Rack&Pinion System

Calculation

Straight Teeth

Helical Teeth

Input

Acceleration Time

t_a=s

Deceleration Time

t_d=s

Constant Speed Time

t_cs=s

Dwell Time

t_dw=s

System Inclination (degrees)

γ=°

Traveling Weight

m=kg

Speed

v=m/s

Static Friction Coefficient

μ_s=

Service Factor

K_A=

System Efficiency

η=

Pinion Pitch Diameter

d=mm

Pinion Inertia

J_P=kg·cm²

Pinion Pressure Angle (degrees)

α=°

Pinion Helix Angle (degrees)

β_d=°

Pinion Helix Angle (arcmin)

β_m='

Pinion Helix Angle (arcsec)

β_s="

Machining Force

F=N

Motor Moment of Inertia

J_M=kg·cm²

Max. Motor Speed During Cycle

n₁=rpm

Gearbox Moment of Inertia

J_g=kg·cm²

Positioning Accuracy

A_p=mm

The formulas used for these calculations are available in this PDF.

Results

Machine

Cycle Duration

t_cycle=s

Cycles per Minute

Z=

Duty Cycle

ED=%

Friction Force

F_f=N

Acceleration Force

F_acc=N

Deceleration Force

F_dec=N

Force Due to Gravity

F_w=N

Max. Tangential Force on Pinion

F_{t max}=N

Max. Radial Force on Pinion

F_{r max}=N

Max. Radial Force on Pinion

F_{r max}=N

Max. Axial Force on Pinion

F_{ax max}=N

Pinion Helix Angle (degrees)

β=°

Inertias

Total Inertia as Seen by the Motor

J_T1=kg·m²

Load to Motor Inertia Ratio

Λ=

Kinematics

Traversed Distance

L=m

Linear Acceleration

a=m/s²

Linear Deceleration

a=m/s²

Pinion Rotational Speed

n₂=rpm

Motor

Maximum Required Motor Power

P_{1 max}=kW

Maximum Required Motor Torque

T_{1 max}=N·m

Gearbox

Ideal Gearbox Ratio

i=

Ideal Gearbox Backlash (arcmin)

Δφ='

Required Torque on Pinion

T_{2 max}=N·m

Required Torque on Pinion, Adjusted for Service Factor

T_2KA=N·m

Buttons

Reset

Diagrams

Straight Teeth

Helical Teeth