST ed. India: S. Chand & Co ltd.

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