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List of symbols

Symbol Name of the symbol Unit
$ $ bolting-up method, measuring method $\mathrm{ }$
$ $ bolt $\mathrm{ }$
$A_b$ cross‐sectional area of the bolts $\mathrm{mm^2}$
$B_A$ coefficient $ B_A $ $\mathrm{}$
$B_B$ coefficient $ B_B $ $\mathrm{}$
$B_T$ coefficient $ B_T $ $\mathrm{}$
$B_{1A-hub}$ coefficient $ B_{1A-hub} $ $\mathrm{}$
$B_{1A-socket}$ coefficient $ B_{1A-socket} $ $\mathrm{}$
$B_{1A}$ coefficient $ B_{1A} $ $\mathrm{}$
$B_{1B-hub}$ coefficient $ B_{1B-hub} $ $\mathrm{}$
$B_{1B}$ coefficient $ B_{1B} $ $\mathrm{}$
$B_{1T-hub}$ coefficient $ B_{1T-hub} $ $\mathrm{}$
$B_{1T}$ coefficient $ B_{1T} $ $\mathrm{}$
$B_{2A-hub}$ coefficient $ B_{2A-hub} $ $\mathrm{}$
$B_{2A-socket}$ coefficient $ B_{2A-socket} $ $\mathrm{}$
$B_{2A}$ coefficient $ B_{2A} $ $\mathrm{}$
$B_{2B-hub}$ coefficient $ B_{2B-hub} $ $\mathrm{}$
$B_{2B}$ coefficient $ B_{2B} $ $\mathrm{}$
$B_{2T-hub}$ coefficient $ B_{2T-hub} $ $\mathrm{}$
$B_{2T}$ coefficient $ B_{2T} $ $\mathrm{}$
$B_{3A-hub}$ coefficient $ B_{3A-hub} $ $\mathrm{}$
$B_{3A-socket}$ coefficient $ B_{3A-socket} $ $\mathrm{}$
$B_{3A}$ coefficient $ B_{3A} $ $\mathrm{}$
$B_{3B-hub}$ coefficient $ B_{3B-hub} $ $\mathrm{}$
$B_{3B}$ coefficient $ B_{3B} $ $\mathrm{}$
$B_{3T-hub}$ coefficient $ B_{3T-hub} $ $\mathrm{}$
$B_{3T}$ coefficient $ B_{3T} $ $\mathrm{}$
$B_{4A}$ coefficient $ B_{4A} $ $\mathrm{}$
$B_{4B-hub}$ coefficient $ B_{4B-hub} $ $\mathrm{}$
$B_{4B}$ coefficient $ B_{4B} $ $\mathrm{}$
$B_{4T-hub}$ coefficient $ B_{4T-hub} $ $\mathrm{}$
$B_{4T}$ coefficient $ B_{4T} $ $\mathrm{}$
$B_{A-clevis}$ coefficient $ B_{A-clevis} $ $\mathrm{}$
$B_{A-hub}$ coefficient $ B_{A-hub} $ $\mathrm{}$
$B_{A-rod}$ coefficient $ B_{A-rod} $ $\mathrm{}$
$B_{A-socket}$ coefficient $ B_{A-socket} $ $\mathrm{}$
$B_{B-hub}$ coefficient $ B_{B-hub} $ $\mathrm{}$
$B_{T-hub}$ coefficient $ B_{T-hub} $ $\mathrm{}$
$C_c$ coefficient according to load $\mathrm{ }$
$C_{D_0}$ dimensional characteristics of the connection on diameter $ D_0 $ $\mathrm{ }$
$C_{D}$ dimensional characteristics of the connection on diameter $ D $ $\mathrm{ }$
$C_{j-trunnion-clevis}$ coefficient of joint for trunnion and clevis $\mathrm{ }$
$C_{j-trunnion-rod}$ coefficient of joint for trunnion and rod $\mathrm{ }$
$D$ diameter $ D $ $\mathrm{mm}$
$D$ diameter of the shaft $\mathrm{mm}$
$D$ basic major diameter of internal thread (nominal diameter) $\mathrm{mm}$
$D_0$ inner diameter of the hollow shaft $\mathrm{mm}$
$D_1$ diameter $ D_1 $ $\mathrm{mm}$
$D_1$ outside diameter of flange $\mathrm{mm}$
$D_1$ basic minor diameter of internal thread $\mathrm{mm}$
$D_2$ internal diameter of flange $\mathrm{mm}$
$D_2$ basic pitch diameter of internal thread $\mathrm{mm}$
$D_h$ diameter of the hub $\mathrm{mm}$
$E$ Young's modulus $\mathrm{MPa}$
$E_{bolt}$ Young's modulus for bolt $\mathrm{MPa}$
$E_{hub}$ Young's modulus for hub $\mathrm{MPa}$
$E_{shaft}$ Young's modulus for shaft $\mathrm{MPa}$
$F$ force $\mathrm{kN}$
$F_A$ axial force $\mathrm{kN}$
$F_R$ radial force $\mathrm{kN}$
$F_{A-bolt-max}$ maximum axial force in the bolt $\mathrm{N}$
$F_{A-bolt-min}$ minimum axial force in the bolt $\mathrm{N}$
$F_{A-bolt-nom}$ nominal axial force in the bolt $\mathrm{N}$
$H$ height of fundamental triangle $\mathrm{mm}$
$K$ diameter of the bolt circle $\mathrm{mm}$
$K$ diameter of the pin circle $\mathrm{mm}$
$L$ thread length of thread in threaded hole $\mathrm{mm}$
$M_B$ bending moment $\mathrm{Nm}$
$M_T$ twisting moment $\mathrm{Nm}$
$M_{B-bolt}$ bending moment the bolt $\mathrm{Nm}$
$M_{bolt}$ bolt tightening torque $\mathrm{Nm}$
$P$ pitch $\mathrm{mm}$
$P_B$ bearing stress $\mathrm{MPa}$
$P_{B-cotter-socket}$ bearing stress in the cotter and socket $\mathrm{MPa}$
$P_{B-cotter-spigot}$ bearing stress in the cotter and spigot $\mathrm{MPa}$
$P_{B-key-hub}$ bearing stress in the key and hub $\mathrm{MPa}$
$P_{B-key-shaft}$ bearing stress in the key and shaft $\mathrm{MPa}$
$P_{B-pin-flange-1}$ bearing stress in the pin and flange 1 $\mathrm{MPa}$
$P_{B-pin-flange-2}$ bearing stress in the pin and flange 2 $\mathrm{MPa}$
$P_{B-pin-hub}$ bearing stress in the pin and hub $\mathrm{MPa}$
$P_{B-pin-shaft}$ bearing stress in the pin and shaft $\mathrm{MPa}$
$P_{B-thread}$ bearing stress in the thread $\mathrm{MPa}$
$P_{B-trunnion-clevis}$ bearing stress in the trunnion and clevis $\mathrm{MPa}$
$P_{B-trunnion-rod}$ bearing stress in the trunnion and rod $\mathrm{MPa}$
$P_{B-washer}$ bearing stress in the washer $\mathrm{MPa}$
$P_{all-B-bolt}$ allowable bearing stress the bolt $\mathrm{MPa}$
$P_{all-B-clevis}$ allowable bearing stress the clevis $\mathrm{MPa}$
$P_{all-B-cotter}$ allowable bearing stress the cotter $\mathrm{MPa}$
$P_{all-B-flange-1}$ allowable bearing stress the the flange 1 $\mathrm{MPa}$
$P_{all-B-flange-2}$ allowable bearing stress the the flange 2 $\mathrm{MPa}$
$P_{all-B-hub}$ allowable bearing stress the hub $\mathrm{MPa}$
$P_{all-B-key}$ allowable bearing stress the key $\mathrm{MPa}$
$P_{all-B-pin}$ allowable bearing stress the pin $\mathrm{MPa}$
$P_{all-B-rod}$ allowable bearing stress the rod $\mathrm{MPa}$
$P_{all-B-shaft}$ allowable bearing stress the shaft $\mathrm{MPa}$
$P_{all-B-socket}$ allowable bearing stress the socket $\mathrm{MPa}$
$P_{all-B-spigot}$ allowable bearing stress the spigot $\mathrm{MPa}$
$P_{all-B-trunnion}$ allowable bearing stress the trunnion $\mathrm{MPa}$
$S_F$ safety factor $\mathrm{ }$
$S_s$ coefficient of max. stress increase $\mathrm{ }$
$S_{y-bolt}$ the minimum yield strength of the bolt $\mathrm{MPa}$
$S_{y-clevis}$ the minimum yield strength of the clevis $\mathrm{MPa}$
$S_{y-cotter}$ the minimum yield strength of the cotter $\mathrm{MPa}$
$S_{y-flange-1}$ the minimum yield strength of the flange 1 $\mathrm{MPa}$
$S_{y-flange-2}$ the minimum yield strength of the flange 2 $\mathrm{MPa}$
$S_{y-hub}$ the minimum yield strength of the hub $\mathrm{MPa}$
$S_{y-key}$ the minimum yield strength of the key $\mathrm{MPa}$
$S_{y-pin}$ the minimum yield strength of the pin $\mathrm{MPa}$
$S_{y-rod}$ the minimum yield strength of the rod $\mathrm{MPa}$
$S_{y-shaft}$ the minimum yield strength of the shaft $\mathrm{MPa}$
$S_{y-socket}$ the minimum yield strength of the socket $\mathrm{MPa}$
$S_{y-spigot}$ the minimum yield strength of the spigot $\mathrm{MPa}$
$S_{y-trunnion}$ the minimum yield strength of the trunnion $\mathrm{MPa}$
$T_a$ ambient temperature $\mathrm{°C}$
$T_{hub}$ temperature for hub $\mathrm{°C}$
$T_{shaft}$ temperature for shaft $\mathrm{°C}$
$a$ thickness the rod $\mathrm{mm}$
$a$ length square head with load $\mathrm{mm}$
$a_1$ length square head without load $\mathrm{mm}$
$a_c$ assembly clearance $\mathrm{mm}$
$b$ thickness the clevis $\mathrm{mm}$
$b$ distance of the resultant of the pressure $\mathrm{mm}$
$b$ width key $\mathrm{mm}$
$d$ diameter of the pin $\mathrm{mm}$
$d$ trunnion diameter $\mathrm{mm}$
$d$ diameter $ d $ $\mathrm{mm}$
$d$ spigot diameter $\mathrm{mm}$
$d$ basic major diameter of external thread (nominal diameter) $\mathrm{mm}$
$d_1$ basic minor diameter of external thread $\mathrm{mm}$
$d_2$ basic pitch diameter of external thread $\mathrm{mm}$
$d_3$ basic smaller diameter of external thread $\mathrm{mm}$
$d_3$ basic smaller diameter of external thread $\mathrm{mm}$
$d_8$ diameter square head $\mathrm{mm}$
$d_9$ free diameter $\mathrm{mm}$
$d_h$ diameter of bolt holes $\mathrm{mm}$
$d_w$ outer diameter of the washer $\mathrm{mm}$
$d_{nut-or-bolt-head}$ mean contact diameter under nut or bolt head $\mathrm{mm}$
$h$ height key $\mathrm{mm}$
$h_1$ length the rod $\mathrm{mm}$
$h_1$ length the spigot $\mathrm{mm}$
$h_2$ length the clevis $\mathrm{mm}$
$h_2$ length the socket $\mathrm{mm}$
$h_h$ the height of the key in the hub $\mathrm{mm}$
$h_s$ the height of the key in the shaft $\mathrm{mm}$
$i$ number of pins $\mathrm{ }$
$i$ number of keys $\mathrm{ }$
$i$ number of bolts $\mathrm{ }$
$l$ length pin $\mathrm{mm}$
$l$ length square head in the hub $\mathrm{mm}$
$l$ bolt connection length $\mathrm{mm}$
$l$ functional coupling length $\mathrm{mm}$
$l$ length key $\mathrm{mm}$
$l_1$ width the rod $\mathrm{mm}$
$l_2$ width the clevis $\mathrm{mm}$
$l_t$ tolerance of key length $\mathrm{mm}$
$p_{max}$ max. contact pressure $\mathrm{MPa}$
$p_{min}$ min. contact pressure $\mathrm{MPa}$
$r$ radius $\mathrm{mm}$
$r_1$ max. rounding the key $\mathrm{mm}$
$r_2$ groove rounding $\mathrm{mm}$
$s$ gap $\mathrm{mm}$
$s$ width square head $\mathrm{mm}$
$s$ thickness the cotter $\mathrm{mm}$
$s$ flange thickness $\mathrm{mm}$
$s_1$ length pin in flange 1 $\mathrm{mm}$
$s_2$ length pin in flange 2 $\mathrm{mm}$
$t$ width between pins $\mathrm{mm}$
$t$ depth in the shaft $\mathrm{mm}$
$t_1$ depth in the hub $\mathrm{mm}$
$t_t$ tolerance of the groove height in the shaft $\mathrm{mm}$
$t_{1t}$ tolerance of the groove height in the hub $\mathrm{mm}$
$v$ width the cotter $\mathrm{mm}$
$Δ_{max}$ max. Interference $\mathrm{mm}$
$Δ_{min}$ min. Interference $\mathrm{mm}$
$α$ angle between pins $\mathrm{rad}$
$α_{hub}$ coefficient of thermal expansion for hub $\mathrm{K^{-1}}$
$α_{shaft}$ coefficient of thermal expansion for shaft $\mathrm{K^{-1}}$
$ε$ scatter value $\mathrm{ }$
$μ$ friction coefficient $\mathrm{ }$
$μ_{flanges}$ friction between flanges $\mathrm{ }$
$μ_{nut-or-bolt-head}$ friction under the nut or bolt head $\mathrm{ }$
$μ_{thread}$ friction in the thread $\mathrm{ }$
$ν_{hub}$ Poisson's ratio for hub $\mathrm{ }$
$ν_{shaft}$ Poisson's ratio for shaft $\mathrm{ }$
$σ_{A-bolt}$ axial stress the bolt $\mathrm{MPa}$
$σ_{A-clevis}$ axial stress in the clevis $\mathrm{MPa}$
$σ_{A-hub}$ axial stress in the hub $\mathrm{MPa}$
$σ_{A-rod}$ axial stress in the rod $\mathrm{MPa}$
$σ_{A-shaft}$ axial stress in the shaft $\mathrm{MPa}$
$σ_{A-socket}$ axial stress in the socket $\mathrm{MPa}$
$σ_{A-spigot}$ axial stress in the spigot $\mathrm{MPa}$
$σ_{B-bolt}$ bending stress in the bolt $\mathrm{MPa}$
$σ_{B-cotter}$ bending stress in the cotter $\mathrm{MPa}$
$σ_{B-hub}$ bending stress in the hub $\mathrm{MPa}$
$σ_{B-shaft-hub}$ bending stress in the weakened part of the shaft-hub $\mathrm{MPa}$
$σ_{B-shaft}$ bending stress in the shaft $\mathrm{MPa}$
$σ_{B-thread}$ bending stress in the thread $\mathrm{MPa}$
$σ_{B-trunnion}$ bending stress in the trunnion $\mathrm{MPa}$
$σ_{R-hub-D}$ radial stress in the hub on diameter $ D $ $\mathrm{MPa}$
$σ_{R-shaft-D_0}$ radial stress in the shaft on diameter $ D_0 $ $\mathrm{MPa}$
$σ_{R-shaft-D}$ radial stress in the shaft on diameter $ D $ $\mathrm{MPa}$
$σ_{T-hub-D}$ tangential stress in the hub on diameter $ D $ $\mathrm{MPa}$
$σ_{T-shaft-D_0}$ tangential stress in the shaft on diameter $ D_0 $ $\mathrm{MPa}$
$σ_{T-shaft-D}$ tangential stress in the shaft on diameter $ D $ $\mathrm{MPa}$
$σ_{all-A-bolt}$ allowable axial stress the bolt $\mathrm{MPa}$
$σ_{all-A-clevis}$ allowable axial stress the clevis $\mathrm{MPa}$
$σ_{all-A-hub}$ allowable axial stress the hub $\mathrm{MPa}$
$σ_{all-A-rod}$ allowable axial stress the rod $\mathrm{MPa}$
$σ_{all-A-shaft}$ allowable axial stress the shaft $\mathrm{MPa}$
$σ_{all-A-socket}$ allowable axial stress the socket $\mathrm{MPa}$
$σ_{all-A-spigot}$ allowable axial stress the spigot $\mathrm{MPa}$
$σ_{all-B-bolt}$ allowable bending stress the bolt $\mathrm{MPa}$
$σ_{all-B-cotter}$ allowable bending stress the cotter $\mathrm{MPa}$
$σ_{all-B-flange-1}$ allowable bending stress the flange 1 $\mathrm{MPa}$
$σ_{all-B-hub}$ allowable bending stress the hub $\mathrm{MPa}$
$σ_{all-B-shaft}$ allowable bending stress the shaft $\mathrm{MPa}$
$σ_{all-B-trunnion}$ allowable bending stress the trunnion $\mathrm{MPa}$
$σ_{all-C-bolt}$ allowable combined stress the bolt $\mathrm{MPa}$
$σ_{all-C-hub}$ allowable combined stress the hub $\mathrm{MPa}$
$σ_{all-C-shaft}$ allowable combined stress the shaft $\mathrm{MPa}$
$σ_{all-C-trunnion}$ allowable combined stress the trunnion $\mathrm{MPa}$
$σ_{tresca-bolt}$ combined stress in the bolt $\mathrm{MPa}$
$σ_{tresca-hub-D}$ combined stress in the hub on diameter $ D $ $\mathrm{MPa}$
$σ_{tresca-hub}$ combined stress in the hub $\mathrm{MPa}$
$σ_{tresca-shaft-D_0}$ combined stress in the shaft on diameter $ D_0 $ $\mathrm{MPa}$
$σ_{tresca-shaft-D}$ combined stress in the shaft on diameter $ D $ $\mathrm{MPa}$
$σ_{tresca-shaft}$ combined stress in the shaft $\mathrm{MPa}$
$σ_{tresca-trunnion}$ combined stress in the trunnion $\mathrm{MPa}$
$τ_{S-bolt}$ shear stress in the bolt $\mathrm{MPa}$
$τ_{S-clevis}$ shear stress in the clevis $\mathrm{MPa}$
$τ_{S-cotter}$ shear stress in the cotter $\mathrm{MPa}$
$τ_{S-hub-D}$ shear stress in the hub on diameter $ D $ $\mathrm{MPa}$
$τ_{S-hub}$ shear stress in the hub $\mathrm{MPa}$
$τ_{S-key}$ shear stress key $\mathrm{MPa}$
$τ_{S-pin}$ shear stress in the pin $\mathrm{MPa}$
$τ_{S-rod}$ shear stress in the rod $\mathrm{MPa}$
$τ_{S-shaft-D}$ shear stress in the shaft on diameter $ D $ $\mathrm{MPa}$
$τ_{S-shaft-hub}$ shear stress in the weakened part of the shaft-hub $\mathrm{MPa}$
$τ_{S-shaft}$ shear stress in the shaft $\mathrm{MPa}$
$τ_{S-socket}$ shear stress in the socket $\mathrm{MPa}$
$τ_{S-spigot}$ shear stress in the spigot $\mathrm{MPa}$
$τ_{S-thread}$ shear stress in the thread $\mathrm{MPa}$
$τ_{S-trunnion}$ shear stress in the trunnion $\mathrm{MPa}$
$τ_{T-hub-D}$ torsion stress in the hub on diameter $ D $ $\mathrm{MPa}$
$τ_{T-hub}$ torsion stress in the hub $\mathrm{MPa}$
$τ_{T-shaft-D_0}$ torsion stress in the shaft on diameter $ D_0 $ $\mathrm{MPa}$
$τ_{T-shaft-D}$ torsion stress in the shaft on diameter $ D $ $\mathrm{MPa}$
$τ_{T-shaft}$ torsion stress in the shaft $\mathrm{MPa}$
$τ_{all-S-bolt}$ allowable shear stress the bolt $\mathrm{MPa}$
$τ_{all-S-clevis}$ allowable shear stress the clevis $\mathrm{MPa}$
$τ_{all-S-cotter}$ allowable shear stress the cotter $\mathrm{MPa}$
$τ_{all-S-flange-1}$ allowable shear stress the flange 1 $\mathrm{MPa}$
$τ_{all-S-hub}$ allowable shear stress the hub $\mathrm{MPa}$
$τ_{all-S-key}$ allowable shear stress the key $\mathrm{MPa}$
$τ_{all-S-pin}$ allowable shear stress the pin $\mathrm{MPa}$
$τ_{all-S-rod}$ allowable shear stress the rod $\mathrm{MPa}$
$τ_{all-S-shaft}$ allowable shear stress the shaft $\mathrm{MPa}$
$τ_{all-S-socket}$ allowable shear stress the socket $\mathrm{MPa}$
$τ_{all-S-spigot}$ allowable shear stress the spigot $\mathrm{MPa}$
$τ_{all-S-trunnion}$ allowable shear stress the trunnion $\mathrm{MPa}$
$ψ$ angle of inclination of the tangent to the bending line $\mathrm{rad}$