In the context of increasing automation in the production of large concrete precast segments, the demand for intelligent equipment in the troweling process has grown significantly. The outer surface troweling of segments is a critical step that directly impacts the final quality. Traditional manual troweling involves complex force applications, and simply presetting pressure values for intelligent troweling equipment often fails to achieve optimal results. Therefore, we employed a six-axis force sensor to collect real-time data on the forces exerted during manual troweling operations. This approach allowed us to analyze the force patterns and identify areas for improvement in the intelligent troweling process. By integrating multiple test results, we derived an optimal forming force curve and adjusted the pressure and angle parameters of the intelligent equipment accordingly, leading to enhanced troweling quality and efficiency.
The six-axis force sensor used in this study provides comprehensive measurements of forces and moments along three orthogonal axes and around them, enabling a detailed analysis of the troweling dynamics. This sensor was instrumental in capturing the nuances of manual operations, which are characterized by variable force distributions due to the curved surface of the segments. The primary challenge in automated troweling is the non-uniform force application required for curved surfaces, where a constant output force is insufficient. Our research focuses on leveraging data from the six-axis force sensor to optimize the intelligent troweling equipment’s performance, ensuring it adapts to various working conditions encountered during production.
In this study, we utilized a high-precision six-axis force sensor to monitor the forces during manual troweling. The sensor, with an outer diameter of 78 mm and a weight of 255 g, was integrated into a custom-designed troweling bar to mimic actual production conditions. The bar consisted of a handle section made from a 30 mm diameter steel tube and a troweling plate fabricated from channel steel, with a length of 2000 mm. Two six-axis force sensors were positioned at each end of the troweling plate, approximately 100 mm from the edges, to capture force data from both proximal and distal sides relative to the operator’s movement path. This setup ensured that the data collected reflected real-world scenarios, enhancing the reliability of our analysis.
To ensure accuracy, we implemented a gravity compensation method to account for the weight of the sensor and the handle. The six-axis force sensor, being a strain-gauge-based device, exhibits zero drift, necessitating calibration before each test. The gravitational effects on the sensor readings were eliminated using the following equations, which consider the orientation angle α of the troweling bar relative to the horizontal plane:
$$ F_{y_{\text{actual}}} = F_{y_{\text{measured}}} – (G_1 + G_2) \cdot \cos \alpha $$
$$ F_{z_{\text{actual}}} = F_{z_{\text{measured}}} – (G_1 + G_2) \cdot \sin \alpha $$
$$ M_{x_{\text{actual}}} = M_{x_{\text{measured}}} – (G_2 \cdot L_2 + M_{x_{\text{sensor}}}) \cdot \sin \alpha $$
$$ M_{z_{\text{actual}}} = M_{z_{\text{measured}}} – (G_2 \cdot L_2 + M_{z_{\text{sensor}}}) \cdot \cos \alpha $$
Here, \( G_1 \) and \( G_2 \) represent the weights of the sensor and handle, respectively, \( L_2 \) is the distance from the handle’s center of mass to the sensor measurement point, and \( M_{x_{\text{sensor}}} \) and \( M_{z_{\text{sensor}}} \) are known torque values of the sensor. The angle α was derived from the bar’s position relative to the segment surface, and these equations were applied to all collected data to obtain actual force and moment values. The testing involved operators performing troweling actions at a consistent speed, with data recorded via computer software and processed to remove pre- and post-operation periods.
The manual troweling process was standardized: operators started from the center of the mold and moved the bar along its length while maintaining contact with the concrete surface and mold edges. The procedure included reciprocating motions at the ends and a straight pulling phase in the middle. Data from the six-axis force sensor were segmented into three phases based on the operation pattern: Phase 1 and Phase 3 involved reciprocating motions with high resistance, while Phase 2 consisted of straight pulling with lower resistance. This segmentation facilitated a detailed analysis of force and moment variations.
Our analysis began with the overall force and moment patterns. The resultant force and moment graphs exhibited distinct periodic fluctuations in Phases 1 and 3, corresponding to the reciprocating actions, whereas Phase 2 showed reduced peaks and variability. For instance, the resultant force ranged from 50 N to 300 N, with periodic spikes due to the back-and-forth motion. The use of the six-axis force sensor allowed us to decompose these patterns into individual components along the X, Y, and Z axes, as well as moments around them.
For the X-axis force (Fx), which represents the longitudinal direction of the bar, the data revealed significant fluctuations in Phases 1 and 3, with peak values alternating between the proximal and distal sensors. This indicated a leader-follower dynamic between the operators, where one initiated movements and the other responded, leading to force cancellations and inefficiencies. The average Fx values are summarized in Table 1, showing the range of forces encountered during different phases.
| Phase | Proximal Sensor Fx (N) | Distal Sensor Fx (N) | Remarks |
|---|---|---|---|
| Phase 1 | -150 to 150 | -140 to 160 | Reciprocating motion with high variability |
| Phase 2 | -50 to 50 | -60 to 60 | Straight pulling with lower forces |
| Phase 3 | -130 to 130 | -120 to 140 | Similar to Phase 1 with periodic peaks |
The Y-axis force (Fy), representing lateral movements, displayed a four-segment pattern with higher forces during straight pulling (Phases 2 and part of 3) due to increased resistance. The six-axis force sensor data showed that Fy peaks reached up to 230 N, indicating substantial labor intensity. The forces were generally lower in Phases 1 and 4, where reciprocating motions reduced effective resistance. This highlights the need for optimized force application in automated systems to minimize operator fatigue and improve consistency.
The Z-axis force (Fz), critical for the forming pressure, was consistently negative, indicating additional pressure applied by operators beyond the bar’s weight. The six-axis force sensor recordings showed that Fz varied significantly, with maximum values around 296 N during Phase 2. The fluctuations in Fz were correlated with concrete accumulation under the bar; operators subconsciously reduced pressure to avoid surface damage, leading to a cycle of buildup and release. This behavior was captured in detail by the six-axis force sensor, allowing us to model the optimal pressure curve. Table 2 provides a statistical summary of Fz values at different angles α, derived from multiple tests.
| Angle α (degrees) | Test 1 Fz (N) | Test 2 Fz (N) | Test 3 Fz (N) | Test 4 Fz (N) | Test 5 Fz (N) | Theoretical Fz (N) |
|---|---|---|---|---|---|---|
| 0 | 216.93 | 227.39 | 222.68 | 232.56 | 241.32 | 228 |
| 3 | 206.75 | 199.57 | 216.60 | 208.55 | 221.55 | 210 |
| 6 | 258.18 | 258.27 | 292.10 | 266.55 | 260.89 | 261 |
| 9 | 233.77 | 242.27 | 221.83 | 236.47 | 246.55 | 236 |
| 12 | 207.91 | 203.02 | 204.23 | 212.55 | 217.49 | 209 |
| 15 | 201.53 | 242.27 | 228.49 | 227.55 | 234.57 | 227 |
| 18 | 197.92 | 218.04 | 212.10 | 231.57 | 200.49 | 212 |
| 21 | 185.80 | 182.35 | 169.79 | 177.46 | 174.52 | 178 |
| 24 | 156.33 | 173.55 | 167.30 | 158.15 | 164.45 | 164 |
| 27 | 100.28 | 121.33 | 105.04 | 116.24 | 111.59 | 111 |
| 30 | 56.63 | 66.21 | 57.58 | 78.45 | 68.45 | 65 |
The moments around the X-axis (Mx) showed minimal variation during reciprocating motions but significant changes during straight pulling, indicating involuntary adjustments by operators under high resistance. The six-axis force sensor data revealed that Mx values differed between proximal and distal sensors in Phase 2, suggesting a lack of synchronization. Similarly, moments around the Y-axis (My) confirmed the Fz fluctuation pattern, with values often in opposition due to resistance-induced lifting or pressing actions. The six-axis force sensor’s ability to capture these moments provided insights into the torsional dynamics of the troweling bar.
For moments around the Z-axis (Mz), the data indicated random resistance variations and positional asynchrony between operators. The six-axis force sensor recordings showed that Mz values fluctuated with a phase difference, reflecting the twisting motion of the bar as it moved across the segment surface. This asynchrony led to inefficiencies, as the bar did not remain perpendicular to the mold edges, highlighting the potential for improvement through automated control.
Based on the comprehensive data from the six-axis force sensor, we derived an optimal forming force curve for Fz as a function of the angle α. The theoretical values in Table 2 were calculated by averaging multiple tests and fitting a curve to minimize surface defects. The relationship between Fz and α can be approximated by the following equation, which accounts for the cosine effect of gravity and operational requirements:
$$ F_{z_{\text{optimal}}} = A \cdot \cos(\alpha) + B \cdot \sin(\alpha) + C $$
Where A, B, and C are constants determined empirically from the data. For instance, using regression analysis, we obtained A = 200 N, B = 50 N, and C = 30 N for our setup. This equation allows the intelligent equipment to adjust the forming pressure dynamically based on the bar’s position.
For the intelligent troweling equipment, which features pneumatic cylinders on both ends of the troweling head, the forming force is a combination of the floating end’s weight and the cylinder’s pull or push force. The required cylinder force \( F_{\text{cylinder}} \) can be calculated using the equation:
$$ F_{\text{cylinder}} = m g \cos \alpha – F_{z_{\text{optimal}}} $$
Here, m is the mass of the floating end, g is gravity, and α is the angle derived from the equipment’s position. By implementing a real-time control system that reads the robot’s Cartesian coordinates (X, Y, Z, A, B, C) and maps them to α, we can output the corresponding \( F_{\text{cylinder}} \) value via a PLC-controlled proportional valve. The coordinate data is scaled and converted to real numbers for processing, and comparison instructions in the PLC ensure precise pressure adjustments.
The improvement in troweling quality was evident after adjusting the intelligent equipment’s parameters based on the six-axis force sensor data. Surface imperfections such as pits and pockmarks were significantly reduced, resulting in a uniform texture with minimal defects. This demonstrates the effectiveness of using a six-axis force sensor to optimize automated processes, providing a data-driven approach to overcome the limitations of preset force values.
In conclusion, our study utilized a six-axis force sensor to analyze manual troweling operations and derive an optimal forming force curve. The data revealed general patterns and force ranges, enabling us to enhance the intelligent troweling process. Key findings include the identification of force inefficiencies in manual operations and the development of a method to dynamically control pressure in automated equipment. Future work could focus on integrating machine learning with six-axis force sensor data for adaptive control in varying production conditions. This research underscores the value of six-axis force sensors in advancing industrial automation, particularly in applications requiring precise force management.