<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.4 20241031//EN" "JATS-journalpublishing1-4.dtd">
<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" article-type="research-article" dtd-version="1.4" xml:lang="en">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher-id">jamp</journal-id>
      <journal-title-group>
        <journal-title>Journal of Applied Mathematics and Physics</journal-title>
      </journal-title-group>
      <issn pub-type="epub">2327-4379</issn>
      <issn pub-type="ppub">2327-4352</issn>
      <publisher>
        <publisher-name>Scientific Research Publishing</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.4236/jamp.2026.145097</article-id>
      <article-id pub-id-type="publisher-id">jamp-151633</article-id>
      <article-categories>
        <subj-group>
          <subject>Article</subject>
        </subj-group>
        <subj-group>
          <subject>Physics</subject>
          <subject>Mathematics</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title>Process Optimization from Machining to Casting for Lead Cones Used in the Terminal-Peak Sawtooth Shock</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name name-style="western">
            <surname>Guo</surname>
            <given-names>Chunxia</given-names>
          </name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <name name-style="western">
            <surname>Liu</surname>
            <given-names>Jiayang</given-names>
          </name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <name name-style="western">
            <surname>Liu</surname>
            <given-names>Zhaoliang</given-names>
          </name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <name name-style="western">
            <surname>Leng</surname>
            <given-names>Jianping</given-names>
          </name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <name name-style="western">
            <surname>Hou</surname>
            <given-names>Haibing</given-names>
          </name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <name name-style="western">
            <surname>Deng</surname>
            <given-names>Qinghui</given-names>
          </name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <name name-style="western">
            <surname>Ge</surname>
            <given-names>Yaqing</given-names>
          </name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
      </contrib-group>
      <aff id="aff1"><label>1</label> Sichuan Aerospace Chuannan Initiating Explosive Technology Limited, Sichuan, China </aff>
      <author-notes>
        <fn fn-type="conflict" id="fn-conflict">
          <p>The authors declare no conflicts of interest regarding the publication of this paper.</p>
        </fn>
      </author-notes>
      <pub-date pub-type="epub">
        <day>15</day>
        <month>05</month>
        <year>2026</year>
      </pub-date>
      <pub-date pub-type="collection">
        <month>05</month>
        <year>2026</year>
      </pub-date>
      <volume>14</volume>
      <issue>05</issue>
      <fpage>2013</fpage>
      <lpage>2018</lpage>
      <history>
        <date date-type="received">
          <day>20</day>
          <month>04</month>
          <year>2026</year>
        </date>
        <date date-type="accepted">
          <day>26</day>
          <month>05</month>
          <year>2026</year>
        </date>
        <date date-type="published">
          <day>29</day>
          <month>05</month>
          <year>2026</year>
        </date>
      </history>
      <permissions>
        <copyright-statement>© 2026 by the authors and Scientific Research Publishing Inc.</copyright-statement>
        <copyright-year>2026</copyright-year>
        <license license-type="open-access">
          <license-p> This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ( <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link> ). </license-p>
        </license>
      </permissions>
      <self-uri content-type="doi" xlink:href="https://doi.org/10.4236/jamp.2026.145097">https://doi.org/10.4236/jamp.2026.145097</self-uri>
      <abstract>
        <p>To reduce the cost of the terminal-peak sawtooth shock tests while satisfying technical specifications, this study explores the feasibility of replacing machining with casting for lead cones used in the terminal-peak sawtooth shock. The results show that the terminal-peak sawtooth shock pulses produced by the cast lead cones satisfy test requirements. Meanwhile, the casting route exhibits superior material utilization efficiency, lower production cost, and simpler process flow. Compared with the traditional machining, the manufacturing cost of the 0.5 kg lead cone processed by the casting has decreased by 60.73%.</p>
      </abstract>
      <kwd-group kwd-group-type="author-generated" xml:lang="en">
        <kwd>Lead Cone</kwd>
        <kwd>Casting</kwd>
        <kwd>Process Optimization</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec1">
      <title>1. Introduction</title>
      <p>To assess the functional reliability of aerospace products, these products must undergo shock environment tests [<xref ref-type="bibr" rid="B1">1</xref>]. The terminal-peak sawtooth shock test is a widely used method for shock motion tests [<xref ref-type="bibr" rid="B2">2</xref>][<xref ref-type="bibr" rid="B3">3</xref>]. Currently, both at home and abroad, the terminal-peak sawtooth shock test is usually conducted by combining a lead cone with a drop-type shock test bench [<xref ref-type="bibr" rid="B4">4</xref>]. Specifically, the deformation of the lead cone is utilized to generate the terminal-peak sawtooth shock pulse. Consequently, the size and shape of the lead cone directly influence the accuracy of test data. However, there are no overly strict requirements for the mechanical properties of the lead cone material.</p>
      <p>At present, the production of lead cones generally adopts the traditional bar cutting process. Although this process can ensure the dimensional accuracy of components, it has some disadvantages. Firstly, the material utilization rate is low. The cutting process is of the “removal type”, removing a large amount of unnecessary material from lead bar raw materials. The generated waste cannot be directly recycled, leading to raw material waste. Secondly, lead cones are disposable consumables. They have high demand and a long production cycle, making it difficult to meet mass production requirements. Thirdly, the production cost is high. Excess material loss, as well as labor and equipment consumption from multiple processes, keeps the processing cost of each lead cone at a high level.</p>
      <p>Casting is a manufacturing process in which molten metal is poured into a mold cavity and allowed to cool and solidify, yielding finished components or blanks [<xref ref-type="bibr" rid="B5">5</xref>]. It has the advantages of simple processes, high material utilization rate, high production efficiency, and low production costs for large-scale production of metal parts. It is widely used in the mass production of metal parts. Therefore, this study takes cost reduction as the core objective, focusing on the research and trial production of lead cones. It explores the feasibility of the casting and provides both theoretical and practical support for optimizing the production of lead cones used in the terminal -peak sawtooth shock tests.</p>
    </sec>
    <sec id="sec2">
      <title>2. Introduction to the Structure of the Lead Cone</title>
      <p>During shock testing, the product is secured to a platform. The platform is raised to a prescribed height and then suddenly released, allowing the product and platform to fall freely onto a lead cone. Upon shock, the lead cone is loaded and generates a reverse acceleration. The resulting acceleration curve presents a terminal-peak sawtooth waveform [<xref ref-type="bibr" rid="B6">6</xref>]. The configuration of the test bench is shown in <xref ref-type="fig" rid="fig1">Figure 1</xref>.</p>
      <fig id="fig1">
        <label>Figure 1</label>
        <graphic xlink:href="https://html.scirp.org/file/1724687-rId13.jpeg?20260529015558" />
      </fig>
      <p><bold>Figure 1.</bold>The drop-type shock test bed [<xref ref-type="bibr" rid="B6">6</xref>].</p>
      <p>The lead cone used in the drop shock test bench is generally a conical shape [<xref ref-type="bibr" rid="B7">7</xref>], as shown in <xref ref-type="fig" rid="fig2">Figure 2</xref>. After being shocked, the lead cone undergoes plastic deformation and cannot be reused, thus it is a one-time consumable item. The physical image is shown in <xref ref-type="fig" rid="fig3">Figure 3</xref>.</p>
      <fig id="fig2">
        <label>Figure 2</label>
        <graphic xlink:href="https://html.scirp.org/file/1724687-rId14.jpeg?20260529015558" />
      </fig>
      <p><bold>Figure 2.</bold>The lead cone model.</p>
      <fig id="fig3">
        <label>Figure 3</label>
        <graphic xlink:href="https://html.scirp.org/file/1724687-rId15.jpeg?20260529015559" />
      </fig>
      <p><bold>Figure 3.</bold>The physical diagram of the loss of the lead cone.</p>
    </sec>
    <sec id="sec3">
      <title>3. Design and Implementation of Casting Processing Plan for Lead Cones</title>
      <p>Lead cones are fabricated from metallic lead. This material exhibits a low melting point and excellent melt fluidity, making it highly suitable for casting. Lead ingots are heated and poured into the mold cavity. When preparing the ingredients, raw lead materials are loaded into the furnace. Upon complete melting, the molten metal is stirred immediately to ensure homogeneous composition and uniform temperature distribution. This is beneficial for accelerating the melting of the furnace materials. After confirming that the furnace materials have completely melted, remove the slag. When no floating slag remains on the melt surface, the molten lead is held prior to casting. The casting process flow is shown in <xref ref-type="fig" rid="fig4">Figure 4</xref>.</p>
    </sec>
    <sec id="sec4">
      <title>4. Results</title>
      <p>During casting, all raw materials are fully melted into liquid phase at high temperatures. Therefore, the scrapped lead cones following shock tests can be reprocessed via casting. This allows material reuse and realizes the recycling of raw lead resources.</p>
      <fig id="fig4">
        <label>Figure 4</label>
        <graphic xlink:href="https://html.scirp.org/file/1724687-rId16.jpeg?20260529015559" />
      </fig>
      <p><bold>Figure 4.</bold>The flow of melting and casting process.</p>
      <p>Using the casting, lead cones of three specifications (1.5 kg, 1 kg, and 0.5 kg) have been successfully produced. The corresponding molds and qualified lead cone products are displayed in <xref ref-type="fig" rid="fig5">Figure 5</xref>. In accordance with the specified requirements, the height, bottom diameter and appearance of the lead cone were inspected. Inspection results confirm that their dimensional accuracy and surface quality satisfy the design requirements.</p>
      <fig id="fig5">
        <label>Figure 5</label>
        <graphic xlink:href="https://html.scirp.org/file/1724687-rId17.jpeg?20260529015559" />
      </fig>
      <p><bold>Figure 5.</bold>The physical picture of the molds and the cast lead cones.</p>
      <p>To verify whether cast lead cones satisfy the requirements of terminal-peak sawtooth shock tests, the cast lead cones were used as waveform generators and tested in conjunction with drop-test shock machine. It is well recognized that the specification requirements for terminal-peak sawtooth pulses are determined by the mechanical performance of the test product, which also serves as the evaluation criterion for pulse characteristics. A typical product was selected as the research object, with designated technical indicators including a peak acceleration of (15 ± 1.5) g and a pulse width of (30 ± 3) ms. Corresponding lead cones were manufactured by the casting, and subsequent verification experiments were carried out to validate their performance. The terminal-peak sawtooth acceleration pulse obtained from the verification test is presented in <xref ref-type="fig" rid="fig6">Figure 6</xref>. The peak acceleration is 14.86 g, with a pulse width of 28.75 ms. It can be observed that the test results meet the requirements.</p>
      <fig id="fig6">
        <label>Figure 6</label>
        <graphic xlink:href="https://html.scirp.org/file/1724687-rId18.jpeg?20260529015559" />
      </fig>
      <p><bold>Figure 6.</bold>The terminal-peak sawtooth pulse produced by a cast lead cone.</p>
    </sec>
    <sec id="sec5">
      <title>5. Discussion</title>
      <sec id="sec5dot1">
        <title>5.1. Increase in Material Utilization Rate</title>
        <p>The lead cone is a conical geometry and is conventionally manufactured via machining. The theoretical material utilization rate is 1/3, while the actual rate from production is only 28%. Furthermore, lead cones deformed during shock tests cannot be re-machined. Thus, the machining method prevents material reuse.</p>
        <p>Casting involves melting metallic raw materials into a liquid phase, then poured into a mold to cool and form. During the casting process, the waste residue is removed and discarded. However, the unqualified components and the lead cones that were deformed during the tests can be re-melted and re-cast, enabling material recycling and further enhancing utilization efficiency. Through statistical calculations, the material utilization rate of melt casting reaches approximately 90%, which is significantly higher than the 28% achieved by conventional machining.</p>
      </sec>
      <sec id="sec5dot2">
        <title>5.2. Reduction in Costs</title>
        <p>Through process optimization, the manufacturing route for lead cones was converted from machining to casting, resulting in a significant reduction in processing costs. The production cost of lead cones mainly consists of manufacturing costs (including labor costs, mold amortization, etc.) and raw material expenses. Detailed data are provided in <bold>Table 1</bold>. For a 0.5 kg lead cone, the unit cost decreased from CNY 60 to CNY 23.56, representing a reduction of 60.73%. For a 1 kg lead cone, the cost dropped from CNY 112 to CNY 44.11, a reduction of 60.61%. For a 1.5 kg lead cone, the cost dropped from CNY 165 to CNY 66.67, a reduction of 59.60%.</p>
        <p><bold>Table 1.</bold>A cost comparison table before and after process optimization for a lead cone.</p>
        <table-wrap id="tbl1">
          <label>Table 1</label>
          <table>
            <tbody>
              <tr>
                <td colspan="2">The specifications of the lead cone</td>
                <td>0.5 kg</td>
                <td>1 kg</td>
                <td>1.5 kg</td>
              </tr>
              <tr>
                <td rowspan="4">Machining</td>
                <td>Manufacturing Cost</td>
                <td>10</td>
                <td>12</td>
                <td>15</td>
              </tr>
              <tr>
                <td>Material efficiency</td>
                <td>28%</td>
                <td>28%</td>
                <td>28%</td>
              </tr>
              <tr>
                <td>Material cost</td>
                <td>50</td>
                <td>100</td>
                <td>150</td>
              </tr>
              <tr>
                <td>Unit cost</td>
                <td>60</td>
                <td>112</td>
                <td>165</td>
              </tr>
              <tr>
                <td rowspan="4">Casting</td>
                <td>Manufacturing Cost</td>
                <td>8</td>
                <td>13</td>
                <td>20</td>
              </tr>
              <tr>
                <td>Material efficiency</td>
                <td>90%</td>
                <td>90%</td>
                <td>90%</td>
              </tr>
              <tr>
                <td>Material cost</td>
                <td>15.56</td>
                <td>31.11</td>
                <td>46.67</td>
              </tr>
              <tr>
                <td>Unit cost</td>
                <td>23.56</td>
                <td>44.11</td>
                <td>66.67</td>
              </tr>
              <tr>
                <td colspan="2">Rate of cost reduction</td>
                <td>60.73%</td>
                <td>60.61%</td>
                <td>59.60%</td>
              </tr>
            </tbody>
          </table>
        </table-wrap>
      </sec>
    </sec>
    <sec id="sec6">
      <title>6. Conclusion</title>
      <p>This study investigates the feasibility of fabricating lead cones for terminal-peak sawtooth shock using casting. Experimental validation confirms that the shock pulse generated by cast lead cones satisfy the technical specifications. Relative to conventional machining, it is clear that casting substantially improves material efficiency and considerably reduces production cost. Therefore, the casting process is proven feasible for the manufacture of lead cones.</p>
    </sec>
  </body>
  <back>
    <ref-list>
      <title>References</title>
      <ref id="B1">
        <label>1.</label>
        <citation-alternatives>
          <mixed-citation publication-type="web">Laborary Environmental Test Methods for Military Materiel—Part 18: Shock Test, GJB 150.18A—2009. https://www.doc88.com/p-1713966655782.html</mixed-citation>
          <element-citation publication-type="web">
            <person-group person-group-type="author">
              <string-name>Test, G</string-name>
            </person-group>
            <year>2009</year>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B2">
        <label>2.</label>
        <citation-alternatives>
          <mixed-citation publication-type="journal">Duan, N.N., Lin, Y.Z. and Su, Y.H. (2021) The Shock Characteristics of Tilted Support Spring System with Double Variance under Final Peak Sawtooth Pulse. <italic>Journal of Fuqing Branch of Fujian Normal University</italic>, 39, 473-478.</mixed-citation>
          <element-citation publication-type="journal">
            <person-group person-group-type="author">
              <string-name>Duan, N.N.</string-name>
              <string-name>Lin, Y.Z.</string-name>
              <string-name>Su, Y.H.</string-name>
            </person-group>
            <year>2021</year>
            <article-title>The Shock Characteristics of Tilted Support Spring System with Double Variance under Final Peak Sawtooth Pulse</article-title>
            <source>Journal of Fuqing Branch of Fujian Normal University</source>
            <volume>39</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B3">
        <label>3.</label>
        <citation-alternatives>
          <mixed-citation publication-type="web">Liang, Z.H. (1997) The Principle and Application of the Simple Impact Post-Saw Wave Waveform Generation. <italic>Aero Weaponry</italic>, 1, 26-28. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HKBQ199701007.htm</mixed-citation>
          <element-citation publication-type="web">
            <person-group person-group-type="author">
              <string-name>Liang, Z.H.</string-name>
            </person-group>
            <year>1997</year>
            <article-title>The Principle and Application of the Simple Impact Post-Saw Wave Waveform Generation</article-title>
            <source>Aero Weaponry</source>
            <volume>1</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B4">
        <label>4.</label>
        <citation-alternatives>
          <mixed-citation publication-type="other">Wu, S., Liu, B. and Ding, F. (2004) Present State and Perspectives on Force-Pulse Generator of Product Shock Tester. <italic>Mechanical Engineer</italic>, 2, 11-14.</mixed-citation>
          <element-citation publication-type="other">
            <person-group person-group-type="author">
              <string-name>Wu, S.</string-name>
              <string-name>Liu, B.</string-name>
              <string-name>Ding, F.</string-name>
            </person-group>
            <year>2004</year>
            <article-title>Present State and Perspectives on Force-Pulse Generator of Product Shock Tester</article-title>
            <source>Mechanical Engineer</source>
            <volume>2</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B5">
        <label>5.</label>
        <citation-alternatives>
          <mixed-citation publication-type="book">Li, K.S. (1981) Fundamentals of Casting Process Design. Mechanical Industry Press. (in Chinese) https://xueshu.baidu.com/ndscholar/browse/detail?paperid=1a61017a023ee5bc252fdce2f63a82fb&amp;site=xueshu_se</mixed-citation>
          <element-citation publication-type="book">
            <person-group person-group-type="author">
              <string-name>Li, K.S.</string-name>
            </person-group>
            <year>1981</year>
            <article-title>Fundamentals of Casting Process Design</article-title>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B6">
        <label>6.</label>
        <citation-alternatives>
          <mixed-citation publication-type="other">Zhu, S.H., Fang, D., Niu, J.H., Yang, R., Sun, Y., Li, W.W. and Cao, X. (2022) Numerical Analysis and Experimental Study of the Terminal-Peak Sawtooth Pulses Produced by Drop-Test Shock Machine. <italic>Spacecraft Environment Engineering</italic>, 39, 40-46.</mixed-citation>
          <element-citation publication-type="other">
            <person-group person-group-type="author">
              <string-name>Zhu, S.H.</string-name>
              <string-name>Fang, D.</string-name>
              <string-name>Niu, J.H.</string-name>
              <string-name>Yang, R.</string-name>
              <string-name>Sun, Y.</string-name>
              <string-name>Li, W.W.</string-name>
              <string-name>Cao, X.</string-name>
            </person-group>
            <year>2022</year>
            <article-title>Numerical Analysis and Experimental Study of the Terminal-Peak Sawtooth Pulses Produced by Drop-Test Shock Machine</article-title>
            <source>Spacecraft Environment Engineering</source>
            <volume>39</volume>
          </element-citation>
        </citation-alternatives>
      </ref>
      <ref id="B7">
        <label>7.</label>
        <citation-alternatives>
          <mixed-citation publication-type="thesis">Zhang, M.B. (2018) Pendulum-Type Impact Test Platform and Impact Response Research. Master’s Thesis, Beijing Jiaotong University. (in Chinese) https://cdmd.cnki.com.cn/Article/CDMD-10004-1018131504.htm</mixed-citation>
          <element-citation publication-type="thesis">
            <person-group person-group-type="author">
              <string-name>Zhang, M.B.</string-name>
              <string-name>Thesis, B</string-name>
            </person-group>
            <year>2018</year>
            <article-title>Pendulum-Type Impact Test Platform and Impact Response Research</article-title>
            <source>Master’s Thesis</source>
          </element-citation>
        </citation-alternatives>
      </ref>
    </ref-list>
  </back>
</article>