( ) Calculating the Nominal Life. Nominal Life Equation for an LM Guide Using Balls. Nominal Life Equation for the Oil-Free LM Guide L = ( C L =

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Megan Bates
6 years ago
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1 Point of Selection The service life of an LM Guide is subject to variations even under the same operational conditions. Therefore, it is necessary to use the nominal life defi ned below as a reference value for obtaining the service life of the LM Guide. The nominal life means the total travel distance that 90% of a group of units of the same LM Guide model can achieve without fl aking (scale-like pieces on the metal surface) after individually running under the same conditions. Nominal Life Equation for an LM Guide Using Balls fh ft fc L ( C ) fw PC 50 LM Guide L : Nominal life (km) C : Basic dynamic load rating (N) P C : Calculated load (N) f H : Hardness factor (see Fig.0 on ) f T : Temperature factor (see Fig. on ) f C : Contact factor (see Table2 on ) f W : Load factor (see Table on ) Nominal Life Equation for the Oil-Free LM Guide L F0 ( ) fw PC L : Nominal life (km) F 0 : Permissible load (N) P C : Calculated load (N) f W : Load factor (see Table on ) Note) The life here means the service of life of the S fi lm based on wear. Since the service life of the S fi lm may vary according to the environment or the operating conditions, be sure to evaluate and validate the life under the service conditions and operating conditions at the customer.

2 Nominal Life Equation for an LM Guide Using Rollers L ( C fh ft fc ) fw PC 0 00 L : Nominal life (km) C : Basic dynamic load rating (N) P C : Calculated load (N) f H : Hardness factor (see Fig.0 on ) f T : Temperature factor (see Fig. on ) f C : Contact factor (see Table2 on ) f W : Load factor (see Table on ) Once the nominal life (L) has been obtained, the service life time can be obtained using the following equation if the stroke length and the number reciprocations are constant. Lh 2 L 0 6 ls n 60 L h : Service life time (h) l s : Stroke length (mm) n : Number of reciprocations per minute (min - )

3 Point of Selection f H : Hardness Factor To ensure the achievement of the optimum load capacity of the LM Guide, the raceway hardness must be between 58 and 64 HRC. If the hardness is lower than this range, the basic dynamic load rating and the basic static load rating decrease. Therefore, it is necessary to multiply each rating by the respective hardness factor (f H ). Since the LM Guide has suffi cient hardness, the f H value for the LM Guide is normally.0 unless otherwise specified. Hardness factor fh Raceway hardness (HRC) Fig.0 Hardness Factor (f H ) LM Guide f T :Temperature Factor If the temperature of the environment surrounding the operating LM Guide exceeds 00, take into account the adverse effect of the high temperature and multiply the basic load ratings by the temperature factor indicated in Fig.. In addition, the selected LM Guide must also be of a high temperature type. Note) LM guides not designed to withstand high temperatures should be used at 80 C or less.please contact THK if application requirements exceed 80 C. Temperature factor ft Raceway temperature ( ) Fig. Temperature Factor (f T ) f C : Contact Factor When multiple LM blocks are used in close contact with each other, it is diffi cult to achieve uniform load distribution due to moment loads and mounting-surface accuracy. When using multiple blocks in close contact with each other, multiply the basic load rating (C or C 0 ) by the corresponding contact factor indicated in Table2. Note) If uneven load distribution is expected in a large machine, take into account the respective contact factor indicated in Table2. Table2 Contact Factor (f C ) Number of blocks used in close contact Contact factor f C or greater 0.6 Normal use

4 f W : Load Factor In general, reciprocating machines tend to involve vibrations or impact during operation. It is extremely difficult to accurately determine vibrations generated during high-speed operation and impact during frequent start and stop. 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 Table, which contains empirically obtained data. Vibrations/ impact Faint Weak Medium Strong Table Load Factor (f W ) Speed (V) Very low V 0.25m/s Slow 0.25<V m/s Medium <V 2m/s High V>2m/s f W to.2.2 to.5.5 to 2 2 to.5

5 Point of Selection Example of () - with Horizontal Mount and High-speed Acceleration [Conditions] Model No. : HSR5LA2SS2500LP- (basic dynamic load rating: C 65.0 kn) (basic static load rating: C kn) Mass : m 800 kg m kg Speed : V 0.5 m/s Time : t 0.05 s t s t 0.5 s Acceleration : 0 m/s 2 Stroke. m/s 2 : l S 450 mm Distance: l mm l 400 mm l 2 20 mm l 50 mm l mm l 5 50 mm Gravitational acceleration g9.8 (m/s 2 ) LM Guide No.4 l2 No. l m2g mg l No. No.2 V m/s l0 t t2 t s mg s s2 s mm ls mm m2g l5 l4 Ball screw Fig.2 Condition

6 Load Applied to the LM Block Calculate the load applied to each LM block. During uniform motion Applied load in the radial direction P n mg mg l2 m g l m2g P 289N 4 2 l 4 mg mg l2 m g l m2g P2 4459N 4 2 l 4 mg mg l2 mg l m2g P 479N 4 2 l 4 mg mg l2 mg l m2g P4 9N 4 2 l 4 During leftward acceleration Applied load in the radial direction Pla n Pla Pla2 Pla Pla4 m α l5 m2 α l4 P N m α l5 m2 α l4 P N m α l5 m2 α l4 P N m α l5 m2 α l4 P N Applied load in the lateral direction Ptla n m α l Ptla. N m α l Ptla2. N m α l Ptla. N m α l Ptla4. N During leftward deceleration Applied load in the radial direction Pld n Pld Pld2 Pld Pld4 m α l5 m2 α l4 P N m α l5 m2 α l4 P N m α l5 m2 α l4 P N m α l5 m2 α l4 P N

7 Point of Selection Applied load in the lateral direction Ptld n m α l Ptld. N m α l Ptld2. N m α l Ptld. N m α l Ptld4. N During rightward acceleration Applied load in the radial direction Pra n LM Guide Pra Pra2 Pra Pra4 m α l5 m2 α l4 P N m α l5 m2 α l4 P N P m α l5 m2 α l4 2.4 N P4 m α l5 m2 α l N Applied load in the lateral direction Ptra n m α l Ptra. N m α l Ptra2. N m α l Ptra. N m α l Ptra4. N During rightward deceleration Applied load in the radial direction Prd n Prd Prd2 Prd Prd4 m α l5 m2 α l4 P 85.4 N m α l5 m2 α l4 P N m α l5 m2 α l4 P N m α l5 m2 α l4 P N

8 Applied load in the lateral direction Ptrd n m α l Ptrd. N m α l Ptrd2. N m α l Ptrd. N m α l Ptrd4. N Combined Radial And Thrust Load During uniform motion: P E P 289 N P E2 P N P E P 479 N P E4 P 4 9 N During leftward acceleration P E la Pla Ptla N P E la 2 Pla 2 Ptla N P E la Pla Ptla N P E la 4 Pla 4 Ptla N During rightward acceleration P E ra Pra Ptra N P E ra 2 Pra 2 Ptra N P E ra Pra Ptra N P E ra 4 Pra 4 Ptra N During rightward deceleration P E rd Prd Ptrd N P E rd 2 Prd 2 Ptrd N P E rd Prd Ptrd N P E rd 4 Prd 4 Ptrd N During leftward deceleration P E ld Pld Ptld N P E ld 2 Pld 2 Ptld N P E ld Pld Ptld N P E ld 4 Pld 4 Ptld N Static Safety Factor As indicated above, the maximum load is applied to the LM Guide during the leftward acceleration of the second LM block. Therefore, the static safety factor (f s ) is obtained in the following equation. C fs.5 PEla

9 Point of Selection Average Load P mn Obtain the average load applied to each LM block. Pm Pm2 (PEl a S PE S2 PEl d S PEra S PE S2 PErd S) ( ) N (PEl a2 S PE2 S2 PEl d2 S PEra2 S PE2 S2 PErd2 S) ( ) LM Guide Pm Pm N (PEl a S PE S2 PEl d S PEra S PE S2 PErd S) ( ) N (PEl a4 S PE4 S2 PEl d4 S PEra4 S PE4 S2 PErd4 S) ( ) N Nominal Life L n The nominal life of the four LM blocks is obtained from the corresponding nominal life equations shown below. L ( L2 ( L ( L4 ( C fw Pm C fw Pm2 C fw Pm C fw Pm4 ) km ) km ) km ) km (where f w.5) Therefore, the service life of the LM Guide used in a machine or equipment under the conditions stated above is equivalent to the nominal life of the second LM block, which is 44,800 km.

10 Example of (2) - with Vertical Mount [Conditions] Model No. : HSR25CA2SS500L- (basic dynamic load rating: C 27.6 kn) (basic static load rating: C kn) Mass : m 0 00 kg m 200 kg m 2 00 kg Distance : l 0 00 mm l 80 mm l 2 50 mm Stroke : l S 000 mm l 280 mm l 4 50 mm l mm The mass (m 0 ) is loaded only during ascent; it is removed during descent. Gravitational acceleration g9.8 (m/s 2 ) l l Ball screw No. No.2 mg m0g m0g mg l0 No.4 m2g No. m2g l2 l4 l5 Fig. Condition

11 Load Applied to the LM Block During Ascent Load applied to each LM block in the radial direction Pu n during ascent Point of Selection Pu mg l4 m0g l 55.6 N Pu2 Pu Pu4 mg l4 mg l4 mg l4 m0g l m0g l m0g l 55.6 N 55.6 N 55.6 N LM Guide Load applied to each LM block in the lateral direction Ptu n during ascent Ptu mg l2 m0g l 75.7 N Ptu2 mg l2 m0g l 75.7 N Ptu mg l2 m0g l 75.7 N Ptu4 mg l2 m0g l 75.7 N During Descent Load applied to each LM block in the radial direction Pd n during descent Pd mg l N Pd2 mg l N Pd mg l N Pd4 mg l N Load applied to each LM block in the lateral direction Ptd n during descent Ptd mg l2 245 N Ptd2 mg l2 245 N Ptd mg l2 245 N Ptd4 mg l2 245 N

12 Combined Radial And Thrust Load During Ascent P Eu P u Pt u 7. N P Eu2 P u2 Pt u2 7. N P Eu P u Pt u 7. N P Eu4 P u4 Pt u4 7. N During Descent P Ed Pd Ptd 4. N P Ed2 Pd 2 Ptd 2 4. N P Ed Pd Ptd 4. N P Ed4 Pd 4 Ptd 4 4. N Static Safety Factor The static safety factor (f S ) of the LM Guide used in a machine or equipment under the conditions stated above is obtained as follows. fs C PEu2 7. Average Load P mn Obtain the average load applied to each LM block. Pm Pm2 Pm Pm4 (PEU ls PEd ls) 495. N (PEU2 ls PEd2 ls) 495. N (PEU ls PEd ls) 495. N (PEU4 ls PEd4 ls) 495. N Nominal Life L n The nominal life of the four LM blocks is obtained from the corresponding nominal life equations shown below. (where f w.2) Therefore, the service life of the LM Guide used in a machine or equipment under the conditions stated above is 82,000 km.

The basic dynamic load rating C is a statistical number and it is based on 90% of the bearings surviving 50 km of travel carrying the full load.

The basic dynamic load rating C is a statistical number and it is based on 90% of the bearings surviving 50 km of travel carrying the full load. Technical data Load Rating & Life Under normal conditions, the linear rail system can be damaged by metal fatigue as the result of repeated stress. The repeated stress causes flaking of the raceways and