Abstract : This paper focuses on the precise design of steel ball positioning indexing plate mechanisms in CNC machine tools, rotary combination machine tools, and various rotary worktables. It analyzes the factors affecting indexing and positioning accuracy, proposes solutions, and provides application examples. In CNC machine tools, rotary combination machine tools, and various rotary worktables, the indexing, rotation, and positioning of commonly used indexing worktables are performed automatically according to the instructions of the control system. Each rotation rotates a certain angle (90°, 60°, 45°, etc.). However, the mechanism that realizes the worktable rotation is difficult to achieve the required indexing accuracy. Therefore, a dedicated positioning element is needed to ensure this. Thus, the indexing positioning element is often a key part of the design, manufacturing, and adjustment of the indexing worktable. Currently, commonly used positioning elements include pin positioning, backing positioning, gear plate positioning, and steel ball positioning. To achieve high-precision indexing, steel ball positioning indexing plate mechanisms are widely used. It possesses some advantages of gear-type positioning, including automatic centering and high indexing accuracy, and is simple to manufacture. The steel balls can be purchased externally, making it ideal for high-precision indexing rotary tables with smaller dimensions. Steel ball positioning utilizes the principle that the diameter of the steel balls can be pre-selected to a range with minimal error, thereby achieving precise indexing accuracy. This paper presents the structural design of the steel ball positioning indexing plate mechanism, analyzes the factors affecting its indexing accuracy, and proposes solutions. 1. Structural Working Principle The steel ball positioning indexing plate mechanism relies on a high-precision base disc 4 and high-precision steel balls to improve the accuracy of the indexing mechanism. 120 ￠8 steel balls are arranged without gaps on a base cylinder with a diameter of ￠297.61238 mm, contacting the same end face. A clamping ring 5 is fitted around the steel balls, with a 30° bevel facing the balls. When the clamping ring tightens, it presses the steel balls firmly against the base cylinder and the end face. In addition, to prevent the steel balls from rotating circumferentially and damaging the indexing, a high-strength steel wedge-shaped cylindrical pin 12 is installed between a pair of steel balls. Its head is a 45° wedge surface to ensure high-precision indexing. This mechanism can be used to process high-precision indexed workpieces such as toothed discs (i.e., end-face toothed indexing discs). 2. Analysis of Factors Affecting Indexing Accuracy and Solutions 2.1 Selection of Steel Balls The dimensional accuracy of the steel balls is the determining factor for the indexing accuracy. Therefore, the accuracy of the steel balls is ensured by pre-selection. Using a micrometer with a diameter error of 1 micrometer, 240 steel balls with a pre-selected diameter error of 1 micrometer are selected. Ideally, the diameter error and roundness of the steel balls should be pre-selected to be below 0.5 micrometers. 2.2 Machining of the Base Disc The base circle diameter of the base disc requires high precision. The calculation of the base circle diameter is as follows: For example, the diameter of the steel ball is ￠8 mm. Given that the circumference is divided into equal parts n = 120, ∠AOB = 3°. AB is the line connecting the centers of the steel spheres, so AB = 8. OC is the angle bisector of ∠AOC in the triangle, therefore △ACO is a right triangle. Since ∠AOC = 1°30′, then: AO = AC/sin1º30° = 4/0.02617695 = 152.80619 mm. Therefore, the diameter d of the base cylinder of base disk 4 is: d = 2 × ao = 2(AO - Aa1) = 297.61238 mm (where Aa is the radius of the steel sphere, Aa = 4 mm). Grinding and measuring the base circle is quite difficult. To solve this problem, we adopted the following processing method: First, grind the two planes of the hardened base circle disc to be within 0.01 mm of parallelism. Then, using the planes as a reference, grind the inner hole, ensuring that the perpendicularity between the planes and the center of the inner hole is 0.001/100 mm. Next, install a specially made mandrel and grind the base circle using the inner hole and end face as references. Grind the end face simultaneously with the base circle. After grinding ￠297.6123 mm to +0.1 mm, each reduction of 0.01 to 0.02 mm is considered one pass, during which the workpiece and mandrel are removed together (the parts must not be removed from the mandrel). 2.3 Pre-assembly: The pre-machined parts, clamping ring, and 120 selected steel balls are trial-assembled on the table. The maximum gap between the steel balls is measured using a precision feeler gauge. Then, the part is ground down to a diameter equivalent to 1/3 of the maximum gap. This grinding and trial assembly process is repeated multiple times until the gap between the steel balls can no longer be measured. The measured diameter at this point should be the calculated size. This process requires extreme care and meticulous attention, and attention should be paid to good cleanliness and ambient temperature. During grinding, the grinding wheel should be kept stable, and the outer diameter and end face should be ground down simultaneously. When the part is mounted on the mandrel and rotates between the two centers of the grinding machine, the maximum point of vibration should not exceed 0.01 mm. The hardness of the base circle cylindrical surface is best above HRC55. If the hardness is too low, indentations will form after repeated pressing and releasing of the steel balls, and the indexing accuracy will decrease accordingly. 2.4 Measurement Method for Base Circle Division Accuracy: Specific methods include using a polyhedron and a collimator, or using a collimator and a reflector to determine the error. 3. Application Example In this device, the steel ball pre-selection accuracy is below 0.002 mm. Using a 1-second collimator and a reflector, the maximum cumulative error of the division accuracy is 4 seconds. Using this indexing plate mounted on a spline grinding machine, a toothed disc with a diameter of 120 mm and 120 divisions was initially measured. After meshing, the meshing number calculated according to the number of teeth reached more than 95%, and the contact surface along the tooth height and tooth width reached more than 70%. After installing this pair of toothed discs on the turret power head and conducting a comprehensive inspection, the division error was within 0.02 mm (repeatability error), which greatly improved the machining accuracy. 4. Precautions (1) When assembling the clamping ring, it is more appropriate to keep the gap between the clamping ring and the platform within 0.1 mm when the steel ball contacts the inclined surface. (2) The steel ball clamping of the indexing plate adopts the above structure. How much torsional torque it can withstand needs to be further tested. (Based on current practical use, this device can achieve relatively high indexing accuracy for grinding precision lines and drilling small holes.) This indexing plate is not suitable for cutting processes with high torque or impact.