Application Area 8: Cam Hinge Optimization

A cam hinge is used in many appliances (ovens and refrigerators, for example). The function of the cam hinge is to let the door stay at arbitrary position freely during the opening or closing operation. By doing so, it ensures that a minimum amount of force is required to open or close the appliance.

The figure below shows a side-view of a simplified oven. The green door hinges about point O and opens or closes as shown. As the door opens, the bottom surface AB (highlighted in yellow) slides over a pin P.



Figure 1.
Objective
Modify the cam profile AB so that the torque required to move it from the closed to the open position is minimized. We wish to minimize the torque during the entire range of operation. The cost function is:
c o s t = ∫ T = 0 T = F i n a l τ ( t ) 2 d t MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8srps0l bbf9q8WrFfeuY=Hhbbf9v8qiqrFr0xc9pk0xbba9q8WqFfea0=yr0R Yxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeGabeqadiWa ceGabeqabeqadeqadmaakeaaieGaqaaaaaaaaaWdbiaa=ngacaWFVb Gaa83Caiaa=rhacqGH9aqpcaWFGcWaaybCaeqal8aabaaabaaaneaa peGaey4kIi=aa0baa4qaaiaa=rfacqGH9aqpcaaIWaaabaGaa8hvai abg2da9iaa=zeacaWFPbGaa8NBaiaa=fgacaWFSbaaaaaakiaa=r8a daqadaWdaeaapeGaa8hDaaGaayjkaiaawMcaa8aadaahaaWcbeqaa8 qacaaIYaaaaOGaa8hOaiaa=rgacaWF0baaaa@4BA4@
τ ( t ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaebbnrfifHhDYfgasaacH8srps0l bbf9q8WrFfeuY=Hhbbf9v8qiqrFr0xc9pk0xbba9q8WqFfea0=yr0R Yxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeGabeqadiWa ceGabeqabeqadeqadmaakeaaieGaqaaaaaaaaaWdbiaa=r8adaqada WdaeaapeGaa8hDaaGaayjkaiaawMcaaaaa@360A@ is the instantaneous value of the torque at an open position
Design Variables
The cam profile is defined a parametric curve, such as it is parametrically defined as a function of the knots of a B-spline. The knot coefficients are the design variables. Give a set of knot coefficients, a unique, smooth curve can be reproduced. In this example there are 8 knot coefficients. The initial guess for the profile is that it is a straight line.
Results
The optimized cam profile is shown in the figure below.


Figure 2.
A comparison of the effort required to open the door for the initial and optimized designs is shown below.


Figure 3.