The following example calculations illustrate the procedure for some typical problems.

Example 1: Equivalent load P per roller

Load and design verification

Assumption:

Input parameters

  • Linear guides type R 6
  • AC 6 cage with 8 rollers (= RA)
  • F = 350 N
  • X = 120 mm
Example 1 diagram – single guideway configuration

Example 1 diagram – single guideway configuration

Example 1 diagram – dual guideway top view

Example 1 diagram – dual guideway top view

For the roller cage type AC 6 the following applies:

Cage-specific parameters

Kt = (RA – 1) · t = (8 – 1) · 9 = 63
Rtmin = 1 roller
C = 530 N (per chapter 5.1 techn. specifications of AC 6 cage)
Calculation for P per roller

Load equation and result

P = (F · X) / (Kt · 2) · (1 / Rtmin) = (350 · 120) / (63 · 2) · (1 / 1) = 334 N

P is smaller than C. The design is correct in this way.

Design verification passed.

Note:

Load component annotation

The asymmetric distribution of force is most safely taken into account when the load on the number of load bearing rolling elements (Rtmin) for the guideway is reduced.

Design guidance note

Symbol definitions

PEquivalent load in N per rollerEquivalent load in N per roller
Fload in Nload in N
CMax. permissible load carrying capacity per rolling element in NMax. permissible load carrying capacity per rolling element in N
XLever arm distance on x-axis in mmLever arm distance on x-axis in mm
RATotal available rolling element per cageTotal available rolling element per cage
RtminCorrection factorCorrection factor
tcage division in mmcage division in mm
KtLoad-bearing length in mmLoad-bearing length in mm

Example 2: Equivalent load P per roller

Load and design verification

Assumption:

Input parameters

  • Linear guides type R 6
  • Roller cage type AC 6 cage with 20 rollers (= RA)
  • F = 6'500 N
  • C = 530 N (per chapter 5.1 techn. specifications of AC 6 cage)
Example 2 diagram – dual guideway configuration

Example 2 diagram – dual guideway configuration

RT = RA / 2 = 20 / 2 = 10 rollers
Calculation for P per roller

Load equation and result

P = F / 2 · 1 / RT = 6'500 / 2 · 1 / 10 = 325 N

P is smaller than C. The design is correct in this way.

Design verification passed.

Symbol definitions

wDistance from cage start to the middle of the first rolling element in mmDistance from cage start to the middle of the first rolling element in mm
tcage division in mmcage division in mm
PEquivalent load in N per rollerEquivalent load in N per roller
Fload in Nload in N
CMax. permissible load carrying capacity per rolling element in NMax. permissible load carrying capacity per rolling element in N
RATotal available rolling element per cageTotal available rolling element per cage
RtNumber of load-bearing rolling elements per cageNumber of load-bearing rolling elements per cage

Example 3: Equivalent load P per ball

Load and design verification

Assumption:

Input parameters

  • Rigid slide structure
  • Linear guides type R 6
  • Cage type AK 6 with 12 balls (= RA); t = 9 mm (according to chapter 5.1, technical data for the AK 6 cage)
  • F = 240 N
  • X = 75 mm (distance F to opposing force)
  • C = 65 N (according to chapter 5.1, technical data for the AK 6 cage)
Example 3 ball cage side view

Example 3 ball cage side view

Example 3 dual guideway top view

Example 3 dual guideway top view

RA = RT = 12 balls
Rtmin = 3 = Rt / 4 (according to diagram on page 101)
Kt = (RA – 1) · t
Calculation for P per ball

Load equation and result

P = F / Kt · X / 2 · 1 / Rtmin = 240 / 99 · 75 / 2 · 1 / 3 = 30 N

P is smaller than C. The design is correct in this way.

Design verification passed.

Symbol definitions

tcage division in mmcage division in mm
PEquivalent load in N per ballEquivalent load in N per ball
Fload in Nload in N
CMax. permissible load carrying capacity per rolling element in NMax. permissible load carrying capacity per rolling element in N
RtminCorrection factorCorrection factor
RATotal available rolling elements per cageTotal available rolling elements per cage
RtNumber of load-bearing rolling elements per cageNumber of load-bearing rolling elements per cage
KtLoad-bearing length in mmLoad-bearing length in mm

Example 4: Equivalent load P per roller and the suitable size for RNG guideways

Load and design verification

Assumption:

Input parameters

  • Type RNG linear guideways
  • Roller cage type KBN with 10 rollers (RA)
  • F = 15'000 N
  • X = 50 mm
  • Q = 100 mm
Example 4 RNG guideway configuration

Example 4 RNG guideway configuration

RT = RA / 2 = 10 / 2 = 5 rollers
Calculation for P per roller

Load equation and result

P1 = (F · X) / Q · 1 / RT = (15'000 · 50) / 100 · 1 / 5 = 1'500 N
P2 = F / RA = 15'000 / 10 = 1'500 N
P = P1 + P2 = 1'500 + 1'500 = 3'000 N
Definition of the suitable guideway size:

Size selection criterion

According to product specification for the KBN cage (chapter 5.2 or 5.3) if C = 3'900 N were to be selected.

The roller size 9 is suitable. Thus select cage KBN 9 and the linear guideway RNG 9, provided the service life has been fulfilled.

Symbol definitions

P (P1, P2)Equivalent loads in N per rollerEquivalent loads in N per roller
Fload in Nload in N
XLever arm distance on x-axis in mmLever arm distance on x-axis in mm
QMedium linear guideway distance in mmMedium linear guideway distance in mm
CMax. permissible load carrying capacity per rolling element in NMax. permissible load carrying capacity per rolling element in N
RATotal available rolling element per cageTotal available rolling element per cage
RtNumber of load-bearing rolling elements per cageNumber of load-bearing rolling elements per cage

KBN cage dimensions and load capacity

Type Size Dw (mm) t (mm) w (mm) C per roller (N)
KBN44.56.5approx. 4850
66.58.5approx. 51'800
9912approx. 7.53'900
121215approx. 96'500

Example 5: Equivalent load P per needle

Load and design verification

Assumption:

Input parameters

  • Linear guideways type N/O 2025
  • SHW 15 cage, cage length K = 194 mm (w = 2.9 mm according to techn. specifications of the SHW 15 cage)
  • t = 4 mm
  • F = 5'000 N
  • X = 280 mm
  • Q = 75 mm
  • C = 750 N (according to techn. specifications for the AC 15 cage)
Example 5 N/O 2025 needle guideway configuration

Example 5 N/O 2025 needle guideway configuration

RA = ((K – 2w) / t + 1) · 2 = ((194 – 5.8) / 4 + 1) · 2 = 96 needles
Rt = RA / 2 = 48 needles
Calculation for P per needle

Load equation and result

P = (F · X) / Q · 1 / Rt = (5'000 · 280) / 75 · 1 / 48 = 389 N

P is smaller than C. The design is correct in this way.

Design verification passed.

Symbol definitions

wDistance from cage start to the middle of the first rolling element in mmDistance from cage start to the middle of the first rolling element in mm
tcage division in mmcage division in mm
PEquivalent load in N per needleEquivalent load in N per needle
Fload in Nload in N
XLever arm distance on x-axis in mmLever arm distance on x-axis in mm
QMedium linear guideway distance in mmMedium linear guideway distance in mm
CMax. permissible load carrying capacity per rolling element in NMax. permissible load carrying capacity per rolling element in N
RtNumber of load-bearing rolling elements per cageNumber of load-bearing rolling elements per cage
RATotal available rolling element per cageTotal available rolling element per cage
KCage length in mmCage length in mm

Example 6: Equivalent load P per roller

Load and design verification

Assumption:

Input parameters

  • Rigid structure
  • Linear guides type R 12
  • Cage type AC 12, length K = 400 mm
  • F = 2'000 N
  • X = 500 mm
  • X1 = 200 mm
  • Q = 100 mm
  • C = 2'500 N (see chapter 5.1, technical specifications for the AC 12 cage)
Example 6 R 12 configuration with AC 12 cage

Example 6 R 12 configuration with AC 12 cage

For the roller cage AC 12 the following applies:

Cage-specific parameters

Kt = K – 2w = 400 – 22 = 378 mm
RA = Kt / t + 1 = 378 / 18 + 1 = 22 rollers
Rt = RA / 2 = 22 / 2 = 11 rollers
X > Kt = Rt / 4 (according to the diagram on page 101)
RTQ = Rt
RTL = Rt / 4 = 11 / 4 = 2.75 rollers (rounded down to 2)
Calculation for P per roller

Calculation step

Load laterally

Directional load component

PQ = (F · X1) / Q · (1 / RTQ) = (2'000 · 200) / 100 · (1 / 11) = 364 N

Load longitudinally

Directional load component

PL = (F · X) / (Kt · 2) · (1 / RTL) = (2'000 · 500) / (378 · 2) · (1 / 2) = 662 N
P = PQ + PL = 364 + 662 = 1'026 N

P is smaller than C. The design is correct in this way.

Design verification passed.

Symbol definitions

wDistance from cage start to the middle of the first rolling element in mmDistance from cage start to the middle of the first rolling element in mm
tcage division in mmcage division in mm
PEquivalent load in N per rollerEquivalent load in N per roller
Fload in Nload in N
XLever arm distance on x-axis in mmLever arm distance on x-axis in mm
X1Lever arm distance 1 on x-axis in mmLever arm distance 1 on x-axis in mm
QMedium linear guideway distance in mmMedium linear guideway distance in mm
CMax. permissible load carrying capacity per rolling element in NMax. permissible load carrying capacity per rolling element in N
RtNumber of load-bearing rolling elements per cageNumber of load-bearing rolling elements per cage
RATotal available rolling element per cageTotal available rolling element per cage
KCage length in mmCage length in mm
KtLoad-bearing length in mmLoad-bearing length in mm
...LLongitudinallyLongitudinally
...QLaterallyLaterally

Example 7: Equivalent load P for recirculating unit

Load and design verification

Assumption:

Input parameters

  • Recirculating unit type SR 6-100
  • Linear guides type R 6
  • Rt = 2 recirculating unit
  • F = 6'000 N
  • C = 2'150 N (see chapter 6.3, technical specifications for the recirculating unit)
Example 7 SR 6-100 recirculating unit configuration

Example 7 SR 6-100 recirculating unit configuration

Calculation for P

Calculation step

P = F / 2 · 1 / Rt = 6'000 / 2 · 1 / 2 = 1'500 N

P is smaller than C. The design is correct in this way.

Design verification passed.

Symbol definitions

PEquivalent loads in NEquivalent loads in N
Fload in Nload in N
CMax. permissible load carrying capacity in NMax. permissible load carrying capacity in N
RtNumber of load-bearing recirculating unitsNumber of load-bearing recirculating units

Example 8: Moment load M longitudinally and laterally

Load and design verification

Assumption:

Input parameters

  • Recirculating unit type SR 6-150
  • Linear guideways type RD 6
  • ML = 112 Nm (according to chapter 6.3, technical specifications for the recirculating unit)
  • X = 45 mm (distance F to opposing force)
  • F = 2'000 N
Example 8 moment load configuration

Example 8 moment load configuration

Calculation for M

Calculation step

M = F · X = 2000 · 0.045 = 90 Nm

The moment load M is below the permissible load ML. Thus the design is correct.

Symbol definitions

MMoment load in Nm longitudinally and laterallyMoment load in Nm longitudinally and laterally
MLPermitted moment load in Nm longitudinally and laterallyPermitted moment load in Nm longitudinally and laterally
Xdistance in mmdistance in mm
Fload in Nload in N

Example 9: Equivalent loads PL and PQ

Load and design verification

Assumption:

Input parameters

  • Recirculating unit top type NRT 26 111 (C = 98'000 N)
  • Recirculating unit bottom type NRT 19 077 (C = 43'000 N)
  • Recirculating unit side type NRT 19 077 (C = 43'000 N)
  • K = 700 mm
  • K1 = 450 mm
  • Rtmin = 0.5 (according to table on page 101)
  • F = 83'000 N
  • X = 500 mm
  • Y = 100 mm
Example 9 NRT recirculating unit configuration

Example 9 NRT recirculating unit configuration

Calculation for PL and PQ

Load longitudinally

Directional load component

PL = (F · X) / (K · 2) · 1 / RTmin = (83'000 · 500) / (700 · 2) · 1 / 0.5 = 59'286 N

Load laterally

Directional load component

PQ = (F · Y) / (K1 · 2) · 1 / Rtmin = (83'000 · 100) / 450 · 1 / 0.5 = 36'889 N

Symbol definitions

Symbol Description (unit) Detail
PEquivalent load in NEquivalent load in N
PLEquivalent load longitudinally in NEquivalent load longitudinally in N
PQEquivalent load laterally in NEquivalent load laterally in N
Fload in Nload in N
Xdistance in mmdistance in mm
Ydistance in mmdistance in mm
CMax. permissible load carrying capacity per recirculating unit in NMax. permissible load carrying capacity per recirculating unit in N
RtminCorrection factorCorrection factor
KSpacing between the recirculating units in mmSpacing between the recirculating units in mm
K1Spacing between the recirculating units in mmSpacing between the recirculating units in mm
ESC