Stand Mixer Design Evaluation

Overview

For ME41 (Engineering Design II) our team took apart a "Kitchen in the Box" 3.2 quart stand mixer and worked out whether it was actually designed well. Three subsystems do the real work: a spur-and-planetary gear train, ball bearings in a plastic housing, and a tilt-head hinge with a safety switch. Nothing came with specs, so we measured, counted or back-calculated the numbers below ourselves, then ran them through free-body diagrams, life calculations and FEA using Shigley's.

A spur plus planetary train that turns motor speed into mixing torque.

• Got the paddle speed, 165 RPM around the bowl, from slow-motion video, then counted every tooth in the train: a 13-tooth motor pinion, 95, 9 and 75-tooth spurs, a 41-tooth ring and a 13-tooth planet.
• Train value e = (13 x 9) / (95 x 75) = 0.0164, so the motor runs at roughly 10,050 RPM. From the 300 W plate that is about 0.29 N-m no-load torque.
• The planetary stage adds 2.15x, giving 28.3:1 overall, about 8.1 N-m at the paddle and roughly 153 N at the beater edge (r = 5.3 cm).
• Modelled the gears in Onshape (20 degree pressure angle, 1.25 mm module, one-third root fillet, 0.02 cm backlash). Ran a SolidWorks motion study and a static FEA in AISI 4130 steel and PA6 nylon, with a control mesh at the tooth contacts under 2.09 N-m.
• The steel is fine and the nylon runs well below its limit, but the factor of safety only just clears 1 in the worst spots. Not much room for overload or material variation.

One deep-groove ball bearing on the intermediate shaft takes the belt and gear loads.

• It is a 608 deep-groove ball bearing (8 x 22 x 7 mm, 3.3 kN dynamic rating) in an injection-moulded glass-filled nylon housing.
• Load path: belt tension to pulley to intermediate shaft at 17.4 N-m. That is a 2320 N radial belt load plus a 253 N gear separating force, or 2570 N radial and 257 N axial at the bearing.
• ABMA equivalent load is 2714 N, so L10 = (C / P) cubed x 1e6 = 1.8 million revolutions. About 182 hours at 165 RPM, or 136 to 234 hours over a plus or minus 300 N band on the rating.
• That short life is almost all down to the constant belt tension. Housing flex, press-fit creep, grease breakdown and start-stop cycling all push the real number lower, so the bearing will go loose or noisy long before a gear fails.

The tilt-head lock, its torsion spring, and the switch that cuts power when the head is up.

• Pressing the button slides a travel rod back so its thin section clears the curved latch slots. The head swings through 60 degrees and a compression spring pushes the thick section back in to lock it. The same motion trips a switch that cuts motor power whenever the head is up.
• Treating the head as a rigid body (about 2.0 kg, centre of mass 0.20 m from the hinge), its weight alone is a 3.9 N-m moment. A hard 50 N push from the user takes that to 11.4 N-m.
• The torsion spring (2.2 mm wire, 8 active coils) gives about 0.79 N-m of restoring torque at around 910 MPa wire stress, against a 2050 MPa music-wire yield. Factor of safety about 2.3.
• Latch contact pressure is 3 MPa in normal use and 10 MPa under the hard push, both well under yield, so slot wear sets the life rather than strength. The travel rod sees about 2 MPa axially, which is nothing.

Gear train CAD & FEA

SolidWorks static study of the driven spur pair under 2.09 N-m, with a control mesh at the tooth contacts.

Full report

Tools