The Snap Clips are the part of the body that provide a quick way to attach and remove the syringe. To optimise this piece, the goal is to minimise its cost by analysing the required material properties and part dimensions that would produce a specified maximum force of 15-25 N on the syringe.
Collecting Data
Using an angle of 25° for the amount of overhang on the clip, the maximum deflection of the ends of the clips, δ, is calculated to be approximately 1 mm, since the syringe has a diameter of 16.7 mm.
By applying Finite Element Analysis to the clip, the maximum stress on the part and the reaction force from the clip ends could be calculated for varying widths of the clip and elastic moduli of the material.
The graphs below show the relationship between each of these variables.
This results in the following relationships:
Varying the width has little to no effect on the maximum stress experienced by the clip.
The maximum stress is proportional to the elastic modulus of the material.
The Force on the clip ends is proportional to both the width of the clip and the modulus of the material.
By interpolating between these equations, a more general equation for the force on the clips was found to be:
F = 8.244E + 1.161W - 8.105 Where:
F = Force on clip ends (N)
E = Elastic modulus of material (GPa)
W = Width of clip (mm)
Calculations
Objective: Minimise cost Constraints:
Force: 15 N < F < 25 N (Reasonable force for clip use)
Width: 4 mm < W < 10 mm (Reasonable width of clip)
Applying Constraints: Rearranging the equation for force to find E in terms of F and W allows us to calculate the maximum and minimum allowable values for the elastic modulus. These are found to be:
max(E) = 3.4524 GPa (at F = 25 N, W = 4 mm)
min(E) = 1.3946 GPa (at F = 15 N, W = 10 mm)
These constraints are plotted on the Modulus-Strength diagram as horizontal lines. The area between these lines contains suitable materials based on these constraints
The stress constraint is σy/E > 1.6784e-2. This is plotted on the same diagram. The area below this line contains suitable materials based on this constraint
This restricts the material selection to polymers only, with PTFE, PE and PP and some other plastics being unsuitable.
Minimising Cost: The total cost of the part is proportional to the product of its volume and cost per unit volume. The volume only varies with the width of the part, which can be substituted by the equation containing force and elastic modulus. This gives, for a specific force on the clip ends, that the cost is proportional to the product of the elastic modulus of the material and its cost per unit volume. Plotting this line on the Modulus-Cost diagram and minimising it to fit the previously suitable materials shows that Polystyrene would be the optimum material for the clips.