Elementos de Máquinas - Guias de Esferas

7/28/2019 Elementos de Mquinas - Guias de Esferas

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4.1.

Flowchart


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4.1 Flowchart

A-66

4. Selecting the Correct Type of LM Guide

Type and size changed

Span, No. of blocks, and No. of rails changed

Set the conditions for the design of loads on the LM Guide.- Space available for the guide part- Dimensions (span, No. of blocks, No. of rails, and thrust)- Installation direction (horizontal, vertical, tilted, wall-hung, or suspended)- Magnitude of the applied load, direction, and location- Frequency of use (duty cycle)

Select the correct type for the operating conditions and assume an approximate size.

SSR, SR, SHS, HSR, JR, CSR, SNR, NR, HRW, GSR, RSR, and HCR

Calculate the load that an LM block exerts on the LM Guide.

Convert the load that an LM block exerts in each direction into an equivalent load.

Verify the value of the static safety factor for the basic static-load rating and maximum applied load.

Average the applied loads which fluctuate during operation, and convert them into a mean load.

Calculate the running distance using the service-life equation.

Convert the running distance obtained into the service life in hours.

Determine the lubricants (grease, oil, special lubrication, etc.) to be used.Determine the lubrication method (periodic greasing, forced lubrication, etc.) to be used.Determine the material (standard, stainless steel, etc.) to be used.

Determine the surface treatment (anticorrosion, appearance protection, etc.) to be provided.Design contaminant protection (bellows, telescopic cover, etc.).

Is the static safetyfactor verified?

Does the valueobtained satisfy the required

service life?

Select the correct type.

Calculate the applied load.

Calculate the equivalent load.

Calculate the static safety

factor.

Calculate the mean load.

Calculate the nominal life.

Calculate the service life in

hours.

Safety design.

Completion of selection.

1

2

3

4

5

6

7

8

11

YES

YES

NO

NO

Set the operating conditions.

- Velocity (acceleration)- Stroke length- Required service life- Motion precision- Service environment


3/32A-67

A-II

Determine the redial clearance to be used. Determine the fastening methods to be used. Determine the rigidity at the fastened areas.

Determine the accuracygrade to be applied.

Determine the mounting-surface precision to be used.

Forecast the rigidity. Set the precision.9 10


4/32

4.2 Applied Load Direction andLoad Rating

The LM Guide can bear loads and moments in all

directions resulting from the installation direction and

location of the guide system, the location of the center

of gravity of a moving object thereon, the location at

which thrust occurs, the acceleration, the machiningresistance, and the like.

A-68

Fig. 30 Applied Load Direction

Reverse-radial load Radial load

Lateral load Lateral load

Moment

Moment

Moment

Yawing

Rolling

Pitching


5/32

4.2.1 LM-Guide Load Ratings inVarious Directions

The LM Guide can be divided into two major types: the

four-way equal-load type, which has the same load

rating for all radial, reverse-radial, and lateral loads;

and the radial type, which has a high load rating in the

radial direction. With the radial type, load ratings inthe radial, reverse-radial, and lateral directions differ.

If a radial type is used under a load in one of these

directions, multiply the relevant basic load rating

provided in the corresponding dimension table by the

factor specified in the respective section.

A-69

A-II

Load Rating in Each Direction

Four-way equal-load type

Radial type

Load distribution curveType


6/32

4.2.2 Calculating the Load Usingthe Moment-EquivalentFactor

Where a sufficient installation space is not available,

you may be obliged to use just one LM block or two

LM blocks laid over one another for the LM Guide. In

such a setting, the load distribution cannot be uniformand, as a result, an excessive load is exerted in

localized areas (e.g., rail ends). Continued use under

such conditions may result in flaking in those areas,

consequently shortening the service life. In such a

case, calculate true load by multiplying the moment

value by any one of the moment -equivalent factors

specified in Tables 6 through 10.

An equivalent-load equation applicable when a moment

acts on an LM Guide is shown below.

P = KM

where P : equivalent load per LM Guide

K : equivalent moment factor

M : developed moment (Nmm)

KA, KB, and KC represent the equivalent moment factors

in directions MA, MB, and MC, respectively.

Calculation Examples One LM block is used

Model No.: HSR25A1

P = MCKC+MAKA+mg= 98 x 100 x 0.087 + 98 x 200 x 0.13 + 98 = 3500 N

Two LM blocks are used laid over one another.

Model No.: SR20V2

P1 = MC/2 x KC+MAxKA+mg/2

= 49x150/2x0.109+49x200x0.0378+49/2=795.5 N

P1L = MC/2xKC+MAxKA+mg/2

= 49x150/2x0.109+49x200x0.0378+49/2= 5.6 N

P2

= MC

/2xKC

MA

xKA

+mg/2

= 49x150/2x0.10949x200x0.0378+49/2=54.6 N

P2L = MC/2xKC-MAxKA+mg/2

= 49x150/2x0.10949x200x0.0378+49/2=746.5 N

Notes

1. Since an LM Guide in a vertical position receives

only a moment load, there is no need to apply other

loads (mg).

2. In some models, load ratings differ depending on

the direction of the applied load. With such a

model, calculate an equivalent load in a direction inwh ich co nd it io ns ar e co mp arab ly ba d (i. e. a

direction in which a larger moment is applied).

A-70

Fig. 31 Ball Load Effected by a Moment

Moment load

Moment load

LM rail

Ball loadcurve

Ball displacementline

Balldisplacementline Ball load curve

Rows of ballsunder a load

Rows of ballsunder a load

Maximuma

pplied

loadonaball

Maximumb

alldisplacement

Fig. 32 Equivalent Load Calculation for aSystem Using One LM Block

Gravitational acceleration g = 9.8 m/s2

Mass m = 10 kg

Gravitational acceleration g = 9.8 m/s2

Mass m = 5 kg

Fig. 33 Equivalent Load Calculation for aSystem Using Two LM Blocks Laid Over

One Another


7/32A-71

A-II

Table 6 Equivalent Factors (Types SSR, SNR, SNS, and SHS)

KA: Equivalent moment factor in the pitching direction

KB: Equivalent moment factor in the yawing direction

KC: Equivalent moment factor in the rolling direction

Model No.

SSR15W (TB)

SSR15V

SSR20W (TB)

SSR20V

SSR25W (TB)

SSR25V

SSR30W

SSR35W

SNR25 SNS25

SNR25L SNS25L

SNR30 SNS30

SNR30L SNS30L

SNR35 SNS35

SNR35L SNS35L

SNR45 SNS45

SNR45L SNS45L

SNR55 SNS55

SNR55L SNS55L

SNR65 SNS65

SNR65L SNS65L

SHS15

SHS20

SHS20L

SHS25

SHS25L

SHS30

SHS30L

SHS35

SHS35L

SHS45

SHS45L

SHS55

SHS55L

SHS65

SHS65L

KA,, KB

1.93x101 3.40x102

3.27x101 4.36x102

1.67x101 2.91x102

2.55x101 3.86x102

1.31x101 2.34x102

1.99x101 3.08x102

1.10x101 2.01x102

1.01x101 1.74x102

1.25x101 2.36x102

9.94x102 1.95x102

1.10x101 1.98x102

8.62x102 1.64x102

9.63x102 1.78x102

7.56x102 1.47x102

7.47x102 1.43x102

5.74x102 1.17x102

6.31x102 1.21x102

4.91x102 1.00x102

5.48x10

2

1.06x10

2

4.02x102 8.17x103

1.68x101 3.04x102

1.32x101 2.49x102

1.01x101 2.05x102

1.12x101 2.15x102

9.14x102 1.84x102

9.74x102 1.86x102

7.48x102 1.53x102

8.47x102 1.62x102

6.50x102 1.32x102

7.47x102 1.41x102

5.74x102 1.15x102

6.05x102 1.15x102

4.65x102 9.41x103

4.44x102 9.02x103

3.50x102 7.42x103

KC

1.45x101

1.45x101

1.10x101

1.10x101

9.34x102

9.34x102

7.85x102

6.49x102

8.91x102

8.91x102

7.97x102

7.97x102

6.66x102

6.66x102

4.99x102

4.99x102

4.28x102

4.28x102

3.62x10

2

3.62x102

1.39x101

9.91x102

9.91x102

8.63x102

8.63x102

7.15x102

7.15x102

5.85x102

5.85x102

4.38x102

4.38x102

3.75x102

3.75x102

3.18x102

3.18x102

Equivalent Load Calculation for aSystem Using One LM Block

Equivalent Load Calculation for a System UsingTwo LM Blocks Laid Over One Another


8/32A-72




Table 7 Equivalent Factors (Types SR, NR, and NRS)

Model No.

SR15W (TB)

SR15V (SB)

SR20W (TB)

SR20V (SB)

SR25W (TB)

SR25V (SB)

SR30W (TB)

SR30V (SB)

SR35W (TB)

SR35V (SB)

SR45W (TB)

SR55W (TB)

SR70T

SR85T

SR100T

SR120T

SR150T

NR25X NRS25X

NR25LX NRS25LX

NR30 NRS30

NR30L NRS30L

NR35 NRS35

NR35L NRS35L

NR45 NRS45

NR45L NRS45L

NR55 NRS55

NR55L NRS55L

NR65 NRS65

NR65L NRS65L

NR75 NRS75

NR75L NRS75L

NR85 NRS85

NR85L NRS85L

NR100 NRS100

NR100L NRS100L

KA, KB

1.95x101 3.41x102

3.17x101 4.44x102

1.70x101 2.92x102

2.77x101 3.78x102

1.36x101 2.34x102

2.22x101 3.02x102

1.14x101 2.01x102

1.85x101 2.69x102

9.74x102 1.76x102

1.58x101 2.35x102

8.52x102 1.55x102

6.81x102 1.25x102

5.24x102 1.01x102

6.27x102 1.05x102

5.09x102 9.62x103

4.59x102 8.13x103

3.82x102 6.83x103

1.28x101 2.37x102

9.83x102 1.96x102

1.07x101 2.01x102

8.19x102 1.66x102

9.74x102 1.79x102

7.37x102 1.48x102

7.55x102 1.42x102

5.87x102 1.17x102

6.35x102 1.22x102

5.00x102 1.00x102

5.49x102 1.06x102

4.09x102 8.17x103

4.64x102 9.09x103

3.61x102 7.33x103

4.08x102 8.05x103

3.21x102 6.65x103

3.55x102 6.72x103

2.89x102 6.02x103

KC

1.44x101

1.44x101

1.09x101

1.09x101

9.31x102

9.31x102

7.82x102

7.82x102

6.47x102

6.47x102

4.81x102

4.59x102

3.21x102

2.77x102

2.35x102

1.95x102

1.57x102

9.04x102

9.04x102

8.14x102

8.14x102

6.79x102

6.79x102

5.06x102

5.06x102

4.34x102

4.34x102

3.66x102

3.66x102

3.07x102

3.07x102

2.73x102

2.73x102

2.32x102

2.32x102




9/32A-73

A-II




Table 8 Equivalent Factors (Types HSR, CSR, JR, and HRW)

Model No.

HSR8

HSR10

HSR12

HSR15 CSR15

HSR20 CSR20S

HSR20L CSR20

HSR25 CSR25S

HSR25L CSR25

HSR30 CSR30S

HSR30L CSR30

HSR35 JR35

HSR35L CSR35

HSR45 JR45

HSR45L CSR45

HSR55

HSR55L

HSR65

HSR65L

HSR85

HSR85L

HSR100

HSR120

HSR150

HRW12

HRW14

HRW17

HRW21

HRW27

HRW35

HRW50

HRW60

KA, KB

5.17x101 7.89x102

3.91x101 6.14x102

2.61x101 4.25x102

2.07x101 3.39x102

1.56x101 2.59x102

1.21x101 2.18x102

1.30x101 2.33x102

1.01x101 1.93x102

1.12x101 1.97x102

8.63x102 1.64x102

9.77x102 1.77x102

7.55x102 1.47x102

7.82x102 1.39x102

6.04x102 1.16x102

6.52x102 1.19x102

5.03x102 9.86x103

5.21x102 1.05x102

4.03x102 8.07x103

4.34x102 7.84x103

3.35x102 6.54x103

3.02x102 5.93x103

2.74x102 5.43x103

2.52x102 5.01x103

3.01x101 5.29x102

2.40x101 4.43x102

2.40x101 3.79x102

2.01x101 3.29x102

1.51x101 2.69x102

1.01x101 1.84x102

7.55x102 1.40x102

6.71x102 1.24x102

KC

2.47x101

1.96x101

1.65x101

1.33x101

1.00x101

1.00x101

8.70x102

8.70x102

7.14x102

7.14x102

5.88x102

5.88x102

4.44x102

4.44x102

3.77x102

3.77x102

3.17x102

3.17x102

2.35x102

2.35x102

2.00x102

1.75x102

1.39x102

1.22x101

8.86x102

6.06x102

5.41x102

4.76x102

2.90x102

2.22x102

1.67x102




10/32A-74




Table 9 Equivalent Factors (Type GSR)

Model No.

GSR15T

GSR15V

GSR20T

GSR20V

GSR25T

GSR25V

GSR30T

GSR35T

KA, KB

1.95x101 3.19x102

2.77x101 3.87x102

1.56x101 2.59x102

2.22x101 3.14x102

1.30x101 2.18x102

1.85x101 2.65x102

1.12x101 1.86x102

9.77x102 1.64x102

Note: With type GSR, these values apply to cases in which two LM Guides are used.

KC




11/32A-75

A-II

Table 10 Equivalent Factors (Types RSR, RSH, and NSR-TBC)

Model No.

RSR3W

RSR3WN

RSR5

RSR5N

RSR5W

RSR5WN

RSR7M RSH7

RSR7N

RSR7W

RSR7WN

RSR9K RSH9K

RSR9N

RSR9WV

RSR9WN

RSR12V RSH12V

RSR12N

RSR12WV

RSR12WN

RSR15V

RSR15N

RSR15WV

RSR15WN

RSR20V

RSR20N

NSR20TBC

NSR25TBC

NSR30TBC

NSR40TBC

NSR50TBC

NSR70TBC

KA, KB

9.10x101 1.23x101

5.99x101 9.69x102

8.80x101 1.04x101

5.78x101 9.63x102

5.78x101 8.62x102

4.09x101 7.02x102

5.54x101 8.18x102

3.41x101 5.89x102

3.91x101 6.02x102

2.58x101 4.85x102

4.40x101 6.05x102

2.54x101 4.75x102

2.89x101 5.03x102

2.05x101 3.90x102

3.52x101 5.42x102

2.31x101 4.08x102

2.48x101 4.45x102

1.72x101 3.34x102

2.77x101 4.42x102

1.82x101 3.18x102

1.95x101 3.58x102

1.36x101 2.67x102

1.83x101 2.90x102

1.21x101 2.28x102

2.29x101 2.68x102

2.01x101 2.27x102

1.85x101 1.93x102

1.39x101 1.60x102

1.24x101 1.42x102

9.99x102 1.15x102

KC

3.17x101

3.17x101

3.85x101

3.85x101

1.96x101

1.96x101

2.74x101

2.74x101

1.40x101

1.40x101

2.15x101

2.48x101

1.09x101

1.18x101

1.74x101

1.93x101

8.51x102

8.95x102

1.41x101

1.52x101

4.85x102

4.98x102

1.09x101

1.18x101







12/32

4.3 Calculating the Applied Load

4.3.1 Setting Operating Conditions

To obtain the magnitude of an applied load and the

service life in hours, the operating conditions of the

LM system in question must first be set.

The operating conditions should include:1) Mass : m (kg)

2) Direction of the acting load

3) Location of the action point

(e.g., center of gravity) : r2,r3, h1 (mm)

4) Location of the thrust developed :

r4, h2 (mm)

5) LM system arrangement : r0,r1 (mm)

(No. of systems and axes)

6) Velocity diagram

Velocity : V (mm/s)

Time constant : tn (s)

Acceleration : n (mm/s2)

7) Duty cycle

No. of reciprocating cycles per min

: N1 (min-1)

8) Stroke length :rs (mm)

9) Mean velocity : V m (m/s)

10)Required service life in hours : Lh (h)

Vtn

(an = )

A-76

Gravitational acceleration: g = 9.8 m/s2

Fig. 34 Operating Conditions

Velocity

Duty cycle

Velocity diagram


13/32

4.3.2 Calculating the Applied Load

The load applied to the LM Guide varies with the

external force exerted thereon, such as the location of

the center of gravity of an object being moved, the

location of the thrust developed, inertia due to

acceleration and deceleration during starting and

stopping, and the machining resistance.

To select the correct type of LM Guide, the magnitude

of applied loads must be determined in consideration

of the above conditions.

Using the following examples 1 through 10, we will

now calculate the loads applied to the LM Guide.

m : Mass (kg)

rn : Distance (mm)

Fn : External force (N)

Pn : Applied load (N)

(radial and reverse-radial directions)

PnT : Applied load (horizontal direction) (N)

g : Gravitational acceleration (m/s2)

(g = 9.8 m/s2)

V : Velocity

tn : Time constant

n : Acceleration (m/s2)

Vtn

(an = )

A-77

A-II

1

2

Operating conditions Equation for calculating applied load

P1

P2

P3

P4

mg

4

mgR2

2R0

mgR3

2R1

mg

4

mgR2

2R0

mgR3

2R

mg

4

mgR2

2R0

mgR3

2R1

mg4

mgR22R0

mgR32R1

P1

P2

P3

P4

mg

4

mgR2

2R0

mgR3

2R1

mg4

mgR22R0

mgR32R1

mg

4

mgR2

2R0

mgR3

2R1

mg

4

mgR2

2R0

mgR3

2R1

Install in a horizontal position.

(Move the block.)

Measure in uniform motion or at rest.

Install in an overhung horizontal position.

(Move the block.)


Ex-ample


14/32A-78

3

4


P1P4

P1TP4T

mgR2

2R0

mgR3

2R0

P1P4

P1TP4T

P2TP3T

mgR32R1

mg

4

mgR2

2R0

mg

4

mgR2

2R0

Install in a vertical position.


Install on a wall.Measure in uniform motion or at rest.

[Ex.] On the vertical axis of industrial robots

In automatic painting machines and

lifters.

[Ex.] On cross railsLoader travel axis

Ex-ample


15/32A-79

A-II

5

6


P1P4max

P1P4 min

mg

4

mgR1

2R0

mg

4

mgR1

2R0

P1

P1T

P2

P2T

P3

P3T

P4

P4T

mgcos

4

mgcosR2

2R0

mgcos

4

mgcosR2

2R0

mgsin

4

mgsinR2

2R0

mgsinh1

2R1

mgcosR3

2R1

mgsin

4

mgsinR2

2R0

mgsinh1

2R1

mgcosR3

2R1

mgcos

4

mgcosR2

2R0

mgcos

4

mgcosR2

2R

0

mgsin

4

mgsinR2

2R0

mgsinh1

2R1

mgcosR3

2R1

mgsin

4

mgsinR2

2R0

mgsinh1

2R1

mgcosR3

2R1

Move on the LM rail.

Install in a horizontal position.

Install in a laterally tilted position.

[Ex.] XY table

Sliding fork

[Ex.] NC lathe

Carriage (for the lathe)

Ex-ample


16/32A-80

7

8


P1

P1T

P2

P2T

P3

P3T

P4

P4T

mgcos

4

mgcosR2

2R0

mgcos

4

mgcosR2

2R0

mgsin

R

32R0

mgsinh1

2R0

mgcosR3

2R1

mgsinR3

2R0

mgsinh1

2R0

mgcosR3

2R1

mgcos

4

mgcosR2

2R0

mgcos

4

mgcosR2

2R0

mgsinR3

2R0

mgsinh1

2R0

mgcosR3

2R1

mgsinR3

2R0

mgsinh1

2R0

mgcosR3

2R1

During acceleration

P1P4

P2P3

P1TP4T

In uniform motion

P1P4

During deceleration

P1P4

P2P3

P1TP4T

mg

4

m1R2

2R0

m1R2

2R0

m1R3

2R0

m3R2

2R0

m3R2

2R0

m3R3

2R0

mg

4

mg

4

mg

4

mg

4

Install in a longitudinally tilted position.

Install in a horizontal position

subjected to inertia.

[Ex.] NC latheTool rest (for the lathe)

Vtn

n =

Ex-ample

Velocity

Velocity diagram

Time (s)


17/32A-81

A-II

Under force F1

P1P4

P1TP4T

Under force F2

P1 P4

P2 P3

Under force F3

P1P4

P1T P4T

P2T P3T

F1R5

2R0

F1R

42R0

F2R2

2R0

F2R2

2R0

F3R32R1

F3R2

2R0

F3R2

2R0

F2

4

F2

4

F3

4

F3

4

9

10


During acceleration

P1P4

P1TP4T

In uniform motion

P1P4

P1TP4T

During deceleration

P1P4

P1TP4T

m(g1)R2

2R0

m(g1)R

3

2R0

m(g

3)R

22R0

m(g3)R3

2R0

mgR2

2R0

mgR3

2R0

Install in a vertical position subjected to

inertia.

Install in a horizontal position subjected to

external force.

[Ex.] Drill unit

Milling machine

Lathe

Machining center and similar

cutting machine

Vtn

n =

Ex-ample

Velocity

Time

Velocity diagram


18/32

4.4 Calculating the Equivalent LoadThe LM Guide can bear loads and moments in four

directions, including a radial load (PR), reverse-radial

load (PL), and lateral load (PT), simultaneously.

Applied loads include the following:

A-82

PR : Radial load

PL : Reverse-radial load

PT : Lateral load

MA : Moment in the pitching direction

MB : Moment in the yawing direction

MC : Moment in the rolling direction

Calculation example for LM Guide type HSR

The equivalent load when a radial load (PR) and a

lateral load (PT) are applied simultaneously can

be obtained using the following equation:

PE (equivalent load ) = PR + PT

PR : Radial load

PT : Lateral load

Fig. 35 Directions of the Load and Moment Exerted on the LM Guide

Fig. 36 LM-Guide Equivalent Load

Equivalent load PEWhen more than one load (e.g. , radial and lateral

loads) is exerted on the LM Guide simultaneously, the

service life and static safety factors should be

calculated using equivalent load values obtained by

converting all loads involved into radial, lateral, and

other loads involved.

Equivalent-load equationThe equivalent-load equations for the LM Guide differ

by guide type. For details, see the relevant sections.


19/32

4.5 Static Safety FactorTo calculate a load exerted on the LM Guide, the mean

load necessary for calculating the service life and the

maximum load necessary for calculating the static

safety factor must be obtained in advance. In a system

that is subjected to frequent starts and stops and is

placed under machining loads, and one upon which amoment due to an overhang load is forcefully exerted,

an excessive load greater than expected may develop.

When selecting the correct type of LM Guide for your

purpose, be sure that the type you are considering can

bear the maximum possible load, both when stopped

and when in operation. The table below specifies the

standard values for the static safety factor.

fs : Static safety factor

C0 : Basic static-load rating (radial) (N)

C0L : Basic static-load rating (reverse-radial) (N)

C0R : Basic static-load rating (lateral) (N)

PR : Calculated load (radial) (N)

PL : Calculated load (reverse-radial) (N)

PT : Calculated load (lateral) (N)

fH : Hardness factor (see Fig. 37, page A-86)

fT : Temperature factor (see Fig. 38, page A-86)

fC : Contact factor (see Table 13, page A-87)

A-83

A-II

Machine used Loading conditionsfs lower

limit

Ordinaryindustrialmachine

Machine tool

Receives no vibration or impact

Receives vibration and impact

Receives no vibration or impact

Receives vibration and impact

1.0~1.3

2.0~3.0

1.0~1.5

2.5~7.0

Table 11 Standard Values for

the Static Safety Factor (fs)

For large radial loads f S

f S

f S

fHf TfCC 0

PR

fH

f T

fC

C 0LP L

fHf TfCC 0T

PTFor large lateral loads

For large reverse-radialloads


20/32

4.6 Calculating the Mean LoadAn industrial robot grasps a workpiece using its arm as

it advances, moving further under the load. When it

returns, the arm has no load other than its tare. In a

machine tool, LM blocks receive varying loads

depending on the host-system operating conditions.

The service life of the LM Guide, therefore, should becalculated in consideration of such fluctuations in load.

The mean load (Pm) is the load under which the service

life of the LM Guide becomes equivalent to that under

the varying loads exerted on the LM blocks.

The basic equation for calculating the mean load is as

follows:

where

Pm : mean load (N)

Pn : varying load (N)

L : total running distance (mm)

Ln : running distance under load Pn (mm)

Note: This equation and equation (1) below

apply in cases in which the rolling

elements are balls.

A-84

Pm (Pn3Ln)1L3 n

n=1

1) For loads that change stepwise

(1)

where

Pm : mean load (N)

Pn : varying load (N)

L : total running distance (mm)

Ln : running distance under load Pn (mm)

Pm P13L1P23L2 Pn3Ln1L

3

Load

P

Total running distance L


21/32A-85

A-II

2) For loads that change monotonously

(2)

where

Pmin : minimum load (N)

Pmax : maximum load (N)

Pm Pmin 2Pmax1

3

3) For loads that change sinusoidally

a) Pm 0.65Pmax (3) b) Pm 0.75Pmax (4)

Load

P



Load

P


Load

P


22/32

1. Operating conditions

A-86

1 (m/s2)

vt1

P1

P2

P3

P4

mg

4

mg

4

mg

4mg

4

Pa1 P1

Pa2 P2

Pa3 P3

Pa4 P4

m1R2

2 R0m1R2

2 R0m1R2

2 R0m1R2

2 R0

Pd1 P1

Pd2 P2

Pd3 P3

Pd4 P4

m1R2

2 R0m1R2

2 R0m1R2

2 R0m1R2

2 R0

2. Load applied to the LM block

1) In uniform motion 2) During acceleration 3) During deceleration

3. Mean load

Pm1 Pa13s1P1

3s2Pd1

3s3

Pm2 Pa23s1P2

3s2Pd2

3s3

Pm3 Pa33

s1P33

s2Pd33

s3

Pm4 Pa43s1P4

3s2Pd4

3s3

1

RS

3

1

RS

3

1

RS

3

1

RS

3

Note: Pan and Pdn represent loads exerted on the

LM block. The suffix n indicates the block

number in the diagram above.

Mean Load Calculation Example (1) Horizontal Installations Subjected toAcceleration and Deceleration


23/32A-87

A-II

3. Mean load

Pm1 2PR1Pr1

Pm2 2 PR2Pr2

Pm3 2 PR3Pr3

Pm4 2PR4Pr4

1

3

1

3

1

3

1

3

Note: PRn and Prn represent loads exerted on the

LM block. The suffix n indicates the block

number in the diagram above.

2. Load applied to the LM block

1) At the left of the arm 2) At the right of the arm

PR1

PR2

PR3

PR4

mg

4

mgR1

2 R0mg

4

mgR1

2 R0mg

4

mgR1

2 R0mg

4

mgR1

2 R0

Pr1

Pr2

Pr3

Pr4

mg

4

mgR2

2 R0mg

4

mgR2

2 R0mg

4

mgR2

2 R0mg

4

mgR2

2 R0

Mean Load Calculation Example (2) Installations on Rails



24/32

4.7 Service-Life EquationThe service life of the LM Guide can be obtained using

the following equation:

whereL : nominal life (km)

(total distance that can be traveled by at least

90% of a group of LM Guides operated under

the same conditions)

C : basic dynamic-load rating (N)

PC : calculated load (N)

fH : hardness factor (see Fig. 37, page A-86)

fT : temperature factor (see Fig. 38, page A-86)

fC : contact factor (see Table 12, page A-87)

fW : load factor (see Table 13, page A-87)

Once nominal life L is obtained using this equation, the

LM-Guide service life can be calculated using the

following equation, if the stroke length and the number

of reciprocating cycles are constant:

where

Lh : service life in hours (h)

rs: stroke length (mm)

n1 : No. of reciprocating cycles per min (min-1)

fH: Hardness factorTo ensure achievement of the optimum load-bearing

capacity of the LM Guide, the raceway hardness must

be 58 to 64 HRC.

At a hardness below this range, the basic dynamic- and

static-load ratings decrease. The ratings must

therefore be multiplied by the respective hardness

factors (fH).

As the LM Guide has sufficient hardness, fH for the LM

Guide is 1.0 unless otherwise specified.

fT: Temperature factorFor LM Guides used at ambient temperatures over

100C, a temperature factor corresponding to the

ambient temperature, selected from the diagram

below, must be taken into consideration.

In addition, please note that the selected LM Guide

itself must be a model with high-temperature

specifications.

Note: When used at ambient temperatures higherthan 80C, the seals, end plates, and ball

cages used must be changed to those with

high-temperature specifications.

A-88

L 3 50

C

PC

fHfTfCfW

Lh L10

6

2RSn160

Fig. 37 Hardness Factor (fH)

Fig. 38 Temperature Factor (fT)

Raceway hardness (HRC)

HardnessfactorfH

Raceway temperature

TemperaturefactorfT


25/32

fC: Contact factorWhen mult iple LM blocks are used laid over one

another, moments and mounting-surface precision will

affect operation, making it difficult to achieve uniform

load distribution. For LM blocks used laid over one

another, multiply the basic load rating (C or C0) by a

contact factor selected from the table below.

Note: When the non-uniform load distribution can

be predicted, as in a large system, consider

using a contact factor.

fW: Load factorIn general, machines in reciprocal motion are likely to

cause vibration and impact during operation, and it is

particularly difficult to determine the magnitude of

vibration that develops during high-speed operation, as

well as that of impact during repeated starting and

stopping in normal use. Therefore, where the effects

of speed and vibration are estimated to be significant,

divide the basic dynamic-load rating (C) by a load

factor selected from the table below, which was

compiled based on THKs extensive experience.

A-89

A-II

No. of blocks used

2

3

4

5

6 or more

In normal use

0.81

0.72

0.66

0.61

0.6

1.0

Contact factor fC

Table 12 Contact Factor (fC)

Vibration and impact fWVelocity (V)

Very slight

Slight

Moderate

Strong

1~1.2

1.2~1.5

1.5~2.0

2.0~3.5

Very lowV0.25m/s

Low

0.25


26/32

4.8 Calculation Examples

4.8.1 Example 1 (Horizontal installationssubjected to high acceleration anddeceleration)


Model number: HSR35LA2SS + 2500LP-II

(Basic dynamic-load rating : C = 50.2 kN)

(Basic static-load rating : C0 = 81.4 kN)

Mass : m1 = 800 kg Distance :r0 = 600 mm

m2 = 500 kg r1 = 400 mm

Velocity : V = 0.5 m/s r2 = 120 mm

Time : t1 = 0.05 s r3 = 50 mm

t2

= 2.8 s r4

= 200 mm

t3 = 0.15 s r5 = 350 mm

Acceleration :

1 = 10 m/s2

3 = 3.333 m/s2

Stroke : rs = 1450 mm

A-90


Gravitational acceleration: g = 9.8 (m/s2)


27/32

2. Load Exerted on the LM Guide by the LM BlockCalculate the load that each LM block exerts.

1) In uniform motionLoad applied in radial direction Pn

2) During acceleration to the leftLoad applied in radial direction Pran

Load applied in lateral direction Ptran

3) During deceleration to the leftLoad applied in radial direction Prdn

Load applied in lateral direction Ptrdn

A-91

A-II

2891 N

4459 N

3479 N

1911 N

P1

P2

P3

P4

m1g

4

m1gR2

2 R0

m2g

4

m1gR3

2 R1

m1g

4

m1gR2

2 R0

m2g

4

m1gR3

2 R1

m1g

4

m1gR2

2 R0

m2g

4

m1gR3

2 R1

m1g

4

m1gR2

2 R0

m2g

4

m1gR3

2 R1

P1

275.6 N

P2

7625.6 N

P3

6645.6 N

P4

1255.6 N

PRa1

PRa2

PRa3

PRa4

m11R5

2R0

m21 4

2R0

m11R5

2R0

m21R4

2R0

m11R5

2R0

m21R4

2R0

m11R5

2R0

m21R4

2R0

333.3 N

333.3 N

333.3 N

333.3 N

PtRa1

PtRa2

PtRa3

PtRa4

m11 3

2 R0m11R3

2 R0m11R3

2 R0m11R3

2 R0

P1

3946.6 N

P2

3403.4 N

P3

2423.4 N

P4

2966.6 N

PRd1

PRd2

PRd3

PRd4

m13R5

2 R0

m23R4

2 R0

m23R4

2 R0

m13R5

2 R0

m23R4

2 R0

m13R5

2 R0

m23R4

2 R0

m13R5

2 R0

111.1 N

111.1 N

111.1 N

111.1 N

PtRd1

PtRd2

PtRd3

PtRd4

m13R3

2 R0m13R3

2 R0m13R3

2 R0m13R3

2 R0


28/32

4) During acceleration to the rightLoad applied in radial direction Pran

Load applied in lateral direction Ptran

5) During deceleration to the rightLoad applied in radial direction Prdn

Load applied in lateral direction Ptrdn

3. Combined radial and thrust load

1) In uniform motion

PE1 P12891 N

PE2 P24459 N

PE3 P33479 N

PE4 P41911 N

2) During acceleration to the left

PERa1PRa1PtRa1 608.9 N

PERa2PRa2PtRa27958.9 N



3) During deceleration to the left

PERd1PRd1PtRd14057.7 NPERd2PRd2PtRd23514.5 N

PERd3PRd3PtRd32534.5 N

PERd4PRd4PtRd43077.7 N

4) During acceleration to the right

PEra1Pra1Ptra16390.9 N


PEra3Pra3Ptra3 645.7 N


5) During deceleration to the right

PErd1Prd1Ptrd11946.5 N



PErd4Prd4Ptrd4 966.5 N

A-92

P3

312.4 N

P4

5077.6 N

Pra3

Pra4

P1

6057.6 N

P2

1292.4 N

Pra1

Pra2

m11R5

2 R0

m21R4

2 R0

m11R52 R0

m21R42 R0

m11R5

2 R0

m21R4

2 R0

m11R5

2 R0

m21R4

2 R0

333.3 N

333.3 N

333.3 N

333.3 N

Ptra1

Ptra2

Ptra3

Ptra4

m11R3

2 R0m11R3

2 R0m11R3

2 R0

m11R32 R0

P1

1835.4 N

P2

5514.6 N

P3

4534.6 N

P4

855.4 N

Prd1

Prd2

Prd3

Prd4

m13R5

2 R0

m23R4

2 R0

m13R5

2 R0

m23R4

2 R0

m13R5

2 R0

m23R4

2 R0

m13R5

2 R0

m23R4

2 R0

111.1 N

111.1 N

111.1 N

111.1 N

Ptrd1

Ptrd2

Ptrd3

Ptrd4

m13 3

2 R0m13R3

2 R0m13R3

2 R

0

m13R3

2 R0


29/32

4. Static Safety FactorAs shown above, it is during acceleration of the 2nd

LM Guide to the left when the maximum load is

exerted on the LM Guide. Therefore, the static safety

factor (fS) becomes as follows:

5. Mean Load PmnThe mean load on each LM block is as follows:

6. Nominal life LnFrom these calculations, 20,600 km (the running

distance of the 2nd LM block) is obtained as theservice life of the LM Guide used in a machine or

system under the operating conditions specified below.

From the service-life equation for the LM Guide:

A-93

A-II

fS 10.2C0

PERa2

81.4103

7958.9

PERa13S1PE1

3S2PERd1

3S3PEra1

3S1PE1

3S2PErd1

3S3

608.9312.52891

314004057.7

337.56390.9

312.52891

314001946.5

337.5

2940.1 N

PERa23S1PE23S2PERd23S3PEra23S1PE23S2PErd23S3

7958.9312.54459

314003514.5

337.51625.7

312.54459

314005625.7

337.5

4492.2 N

PERa33S1PE3

3S2PERd3

3S3PEra3

3S1PE3

3S2PErd3

3S3

6978.9312.53479

314002534.5

337.5645.7

312.53479

314004645.7

337.5

3520.4 N

PERa43S1PE4

3S2PERd4

3S3PEra4

3S1PE4

3S2PErd4

3S3

1588.9312.51911

314003077.7

337.55410.9

312.51911

31400966.5

337.5

1985.5 N

Pm1

Pm2

Pm3

Pm4

1

2RS1

21450

12RS

1

21450

1

2RS1

21450

1

2RS1

21450

3

3

3

3

3

3

3

3

L1 3 50 73700 km

L2 3 50 20600 km

L3 3 50 43000 km

L4 3 50 239000 km

fW 1.5

C

fW Pm1C

fW Pm2C

fW Pm3C

fW Pm4


30/32

4.8.2 Example 2 (Vertical installations)


Model number: HSR25A2SS + 1500L-II

(Basic dynamic-load rating : C = 19.9 kN)

(Basic static-load rating : C0 = 34.4 kN)

Mass : m0 = 100 kg Distance :r0 = 300 mm

m1 = 200 kg r1 = 80 mm

m2 = 100 kg r2 = 50 mm

r3 = 280 mm

r4 = 150 mm

r5 = 250 mm

Stroke : rS = 1000 mm

The mass (m0) is applied during ascent only. It is

removed during descent.

A-94


Gravitational acceleration: g = 9.8 (m/s2)


31/32

2. Load Exerted on the LM Guide by theLM Block

1) During ascentLoad exerted on the LM Guide in radialdirection Pun by the LM block

Load exerted on the LM Guide in lateraldirection Ptun by the LM block

2) During descentLoad exerted on the LM Guide in radialdirection Pdn by the LM block

Load exerted on the LM Guide in lateraldirection Ptdn by the LM block

3. Combined radial and thrust load

1) During ascent

PEu1Pu1Ptu11731.3 N

PEu2Pu2Ptu21731.3 N

PEu3Pu3Ptu31731.3 N

PEu4Pu4Ptu41731.3 N

2) During descent

PEd1Pd1Ptd11143.3 N

PEd2Pd2Ptd21143.3 N

PEd3Pd3Ptd31143.3 N

PEd4Pd4Ptd41143.3 N

A-95

A-II

1355.6 N

1355.6 N

1355.6 N

1355.6 N

Pu1

Pu2

Pu3

Pu4

m1gR42 R0

m2gR52 R0

m0gR32 R0

m0gR32 R0

m1gR4

2 R0

m2gR5

2 R0

m0gR32 R0

m1gR4

2 R0

m2gR5

2 R0

m0gR32 R0

m1gR4

2 R0

m2gR5

2 R0

375.7 N

375.7 N

375.7 N

375.7 N

Ptu1

Ptu2

Ptu3

Ptu4

m1gR22 R0

m2gR22 R0

m0gR12 R0

m1gR22 R0

m2gR22 R0

m0gR12 R0

m1gR22 R0

m2gR22 R0

m0gR12 R0

m1gR22 R0

m2gR22 R0

m0gR12 R0

898.3 N

898.3 N

898.3 N

898.3 N

Pd1

Pd2

Pd3

Pd4

m1gR4

2 R0

m2gR5

2 R0m1gR4

2 R0

m2gR5

2 R0m1gR4

2 R0

m2gR5

2 R0m1gR4

2 R0

m2gR5

2 R0

245 N

245 N

245 N

245 N

Ptd1

Ptd2

Ptd3

Ptd4

m1gR2

2 R0

m2gR2

2 R0m1gR22 R0

m2gR22 R0

m1gR2

2 R0

m2gR2

2 R0m1gR2

2 R0

m2gR2

2 R0


32/32

4. Static Safety FactorThe static safety factor (fs) of a machine or system

under the operating conditions shown above becomes

the following:

5. Mean LoadThe mean load on each LM block is as follows:

6. Nominal life LnFrom the service-life equation for the LM Guide:

From these calculations, 68,200 km is obtained as the

service life of the LM Guide used in a machine or

system under the operating conditions specified above.

PEU13RSPEd1

3RS 1495.1 N

PEU23RSPEd2

3RS 1495.1 N

PEU33RSPEd3

3RS 1495.1 N

PEU43RSPEd4

3RS 1495.1 N

Pm1

Pm2

Pm3

Pm4

1

2RS

3

1

2RS

3

1

2RS

3

12RS

3

L1 3 50 68200 km

L2 3 50 68200 km

L3 3 50 68200 km

L4 3 50 68200 km

fW1.2

C

fW Pm1C

fW Pm2

CfW Pm3

C

fW Pm4

fS 19.9C0

PEu2

34.4103

1731.3

Elementos de Máquinas - Guias de Esferas

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