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CP Racks & Pinions: Technical Information

Characteristics∧ top

KHK stock CP racks and pinions are suitable in applications where very accurate positioning in linear motion is required. For your convenience, we offer circular pitches of 2.5 to 20 mm and in lengths of 100 to 2000 mm. (FRCP is available to 4000 mm)

About CP Racks & Pinions
About Racks and Pinions The reference pitch of a metric module is computed by multiplying the number of module by π (3.14159). For example, the reference pitch of m 3 rack is 9.425 mm (3 x π). When using a rack and a pinion in a linear motion application, the fact that the pitch is not an integral number presents a difficulty in accurate positioning. This problem is solved by CP racks and pinions where one rotation of a pinion moves it precisely 50, 100, 150, ... or 600 mm. The following table lists the main features. The following table lists the main features.
Catalog No. Note 1 Pitch (mm) Total Length
( ) No. of teeth
Material Heat Treatment Tooth Surface Finish Precision
KHK R 001
( ) denotes
JIS B 1702-1
KStrCPF • KStrCPFD 5, 0 1000 S45C Cut 4 By pairing with KKTSCP pinion, the backlash may be adjusted.
KKRGCPF - H KKRGCPFD - H 5, 0 500, 1000 SCM440 Thermal refined, teeth induction hardened Cut 1 Heat treated ground gears with high precision and strength has excellent cost-performance ratio. J Series products are also available.
KKRGCP • KKRGCPF • KKRGCPD 5, 0 100, 500, 1000 SCM440 Thermal Refined Ground 1 High strength and abrasion-resistant for precision linear motion.
KSRGCP • KSRGCPF • KSRGCPFD 5, 0, 15, 20 100, 500, 1000 S45C Gear teeth induction hardened Ground 3 Reasonably priced ground racks with abrasion-resistant characteristics. J Series products are also available.
KKRCPF 5, 0 1000 SCM440 Thermal Refined Cut 4 Increased strength with SCM440 material which is thermal refined.
KSRCP • KSRCPF • KSRCPFD 2.5, 5, 10, 5, 20 100, 500, 000, 500, 2000 S45C Cut 4 Widely applicable due to low cost and large selection of pitches and lengths.
KSURCPF • KSURCPFD 5, 0 500, 000 SUS304 Solution treated Cut 5 Suitable for food machinery due to SUS304 material’s rust-resistant quality.
KSROCP 2.5, 5, 0 500 S45C Cut 4 Convenient in applications where the rack has reciprocal motion.
KFRCP 5 2000, 3000, 4000 SS400 Cut 8 Cut continuously. Long length and bendable to a contour.
KKTSCP 5, 0 (20~40) SCM440 Thermal refined Cut (N8) By pairing with KStrCPF rack, the backlash may be adjusted.
KSSCPGS 5, 0 (10~25) S45C Thermal refined, teeth induction hardened Ground (N7) Ground Spur Gears with Pinions, can be directly assembled with the shaft bearing, by modifying the pinion.
KSSCPG 5, 0, 15, 20 (20~40) S45C Gear teeth induction hardened Ground (N7) Perform secondary operations to suit your requirement on these ground CP spur gears.
KSSCP 2.5, 5, 10, 5, 20 (20~40) S45C Cut (N8) Low cost and widely applicable, with a large selection of pitches and numbers of teeth.
KSUSCP 5, 0 (20~30) SUS303 Cut (N8) Suitable for food machinery due to SUS303 material's rust-resistant quality.
NOTE 1: The catalog numbers in the above tables with a suffix of F 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.
  • For safer handling and to prevent damage such as deformation, KHK stock CP racks have round chamfering on 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 CP 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.

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
  1. KHK stock CP racks are mated with CP spur gears having the same pitch. Since CP2.5 (m0.796), CP5 (m1.592) and CP10 (m3.183) are very close in size to m0.8, m1.5 and m3 respectively, the selecting the proper mating gear should be verified to make sure that the items are correct. Otherwise, complications could arise.
  2. KSTRCPF and KSTRCPFD Tapered Racks are mated with KTSCP Spur Gears having the same pitch. They can also be mated with other spur gears, however, they can not be used as parallel axis gears due to the setting angles.

2. Caution in Selecting Gears Based on Gear Strength
The gear strength values shown in the product pages were computed by assuming a certain application environment. Therefore, 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 these products in order to compute gear strengths.

Catalog No.
/ Item
Racks Pinions
Calculations assumptions for Bending Strength
Formula NOTE 1 Formula of spur and helical gears on bending strength (JGMA401-01)
No. of teeth of mating gear 30 Same number of teeth
Rotation 100rpm
Durability Over 107cycles
Impact from motor Uniform load
Impact from load Uniform load
Direction of load Bidirectional
Allowable bending stress at root σFlim (kgf/mm²) NOTE 2 32 32 20 20 10.5 24.5 19 28.5 19 10.5
Safety factor SF 1.2
Calculation assumptions for Surface Durability (Except those in common with bending strength)
Formula NOTE 1 Formula of spur and helical gears on surface durability (JGMA402-01)
Kinematic viscosity of lubricant 100cSt (50°C)
Gear support Support on one end
Allowable Hertz stress σHlim (kgf/mm²) 112 79 90 52.5 41.3 99 90 74.5 49 41.3
Safety factor SH 1.15
NOTE 1: The gear strength formula is based on JGMA (Japanese Gear Manufactures Association) specifications. The units for the number of rotions (rpm) and the stress (kgf/mm²) are adjusted to the units needed in the formula. NOTE 2: The allowable bending stress at the root σ Flim 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.
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. Please be sure to see the KHK Racks Technical Information Page when selecting. NOTE 2: Convert CP to m (module) when reference is made to the data in the table. (m=CP/π)

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 CP 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 (CP) 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
    CP2.5 -0.05
    CP5 -0.01
    CP10 -0.1

  4. To use dowel pins to secure racks, attach the racks to the base and drill both simultaneously.
  5. KHK stock CP 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.

2. Points of Caution in Assembling
  1. KHK stock CP 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 backlash table above. 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. KKRGCP 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 KSRCPF and KSRCPFD series have the pitch tolerance of— 0.1/— 0.3 for modules less than Module 2.5, and — 0.1/— 0.4 for larger modules. 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.

Features of KHK Tapered Racks and Pinions∧ top

  1. Easy Adjustment of Backlash Value. Generally, adjustment of backlash value is made by changing mounting distance (adjusting the height of the motor shaft). The backlash of KHK stock tapered racks and pinions are adjustable only by moving the pinion axially.
  2. Reasonable Prices. The precision of KHK stock tapered racks and pinions are obtained by rationalization in the production process with our cutting-edge technologies. This enables us to offer quality tapered racks and pinions in the same price range as the CP racks and pinions. (KSRCPF and KSSC).

Examples of Comparison
  • KSRCP5-1000 and KSSCP5-30 combination produces a backlash value of 0.1 to 0.26.
  • KSTRCPF5-1000 and KKTSCP5-30 combination produces a backlash value of 0.05 or less. (Target value)
Changing Backlash
Note: above backlash values are theoretical values when meshed under ideal conditions. Tapered racks and pinions are not interchangeable with KHK stock CP racks and pinions. Different modules, number of teeth, ground gear versions and custom-made items are available as special orders.
Examples of special applications of Tapered Rack & Pinions
The shaft angle illustrated below can be obtained by changing the assembly orientation of the tapered spur gear or by mating with a regular spur gear.
Example 1
When mating a tapered rack and a tapered pinion, where each hub is set in opposite directions, a 0° shaft angle is obtained. (Axis Parallel).
Example 2
When mating a tapered rack and a tapered pinion, where each hub is set in the same direction, an 8° shaft angle is obtained.
Example 3
When mating a tapered rack and a spur gear, a 4° shaft angle is obtained.