Mathematical performance analysis of a reciprocating-fork hopper feeder

Feeders form a critical part of automated assembly lines. Along with feeding from a bulk supply, they also convert the randomness of parts into a flow in a geometrical pattern and deliver them at a pre-determined rate. This paper mathematically analyses a reciprocating-fork hopper feeder. This system supplies headed parts like bolts and rivets in an upright configuration to the delivery chute through a pneumatically-actuated reciprocating fork which picks up the parts from a rotating bowl. The feed rate performance of the feeder is analysed for three parameters: part population, rate of reciprocation of fork and speed of rotation of bowl. The Design of Experiments (DOE) is done using 2³ full-factorial method. A mathematical model is formulated using Design Expert ® software, to investigate the significance of individual parameters as well as interactions amongst them. Adequacy of the model to predict the performance of the feeder is checked using Analysis of Variance (ANOVA) method. The results obtained are presented graphically and in the form of factorial model which defines the performance characteristics of the feeder. The mathematical model also provides the most appropriate process parameter settings to optimize the feed rate of the feeder under the given constraints.