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Racks: Technical Information

Characteristics∧ top

KHK stock racks are made for high precision linear motion applications. We offer a large selection of racks ranging from module 0.5 to 10 and lengths from 100 to 2000 mm. The following table lists the main features.

Catalog No. Module Total Length (mm) Material Heat Treatment Tooth Surface Finish Precision KHK R 001 Note 3 Features
KKRGF-H KKRGFD-H 1.5~3 500,1000 SCM440 Thermal refined, induction hardened Ground 1 Heat treated ground gears with high precision and strength has excellent cost-performance ratio. J Series products are also available.
KKRG • KKRGF KKRGD Note 1 1~3 100,500, 1000 SCM440 Thermal refined Ground 1 High strength and abrasion-resistant for precision linear motion.
KSRG • KSRGF KSRGFD • KSRGFK Note 1 0.5~6 100,300, 500,1000 S45C Gear teeth induction hardened Note 2 Ground 3 Reasonably priced ground racks with abrasion-resistant characteristics. J Series products are also available.
KSRF-H KSRFD-H 1.5~4 1000 S45C Gear teeth induction hardened Cut 4 Stable Hardened racks with high strength, long life span are reasonably priced. J Series products are also available.
KKRF 1.5~5 1000 SCM440 Thermal refined Cut 4 Increased strength with SCM440 materialwhich is thermal refined.
KSRAF 1.5~4 1000 S45C Cut 4 This gear rack has the same tooth height and face width sizes,more compact and reasonably priced in comparison to SRF Racks
KSR • KSRF • KSRFD • KSRFK Note 1 0.5~10 100,300,500, 1000,1500,2000 S45C Straightened & annealed Cut 4 Low cost, large selections of modules and number of teeth. J Series products are also available.
KSUR • KSURF • KSURFD Note 1 1~4 500,1000 SUS304 Solution treated Cut 5 Suitable for food machinery due to SUS304material's rust-resistant quality.
KPR • KPRF Note 1 1~3 500,1000 MC901 Cut 5 Made form MC nylon, can be used without lubrication.
KBSR 0.5~1 300 C3604 Cut 4 Small pitch racks made of free-cutting brass,excellent workability and high rust resistance.
KDR 0.8~2 2000 Dura con (M25-44) Injection Molded 8 Used in applications due to its flexibility, where metal racks do no have this attribute. Pinions and accessories are also available.
KSRO • KSROS 1~6 500,1000 S45C Straightened & annealed Cut 4 Convenient in applications where the rack hasthe reciprocal motion. S Type is easy to install.
KSURO 1~3 500,1000 SUS303 Cut 5 Same dimensions as SRO racks, except in stainless steel. Use where rust-resistance is required.
KKRHG • KKRHGF Note 1 1~3 100,500, 1000 SCM440 Thermal refined Ground 1 Excellent products with high precision and strength, and low noise and abrasion characteristics.
KSRH • KSRHF • KSRHFD Note 1 2~3 100,500, 1000 S45C Straightened & annealed Cut 5 Effective in reducing noise and vibration due to larger contact ratio of helical gears.
NOTE 1 The catalog numbers in the above table with (F) suffix have both ends machined so that they can be butted against each other to make any desired length. The items with (D) have mounting screw holes for easier assembly. NOTE 2 Products with module less than 0.8 are thermal refined, without their gear teeth being induction hardened. NOTE 3 Precision grade standard of racks are set by KHK. Please see "Precision of Racks" in Selection Hints section for details.
  • For safe handling and to prevent damage such as deformation, KHK stock racks have round chamfering at the corners of the top land of the gear tooth. This rounded chamfered shape is patented by KHK. Because it is effective for reducing noise, all of KHK products, except for BSR and PR racks, have this chamfering treatment.
  • Black colored products are KHK stock gears that have an applied black oxide coating for rust resistance; this 'blackness' is a product characteristic of KHK stock gears.

We proudly offer cutting edge technology for rack production.
Providing quality, affordable products with assurance is our policy. You can count on us for safe and durable produced racks.
Rack Cutting Machine Rack Gearing Machine

Selection Hints∧ top

Please select the most suitable products by carefully considering the characteristics of items and contents of the product tables. It is also important to read all applicable notes before the final selection.

1. Caution in Selecting Mating Gears
Mating Gear Selection Chart
(O = Allowable, X = Not Allowable
Catalog No.
& Helix Hand
  1. a With the exception of helical racks, KHK stock racks can mate with any spur gears of the same module. Products with different tooth width can also be mated as a pinion.
  2. There are limited choices for of mating gears for KKRHG • KKRHGF Ground Helical Racks and Helical Racks. There are limited choices for of mating gears for KKRHG(F) Ground Helical Racks and KSH Helical Racks. Be sure to check the helix hand (right or left) when selecting.

2. Caution in Selecting Gears Based on Gear Strength
Allowable bending strength and surface durability values shown in product tables were computed by assuming a certain application environment. They should be used as reference only. We recommend that each user computes his own values by applying the actual usage conditions. The table below contains the assumptions established for various products in order to compute gear strengths.


Calculation Assumptions for Bending Strength of Gears
Formula Note 1 Formula of spur and helical gears on bending strength (JGMA401-01) The Lewis formula
No. of teeth of mating gear 30 (30)
Rotation 100rpm (100rpm)
Durability Over 107 cycles Allowable Bending Stress(kgf/mm²)
Impact from motor Uniform load 1.15 (40°C with No Lubrication) m 0.8 4.0
m 1.0 3.5
m 1.5 1.8 Note 4
m 2.0 1.2
(Grease lubrication 40°C)
Impact from load Uniform load
Direction of load Bidirectional
Allowable bending stress at root σFlim (kgf/mm²) Note 2 32 32 20 (24.5) Note 3 20 10.5 4
Safety factor SF 1.2
Calculation assumptions for Surface Durability (Except where it is common with Bending Strength)
Formula Note 1 Formula of spur and helical gears on bending strength (JGMA401-01)    
Kinematic viscosity of lubricant 100cSt (50°C)    
Gear support Supported on one end.    
Allowable Hertz stress σHlim (kgf/mm²) 112 79 90 (62.5) 52.5 41.3      
Safety factor SH 1.15    
NOTE 1: JGMA (Japanese Manufacturers' Association), "MC Nylon Technical Data" of Nippon Polypenco Limited and "Duracon Gear" of Polyplastic Co. The units for rotational speed (rpm) and the load (kgf/mm²) were matched to the units needed in the equation. NOTE 2: The allowable bending stress at root σFlim is calculated from JGMA401-01, and set to 2/3 of the value in the consideration of the use of planetary-, idler-, or other gear systems, loaded in both directions. NOTE 3: For KSRG, or KSRGF Ground Racks, with a module less than 0.8, the rack teeth are not induction hardened. Allowable bending stress and allowable hertz stress are referred to the value shown in the parentheses. NOTE 4: The values for DR m 1.5 racks were assumed by KHK. Usage conditions for KSSDR (DR Rack Pinion) are the same for the KSSCP Pinion.
Bending Damage Definition of bending strength by JGMA 401-01(1974)
The allowable bending strength of a gear is defined as the allowable tangential force at the pitch circle based on the mutually allowable root stress of two meshing gears under load.

Surface Damage Definition of surface durability by JGMA 402-01(1974)
The surface durability of a gear is defined as the allowable tangential force at the pitch circle, which permits the force to be transmitted safely without incurring surface failure.

3. Selecting Racks by Precision
The precision standards of KHK stock racks are established by us. The table below indicates the tolerance ranges of our racks.

  1. Pitch Errors of Racks (KHK R 001)
    Our precision grades for pitch errors are established by referring to JIS Standards. The precision grades are set from 1 to 8, in accordance with the tolerance of a single pitch error (S.P.E.), adjacent tooth-to-tooth error (T.T.E.), and the total composite error (T.C.E.) for each module and length.
    Precision Grades of Racks (KHK R 001)
    Grade Pitch Error over m0.4 up to 1 over m1 up to 1.6 over m1.6 up to 2.5 over m2.5 up to 4 over m4 up to 6 over m6 up to 10
    Rack Length (nominal)
    1000 or less 1500 up to 2000 1000 or less 1500 up to 2000 1000 or less 1500 up to 2000 1000 or less 1500 up to 2000 1000 or less 1500 up to 2000 1000 or less 1500 up to 2000
    1 S.P.E. 10 10 12 11 12 11 13 13 14 14 16
    T.T.E. 10 11 13 12 14 13 15 14 16 16 18
    T.C.E. 28 29 33 30 35 32 37 35 40 40 45
    2 S.P.E. 14 14 17 15 17 16 18 18 20 20 23
    T.T.E. 16 16 19 17 19 18 21 20 24 24 27
    T.C.E. 39 41 48 43 49 46 53 50 57 58 64
    3 S.P.E. 20 20 24 21 25 23 26 25 29 29 32
    T.T.E. 22 24 28 25 29 27 31 30 34 34 40
    T.C.E. 56 57 67 60 70 64 74 71 80 81 91
    4 S.P.E. 28 29 33 30 35 32 37 35 40 40 45
    T.T.E. 33 34 42 38 43 40 46 44 50 51 57
    T.C.E. 79 81 95 85 99 91 105 100 115 115 130
    5 S.P.E. 39 41 48 43 49 46 53 50 57 58 64
    T.T.E. 49 51 59 53 62 57 69 66 75 76 85
    T.C.E. 110 115 135 120 140 130 145 140 160 160 180
    8 S.P.E. 206 206 212 212 219 219
    T.T.E. 330 330 339 339 350 350
    NOTE: Since the pitch accuracy of racks may vary due to humidity, the precision grades are evaluated at the bottom surface of the product, at the temperature of 20°C. The dimensions of the KHK PR Plastic Racks may vary widely due to humidity. Therefore, the total composite error is assumed to be excluded from this accuracy standard.
    Pitch inspection and a sample report using Karl Zeiss UMC-550 Coordinate Measuring Machine. (KHK R 001 Grade 1)
    Pitch Inspection Pitch Inspection Graph

  2. Precision of Rack Blanks
    Tolerance on Face Width and Height
    Face Width
    Precision grade (KHK R 001)
    / Face width & height
    Grade 1 Grades 3 to 4
    (Excludes thermal refined racks)
    Grades 5
    (Includes thermal refined racks)
    Grade 8
    Below 6 0 -0.09 ±0.25
    6 up to 10 0 -0.05 0 -0.09 0 -0.22 ±0.30
    10 up to 18 0 -0.05 0 -0.11 0 -0.27 ±0.35
    18 up to 30 0 -0.05 0 -0.13 0 -0.33 ±0.40
    30 up to 50 0 -0.05 0 -0.16 0 -0.39
    50 up to 90 0 -0.05 0 -0.19 0 -0.46
    CAUTION: The width and height tolerances of KHK R 001 grades 3 to 5 products are measured at 1mm inside from each corner. Dimensional tolerance for plastic racks is the value obtained when machining is performed, and the maximum tolerance value is +0.2 x Module (+0.40 for m2 products.), with consideration for aging.

    Maximum Curvature Values (Flatness Tolerance L)
    Curvature Values
    Precision grade (KHK R 001)
    / Length (nominal)
    Grade 1 Grade 3 Grades 4 & 5
    500 0.05 0.1 0.2
    1000 0.05 0.2 0.3
    1500 0.3
    2000 0.4
    CAUTION: The straightness tolerances of round racks are 0.15/500 mm and 0.2/1000 mm.
    Rack Diameter

    Tolerance on Diameter of Round Racks
    KHK Stock Round Racks have diameter tolerances of h10 for Ø60 (KSRO6-1000) round racks, and h9 for others.

    Tolerance on Overall Length
    Type of product Module Allowable error
    Type F racks with machined ends 0.5 (–0.1) (–0.3)
    0.8 (CP2.5) (–0.1) (–0.5)
    1 up to 2.5 (–0.2) (–0.6)
    Over 2.5 (–0.2) (–0.8)
    FRCP, DR flexible racks Uniform ±10
    Other racks Uniform +3 –2
    CAUTION: For Type-F racks with machined ends, the dimensional tolerance is a calculated value according to assumed usage conditions, without consideration of pitch errors and aged deterioration.

  3. Backlash of Rack Tooth

    Backlash of Rack Tooth (Amount of Tooth Thinning)
    Precision grade (KHK R 001)
    / Module ( m ) or Pitch ( CP )
    Grade 1 Grade 3 Grade 4 Grade 5
    Excludes thermal refined racks Includes thermal refined racks Hardened racks Stainless steel/Helical racks Plastic racks
    m0.5 0~0.07 0.02~0.10
    m0.8, CP2.5 0~0.05 0~0.08 0.03~0.12 0.03~0.14 0.03~0.14 0.03~0.14
    m1 0~0.05 0~0.10 0.03~0.12 0.03~0.14 0.03~0.14 0.03~0.14 0~0.20
    m1.5, CP5 0~0.05 0~0.10 0.04~0.13 0.04~0.15 0.04~0.15 0.04~0.15 0~0.21
    m2 0~0.05 0~0.10 0.05~0.14 0.05~0.16 0.05~0.16 0.05~0.16 0~0.22
    m2.5 0~0.05 0~0.10 0.06~0.16 0.06~0.18 0.06~0.18 0.06~0.18 0.06~0.18
    m3, CP10 0~0.05 0~0.10 0.07~0.18 0.07~0.20 0.07~0.20 0.07~0.20 0~0.24
    m4 0~0.10 0.08~0.22 0.08~0.24 0.08~0.24 0.08~0.24 0~0.27
    m5, CP15 0~0.10 0.09~0.24 0.09~0.26 0.09~0.26 0.09~0.26
    m6, CP20 0~0.10 0.10~0.28
    m8 0.13~0.32
    m10 0.15~0.34
    NOTE: The values shown in the table are amount of tooth thinning. The theoretical backlash of assembled rack and pinion is given by:
    Rack & pinion backlash = Amount of tooth thinning of the rack + Amount of tooth thinning of the pinion
    Amount of tooth thinning of the rack : See above table.
    Amount of tooth thinning of the pinion : Take 1/2 of backlash given in the product table.

Application Hints∧ top

In order to use KHK stock gears safely, carefully read the Application Hints before proceeding. If there are questions or if you require clarifications, please contact our technical department.

1. Caution on Performing Secondary Operations
  1. Secondary operations can be performed on all KHK stock racks except for the racks with their gear teeth induction hardened. To avoid problems of gear precision, do not reduce the face width. The precision of ground racks and racks with mounting holes may drop if you do not exercise extreme caution during installation or while modifying.
  2. Pitch lines of racks are controlled by using the bottom surface as the reference datum and over-pin measurements on tooth thickness. If you machine the bottom surfaces, the precision of the racks may be affected.
  3. When connecting two racks, the machining of the mating ends requires careful consideration. The meshing will be poor if the pitch straddling the connection has a positive tolerance. We recommend a minus tolerance on pitch of at the connection. The below is an indication of pitch tolerance for each module.
    Pitch Formula
    Module Pitch (p) Tolerance
    m0.5 1.57 -0.05 -0.15
    m0.8 2.51 -0.05 -0.25
    m1 3.14 -0.1 -0.3
    m1.5 4.71
    m2 6.28
    m2.5 7.85 -0.1 -0.4
    m3 9.42
    m4 12.57
    m5 15.71
    m6 18.85
    m8 25.13
    m10 31.42

  4. To use dowel pins to secure racks, attach the racks to the base and drill both simultaneously.
  5. KHK stock racks made of S45C and SCM440 (except for ground racks) can be induction hardened. However, the precision of pitch is decreased.
  6. To be able to handle parts safely, all burrs and sharp corners should be removed after the secondary operations are done.
  7. If you are going to modify the gear by gripping the teeth, please exercise caution not to crush the teeth by applying too much pressure. Any scarring will cause noise during operation.

1. Points of Caution in Assembling
  1. KHK stock racks are designed to give the proper backlash when assembled using the mounting distance given by the formula below (mounting distance tolerance of H7 to H8 required). The backlash values are given in the table on page 375. Make sure that the mounting distance stays constant for the length of the rack.

    Mounting distance a = Height of pitch line of rack + Pitch radius of pinion
    Mounting Distance
  2. KKRG type of KHK stock ground racks have four surfaces ground parallel to within 10~15μm. To maintain true angle, they should be mounted on high precision bases as shown below. It is even possible to correct for the angular errors of racks by compensating the mounting base. With recent increases in the requirement for zero backlash linear drives, such accurate assembly as shown is becoming more important.
  3. If the racks are not secured properly to the base, they could shift during operation and cause unexpected problems. It is very important to insure firm mounting by the use of dowel pins or similar devices.
  4. Machined end type racks such as KSRF and KSRFD series have the pitch tolerance of -0.05 to -0.4mm at the end face. If you try to connect the racks without any space, the pitch at the connection will be too small and will cause problems. Please follow the following diagrams for assembly.

    An example of Rack Joining, we recommend the following method.
    Rack Gauge Diameter Rack
    CAUTION: Joining gauge racks for helical racks must have the opposite hand from the racks Please use Module 1~10 100 racks as a joining gauge rack, or alternatively the rack of the same specifications on hand.

Application Examples

Application Example
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