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I have designed a plastic part shown in blue that will be injection moulded. The part is a lever that takes 1 mm of movement downward and outputs 6 mm of movement upward. Circled in green is a hinge and red indicates the direction of the force. I need this hinge to be able to take this 1 mm of movement over thousands of cycles.

I have outlined the 3 main characteristics that I am looking for:

  1. A small Young modulus value so that it offers minimal resistance to bending
  2. The ability to spring back to its original shape after thousands of cycles
  3. Minimal density as it needs to be as light as possible

I need help specifying and defining actual values so that I can select a material from Matweb.

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  • $\begingroup$ Then you should use the same type of material as for the lever arm, maybe a different grade. $\endgroup$
    – r13
    Apr 28, 2021 at 1:29
  • $\begingroup$ PP supposedly, assuming you're talking about a "living hinge". However it would conflict somewhat with requirement #2 $\endgroup$
    – Pete W
    Apr 28, 2021 at 2:25
  • $\begingroup$ @r13 The entire part is made of the same plastic piece with the hinge being thinned out. $\endgroup$
    – MechFlag
    Apr 28, 2021 at 3:34

2 Answers 2

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If I understand correctly you need the part to be able to rotate around point B, so that the AB section remains vertical, while the BCD rotates.

enter image description here

In that case, the following is not really an answer, just a heads up, that there are other properties that will have a detrimental effect on the properties:

  • The horizontal distance between the fulcrum and the hinge.

The properties of the material will be vastly different, if the horizontal distance between the fulcrum and the hinge is 10 [mm] or 1 [m]. The reason is that the required angle between the vertical part (AB) and the lever part (BCD) would be significantly different.

  • Cross-sectional properties of the material and loads

If you use any ductile material (even if its ductility is small) then you could achieve the desired effect if the cross-section at the hinge is sufficient small. However, then you are running into the problem of not stressing the material too much before breaking.

Therefore, in order to determine the properties of the material you need to also know cross-sectional properties of the area near the plastic hinge and also the loads transmitted through the material.

  • Rate of cycles

Although this parameter is not as important, it may come into play if the repetition rate is too high; e.g. 1000 repetitions in 5 seconds, its different that 1000 repetitions in a month.

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  • $\begingroup$ You're correct. Part ABCD is all one piece of plastic, where hinge AB is a cored out piece of plastic. Similar to a living hinge, the difference here is that the part returns to its original shape when it is not stressed. The horizontal distance is fixed, but the angle can be changed (how close point B is to the bottom surface). The cross-sectional area is a uniform 2 mm x 2 mm and thins out to 0.25 mm at the hinge. The force its subjected to is entirely dependent on the hinge's Youngs Modulus; which is why I need it to be as weak as possible, but still maintains elasticity. Thank you $\endgroup$
    – MechFlag
    Apr 28, 2021 at 3:33
  • $\begingroup$ Then you'd be better off having the section BC, as close to vertical as possible. That would minimise the rotation around plastic hinge at B. E.g. if it was 90.1 degress with the horizontal axis you'd probably would have any plastic hinge (the length would also be enormous). In any case, keep in mind of other issues, like buckling. $\endgroup$
    – NMech ♦
    Apr 28, 2021 at 3:42
  • $\begingroup$ Also, consider updating the question with the data in your comment. Other people will also find it helpful and maybe you'll get better responses. To be honest to me there is still information missing before being able to start crunching numbers. $\endgroup$
    – NMech ♦
    Apr 28, 2021 at 3:44
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In order to match your first two desired characteristics, the material under load must 1) not be stressed beyond yield and 2) keep the resulting strain/deformation stay within the elastic range.

enter image description here

In your design, you need to first determine the beam geometry, arranged in a manner such that it is in balance and in equilibrium about the support joint C. Then determine the load P that will initiate the rotation but not overturn the structure. The last, find the resulting primary forces (M) due to P and weight W, and the secondary force due to the displacement (eccentricity).

The displacement $\delta$ is a function of P, E and the rotation angle $\theta$, and it relates to the linear strain $\epsilon$. By setting $\epsilon = \epsilon_y$, you can solve the elastic modulus E = fy/$\epsilon_y$ for the given load P. At this point, you can see it will take several iterations to reach the desirable elastic modulus.

enter image description here

One note to your design is that the beam is weakened at point B by the borehole, but it does not constitute a "hinge" until the combined stress has reached yield on the remaining sections (on sides of the hole), a plastic hinge has thus formed. However, you need to pay attention to the stress concentration and premature buckling though.

Another note is the repetitive/cyclical nature of the loading will leads to fatigue, which needs to be included in the stress calculations too.

The calculation is quite involved and tedious, therefore, it is recommended to seek technical help from a mechanical or structural engineer to select a material that is suitable for your application with the least weight.

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  • $\begingroup$ I would like to add that point C is not fixed to anything and that the entire structure is free to float. C becomes the fulcrum and is free to slide when P is applied. In actual use, the hinge will be stressed rarely. However, to pass testing I need to run it through many cycles. Is the displacement referring to the movement of point A from side to side? Also, could you explain which values I need to work out to plug into the elastic modulus equation? Thank you $\endgroup$
    – MechFlag
    Apr 29, 2021 at 22:56
  • $\begingroup$ @MechFlag 1) Without knowing the complete scheme, I can't comment on the idea of letting point "C" free float, eventually, you will need some mechanism to hold the fulcrum in place, in a manner fitting your purpose and is feasible. 2) The deflection of point "A" occurs in both directions (x & y). It is the result of the displacement of the member AB induced by the displacement of the member BC. The deflection is a function of material property (E) and structure geometry (I - the moment of inertia), through setting the deflection limit and trial I, you can backward work out E. $\endgroup$
    – r13
    Apr 29, 2021 at 23:36
  • $\begingroup$ @MechFlag Your problem is quite involved that hand calculation will be very difficult without some simplifications and assumptions, also the number of required calculations can be prohibitive. Thus it is recommended to work with an engineer, and solving the matter through computer method. $\endgroup$
    – r13
    Apr 29, 2021 at 23:42
  • $\begingroup$ Point C is free floating by nature. Where the only fixed point is A. I have 3D printed the design, and it works just fine. What I'm trying to do is minimise the force point C applies to the bottom barrier. This done by joint design and material selection. I have done FEA to replicate its performance in CAD, and found that; with PP as the material, the Von Mises Stress is 15.75 MPa at the hinge. $\endgroup$
    – MechFlag
    May 3, 2021 at 0:55
  • $\begingroup$ You are contradicting what was provided in the original write-up, which described point A as moving downward while loaded, but now it is fixed. Anyway, cong on the successful completion. $\endgroup$
    – r13
    May 3, 2021 at 1:43

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