# Gear rack limitations

Gear racks are more than just a bar with teeth and their design must take into account several factors.

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Gear racks are a popular gear style. They convert rotational motion into linear motion. Simply speaking, a gear rack is a section of a spur gear with an infinite pitch radius. Typically machined from a bar shaped material, racks can be square, round, or rectangular in cross section and the teeth can be either parallel to the base or offset at an angle.

One issue when designing a rack system is to set the length of the gear rack. Racks are limited in length by the length of the rack milling machine bed. Practically speaking, this means that a 10-meter continuous length rack is not readily available. One solution for this situation is to produce racks with finished ends. A simple end on a gear rack implies that the producer measures a fixed length on the machined rack and, using a band saw or similar cutting tool, slices the rack at the desired length. This can easily result in a partial tooth or an incomplete tooth at one end of the rack. A rack with finished ends is produced oversized and the rack ends are machined to result in a full gear tooth on each end. This results in a rack that is slightly larger than the nominal length  but permits the racks to be butted end-to-end in order to form a functional infinite length. To join together two finished-end gear racks, you need to employ the use of a joining gage. By inverting the joining gage rack over the gap between the two finished end racks (Figure 1), you properly space the two racks so that the pinion does not bind or jump when transitioning from rack A to rack B.

If you do not have a joining gage rack, then you can you use two pins and a caliper to measure the distance between the two end teeth in order to determine if the racks are set to the proper spacing. In the formula shown in Figure 2, m is the module of the rack and d is the diameter of the pin.

Another issue with gear racks is the introduction of tapped or bolt holes through one or more faces on the rack. In Figure 3, dimension E is critical. If it is too small, the bolt hole counterbore will be too close to the base of the rack, resulting in material loss and poor performance of the bolt. If the dimension E is too large, then the bolt counterbore will interfere with the tooth root of the rack teeth. This will cause premature failure of the rack teeth due to the lack of structural integrity. Similarly, tapped holes through the base of the rack should not be too deep such that they impact the tooth root. The rule of thumb is that the material should not be removed within a distance of 1.5 times the tooth height of the rack. For a module 2 rack, the tooth height is 4.5 millimeters. As such, the nearest hole should be more than 6.75 millimeters from the tooth root.

Another issue with gear racks is straightness. As noted by L in Figure 4, gear racks have a natural deviation from the nominal plane. This distortion can be inherent in the supplied material, it can be caused by the tooth milling process, it can be caused by the heat treatment process, or it can be any combination of the three. Because of this distortion, all racks need to be straightened after the milling process and most are face ground after heat treatment. One issue that occurs with heat-treated racks with bolt holes, is that the bolt holes typically are machined prior to heat treating as the material is too hard, post hardening, to add them. However, the straightening and grinding process will change the positional tolerance of these holes and may cause them to be out of specification. In order to account for this issue, it is best to specify oval holes for these types of racks.

Similar to the straightness of the length of a gear rack is the parallelism of the rack faces. Although exaggerated, the image on the right in Figure 5 details the true shape of a square bar. The image on the left is the theoretical shape. When specifying locations of tapped or bolt holes, it is important to realize that the holes will be machined where the actual material is present; however, the holes will be inspected based on the outer most material point. This means that a bolt may sit deeper into the rack face than called for in the design.

When designing a gear rack, it is important to calcuate the pitch size to account for the strength requirements of the application, the material and hardness to account for the duty cycle and wear of the rack in the application, and to realize the design limitation of the geometry of the material.

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is general manager of KHK USA Inc, a subsidiary of Kohara Gear Industry with a 24-year history of working in the industrial automation industry. He is skilled in assisting engineers with the selection of power-transmission components for use in industrial equipment and automation. Dengel is a member of PTDA and designated as an intern engineer by the state of New York. He is a graduate of Hofstra University with a Bachelor’s of Science in Structural Engineering.