Gear train-motor kinematic analysis

Gear Train

The gear train is composed by 7 gears. There are two outputs; the output I am concerned with is output two, which is where the mixer is connected. The other output is used to connect attachments that the company sells, such as a food processor or a pasta machine, but it is not relevant for my analysis.  Images of the gear train and a schematic are shown on the side. For the mixer output, we first have a connection of two helical gears, with the second one on the same shaft as a worm gear. This worm gear connects with a worm follower, which is attached to the central shaft of the mixer. This central shaft is connectes to a planetary gear set, which gives the final output.

From the video we can see that the mixer has two angular motions. One is the angular motion of the arm around the center of the mixer. The other motion is the motion of the planet about its own axis. These motions are in opposite directions, the arm spins counterclockwise, while the planet spins clockwise about its own axis. This allows for better mixing, since mixing occurs in to different directions simultaneously. 

Video 2: Mixer in operation

Results and analysis

Results were calculated for the transmission ratios of the two gears of interest. As you can see, the speed is greatly reduced from the motor to the output, and consequently the torque is greatly amplified. For a mechanism like this, a high torque is fundamental because dough made out of flour usually becomes very thick and viscous, and a low torque mechanism wouldn't be able to mix it properly. The mixer uses an electric motor, which achieves high rotational speeds to the expense of torque. Therefore the torque provided by the motor has to be increased before bringing it to the output, this is what this gear train achieves.

The plot below clearly shows the comparisons between the speed of the motor and the speed of the gears at the output. The angular speeds were plotted with respect to the 10 speed settings that the user can adjust. The speeds at the output were measured using a stopwatch, and through the gear train ratios, the motor speed was calculated. The highest speed setting (speed level 10) will result in the highest angular speed but lowest torque at the output and vice versa.

Two plots were plotted for the motor speed, one assuming 100% efficiency and the other one assuming 90% throughout the gear set. Usually well greased gears, such as these ones, have a high efficiency (around 95%), so the actual curve will be somewhere in between the two. The rotational speed of the planet was plotted as well, and as you can see it is negative because it spins in the opposite direction, as mentioned above. The table also shows the exact calculated values for all the speeds.

Figure 6: Plot of velocities of various components of the gear train