Rack & Gearbox Pinion

The dynamics calculations for the Rack & Gearbox Pinion are handled in the exact same way as a Rack & Pinion and a Gearbox. Because the Gearbox-Pinion combination is known and is purchased as one product, and often there is an additional supporting bracket and bearing, the vendor usually allows for a higher rated feed force than if the gearbox and pinion were purchased separately.

Rack Moves

 

Rack is Stationary

Note: As shown in the rack is stationary moving mass formula below, m1 does not include the gearbox mass. This is consistent with the Rack & Pinion mechanism.

 

Symbol Description Units
JDM Inertia of drive mechanism kg-m2
TDM Torque of drive mechanism Nm
aDM Rotational acceleration rad/s2
h Efficiency of drive mechanism 1
q Incline angle above horizontal o
g Acceleration due to gravity = 9.81 m/s2
m Rack friction coefficient  
mLoad Mass of load + payload kg
mCB Mass of counterbalance kg
mRack Mass of rack kg
rPinion Radius of pinion m
mPinion Mass of pinion kg
JPinion Inertia of pinion kg-m2


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