Expressions and Definitions

A

Shaft cross section [mm²]

i

Number of ball circles

α

Coefficient of thermal expansion [1/°C]

JIS

Japanese Industrial Standard

c

Lead compensation

k

Support coefficient, critical speed

C_0a

Static axial load capacity [N]

L₁₀

Nominal life 90% reliability [10⁶ revolutions]

C_a

Dynamic axial load capacity [N]

l_s

Unsupported shaft length [mm]

C_aerf

Required dynamic axial load capacity [N]

l_u

Travel [mm]

Δl_b/t

Axial elastic deformation due to external load F_i [µm]

m

Support coefficient, buckling

Δl_b/t,pr

Axial elastic deformation due to preload F_pr [µm]

n_i

Speed [rpm]

Δl_p

Elongation of the shaft [mm]

n_k

Critical speed [rpm]

Δl_T

Thermal expansion [mm]

n_m

Equivalent Speed [1/min]

d_N

Nominal diameter [mm]

n_max

Maximum Speed [rpm]

DN

D_N value [mm/min]

P

Lead [mm]

Δt

Temperature increase [°C]

P_B

Buckling load [N]

"E"

Tolerance of cumulative lead error (JIS)

P_i

Load capacity per ANSI [lbf]

E

Elasticity modulus [N/mm²]

q_i

Time percentage [%]

ε

Elongation relative to length

R_b

Axial bearing rigidity [N/µm]

e_0a

Mean lead deviation over entire travel l_u

R_nu,ar

Actual nut rigidity [N/µm]

e_2π

Lead error in one revolution (JIS)

R_s

Shaft rigidity [N/µm]

e₃₀₀

Lead error in 300 mm (JIS)

R_t

Rigidity of ball screw [N/µm]

e_p

Tolerance of average lead deviation over entire travel l_u

T

Travel compensation (JIS)

e_sa

Actual lead deviation over entire travel l_u

T_pr

Preload torque

F_i

External load [N]

v_2πa

Lead fluctuation in one revolution

F_i*

Modified external load [N]

v_300a

Lead fluctuation in 300 mm

F_m

Dynamic equivalent load [N]

v_300p

Tolerance of lead fluctuation in 300 mm

F_m*

Modified dynamic equivalent load [N]

v_ua

Lead deviation over entire travel l_u

F_pr

Preload [N]

v_up

Tolerance of lead deviation over entire travel l_u

F_T

Tensioning force [N]